Cosmology

[desiresjab]

Later on in the article, they say on page 4, ex. 11.5:

Z[√-3] is not a Dedekind domain, (which I believe Z[√-5] is). It is not a Dedekind domain because it does not contain every integer in its quotient field.

It appears from the article we may have to pass to the ring of ξ, or whatever that strange symbol is they keep using. This seems to be another level of abstraction to tackle. Happily, it may be the last great hurdle on this particular journey.

[YesNo]

I see that part. I am puzzled by it. I would have thought that Z[√-3] would have all the integers from Q[√-3]. Apparently it is not "integrally closed". That means there must be "integers" in Q[√-3] that are not in Z[√-3]. It looks like one also has to include (1+√-3)/2 = (1/2) + (1/2)√-3. But 1/2 is not an integer in Z.

[desiresjab]

Whatever is in the quotient fileds of √-3 and √-5 only gets there after the proper division, right? Maybe there are some "objects," in the quotient field of Z[[-3], but what the article says is that Z[√-5] contains all the integers in its quotient field, suggesting that Z[√-3] does not. We have exactly the same problem at this point.

If x2+3 is our polynomial, it is also our quotient field modulus, isn't it, or do we simply use √-3?

This only goes to show how great a paucity there is of clear, specific examples in this literature. The phd candidates who write these posted papers would not dare insult those judging their dissertations by anything so lowly and nasty as specific numerical examples all worked out here and there.

Mathematicians write only for those who are 100% up on the language. Even professors do this teaching their courses. They expect everyone to already understand and be intimately familiar with whatever is being studied. Good examples are for neophytes.

I have aired this gripe before. Of course most math articles are not written with me in mind. Nonetheless, I think mathematicians are generally bad writers and bad teachers.

[YesNo]

I agree it isn't clear. I did find a Wikipedia article that is making sense to me at the moment although it is not completely clear: https://en.wikipedia.org/wiki/Quadratic_integer

The quadratic integers are roots of monic quadratic equations. Looking at Q(sqrt(-3)) we can find the ring of integers OQ(sqrt(-3)) which are integrally closed because we take all quadratic integers from Q(sqrt(-3)), but this is larger than the ring Z[sqrt(-3)]. There we are starting with the ring Z not the field Q when we make the extension. I think that is where part of the confusion comes from. What we need to extend the rational integers Z by is not sqrt(-3) but (1+sqrt(-3))/2 to get all the roots of all monic equations where only the sqrt(-3) appears as an algebraic number. However if we are looking at a field like the rationals Q, which is the field of fractions of Z, we can simplify this to Q(sqrt(-3)) because 1/2 is in Q already. It is not in Z unless we put it in there some how.

The monic quadratic equations containing sqrt(-3) in the root somewhere would be x2 + 3 = 0 and x2 + x + 1 = 0. The second is a factor of x3 - 1 making that root one of the cubic roots of unity.

The challenge is to understand the concepts and then maybe write a clearer exposition.

Edit: Here's another link. I like the first answer and the way the question was formed: http://math.stackexchange.com/questions/1198188/why-is-quadratic-integer-ring-defined-in-that-way

[desiresjab]

That article seems to have about everything in it that is needed for understanding the subject the way I would like to. It is a very tough piece. I have stayed away from it because it hurts my brain and I have not been feeling that well. But now I feel okay and I need to go after it. The fine points are somewhat explained. But of course there are always things you wish they had cleared up in any article on the subject.

In order to properly understand ideals all these related areas like field extensions and polynomial rings must be comprehended. So in the end it is a much bigger task to learn than quadratic reciprocity was.

[YesNo]

In a sense the task is large, but like a huge jigsaw puzzle. Once one gets a piece in place, it's there. Remembering is easier after one has forgotten it.

My confusion with the earlier link was that it talked about Z[sqrt(-3)], but that is an example of a ring that is not a Dedekind domain. It shows that they exist. One needs to start with Q, the rationals. Then note that Z is the ring of integers, OQ, in Q. An algebraic integer in an algebraic number field is the root of a monic polynomial with integer coefficients. In the case of Q, the monic polynomial is x - n = 0 where n is an integer. We get the expected ring of integers, Z.

[desiresjab]

What is true for 3 and -3 is true for all 4n+3 type primes, correct? That would make things a bit easier to organize.

[YesNo]

The -3 is a 4n+1 type. If you add 4 to -3 you get 1. The quadratic algebraic integers, those that are roots of monic polynomials of degree 2, separate into two groups depending on mod 4 (except for 2 which is handled separately).

Two things come to mind:
(1) How does one tell which are the integers in a quadratic number field, like Q(sqrt(-3)) or Q(sqrt(-5))?
(2) Is the ring of integers, such as OQ(sqrt(-3)), a unique factorization domain?

The first question is resolved by checking if the number is congruent to 1 or 3 mod 4. The second is resolved by using ideals, so unique factorization is possible in the Dedekind domains with ideals. I think the number of UFDs for algebraic numbers that are square roots of negative integers are finite, if one does not use ideals. I will have to check that.

[desiresjab]

Yes, only 3 is a 4n+3 type.

I am confused by this notation: OQ(sqrt(-3)).

Can you say it in English, please?

* * * * *

What I meant to say is that what is true of one 4n+3 number is true of another. Rather, I meant to ask if that is strictly true.

[YesNo]

The OQ(sqrt(-3)) is the notation for the ring of integers from the field of algebraic numbers Q(sqrt(-3)). I think the O notation comes from Dedekind. Sometimes that ring of integers can be represented by something like Z[sqrt(-3)], which is a ring of a + b*sqrt(-3) where a and b are in Z or where a and be are what we normally think of as integers, or "rational integers". Sometimes it is not, as in this particular case, which is why I think Z[sqrt(-3)] was used as an example. Because -3 is congruent to 1 mod 4, we also have integers that look like this (a + b*sqrt(-3))/2. So the notation using O gives the ring of integers from a field which could be different from just extending Z by the same algebraic number. In the case of Q, the rationals, OQ is just Z. So for the field Q we don't need new notation because there is no difference from what we would expect the ring of integers to be.

One other notation that can be confusing: If one is extending a field the notion of "vector space" is used which is a special kind of "module" and one uses parentheses, such as, Q(sqrt(-3)). What makes it special is Q has all of its inverses. If one is extending a general ring (not necessarily a field) one uses the more general concept of a "module" and the notation changes to brackets such as Z[sqrt(-3)]. Here's some discussion of that difference: https://www.quora.com/What-is-the-difference-between-a-vector-space-over-a-field-and-a-module-over-a-ring

[desiresjab]

Mod 3 there is no object which when squared equals -1 (mod 3), for -1 is equivalent to 2 (mod 3).

Mod 5 the case is different. We do not even have to adjoin √-1 to our ring, because -1 is already there, since (√-1)2 is equal to 4.

This simple truth hung me up for quite a while.

When something snags me I find it almost impossible to move foreward until I have resolved the problem. Finally I have resolved this one, partly at least. I think you are well beyond me now, I hope not out of yelling distance. A new plateau of understanding may now pour over me quickly.

The article said its quotient field contained all numbers within itself. There is nothing I can square (mod 5) to get 3, however, so it still appears to matter what one is trying to adjoin.

[YesNo]

I think it is only mod 4 that is of interest here, not mod 3 or mod 5.

For quadratic algebraic number fields, that is fields where the numbers are roots of quadratic equations like ax2+bx+c=0, the way to tell what algebraic numbers are integers is given by the rule that if we extend Q by the square root of a negative integer, then if that negative integer, -t, is congruent to 3 mod 4 then the algebraic integers are what we would expect them to be, numbers like a+b*sqrt(-t). If -t is congruent to 1 mod 4 then we have to also include a/2+b/2*sqrt(-t) as integers. This comes from using the quadratic formula to find x = (-b+-sqrt(b2-4ac)/2a. That 2 in the denominator does not cancel out in this case. The a = 1 because that is required for an algebraic number to be an algebraic integer. It has to be monic.

Don't worry about being out of reach. If I can't explain it, then I don't really understand it well enough and I don't understand this myself all that well. Also, I might have some of this wrong.

[desiresjab]

I have been traveling again, and I will have to do even more later this week or early next. While I am away I have no computer to do research on, so I concentrate on organizing as many details as I can remember on these math subjects, or what I can put down on paper.

Ideals and field extensions are parts of the classical theory of pure mathematics. I seriously doubt that ideals have found "many," applications outside of conducting more pure research. Also I would be only slightly more surprised if ideals had not already found "some," applications outside of pure mathematics.

Almost nothing is known about fields beyond quadratic fields. It was only for some quadratic fields that ideals recovered unique factorization. In the future I expect much more to be known about higher order fields. Perhaps the complexity will eventually be unraveled by quantum computers. At such a time more applications would come into being. Some of them might be more reliable and secure encryption techniques, as happened with the congruence theory of Gauss, a math language which did not find its big application outside of pure mathematics for a full 200 years.

Right now I feel like tackling more math. The harder it gets, the less I feel like diving in, so I had better take advantage of every time I feel like pushing my boundaries.

[YesNo]

There is probably a lot that is not known also because the questions haven't been asked, but I don't know what the limits are. I ran into this article on "monogenic" fields which have an example of a cubic field that is not monogenic: https://en.wikipedia.org/wiki/Monogenic_field

So here is another technical term, "monogenic", and also, "power integral basis". These terms are more pieces in the jigsaw puzzle.

[desiresjab]

I think it is only mod 4 that is of interest here, not mod 3 or mod 5.

For quadratic algebraic number fields, that is fields where the numbers are roots of quadratic equations like ax2+bx+c=0, the way to tell what algebraic numbers are integers is given by the rule that if we extend Q by the square root of a negative integer, then if that negative integer, -t, is congruent to 3 mod 4 then the algebraic integers are what we would expect them to be, numbers like a+b*sqrt(-t). If -t is congruent to 1 mod 4 then we have to also include a/2+b/2*sqrt(-t) as integers. This comes from using the quadratic formula to find x = (-b+-sqrt(b2-4ac)/2a. That 2 in the denominator does not cancel out in this case. The a = 1 because that is required for an algebraic number to be an algebraic integer. It has to be monic.

Don't worry about being out of reach. If I can't explain it, then I don't really understand it well enough and I don't understand this myself all that well. Also, I might have some of this wrong.

What I need are a few specific examples worked out with all the algebra. If I can see it just once I can figure out how the discriminant figures into this. The problem with any examples I have seen is that they suddenly introduce new variables to make the job harder. Often I cannot see which step to take. For instance, when they say it is obvious so and so is the minimum equation for so and so, I will not see why or how they got the answer.

A few examples geared just for me would make everything clear, I am convinced, but that luxury usually does not exist in math.

Of course I understand that if the discriminant is negative then we intorduce the complex numbers through a field extension. I cannot reproduce the algebra involved. I would have to see it once.

[YesNo]

Here is a video describing the discriminant for a quadratic equation: http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/discriminant-quadratic-formula/discriminant/discriminant-definition You may already know this.

If the square root of the discriminant is not an integer, then the root (which could be either a real or a non-real complex number) is not a rational number. That is, it is not in the field of rational numbers, Q. We could extend this field by creating an object that has all of Q plus one of these non-rational roots. That would also be a field, and its structure would be a two-dimensional vector space. One of the dimensions would have 1 as the base and the other would have this non-rational root, r. The base would look like this: (1,r). The field extension of Q is written like this Q(r). If a and b are arbitrary rational numbers, that is elements of Q, then a number in this new field would look like this: a + br.

Now suppose we don't extend Q but instead extend Z, the ring of integers of Q. Z is not a field, but the extension would be similar and called a module. This is not always a Dedekind domain with ideals forming a unique factorization domain. However, we still could extend Z and see what we get. If we are extending a ring that is not a field the notation would be modified to Z[r], but the idea of the extension is the same. If a and b are integers, that is elements of Z, then a + br would be in Z[r].

Since the ring of integers OQ(r) may be larger than Z[r], we need some way to tell when they are not the same. The discriminant does this. If the discriminate is congruent to 1 mod 4, then we have to include the root that has a 2 in the denominator which is what the earlier link referenced when it discussed Z[sqrt(-3)].

[desiresjab]

Very good. It seems like I have most of the theory under control. Cannot look at the link yet, for I must travel again. Yes, I am no stranger to the quadratic formula. I just have to see exactly how it fits into all this business.

There is always some unpleasant algebra if one wants to view these things in detail. That will be my last step. We are almost done with ideals and the whole 19th century business of settling the theory of equations. Be back in four or five days this time.

[YesNo]

You probably know what is in the link. It just talks about the discriminant for a quadratic polynomial. However, there are a lot of questions. It is worthwhile solving questions at the end of chapters in a text book. I have been reading Saul Stahl, "Introductory Modern Algebra: A Historical Approach". It is an undergraduate level survey of algebra with many questions. If we get a common text with problems that might be a way to go deeper into this subject. What books are you reading?

Here's a question I found interesting about quadratic equations associated with the idea of "algebraic expressions", that is, the ability to write the roots of an equation as an algebraic expression using the coefficients of the equation: Given two numbers, r and s, and the quadratic equation, x2-(r+s)x+rs = 0, show that r and s are the two roots of that equation.

[desiresjab]

We know we are on the lookout for UFD's (Unique Factorization Domains). It is nice to know then that all PID's (Principal Ideal Domains) are UFD's and all ideals in Z are Principal, for nice consolidation.

Irreducible ideals and prime ideals are not always the same in ideal language, but irreducible maximal ideals are always prime ideals.

Without becoming a grinding algorist, one can then follow the language of ideals as written in math the way a non-native pidgin speaker pieces together a newspaper bulletin in a foreign language.

[desiresjab]

The last paragraph of your second to the last post spills a lot of light on the significance of the discriminant in the theory: It is the discriminant itself whose value (mod 4) we are looking at to make our determination of what can be regarded as an algebraic integer.

Are some numbers with an irreducible 2 in the denominator then algebraic integers, or do they become mere algebraic numbers because of their denominator, causing a domain switch as a result?

[YesNo]

That's how I follow it also, in bits and pieces. I get stuck, I stop and look for clues elsewhere.

I have heard that the reason to look at algebraic number fields and their rings of integers is to help us understand better the rational integers, Z. I wonder what insights have been gained? Perhaps insights into Fermat's Last Theorem? Just one of the many questions I have at the moment.

[YesNo]

The last paragraph of your second to the last post spills a lot of light on the significance of the discriminant in the theory: It is the discriminant itself whose value (mod 4) we are looking at to make our determination of what can be regarded as an algebraic integer.

Are some numbers with an irreducible 2 in the denominator then algebraic integers, or do they become mere algebraic numbers because of their denominator, causing a domain switch as a result?

I think they would be algebraic integers, not just algebraic numbers. They don't look like integers because they can't be written as r + st where r and s are in Z, but they are integers because they are roots of a monic polynomial, that is, one where the coefficient of the x2 term is 1.

[desiresjab]

But do we even need to look at the discriminat for that? Can't we just determine the value (mod 4) of the number originally adjoined to our field? Doesn't this accomplish the same thing while being much easier to perform?

What is different about the quotient fields (rings?) of √-5 and √-3 mentioned early in one of the articles we have been referencing back and forth?

I believe numbers of the form a/2 + br/2 can be algebraic integers though they do not appear to be. It may come down to what they can do. Can they help recover unique factorization? Do they qualify as an algebraic integer, or does their denominator represent a weakening which demotes these numbers to mere algebraic numbers but which are still useful for the purposes of ideals, i.e., which still qualify to help?

[YesNo]

I woke up this morning thinking about why integers are defined as roots of monic polynomials. I probably don't have the full picture.

I can see how the integers Z can be defined using first degree monic polynomials. (A monic polynomial is a polynomial over the rationals Q, all coefficients are rational numbers, that when written as a polynomial over Z by getting rid of any denominators the highest nonzero coefficient is 1.) A first degree polynomial looks like this x+3/2 = 0. That has 1 as the coefficient of the highest term, x, but it is not monic because 3/2 is not an integer. It could be written as 2x + 3 = 0 which shows the coefficient of the highest term, 2, is not 1. So the root of that polynomial, 3/2, is not an integer, which is what we expect. If we look at 4x + 12 = 0 and divide by 4, we get x + 3 = 0. That is a monic polynomial since all coefficients are integers and the highest term has 1 as a coefficient. The root is 3 which we know is an integer.

If we try to do the same thing for second degree polynomials we find that the roots of some of these monic polynomials look like a/2 + br/2. That is because the quadratic formula has a 2 in the denominator. Sometimes this 2 cancels out. Whether it does or not depends on the discriminant. If the discriminant is -3 it doesn't cancel out so if we consider the ring of integers in Q(√-3) some of them will look like a/2 + b√-3/2 where a and b are integers. So the ring of integers of Q(√-3), written OQ(√-3), has more elements than the ring formed by extending Z with √-3, that is, Z[√-3].

What are the differences? It turns out the ring of integers of Q(√-3) is a unique factorization domain, but Z[√-3] isn't even a Dedekind domain.

If we look at Q(√-5), the discriminant, -5, is congruent to 3 mod 4 and so there are no integers in the ring of integers of Q(√-5) that look like a/2 + b√-5/2. The 2 in the denominator of the quadratic formula for roots of monic polynomials with -5 as the discriminant cancel out. They all look like a + b√-5. So the ring of integers of Q(√-5) is the same as Z[√-5]. The problem is this ring of integers does not have unique factorization. We will need to use ideals (special subsets of elements) to recover unique factorization rather than individual elements from that ring of integers.

For the first question, looking at the number originally adjoined to the field Q is almost the same thing as looking at the discriminant. For example when we adjoin √-5 to Q to get the algebraic number field Q(√-5), -5 is the discriminant. It just has a radical sign over it. The discriminant is the part under the radical sign in the quadratic formula.

The discriminant does not tell us if the ring of integers will be a unique factorization domain or not. It only tells us if there are integers of the form a/2 + br/2 in the ring of integers of Q extended by the square root of the discriminant. I don't know how they determined which of these algebraic number fields have unique factorization. That would be another piece of the puzzle for me to find out.

[breslevmeir]

i like

[desiresjab]

I believe the root of 4x+12 would be -3 not 3.

That polynomials must be reduced to a minimum polynomial which has to be monic to be of use to us in recovering unique factorization, is understood. However, it seems to me that finding the minimum polynomial for even simple equations is not particularly simple and can involve a lot of algebraic labor.

I still do not see enough to relate this subject to quadratic reciprocity, which I find disturbing. I keep asking myself if the extra factor of 2 in 4n numbers which we observed in the Eisenstein diagram has anything to do with the different behavior of 4n+1 and 4n+3 numbers we observe here. Where does the expression of that extra 2 take place in this arena, if there is any? The only place I can see so far where there is an extra 2 sticking out like a sore thumb is in the denomoinator of those numbers of the form a/2 + br/2, but I do not see clearly if and how they relate.

And I still cannot decide if OQ(√-3) represents a quotient ring, i.e., the kind often represented by R/I. Those rings usually involve division by an ideal which contains a complex number, from what I have seen.

For instance, the possible remainders when dividing by 3i (which involves the Ideal of (3)), are 0, i, 1, 1+i, 1+2i, 2, 2i, 2+i, 2+2i, which is an example given in the chapter 11 link.

Having a way to state long chains of mathematical symbols in spoken language is important to me.

For something like R[√-3], I simply say R adjoined to the square root of -3.

I say it the same way for Q(√-3), and I am wondering if there is a more appropriate way to speak it once we reach the Rationals.

[YesNo]

Yes, you are right. It is -3 and not 3. I got it wrong.

For first and second degree polynomials finding the roots are easy. There exist general algebraic formulas for third and fourth degree polynomials, so the general case is relatively easy there as well, but I think it stops with fifth degree polynomials. No general formula exists. So, I agree it gets harder to find roots of higher degree polynomials.

I don't see where it relates to quadratic reciprocity at the moment either. Given a monic polynomial of second degree, one has something like x2+bx+c where b and c are integers. Then use the quadratic formula to find the roots and see why knowing whether the discriminant is congruent to 1 or 3 mod 4 determines if we will be able to cancel out the 2 in the denominator of the quadratic formula. I think the details were given in one of the links for math stackexchange.

The ring of integers OQ(√-3) would not be quotient ring. It would be an infinite ring like the integers, Z. To get a quotient ring one would have to take an ideal and mod out by it: http://mathworld.wolfram.com/QuotientRing.html I suspect a quotient ring would be a finite ring (at least for Z). The ring of integers is an infinite ring containing all the integers in the algebraic number field Q(sqrt(-3)).

I use the following words which might not be correct terminology: R[√-3] is a module over the ring R extended with the square root of -3.

Q(√-3) would be a vector space (or module) over the field (ring) of rational numbers, Q, extended with the square root of -3. It is an algebraic number field. https://en.wikipedia.org/wiki/Algebraic_number_field

[YesNo]

Here is the stackexchange article: http://math.stackexchange.com/questions/1198188/why-is-quadratic-integer-ring-defined-in-that-way See Adam Hughes response to the question. This is where the mod 4 criteria is helpful. There is nothing about quadratic residues in the answer that I see.

However, reading this again I now picked up on the idea of "integral closure" which might be another key to understanding this better. Here is a definition of an "integral element": https://en.wikipedia.org/wiki/Integral_element As I see it at the moment, using this term, the reason why Z[√-3] is not the way to get to the ring of integers of the algebraic number field Q(√-3) is because Z[√-3] is not integrally closed in Q(√-3). It needs more integral elements from Q(√-3).

I don't understand this either, but that it seems to make sense makes it worth trying to understand better.

[desiresjab]

Here is the stackexchange article: http://math.stackexchange.com/questions/1198188/why-is-quadratic-integer-ring-defined-in-that-way See Adam Hughes response to the question. This is where the mod 4 criteria is helpful. There is nothing about quadratic residues in the answer that I see.

However, reading this again I now picked up on the idea of "integral closure" which might be another key to understanding this better. Here is a definition of an "integral element": https://en.wikipedia.org/wiki/Integral_element As I see it at the moment, using this term, the reason why Z[√-3] is not the way to get to the ring of integers of the algebraic number field Q(√-3) is because Z[√-3] is not integrally closed in Q(√-3). It needs more integral elements from Q(√-3).

I don't understand this either, but that it seems to make sense makes it worth trying to understand better.

The article says that below is the minimum polynomial for a+b√D. I am not sure how they got that. I realize it is a simple concept and manipulation, but I am unable to make this small leap. It would help a lot if you performed the manipulations that got it to the form below. I am not sure how to get a involved.

pα(x)=x2−2ax+(a2−Db2)

[desiresjab]

I say the following as, "Z mod six Z," taking my example from the abstract algebra course I watched last year.

Z6/6Z

[YesNo]

The article says that below is the minimum polynomial for a+b√D. I am not sure how they got that. I realize it is a simple concept and manipulation, but I am unable to make this small leap. It would help a lot if you performed the manipulations that got it to the form below. I am not sure how to get a involved.

pα(x)=x2−2ax+(a2−Db2)

If a+b√D is a root, then so is a-b√D a root. Multiplying the two linear polynomials together we get (x - (a+b√D))(x - (a-b√D)) = x2 - (a+b√D)x - (a-b√D)x + a2-Db2 = x2−2ax+(a2−Db2)

If one lets r and s be two roots of a quadratic equation, multiplying linear polynomials together leads to a general solution: (x - r)(x - s) = x2 - (r+s)x + rs The coefficient of the x term is negative the sum of the roots and the unit term is the product of the roots.

[desiresjab]

If a+b√D is a root, then so is a-b√D a root. Multiplying the two linear polynomials together we get (x - (a+b√D))(x - (a-b√D)) = x2 - (a+b√D)x - (a-b√D)x + a2-Db2 = x2−2ax+(a2−Db2)

If one lets r and s be two roots of a quadratic equation, multiplying linear polynomials together leads to a general solution: (x - r)(x - s) = x2 - (r+s)x + rs The coefficient of the x term is negative the sum of the roots and the unit term is the product of the roots.

Alrightee, that is clear enough. I got it. I should have had it before, but sometimes merely hearing someone you trust say something clears it up better than texts. Of course I am supposed to know what you had to write out, having already seen it multiple times, but somehow it did not completely stick. As long as I finally comprehend things, I cannot concern myself with the time it takes, since that slows me down even more.

[desiresjab]

If a+b√D is a root, then so is a-b√D a root. Multiplying the two linear polynomials together we get (x - (a+b√D))(x - (a-b√D)) = x2 - (a+b√D)x - (a-b√D)x + a2-Db2 = x2−2ax+(a2−Db2)

If one lets r and s be two roots of a quadratic equation, multiplying linear polynomials together leads to a general solution: (x - r)(x - s) = x2 - (r+s)x + rs The coefficient of the x term is negative the sum of the roots and the unit term is the product of the roots.

I seem to have carelessly lost a long post that was supposed to go here.

[desiresjab]

The minimum polynomial when extending a field by √5 is

x2=5, or x2-5=0. Applying the quadratic formula:

-0+-(√02-4·1·-5)/2= +-√4·5=2√5

For √-5, which is a 4n+3 number, the minimum polynomial is

x2=-5, or x2+5=0 Applying the quadratric formula:

-0+-√-20, which merely reduces to 2√-5

I do not see the real difference in terms of 5 being a 4n+1 number and -5 being a 4n+3 number. In both cases above, the 2 beneath the discriminants factors out. What simpleton mistake have I made this time? I have to be looking at something major wrong.

[YesNo]

Your questions make me wonder what is meant by a minimal polynomial. I think it means that given a root, such as √5 or (1+√5)/2, the minimal polynomial of that root is a polynomial with rational coefficients with minimal degree. If we have square roots of non-square integers, these would have a second degree polynomial as their minimal polynomials. Rational numbers would have first degree polynomials as their minimal polynomial. One can always multiply that polynomial by some other linear polynomial, say x-7, to get a larger degree polynomial. The minimal polynomial is associated with specific algebraic numbers, the roots of that polynomial. (The term of the minimal polynomial with the largest degree should have 1 as its coefficient. This guarantees uniqueness of that polynomial. It can be found since the coefficients of the minimal polynomial are over a field such as the rationals, Q.)

What one has with Q(√5) are all of the algebraic numbers that can be written as a + b√5 with a and b being rational numbers. All the rational numbers are in this field because b could be 0.

What the discriminant being congruent to 1 or 3 mod 4 is supposed to tell us is whether there exist algebraic integers in Q(√5) that have a 2 in the denominator or not. The 2 won't cancel in all cases if 5 is congruent to 1 mod 4.

What does it mean to be an algebraic integer rather than just another algebraic number? The minimal polynomial has integer coefficients and the coefficient of the largest non-zero term is 1.

As an example, consider (1+√5)/2.

This is an algebraic number in Q(√5) because (1/2)+(1/2)√5 is of the form a + b√5 where a and b are rational numbers, in this case both rational numbers are 1/2.

To find its minimal polynomial, I used the idea that if (1+√5)/2 is a root then so is (1-√5)/2. (That might be worth trying to prove, but I can't think of the proof at the moment.) If r and s are roots of a quadratic polynomial, then (x - r)(x - s) = x2 - (r+s)x + rs. So, to get the middle term I add the two roots (1+√5)/2 and (1-√5)/2. I get 1 and then subtract it. To get the unit term I multiply those two roots to get -1. So the minimal polynomial is x2-x-1. Using the quadratic formula, I check that (1+√5)/2 is a root of that polynomial.

Is it an algebraic integer? Yes. The coefficients of its minimal polynomial are all integers and the highest term has coefficient of 1.

So Q(√5) has algebraic integers that have a 2 in the denominators as the determinant tells us to expect. That means the ring of integers of Q(√5) cannot be completely represented by Z[√5]. There are algebraic integers in Q(√5) that don't have this 2 in the denominator (such as all the rational integers and √5), but we are only interested in knowing if some of them need that 2 in the denominator.

[desiresjab]

Great post. Nice amount for me to think about.

[desiresjab]

Your questions make me wonder what is meant by a minimal polynomial. I think it means that given a root, such as √5 or (1+√5)/2, the minimal polynomial of that root is a polynomial with rational coefficients with minimal degree. If we have square roots of non-square integers, these would have a second degree polynomial as their minimal polynomials. Rational numbers would have first degree polynomials as their minimal polynomial. One can always multiply that polynomial by some other linear polynomial, say x-7, to get a larger degree polynomial. The minimal polynomial is associated with specific algebraic numbers, the roots of that polynomial. (The term of the minimal polynomial with the largest degree should have 1 as its coefficient. This guarantees uniqueness of that polynomial. It can be found since the coefficients of the minimal polynomial are over a field such as the rationals, Q.)

What one has with Q(√5) are all of the algebraic numbers that can be written as a + b√5 with a and b being rational numbers. All the rational numbers are in this field because b could be 0.

What the discriminant being congruent to 1 or 3 mod 4 is supposed to tell us is whether there exist algebraic integers in Q(√5) that have a 2 in the denominator or not. The 2 won't cancel in all cases if 5 is congruent to 1 mod 4.

What does it mean to be an algebraic integer rather than just another algebraic number? The minimal polynomial has integer coefficients and the coefficient of the largest non-zero term is 1.

As an example, consider (1+√5)/2.

This is an algebraic number in Q(√5) because (1/2)+(1/2)√5 is of the form a + b√5 where a and b are rational numbers, in this case both rational numbers are 1/2.

To find its minimal polynomial, I used the idea that if (1+√5)/2 is a root then so is (1-√5)/2. (That might be worth trying to prove, but I can't think of the proof at the moment.) If r and s are roots of a quadratic polynomial, then (x - r)(x - s) = x2 - (r+s)x + rs. So, to get the middle term I add the two roots (1+√5)/2 and (1-√5)/2. I get 1 and then subtract it. To get the unit term I multiply those two roots to get -1. So the minimal polynomial is x2-x-1. Using the quadratic formula, I check that (1+√5)/2 is a root of that polynomial.

Is it an algebraic integer? Yes. The coefficients of its minimal polynomial are all integers and the highest term has coefficient of 1.

So Q(√5) has algebraic integers that have a 2 in the denominators as the determinant tells us to expect. That means the ring of integers of Q(√5) cannot be completely represented by Z[√5]. There are algebraic integers in Q(√5) that don't have this 2 in the denominator (such as all the rational integers and √5), but we are only interested in knowing if some of them need that 2 in the denominator.

Are you saying...well, exactly what are you calling an algebraic integer--x2-x-1, or one of its roots? Do those roots with a 2 in the denominator become classified as algebraic integers whenever they are the roots of monic polynomials?

Even when you do a great job I still have dumb questions, you see.

[YesNo]

The algebraic integers are the roots of monic polynomials with integer coefficients, that is with coefficients in Z. Algebraic numbers in general are defined in a similar way. They are the roots of monic polynomials with rational coefficients, that is with coefficients in Q.

For quadratic number fields sometimes those roots have a 2 in the denominator such as (1-√5)/2 which comes from the quadratic formula with the 2a in the denominator.

[desiresjab]

Yes, very good. Your explanations are quite acceptable. I take it, then, that an algebraic number with a denominator of 2 does not become an algebraic integer just because it happens to be the root of a monic polynomial with integer coefficients. It is still only an algebraic number, but an important one now on equal footing with an algebraic integer that is a root because it is a root itself.

The denominator of these roots tells us whether the root is an algebraic integer or merely a "rootish," algebraic number.

Multiplying the roots together as you did one can see some action in the denominator. However, working with the quadratic formula in the usual high school fashion, nothing seems to reveal itself with regard to 4n. At that level I do not detect anything about that which we are speaking. I already know there will be an unreduced 2 in the denominator at the end, or there will not be, and I know why it will or will not be there.

I feel I am getting pretty close, but there are still small pieces here and there I do not have in place yet.

When you start out with a field extension you already can see what "type," the root will be, whether it will be a 4n+1 or a 4n+3 number, for instance. When you start out with the quadratic formula you are trying to determine what the roots are. Once you find a root you could always assume a field extension was made earlier. I do not see anything discouraging me from looking at it this way.

Unless I am making a field extension, I have to use the quadratic formula to find roots, and therefore will not know the relationship of my roots to 4n in advance, or not until the formula has worked its root-finding magic.

At least that is my current view of the whole situation. Some of it is bound to be deficient, I suppose, downright incorrect, or short-sighted.

[desiresjab]

And, by God, I believe I know (at least I hope I am right) that every algebraic integer is the root of some minimum polynomial with integer coefficients. But of course every root is not reciprocatively an algebraic integer (because we know of the existence of some monic polynomials with integer coefficients whose roots are yet of the form a/2 + br/2).

I am just musing out loud to see if I am correct or incorrect on a few ideas. Jigsaw puzzles are completed at exponential acceleration as time increases.

[YesNo]

An algebraic number I think could be defined as the root of a monic polynomial where the coefficients come from the rational numbers, Q. The reason to use a monic polynomial is to avoid having many of these minimal polynomials. For example, x - 7 = 0 gives the same root, 7, as 2x - 14 = 0 does. Since the rational numbers form a field, they have inverses so we can divide by the coefficient of the term with the highest power of x and make it 1. For example, 2x - 3 = 0 can be written as x - (3/2) = 0 and the root 3/2 is an algebraic number. In this case it is a rational number as well.

If it turns out that this minimal, monic polynomial has all integer coefficients, then one defines that root as being not only an algebraic number, but also an algebraic integer no matter what it looks like. That means (1-√5)/2, even though there is a 2 in the denominator, is also an algebraic integer. It is the root of a minimal, monic polynomial with integer coefficients. So it is an algebraic integer.

If we are looking at quadratic algebraic number fields, that is fields where the rationals Q are extended by the square root of a non-square integer, such as √5, then checking whether 5 is congruent to 1 or 3 mod 4 will tell us if the algebraic integers could have a 2 in the denominator or not.

[desiresjab]

An algebraic number I think could be defined as the root of a monic polynomial where the coefficients come from the rational numbers, Q. The reason to use a monic polynomial is to avoid having many of these minimal polynomials. For example, x - 7 = 0 gives the same root, 7, as 2x - 14 = 0 does. Since the rational numbers form a field, they have inverses so we can divide by the coefficient of the term with the highest power of x and make it 1. For example, 2x - 3 = 0 can be written as x - (3/2) = 0 and the root 3/2 is an algebraic number. In this case it is a rational number as well.

If it turns out that this minimal, monic polynomial has all integer coefficients, then one defines that root as being not only an algebraic number, but also an algebraic integer no matter what it looks like. That means (1-√5)/2, even though there is a 2 in the denominator, is also an algebraic integer. It is the root of a minimal, monic polynomial with integer coefficients. So it is an algebraic integer.

If we are looking at quadratic algebraic number fields, that is fields where the rationals Q are extended by the square root of a non-square integer, such as √5, then checking whether 5 is congruent to 1 or 3 mod 4 will tell us if the algebraic integers could have a 2 in the denominator or not.

Ah, in red is what I have been driving at and harping on, I don't know why. It was an instinct or the unconscious memory of something I read. It seems now that these numbers with 2 in the denominator can indeed be classified as algebraic integers as long as they are the roots of monic polynomials with integer (no, rational) coefficients.

Hmmm...I still don't know if it is rational coefficients or integer ones.

[desiresjab]

Well, lad, the only thing we have not done is the long, 19th century algebraic manipulations where these ideas came from. I don't know if we need to do that. Between your forced didacticism and my own efforts understanding seems to have arrived.

* * * * *

Now we must ask: have we moved an inch, cosmologically speaking? What do ideals (and for that matter quadratic reciprocity) have to do with cosmology?

Well, do not forget, the deeper structure which we believe silently rules the universe and ourselves is what we hoped to catch a glimpse of by delving into exotic maths. Whether we have done that is a matter for debate, perhaps.

Even when numbers look exhausted and capable of no more order, enough genius is always able to find more structure nested in them. Ideals demonstrate this. I deals did not capture the ultimate order. Ideals could (ideally) apply in only some of the cases where unique factorization is not possible among the integers, polynomials et al. The theory made inroads, it did not settle all matters once and for all; it pointed a way forward.

We will continue to discover deeper and less accessible structures within numbers themselves, which will eventually connect to our own consciousness, I believe. Our consciousness likely hails from some deep structure we have barely glimpsed. Someday a connection will be made between us and the arithmetic structure we keep unraveling, is my one trusted belief.

[YesNo]

I don't know if there is any cosmological significance in this, but there may be. I have enjoyed thinking about it and I did read most of Dedekind's book finally after having forgotten I bought it long ago.

Symmetry is supposed to be related to cosmological ideas. I forget how at the moment. That might be a place to continue pursuing the relationship between cosmology and mathematics. Then, of course, there is also a study of tensors and the Lorentz transformation for special relativity. Here is Einstein's "The Meaning of Relativity" which I have read parts of in the past: http://www.gutenberg.org/files/36276/36276-pdf.pdf?session_id=7a9ac090965e91860290ffa88e68a2f 9e44ff27b

One place where I think mathematics leads cosmologists astray is in a belief in constants. For example, is the speed of light really a constant? Is big G, the gravitational constant, really constant? It is convenient for the mathematics that they are constant, but I don't know how we would be able to tell.

[desiresjab]

The orchestration of coordinated activity of microtubules in brain neurons is one of the initial steps to understanding consciousness as a mathematical phenomenon, i.e., one which can be explained and predicted using mathematical tools some of which might not yet exist.

When there is enough "accord," the microtubules act in unison like a school of swallows banking and twisting at high speed without collisions.

I put accord in quotations. Call it a metaphor for consciousness. Scientists are busy constructing models of consciousness in 248 dimensional matrices compressed to 8 dimensions. They are looking for ways to make the swallows act in unison.

These are the initial baby steps. Where we get to is anyone's guess. My pal YesNo is quite convinced by the Searles argument that strong AI will never come about. Actually, I take YesNo more seriously than I take Searles. To me, Searles has constructed a semantic argument I do not feel compelled to even challenge. It is like one of those old semantic arguments by Kant or Spinoza that seem quaint and innocent enough these days to bring a smile to our lips at yesterday's children.

* * * * *

There is this notion (unshakeable for most) that our own intelligence is real intelligence, and everything else, if it is not made of meat or DNA, is an artificial intelligence.

I beg to differ. Only if we came about entirely without the aid of any form of consciousness is our intelligence the "natural one," the real one. Otherwise, we ourselves are created, and therefore artificial.

If our intelligence (earthly) is therefore artificial, having been aided into existence or manifestation by any form of consciousness whatsoever, then I say the job of creating artificial intelligence is already a done deal, having been accomplished at least once to date.

By extrapolation I might contend that since YesNo and others believe in a consciousness that permeates individual atomic particles, the form of intelligence we represent can hardly have been attained without contact with any individual particles! This makes us and our intelligence artificial since we defined artificial as having been aided in any way by any form of consciousness, even the wee consciousness found in individual particles.

[desiresjab]

I did not see that you had come back to answer.

Yes, symmetry is a major idea. To really study it one should probably delve head first into group theory. Boy, I don't know if I am ready for that right now. I will go only where I have to out of intrigue. Dumb people have to limit their enterprises in some way. I do it by interest alone, letting nothing else interfere. There is always something in math I feel dumb for not knowing, and this provides my main drive. But the motivation is to follow structure deeper.

[desiresjab]

Would you draw any distinctions between constants from physics like the speed of light and a geometrical constant like pi or an arithmetical one like e? For it seems like a number which is its own derivative will not change under any circumstances I can predict.

[YesNo]

The most that anyone can come up with is a model of reality. This is an objective map. It helps make predictions but just because we have a map does not mean that map IS reality. At most it is only a part of reality that we find interesting enough to want to make predictions about. In particular it does not contain our subjective perspective on reality.

The reason I reject AI (both strong and weak version) is because the AI computer is a deterministic-random machine. It is pure objectivity, like a table or chair. It cannot make a choice that is not part of an optimization process that can explain the decision. We can make such choices. A photon can make such "choices" as well. There is no programming or optimization underlying quantum indeterminism because there are no hidden variables to explain the indeterminism.

[YesNo]

Would you draw any distinctions between constants from physics like the speed of light and a geometrical constant like pi or an arithmetical one like e? For it seems like a number which is its own derivative will not change under any circumstances I can predict.

In mathematics, the constants such as pi or e do not change. They are not empirically derived. However, physical "constants" are empirically measured. They are useful up to a certain number of decimal places. We assume they are good for any number of decimal places and that they do not change with time. But how are we going to know that empirically?

[desiresjab]

We have grasped the essence of ideals. I feel my understanding of ideals is on a par with my grasp of QR. It is time to move on unless someone has a cogent remark about ideals at this point.

I do not have an area of math in mind to visit next that I feel relates to cosmology or the deeper understanding of structure in the universe. Exploring fancy counting methods from probablity theory would be interesting and fun but seems far away from cosmological pursuits to me. We only want math involved if it offers the possibility of deep glances at structure, not math merely for the sake of having it.

YesNo may have an area in mind that he feels is relevant.

* * * * *

Belief #1

For the moment, I would like to turn back to what I feel is the surest idea in my philosophy.

For the universe--for all things--to come out of nothingness, is impossible. For nothingness means not only the tangible but the intangible as well. In true nothingness, there would be no existence of any kind. Even the potential for something to exist later is not permissible in nothingness, for that potential would be something which existed, though not tangible.

The forced result is that something had to always exist. There never was a time or a state in which pure nothingness prevailed. Pure nothingness cannot be, it is only a concept of the imagination.

It is logically undenaible that there is something eternal in the universe. Lacking a better name, that thing is existence itself, at the minimum, and perhaps God or consciousness, if we but knew the truth.

* * * * *

Belief #2

In any possible universe with physics, 2 is the successor of 1. Universes which run backwards, universes which are p-adic, and all other apparent exceptions are easily remedied by a simple re-labling, e.g., the last event in a universe which runs backwards would become the first event under the re-labling, easily allaying the problem and casting it in its proper light as no more than a labling phenomenon. Under this belief it is forced that all universes will submit to our mathematical labling. No universe has a choice to refuse, for we are guaranteed to find mathematical lables that apply.

[YesNo]

I agree with your two beliefs.

Symmetry or invariance may be a useful way to see the structure of physical models of the universe. https://en.wikipedia.org/wiki/Symmetry_(physics) I haven't looked at this closely. Relativity is an "invariance" when measuring differences between two events in space-time from any frame of reference. What invariances are there in physical models? Philosophically, what does this tell us about reality?

I have been re-reading Moffat's "Reinventing Gravity". I would like to understand the theory of gravity well enough to make more sense out of Moffat's modification of it. It appears that Einstein's theory of gravity breaks down when discussing galaxies and larger clusters of galaxies. It no longer makes accurate predictions unless one assumes there is dark matter and dark energy present.

Then there is also quantum physics. It is easy to confuse the model with reality here, but one has to know the model to philosophically assess the confusion. These all tie together. I don't think it is possible to compress an atom into a black hole which makes me wonder if black holes are possible. If they are not then Einstein's theory of gravity needs to be modified.

For me, the whole question is philosophical, but I need to understand the mathematics and physical theory to ground that philosophy.

[desiresjab]

It usually seems to me that the deepest propositions from physics are doomed to failure and usurpation. For instance, What is the nature of matter? is to me likely a doomed question any one answer to which we will never settle on for long. Compared to this, the absolute truth of Quadratic Reciprocity stands out like a granite monument of absolute and unchanging consistency.

Each temporary answer we accept along the way will take us far and enable many new miracles of technology. But in the end each will show its limitations and contradictions which prepare the way for a new theory to supplant it.

Each new advancement will have a mathematical framework, sometimes consisting of newly invented or discovered mathematics. When the physical theory it once supported has been supplanted, the skeletal remains of these systems will consist of a funeral scaffolding of mathematics which remains true of itself without the insufficient physical theory it was once thought to support.

In other words, it is not mathematics which we cannot know with certainty, but the nature of physical reality which eludes and will continue to eldue us. Each best theory of physical reality will become insufficient and contradictory. On the other hand, addition, subtraction, derivatives, integrals and matrices are just as useful, true and efficient as they ever were at containing certain aspects of physical relaity.

[YesNo]

That's how I see it also. Mathematics is certain. Technology, when it works, is useful. Physical theory changes.

I found Frank Wilczek's "A Beautiful Question" in the library. It is about symmetry and physics. I expect it to be a survey of ideas he finds beautiful in science.

[desiresjab]

I have avoided studies of symmetry because I feel one must know a lot of Group Theory, since that theory is known for ideas on symmetry. But, yes, it is highly provocative, and probably bears a good relationship to the deeper structures we are seeking.

[YesNo]

I stopped reading Wilczek's book after reading the introduction. All of a sudden I felt like it might not be what I needed at the moment.

I am sort of avoiding symmetry for the same reason, but if I think of symmetry as a way to achieve "invariance" in physics theory I start looking at it differently. I do have Carmichael's Introduction to Groups of Finite Order. That will take some time to read and most of it may not be relevant to physics.

[desiresjab]

I am not searching for religion. But one person I am acquainted with through music and who can suddenly turn anti-religious in the typical ranting way, has already tentatively grouped me with the "religious kooks," I can tell, because I related my recent reflections to him. The fact that I even related them to him indicates the paucity of philosophical minds in this berg.

* * * * *

Let us recap. Over in the thread The Fall under the category of Religion, I offered a proof of the existence of a consciousness if there was a beginning of everything. It is simple, and I am satisfied with it, for the moment.

Going to Scenario #1 where absolutely nothing existed, we see that something had to exist anyway, namely the potential for all other things to come about, or else we could not be here now.

To hazard what this potential actually consisted of, we were only able to come up with two possibilities:

1 Some sort of Meta thing that could exist under these conditions.

2 A Consciousness, i.e., a Will.

No one offered any other alternatives. We were able to dispel the notion of Meta things quite easily, as it turned out. Not a thing else exists, remember, even ideas and other abstractions. The Meta things are like precursors of things to come. Except there is no, "to come." There is no time. The Meta thing cannot become real. It cannot move from its original condition. Its so-called potential to create real things is only an illusion after all.

The remaining possibility is Consciousness. It is a very good candidate because we know so little about it. It is the only other candidate, which is quite compelling indeed. We do not know where consciousness comes from, what truly restrains and produces it, nor indeed even what it is.

The fact that Consciousness can have an Imagination, means to me that even if Time did not exist, it could be imagined by the Primal Consciousness. The same with light and all the other phenomena of our universe. That is something Meta things cannot do, unless they, too, had imaginations, which would end that part of the discussion, and in fact does end it to my satisfaction. Also, Meta things contain no way of kickstarting the creaton of everything.

By this point in our discussion it is okay to sometimes use the word God, since we mean Primal Consciousness by it, and are not ready to assign qualities to God unless we find there is one.

The basic argument is a very old one called the First Cause argument. What satisfies me is that there is no viable alternative to consciousness. In order for Meta things to be able to perform the tasks that the single concept of consciousness could, it would need to consist of myriad other things, such as built in programs for kickstarting Time, a concept, remember, which does not exist. Without an imagination, Meta things cannot conceive of Time, either. Occam's razor seems to demand that consciousness be our philosophical supposition.

The argument has some contingencies regarding the nature of consciousness and its ability to operate under the condition of nothingness. It is the only candidate that might be able to do this. No one else has put forward another.

That is the conclusion of arguments for Scenario #1.

* * * * *

Scenario #2 is the only other possible Scenario. It is the scenario under which we assume things have existed forever. We have seen that it is an undenaible fact that something always had to exist. In Scenario #1 it turned out to be potential in the form of consciousness with an imagination, as near as we could figure.

Under Scenario #2 the world, as in something or the other, as in everything, always existed, it was not created. This scenario is philosophically a tougher nut to crack. Immediately, it is difficult to ascertain a logical necessity for there being a Primal Consciousness. Things simply always were. Hmmmm...

Such a proposition must surely mean life always existed, too. We are talking about times beyond this universe, a trillion Big Bangs ago. This would amount to an absolute certainty that we are not the first conscious life forms. This is asymptotically close to a certainty. Infinite time before us has produced every individual type of thing before us, because there was infinite time to accomplish it in. There actually is nothing new under the sun, in this scenario. There cannot be.
Dwell on it, you will see.

Lack of dwelling on it is one problem in talking about these things with folk who are just going about their daily business. Unless one has dwelled and meditated on the exact topics for hours on end, they are received as just words, which are then processed in the normal way with all predjudices present, right after the grocery list.

Meditate on the concepts to know the truth.

I will now prove the necessity of God under the remaining Scenraio, #2.

You missed it again. Me, too. But, ah, now I have seen it. People underestimate infinity. They underestimate infinite Time. There has been time under this scenario for everything and anything to come about. So a God came about by necessity. This God would not have created the universe (as in everything), but is a God nonetheless.

I am under no injunction to make my God the creator of the universe. I am not a Christian, Moslem or Hindu.

Infinite time produces everything, since things always existed. We know for a fact that if Scenario #2 is true, that it produced consciousness one way or another, which is a step toward God already.

It is improper to view ourselves as the first to evolve toward the Godly, simply because we cannot be, in a Scenario where Time and Things have always existed. It would be logically erroneous for us to view ourselves as the first who have started toward Godhood. Godhood already has to have been attaineded, one way or another, one scenario or another. We have to live with that. It is logically sound.

That concludes arguments fir the case of Scenario #2. I have proven that under any case imaginable, logically God exists.

* * * * *

No single religion or denomination thereof will approve, I am sure.

Remember, I did not say God was not immortal and had not been around forever. I said that if he wasn't around forever, he was around by now anyway. As far back in time as you want to go, infinite time has already existed before that point.

In a universe with infinite time, there are only finite arrangements of all the particles. Even if it takes an octillion years, the exact arrangement of particles which constitutes you will come around again, and you will be born into a world which is the exactly same, nearly the same, or radically different from the one you know now. All of them will come, and have come, given infinite time.

What has existed? Nothing but everything. If not in this universe, which may be finite, then it has existed in another one. Everything we have imagined in our fiction has already been reality--giant robots fighting mankind's battles, dragons, demon possession, time travel--have all inevitably existed under Scenario #2, plus many more things we have not yet imagijned. The cinch is that anything we do imagine has already happened.

* * * * *

God exists, folks. Like it. Unfortunately, the devil and all his demons necessarily do, too.

A Scenario where God is not all-powerful in the sense of having created everything, comes together logically very nicely once one is over the initial hump of realizing there necessarily is a God in this scenario, too. As powerful as you want to name, but not the creator of the universe. Not infinitely powerful, but as powerful as you can name. But possibly as old as the universe anyway, and at least its ultimate inhabitant.

Like it. There is a God who may or may not have created the universe, but who nonetheless may be as "old," as existence itself.

There it is.

[YesNo]

I am thinking along the same lines. At place where we might disagree is here (for some reason I can't quote a post, so I will just copy it):

"In a universe with infinite time, there are only finite arrangements of all the particles. Even if it takes an octillion years, the exact arrangement of particles which constitutes you will come around again, and you will be born into a world which is the exactly same, nearly the same, or radically different from the one you know now. All of them will come, and have come, given infinite time."

If unconscious things do exist and they can be reduced to particles and we are the result of them then I think this would be true. But (1) do unconscious things exist and (2) are they reducible to particles and (3) is our consciousness reducible to them? If there are unconscious particles then what we are may be infinite, with infinite variability and so in a finite amount of time everything could be different.

[desiresjab]

The idea does imply the old notion of randomness and that particles have no other reason to get together. In a mechanistic universe with infinite time available, particle arrangements are finite and must repeat. I am sure you willl have no objection to that much.

Particle arrangements may draw consciousness to them rather create consciousness.

There is also the possibility that consciousness (God) imparted some of itself to us--the conscious part. Where was it stored, so that generation after generation now imparts it to their own kind who are conscious at birth? I do not believe Amoeba are conscious, because they do not have a reflective sense of self. You are convinced electrons are conscious, so maybe you have no trouble accepting an amoeba into the fold.

Or perhaps (something like the mechanistic view again) certain arrangements naturally provide consciousness into the arrangement. The arrangement did it, mama.

Now a man (this man, at least) has to have a pretty good reason for choosing one of these over the other. So far I do not have that good reason. I refuse to believe and defend something simply because I fervently want it to be true. I want there to be an afterlife. But so far I have not proven or demonstrated convincingly that there is one, I have not shown the logical necessity or the likely existence of one. To say that infinite time would create anything, including an afterlife, is not good enough in this case, as it was in the case of physical particles, since we can posit nothing yet as to the nature of this afterlife, if it did exist--what it is made of, and the like.

Of course, not knowing what consciousness is made of, leaves us in the same conundrun.. I have a strong inkling the afterlife is made only of consciousness, however. This final component of the scenario may be made of only itself, indivisible.

* * * * *

The notion that God created us might only mean he imbued an animal with consciousness, not that he directed our evolution from a single cell. These things must all be reasoned out.

The next place to dwell is on the likely nature of God, since we have shown the existence of at least a primal consciousness. In Scenario #1 we could not prove that God was not already dead, however, just that he had existed in the beginning. In Scenario #2 it did not matter if God had died, for he would come around again, eventually creating a version of God that was not temporal.

* * * * *

I lean heavily toward Scenario #2. Christians would like Scenario #1 better. But I guess I am averse to the idea of beginnings. I already know existence was already here. If existence was here, I think everything about existence was here.

God may be in an existence he did not create. The universe he created may only be this artificial one we experience. That is where God would have absolute and universal power, but perhaps not in the larger Scenario he is part of.

To my way of thinking, we are already artificial, along with our whole universe, if we were indeed "created." All creations are artifice, artificial, not original, purposefully made by another consciousness. We would have to admit we are artificial, if we believe we were created. It should not shock Christians that our reality is less real than the reality of God. In the Bible I believe what God is promising to obedient servants is a further taste of that higher reality.

[YesNo]

I agree with what you say about a mechanistic universe. The arrangement of finite particles would repeatedly return to a same arrangement. However, I don't see our universe as mechanistic. So the argument is hypothetical for me.

I don't see consciousness as dependent on self-reflection. Nor the ability to make a choice depend on self-reflection. Our choices appear with prior causes or they would not be "free". Our self-reflective reason rationalizes these prior free choices. So I could have consciousness, characterized as an ability to make a choice, where ever I could show that neither determinism nor uniformly distributed random processes can explain the behavior of something. That would include quantum reality.

Traditionally God does more than "create" the universe like one might create a computer and then let it run down. That's an atheistic simplification of a God to argue against its existence. I agree with them. Such deities do not exist. Besides they are mechanistic and their existence would assume the universe were mechanistic, which it is not. Such deities have nothing to do with what people who are theistic mean by "God". God also sustains the universe, that is, keeps it in being constantly. So there is no way for Him to be already dead.

In Scenario 1, things had a beginning. In Scenario 2, things are eternal. One needs to know what "things" are. Defining things is as difficult as defining consciousness.

Consider Scenario 1: The universe had a beginning. Some consciousness preceded this beginning, but nothing comes from nothing, so there is no-thing now under that scenario. There is only consciousness that gets manifested to us as objects. Our present universe looks like this given the big bang.

Consider Scenario 2: The universe did not have a beginning, but because we are here, the universe does contain consciousness. We don't know that it contains anything "unconscious". What we see is what reality appears like to us. Supposing there is something unconscious in the universe, then we have to make sense out of how both conscious and unconscious reality can exist together. I don't think it can, so even in Scenario 2, all we have is consciousness.

Are we artificial? It is true that an AI robot is artificial just like the chair I am sitting on. Because of that the robot or the chair, not the reality they are made out of, is not consciousness. But we are conscious. How can something conscious be artificial?

[desiresjab]

You are really stretching, while I am staying logical.

The word "choice," is a bad choice for whether something is manifesting consciousness, because your standards seem so low for what constitutes a choice.

God is only for sure not dead under Scenario #1 where he created "everything," out of his imagination and must still be around to keep the light show going.

* * * * *

For a consciousness unfamiliar with ideas, what starts as an urge could grow into an idea.

The necessary Gods of Scenario #2 did not create the universe. The necessary ones (as in logically demonstrated) are products themselves of a universe infinitely old which has had to produce everything already that it was going to. And given enough time, one of the things it was going to produce were beings that made us look like amoeba at a Mensa meeting, spread out among the stars, or in hidden universes.

If God is next of kin to consciousness, God is not dead, but it had to be mentioned and considered.

Your personal beliefs are pushing way ahead of the discussion and proof. I cannot grant consciousness to particles or state flatly the universe is not mechanistic.

* * * * *

I am willing to logically speculate on certain things, and call them speculations.

In #2 it seems to me we could expect every kind of God, both good and malicious. A God powerful enough to be the devil seems likely. (There I go again trying out of the corner of my eye to rectify my speculations with Christian tradition simply because I grew up in it, when I do not actually believe the relgious part of the tradition any more than I believe Moslem teachings.)

We could expect a malicious God powerful enough to be called the Devil. Judaic/Christian tadition tells me the Devil is so powerful that God can only protect me under certain conditions. I have to behave. A father does not sentence his own "children," to an eternity of the worst kind of punishment for misbehavior, unless he has no choice. So, the God known as the Devil would be quite strong, if Scenario #2 is the real scenario.

Ignoring Biblical sources, we may postulate the devil is either an invader in another God's domain, or a rightful occupant fighting off an invader.

[YesNo]

What we are both doing is rationalizing our prior beliefs. We are both being logical but we haven't convinced the other. That is fine. We shouldn't aim to convince, but to use this opportunity to clarify our position for ourselves, make our rationalizations better.

The reason I use choice is because it is how one could interpret quantum physics. The standards are that the behavior cannot be explained by either determinism or uniformly distributed chance. I don't know what consciousness means for those particles. All we could see is the behavior, so this interpretation is speculation, not science. However, I think it is a more sensible speculation than to say something, like many world does, that an entirely new universe that we can't see pops into existence for every possible outcome at the quantum level to eliminate the choice interpretation.

We agree in Scenario #1 that God sustains, not only creates.

I think I understand that the Gods, both good ones and bad ones, in Scenario #2 would be combinations of particles that just happened to happen. Given an infinite amount of time everything will happen. This argument is similar to the anthropic principle. However, is Scenario #2 even appropriate for the reality we experience. Is reality really reducible to particles and is the universe mechanistic? That has to be established or at least noted that it has not been settled before one can say much about Scenario #2. In Scenario #1 we started with consciousness. That evidently exists because we are conscious.

You used the phrase "manifesting consciousness". The more correct phrase for Scenario #1 is "consciousness manifesting things" because consciousness is the given in Scenario #1. Which brings me back to the question: what are things? We make cultural things, like chairs and computers, out of stuff or things, but culturally what we see are the objects we have made not the underlying stuff they are made out of. None of those things are conscious as a chair or a computer, although the stuff they are made out of may be conscious. The closest we get to creating something conscious is through procreation. The resulting baby is conscious unlike the chair or the computer. I think the reason the baby is different from the computer is because the baby can make choices and the computer can't. That is another reason why I keep coming back to choice.

[desiresjab]

Not being a Christian, I feel no pressure to posit free will, either. I don't know if we have it. We are at least free enough to believe we are making decisions and to see ourselves as having free will. We seem to ourselves just like beings with free will.

In case there is a Judaic/Christian God, it is better that I am not free. If there is a God, then no merciful being would send his children off to an eternity of punishment when they were not responsible for their own actions. Maybe we are only semi-responsible, at best. The Primal Consciousness would know this and cut us a break, if he were really merciful and compassionate.

[YesNo]

I'm not worried about hell. Our ability to make choices, not just imaginary ones and not with absolute freedom, makes sense to me. I see no reason to reject it.

[desiresjab]

Kidnapped and enslaved by the Devil is how I would interpret hell. Evil Gods must take some pleasure in pain. Or maybe their pleasure is in capturing subjects of the altruistic God. It is not out of the question that we are caught in the middle of a battle between these high lords who did not create the universe or all things. Like Pork Chop Hill, we are not important in ourselves, but as symbolic turf.

[YesNo]

As a theme for fantasy fiction, that view of the Devil might work. The only thing I know of the afterlife is what people who have had near-death experiences or people who have received after death communications tell me. I would count the events after the crucifixion of Jesus in those communications and experiences realizing the canonical accounts might have been modified for theological correctness. Personally, I imagine heaven and hell as a different, perhaps expanded, perspective on reality from our current perspectives which are very localized.

I picked up Jeffrey Long and Paul Perry's "God and the Afterlife" in a used book store a few days ago. They research near-death experiences. Often I don't read the books I buy, expecting to read them sometime in the future and then forgetting about them, but you are encouraging me to look at this now.

[desiresjab]

I cannot find any necessity yet for God to be good. An excellent case could be made and has been made that God is evil. I want to believe God is good but I need some evidence.

I cannot expect any religion to have gotten the whole thing right. I think each got only small pieces, in some cases the same pieces, but very small pieces. The common thread was probably wishful thinking. No religion is likely to have come close to the truth.

* * * * *

The Bible is very big on touting the mercy of God. At the same time God shows hardly any mercy at all in the Bible. This very human God is jealous, angers easily, vengeful, and spills blood often. Not a strong recommendation for mercy. I do not presuppose any such qualities in the Primal Consciousness. Maybe it is not the primal consciousness, then, but one of those Gods that came about naturally through Scenario #2 which has no Primal Consciousness to be found that is necessary.

There can be only one cosmological excuse for the strict harshness of the biblical God, if he is as good as advertised--his own impotence at certain acts--it is the only way he can protect his children. If they play in the street he must spank them, though it hurts him. This means the devil is strong. Many people choose to believe in God but deny the devil. If biblical cosmology is true, there must be a devil, from the evidence in the world.

* * * * *

A more acceptable view to many might be that there is only a God and no devil, but that the world the Lord made was wrought with implict dangers and risks. Hence, accident as well as evil can carry a man off.

As anyone can see, proving the existence of God under certain circumstances, is a piece of cake compared to proving his nature. The proof God exists is but a dry thing with little inspiration in it.

* * * * *

Providing that Consciousness really is indivisible, God would be proven to still be alive, under Scenario #1, since the indivisible cannot be further destroyed. Most Christians put their faith in something like this.

God might be the sum total of consciousness in the universe, not just all the consciousness we observe. That it is all connected at some source is an earnest wish of many.

Myself, I care only about one thing--an afterlife. Without an afterlife who cares about anything, really? I do not really believe the afterlife has a price of admission per se, as advertised in the bible, but the threat of punishment was necessary to keep the kids out of the road.

[desiresjab]

I can think of only one reasonable explanation of the biblical God's apparent wish to be worshipped constantly--without constant vigilance we easily lapse back into our animal ways whereby Cain killed Able, etc. Again, not for him, but for us. That would be my rationale.

[YesNo]

There is no necessity to reduce God to any particular religion. So talking about God does not imply accepting Christianity or the Muslim religion or some Hindu religion or a New Age religion. All of these are ways to approach God. There are multiple perspectives on the Biblical God depending on the original sources of the text.

I also don't think there is much of a case for a God that is "evil". That is because near-death experiences do not report such an evil God.

I also don't think there is any point in pursuing the mechanistic Scenario #2 because quantum physics shows that reality is not mechanistic.

[desiresjab]

There is no necessity to reduce God to any particular religion. So talking about God does not imply accepting Christianity or the Muslim religion or some Hindu religion or a New Age religion. All of these are ways to approach God. There are multiple perspectives on the Biblical God depending on the original sources of the text.

I already said I think all the religions together got only a little bit of the truth, sometimes ovelapping. What are you accusing me of? All these religions think they are a way to approach God. So far they haven't done much approaching, from the evidence at hand. One thing about higher consciousness--it does not seem to be contagious. We will always be referring back to religions and human experience.


I also don't think there is much of a case for a God that is "evil". That is because near-death experiences do not report such an evil God.

Well, I think there is not much of a case, either, for a God that is good. It seems pretty resasonable to me that if there are good Gods there might be bad Gods as well.


I also don't think there is any point in pursuing the mechanistic Scenario #2 because quantum physics shows that reality is not mechanistic.

Is there a particular reason you think Scenario #2 has to represent a mechanistic reality? I know "mechanistic," smacks of the antiquated to you and is practically a dirty word. If existence was always here, how does that translate as necessarily mechanistic? I am not saying you are wrong, I just want to know what you mean by the word. Do you think something which evolves by itself is mechanistic because there would be no guiding hand of consciousness, so to speak?

* * * * *

Suppose for a moment that pipelines to higher consciousness do exist. I know that east Injun texts exist which speak in terms of trillions of years of existence, because a long time ago (ahem! relatively speaking) I read some of them. I am not sure if it was the Bahagavad Gita or something else. Man, that is nearing 50 years ago.

Trillons of years is thousands of times older than we scientifically presently suppose our own universe to be. The east Injuns have always been good at numbers. Were they just making up the largest ones they could write in these cases, or did they mean what they said?

[desiresjab]

To have an afterlife is no more unlikely than to have a conscious life. Under scenario #2, just as life happens to be part of it, afterlife might also happen to be part of it.

And what if "Things," are eternal but a master consciousness is also eternal? It seems tro me there could still be God under Scenario #2. And in this case an afterlife of some sort seems very likely to me. I sometimes think of ourselves and of all living things as the sensory organs of this master consciousness, who created us because it needs us and amoeba to experience life at every level. Now that would be a God to me!

An afterlife under Scenario #2 and Scenario #1 seems likely to me, because why would God make throwaway parts? Why would those consciousnesses finally maturing at what they do, be suddenly discarded? God would make permanent beings, especially if he is a good God, because reflective beings desire permanence more than anything else.

[YesNo]

Regarding this question: "I already said I think all the religions together got only a little bit of the truth, sometimes ovelapping. What are you accusing me of?"

There is no accusation. We agree that religions only approximate the truth. They are like someone trying to write out the digits of pi. Some write 3.14. Some write 3.1415. Some go further. Some write 3.212 and get it wrong. No matter how far they go, they are still approximating with these digits. Here's the problem: Is pi itself real? One can't resolve that by saying because 3.14 and 3.1415 are different or not exactly what pi is that pi is not real. The same with God. One can't complain about particular religions and claim that God does not exist. Furthermore, if someone were able to write out all the digits of pi, that would convince me that pi did not exist. Same with God. If some religious texts exactly represented God non-metaphorically that would prove God did not exist.

I don't know what Scenario #2 is if it is not mechanistic. In that scenario, if I understand it, there are a finite or infinite number of particles to which everything, including God and our consciousness, can be reduced with different arrangements of them. With infinite time by chance or determinism all arrangements will occur over an over again. The underlying problem is can such reductions be made?

Last night I watched a set of six interviews on the observer problem in quantum physics: https://www.closertotruth.com/series/what-are-observers If we are talking about particles, we need to get quantum physics involved. The problem is that our only experience of a quantum particle occurs when we make a measurement and then it appears as a particle. We can only see quantum reality as particles. Furthermore, we can't predict exactly what will happen to any specific particle later, but we can give a probability distribution for what we might expect to see. That probability distribution is the wave function. If we could exactly predict what the particle would do there would be no mystery, but now there is this critical mystery: When we are not looking at a particular particle what is it doing? There are three general positions based on these interviews:

1) When we are not looking at the particle it is in a superposition of many possibilities. We are also in those superpositions and this creates a many worlds description of reality. See the interviews of Sean Carroll and Alan Guth.

2) When we are not looking at the particle it is in a superposition of many possibilities, but when we observe the particle those possibilities collapse into one definite particle, which is the only thing we can ever actually measure. This would be the Copenhangen or decoherence position. See the interviews of Laura Mersini-Houghton and Seth Lloyd and perhaps some of Paul Davies.

3) When we are not looking at the particle it has no properties to manifest. The wave function is only valuable for mathematical predictions. It is not reality. When we observe what a particle does it makes a choice. This would by my position. For something similar, see David Chalmers and perhaps some of Paul Davies.

For Scenario #2 to make sense it needs to fit one of those three interpretations.

Regarding this statement: "Well, I think there is not much of a case, either, for a God that is good. It seems pretty resasonable to me that if there are good Gods there might be bad Gods as well."

Perhaps we differ on perspective. I am not concerned with something being "reasonable" without empirical evidence to back it up. That is why I need the information coming from those near-death experiences, mystical experiences or personal experiences of my own subjectivity to tell me if there is an afterlife or a God. I won't trust my reasoning alone to get there without some empirical evidence to back it up. You may be a "rationalist". I am likely best described as an "empiricist".

[desiresjab]

You get stuck on notions, so I have to go against my speculative nature and play the rantionalist. Do you have some empirical evidence for a good God, good God?

You say:

When we observe what a particle does it makes a choice.

It makes a choice, eh? You are like a religious person with this chant, then all you do is refer me to your bibles. Convince some people that quantum particles make choices. How many people have the professional convincers convinced? I am not going to plough through your references. If the people you have read did their job, you should be able to present the case to me.

I can easily improvise an argument that the particle in question did not make a choice. I say it was in a specific place all the time as a particle. Since we were not observing it all of that time, how are we supposed to know where it was or what it was doing? Quantum particles operate under a different set of rules than big objects. Just because we cannot predict their positions as if we were dealing with planets, does not give them consciousness or the ability to make choices. It simply means we are just beginning to understand the rules of the realm, and may be getting ahead of ourselves.

I don't know, and the above is my own improvised argument. You should be able to shoot holes in it. And you should be able to discuss it instead of asking me to plough through a hundred articles and books.

Observation itself may change quantum phenomena. It does not do much to the side of a barn when you shoot a beam of light at it. Photons are in the same size scale as the particles we are using them to observe. So, they will "blow," them around a bit, I suppose.

You keep making the statement, lad. Let's see the evidence now instead of the continual statement repeated. If you have strong reasons, present them. I am only playing devil's advocate because I have to. I am receptive to the idea of "cosmic consciousness," but not ready to state it as truth. You state it as truth. You claim you are empirically convinced. Let's go. That means evidence.

[YesNo]

In response to: "Do you have some empirical evidence for a good God, good God?"

Yes, near-death experiences and after-death communications. They don't report an evil God.

In response to: "You are like a religious person with this chant, then all you do is refer me to your bibles."

I referred you to interviews of people with three very different opinions: (1) many worlds, the materialist perspective, (2) decoherence, the dualist perspective and (3) panpsychism, the idealist perspective. I disagreed with most of the interviewees. They aren't my bibles. I read them or listen to them to see where I differ from them.

In response to: "You claim you are empirically convinced. Let's go. That means evidence."

The evidence is partially in the near-death experiences. These are case studies. The quantum evidence comes from repeatable science experiments. My position is an interpretation of them. I think the idealist interpretation fits the problem better.

I don't think you should accept "cosmic consciousness" without understanding it. It is easy to get stuck in some New Age fog about quantum reality.

[desiresjab]

The near death experiences are not bad evidence, after a fashion, of course. I like it at least. You say they do not report an evil God. Do they report any God at all?

My biggest doubt comes from observing light bulbs blow, and realizing stars (of the right size) expand to a red giant before going out. One may take a split second and the other millions of years, but they seem like similar phenomena on one level of abstraction. There is a little light show from both before they expire. The brain may put on its own light show just before we die. The light show could even be culturally conditioned. For that reason it would be interesting to see the reports of people who came from non-Christian cultures. Are their experiences any different, I wonder.

What is needed is a way of inducing this state into humans we can later revive and get reports from after a prolonged experience. Performing such experiments would walk an ethical tightrope, of course. I can see such experiments providing valuable evidence, relating, possibly, to both dreams and space travel.

I believe astral travel is possible, and I believe experiments can be designed to test that. I tried it as a young man. But I got scared and backed out when it felt like it was beginning to work. Now I would fear for my old body more than my "soul."

The next paradigm in human evolution may well come from an arcane area like this, rather than pure scientific research in physics. This has been my feeling for some time. I believed it before I ever read it. Once that door of possibility is opened a crack, earnest research will begin on a large scale.

One of the drawbacks may be that financially valuable results could be scarce or a long time coming in this field. I think the U.S. administration at the present time is skeptical of even the value of the space program in general. They would be much more interested, for instance, in new allloys that might be produced under the zero gravity of space, than any speculative advances on our nature and origin. The human race has outlasted all administrations so far. Our angle of interest is a changing feature of us.

Some high powered minds like the mighty Brian Josephson have already made the switch to the future line of resesarch. They went southpaw. Probably only their great standing keeps the pitchforks and torches away.

Truth be told, this field of research will always be a magnet for charlatinism, sloppy experiments and results obtained because they were desired. Maintaining scientific discipline and distinguishing disciplined results from a huge tangle of less disciplined, will be key problems in the coming paradigm, as they already are now.

[desiresjab]

I forgot to add that I think it is a trend in physics today to name your theories after appealing human abstractions. In songwritung they are called "Hooks."

Relativity, String Theory, The Big Bang, Many Worlds, Cosmic Inflation...Particle Choices--these are all hooks, carefully chosen names to draw people in, even those named long after their inception. The hooks are so powerful and compelling they gain admirers and become our favorite songs. Hooks will be an even greater problem in the future, I can foresee, making it more difficult to distinguish good research from good names.

[YesNo]

Some of the near-death experiences mention God and that God isn't restricted to one religion or no religion or a particular culture which is as one would expect it to be if it is true. I mentioned earlier a book about this: Long and Perry, "God and the Afterlife" that I skimmed recently. Other information is available at http://www.nderf.org/index.htm Having said that, I don't spend too much time looking at this research except to get a general idea what the results are. Religious groups have to come to terms with this evidence as much as atheists. As a panentheist, these results don't contradict anything that I think is true.

I don't know much about astral travel. I have found out how to see auras. They are easy and safer than astral travel.

I agree with you that one has to avoid foggy results including the fog in established science with their "hooks" as you put it. For example, I don't see how an empirical scientist can even consider many worlds that no one can see as an interpretation for anything. A speculative science fiction writer might find it cool. As a reader I would find it boring. The same thing goes for black or dark stuff in the universe that no one can directly observe that keeps a current gravitation theory afloat. That there exists other gravitation theories that don't require these things is all the more reason to modify the current one and get on with it. However, developing experiments to prove or disprove any of these is worth doing. It improves our skills and knowledge. Part of my interest in looking at scientific results that I question is to ask what is the cultural motivation underlying these beliefs.

I am interested at the moment in "quantum computing". I don't understand what underlies it. It might challenge my idealist perspective but perhaps it doesn't.

[desiresjab]

After doing some cursory reading on Near death experiences, I find the following to be true:

A small percentage of people (anywhere from 1% to 25%) report hell and or demons in their near death esperiences. So perhaps there is some evidence for an evil God after all. The scientific rationale for NDEs is similar to mine. It is interesting that a person sleeping can detect a bright light shined at their eyelids and can give signals back to the experimentor while remaining asleep. My own problem with Lucid Dreaming, and I have had them, is that I wake up every time I become aware I am dreaming.

I don't know what my swami boys up in the Himalayas can do. Reports vary. When talking about this subject expect hyperbole and wishful thinking. The tiger swamis are supposed to live around tigers like house cats and command them. Recently we got a glimpse of their modern spiritualism when they were charged with selling tiger body parts on the black market. Maybe donations were down.

There is not a single human beyond corruption--Papal assistants, tiger swamis, TV ministers. Where does that leave the rest of us? Well, it leaves us without power, always a good place from which to begin a spiritual quest.

Apparently, Christians never see Buddah coming to pick them up in the taxi to heaven, it is always Jesus. Hindus never see Jesus coming. The experiences do seem to have strong cultural inflections.

* * * * *

The only way I can reconcile heaven with a merciful God is if you get what you believe at death. Those who believe in Christian heaven get that. Moslems get a moslem heaven replete with immaculate virgins. I hope there is sort of a library where Christians can check out virgins for a while, too.

That is the preparation for the afterlife we are in. We are here to imagine it so strongly that it shapes it beforehand at quantum level. It is our ticket. One way or another, we are leaving, but there are different destinations. All tickets are not the same. For all we know, only the imaginations of the devout work hard enough to put some extra shape on their afterlife. Other peoples' occasional musings and vague beliefs may not be enough to transform the quantum architecture of a generic afterlife into something more special, which could be the whole point of religious devotion.

[tailor STATELY]

As a man of faith I've been enjoying your recent interchange of ideas and comments and keep coming up with a remembrance of "The King Follett Sermon" by Joseph Smith, Jr. (First President of The Church of Jesus Christ of Latter-day Saints). The "Sermon" isn't canonized by the church, hence Mormon literature, but offers insights to the character of God as revealed to Joseph... http://mldb.byu.edu/follett.htm I've been reflecting upon the "Sermon" and its consequences for years and continue my study within the canon of LDS scripture.

Ta ! (short for tarradiddle),
tailor STATELY

[YesNo]

Religions that have an immanent and transcendent view of God would be "panentheistic" by my view of the word, however different their practices or texts may be. That includes Christians, Hindus, many others and pagans and even some atheists who acknowledge their own subjectivity which is hard not to acknowledge. One thing I disagree with Joseph Smith's writing is this which comes from John and is similar to the beliefs of other Christian religions: "This is life eternal"--to know God and Jesus Christ, whom he has sent." The only part I disagree with is the implication that this is the only way. Life like ours on other planets will not know Jesus, nor will such life in other universes. This can't be the only way.

I don't see anything other than that to disagree with because I don't know enough about it. He did mention something interesting about the Devil:

"The contention in heaven was this: Jesus said there would be certain souls that would not be saved, and the devil said he could save them all. The grand council gave in for Jesus Christ. So the devil rebelled against God and fell, with all who put up their heads for him." http://mldb.byu.edu/follett.htm

That brings up the idea of hell that desiresjab mentioned. Some people do experience hellish near death experiences. I don't think that implies God is evil. Nor do I think that implies there is an eternal hell. Long and Perry have a chapter on hellish experiences in "God and the Afterlife". Long, I assume, wrote, "I never read an NDE describing God casting the NDEr into an irredeemable hellish realm." (page 171) He speculates that they would be there because of "very poor choices" and they "have the free will to both make good choices and return to the heavenly realms".

Regarding cultural influences on what those having an NDE saw, he asked them "Have your religious beliefs/spiritual practices changed specifically as a result of your experience?" 73 percent said they had. (page 189) They may go into these NDEs with a cultural bias, but many come out with a changed perspective.

[tailor STATELY]

Life like ours on other planets will not know Jesus, nor will such life in other universes. This can't be the only way. The doctrine of my faith teaches that our Savior is the Savior of all worlds. A poem by Joseph Smith, Jr. that resonates for me:
For the Lord he is God, and his life never ends,
And besides him there ne’er was a Saviour of men. …
He’s the Saviour, and only begotten of God—
By him, of him, and through him, the worlds were all made,
Even all that career in the heavens so broad,
Whose inhabitants, too, from the first to the last,
Are sav’d by the very same Saviour of ours;
And, of course, are begotten God’s daughters and sons,
By the very same truths, and the very same pow’rs.”
(Times and Seasons 4:82–85.)

... a link to one of my favorite hymns: http://www.timesandseasons.org/harchive/2004/03/if-you-could-hie-to-kolob-lyrics/

[YesNo]

I can see how that would be the case because the divine is "one", but other cultures may use other names and practices to approach the one divine. Although I don't think Christianity is the "only" way to the divine Christianity is still "a" way to the divine and there is no need to convert to something better.

[YesNo]

I have been re-reading John Moffat's "Reinventing Gravity". I am at the part about his theory of the variable speed of light at the beginning of the universe. He rejects the various inflation theories and adjusts Einstein's special relativity so that the speed of light is not a constant. This allows for the universe to be homogeneous without invoking inflation.

One of the ideas that I found interesting is the idea of a "bimetric" separating the speed of light from the speed of gravitational waves. These two would vary between themselves to avoid inflation in a different way from the variable speed of light theory he originated above. Generally it is believed that there is one metric, the speed of light, which is constant and gravitational waves travel at the speed of light.

[YesNo]

Moffat mentioned that he is not the only one who has promoted the variable speed of light in a vacuum as an alternative to inflation to get the universe into a homogeneous state. More generally the variable speed of light in a vacuum has been considered by others. Here is a survey of these ideas: https://en.wikipedia.org/wiki/Variable_speed_of_light

[YesNo]

I just came across another survey article at a deeper level than the Wikipedia article by Jo˜ao Magueijo who Moffat mentioned. It was written in 2003, older than the Moffat summary I am reading written in 2009: http://cds.cern.ch/record/618057/files/0305457.pdf

Also it looks like a test of this may be underway perhaps to complete in the next five years with improved measurements of the "spectral index" for which they made a prediction based on their theory: https://www.theguardian.com/science/2016/nov/28/theory-challenging-einsteins-view-on-speed-of-light-could-soon-be-tested This article is less than a year old.

[YesNo]

I have nearly completed a second reading of Moffit's book. I've come to realize that there are many people who are looking for modified gravity theories because dark matter has so far not been found. One has to do one or the other: modify the gravity theory or find dark stuff.

One blog I found interesting was Sabine Hossenfelder's http://backreaction.blogspot.de/2015/05/testing-modified-gravity-with-black.html Here is the archive header for the paper she references: https://arxiv.org/abs/1502.01677 The Event Horizon Telescope may be a way to falsify either Einstein's general relativity or Moffit's MOG. Here is an update of the project: http://eventhorizontelescope.org/blog/eht-update

[YesNo]

I found out that John Moffat has a more recent book (2014) on the Higgs boson and it is in a local library. He writes very well. Maybe he'll help me figure out what that boson is.

[desiresjab]

If there is a God, and if God knows our future, does not his knowing then preclude our having free will? For if God knows, then it is predestined, is it not? And if it is predestined, our sense of free will and choice is illusory, is it not?

Would God then have made a universe whose future he could not read? Or could he read it if he chose to but simply has the will power and the character never to peek?

Isn't it the position of several major world religions that God knows everything, including the future? I think it is safe to say this was/is the position of many Christians I have known quite well. I cannot remember any scriptual support for the position right now. Maybe there is some.

Anyway, several of the world's major religions believe God is ubiquitous and all-knowing. But it seems to me this idea might be inimical to the idea of free will. Am I wrong?

[YesNo]

If you assume God knows our future exactly, then you have assumed we have no free will.

However, if we do have some free will, then he doesn’t exactly know our future.

Can one reconcile an omniscient God with one who does not know more than probabilistically what we will do in the future? I think one can. If one defines “omniscient” to be knowing everything there is to know, then God would be omniscient and still not know exactly what we will do. We have our free will and God has his omniscience.

I don’t speak for any religion. I am sure some religious people think we have no free will because God knows everything (more than what there is to know). However, I think that leads to a contradiction. Not that it really matters since a religion is about establishing a relationship to God, not obtaining philosophic knowledge.

[desiresjab]

The phrase Some free will is curious. My belief is leaning differently. I believe we may have no free will but are asymptotically close to it, so close we cannot tell if we are free or puppets of fate.

The two phrases Some free will[ and Asymptotically close to free will may be trying to express approximately the same idea. But either leaves me with no idea what God is allowed know so that I may still have free will. Very tricky of God, I must say.

God may have built the discoveries of Godel into the universe. Free will is one of those questions of which we cannot even decide if it has an actual answer or does not.

One question to ask ourselves is whether we ourselves could build something whose future would necessarily remain shrouded in mystery to us? If we can do that, it is easy to assume God can too.

One might naturally argue that we built this country and its future is unknown to us. God made the dirt, we cultivated it and gave our patch its own name.

[desiresjab]

If you assume God knows our future exactly, then you have assumed we have no free will.

However, if we do have some free will, then he doesn’t exactly know our future.

Can one reconcile an omniscient God with one who does not know more than probabilistically what we will do in the future? I think one can. If one defines “omniscient” to be knowing everything there is to know, then God would be omniscient and still not know exactly what we will do. We have our free will and God has his omniscience.

I don’t speak for any religion. I am sure some religious people think we have no free will because God knows everything (more than what there is to know). However, I think that leads to a contradiction. Not that it really matters since a religion is about establishing a relationship to God, not obtaining philosophic knowledge.

Sounds like an opinion to me. The opinion of some would be that religion is about controlling the populace and always has been. The belief you expressed would be exactly what the controllers want the controlled to say.

Besides, how many of the major religions are about having a personal relationship with God? Buddhism is not about that, and I am not sure Hinduism is either. I have never heard any Moslem speak about achieving a personal relationship with God.

It seems this idea of religion being about a personal, loving relationship may simply be because you are a westerner raised in a religion where that happens to be the rare case.

I do not know this for sure. I would like to know what others with more experience and reading in religion have to say about this. Is religion in general really about a personal relationship with God, or is just ours?

Let us not play the silly game of calling any interaction whatsoever a personal relationship. The phrase means more than that. It means something specific. I am not sure that applies to all other religions or even a majority of them. There are probably some people with strong ideas on this on here. I would like to hear their opinions. Not likely that I will, I have found, but I would like to anyway.

[Kate23]

I consider myself to be a cosmologist as well, as everything that is happening in the world has an impact and depends on the Universe. Everything which is around us, and we ourselves, cosist of energetic particles, every little thing in the Universe has the same inner structure, that is why you cannot deny the idea of reincarnation, as energy never comes from nowhere and never goes anywhere, it can only transform into a different object.

[desiresjab]

Dwell on a picture and you may start to see things within it you had not noticed before. Some pictures are made that way purposely, some just contain that potential by accident. You can do the same thing with philosophical concepts. If I dwell on the idea of death long enough it seems not to be the end. I can almost see more. The vision is so murky I cannot be sure what I see, yet the impression is quite strong. It averages out to more an intuition of something, rather than a clear picture. A strong intuition says there is more after death. Can't prove it, cannot even convince you. Near impossible to describe. Still, something is trying to become clear. Not sure how to let it, or if there is a way to improve the image.

[YesNo]

That reminds me of the "contemplation" Plotinus wrote about. It's a different way of seeing reality. Shimon Malin discusses him and Whitehead in "Nature Loves to Hide" as well as this other way of seeing.

[desiresjab]

That reminds me of the "contemplation" Plotinus wrote about. It's a different way of seeing reality. Shimon Malin discusses him and Whitehead in "Nature Loves to Hide" as well as this other way of seeing.

At first, the surprising thing seems to be that human beings are still here. Of all the ill-equipped who would not be likely to survive--but here we are anyway. Before this, no single man had the power to destroy mankind, or at least civilization, in total. That was our saving grace. Ninety wiped out here but ten survived scattered elsewhere. Those were the kind of odds we kept beating. For what? A miserable and a short life, buried in our own feces until the last century. We endured millennia of discomfort for this we call life now.

I first find it surprising that we ended up here. I next find it surprising that we survived, and even seemed to flourish. The compound probability of this trio of surprises together nods toward the belief that the universe is not pointless after all, that unlikely things may be happening because there is a will for them to happen.

[YesNo]

It does seem unlikely that we are here at all.

[desiresjab]

Looking at us, that we made it is really shocking. We all know that many societies were wiped out courtesy of another. One reason we made it is that everyone was not connected yet. The world was full of little feudal fiefdoms disconnected from each other. Villages. Tyrants with the disposition to wipe out the world had not the means. But they could play hell with their neighbors.

Archimedes could figure out the volume of a sphere, but man did not yet know what to do with his feces. Pooping into a hole in your floor into a rivlet running beneath was the ancient equivalent of indoor plumbing

[YesNo]

At least they had a nice view of the river.

[desiresjab]

Not too nice for the folks downstream where the water slowed and turds clogged on bushes and fouled embankments. They are still doing that and worse in India and other places. Public squatting is a tradition. I once figured out what the pile of untreated human waste from a single day globally would look like gathered in one place. Make um big heap.

* * * * *

I read or saw somewhere that a famous cosmologist said the entire universe might be up to 1023 times more extensive than what we know of.

00,000,000,000,000,000,000,000. Well, up to 99 sectillion times larger. I would call that a fairly extensive place.

[YesNo]

As long as it's not infinitely large we have hope to get from one end to the other.

[desiresjab]

Its size suggests its potential diversity.

[YesNo]

This diversity is quite large. Given enough data it might not be possible to have a relativistic and deterministic gravitation theory. That would be something worth trying to show. Indeterminism would not only be at the quantum level but at the gravitation level as well.

[desiresjab]

Now for a tough question: Is infinite diversity possible in a finite universe?

[YesNo]

I would guess not, but I don't know. Assuming the finite number of things are isolated from each other so no infinitesimal distances either.

[desiresjab]

Let's cut right to the chase. Can a finite universe be infinite? That is one thing we are interested in knowing. We can construct finite universes in our minds which have some aspects of infinity. We know that a coastline has some aspects of infinity, therefore we call coastlines infinitely long in fractal geometry. But once the surfaces are too small to reflect a photon the mathematics keeps right on going like there is somewhere to go. This may be wishful thinking.

[desiresjab]

Infinite diversity must be called uniformity!

[YesNo]

Uniformly diverse.

[desiresjab]

Uniformly diverse.

Correct...it swallows its own tail.

[YesNo]

Omnivorously diverse.

[desiresjab]

Paradoxes may merely be vertices on the boundary of the artificial reality in which we find ourselves embedded. Around the edges of our "universe," and only there, might traces of the imperfect and fictional nature of our simulated reality become evident to a few skeptical outcasts among us. It is not inconceivable for someone in the future to prove that our reality--our universe--is artificial. What does that mean? It means a construct. Certainly there are those who will argue that no construct can ever be complex enough to represent parts of reality we already know, such as consciousness, for instance. Their doubt comes no closer to constituting a proof than my lack of doubt does. What the above also means is that we would have to accept that it is we who are the artificially intelligent life form. If we were created instead of occurring entirely randomly, then we are artifice, and not our own.

[YesNo]

If we were created we could be called artificial from the perspective of the creator.

[desiresjab]

If we were created we could be called artificial from the perspective of the creator.

Yes indeed.

At this point a created universe like ours "seems," so much more likely than a randomly generated one that it is frustrating to make so little progress demonstrating it.

One has to suspect that even without a God or conscious sub atomic particles to assist it, mankind is on the road to immortality. Lifespans will grow longer. Then man will learn how to prolong a cyber essence indefinitely which can synthesize experience.

We were born too soon. It may only be later generations which get in on the immortality act of science and mankind. People of the future would hate to be born right now. How much would you have hated living in pre civil war America, even? Not even knowing there were other galaxies; Not even knowing the age of the world; Not even knowing the age of the universe; Not even knowing how to hygienically dispose of your feces en masse; Only having conquered darkness with whale oil; Advanced transportation was a good horse and buggy.

But worse than all of the above were the backwards notions on everything from race relations to religion to education one would have encountered. A sense of mystery was still there surrounding such phenomena as the pyramids. But when you look at their overall understanding and overall standard of living & development, one wipes one's brow that it was them and not us. For we could easily have been born into a more ignorant and backwards time.

That is exactly how men in the future will see it, and how they will see us. "No thanks," would be their reply to living in our era of backward ignorance. They themselves will live thousands of years, or longer, and be able to do things now considered worthy of only pure fantasy fiction.

[YesNo]

I suspect there is also a way, say through Plotinus's creative contemplation, for creation to occur without it being artificial. It is not really a making of something.

[desiresjab]

I suspect there is also a way, say through Plotinus's creative contemplation, for creation to occur without it being artificial. It is not really a making of something.

A willful creator is more likely than random interaction of "unbiased," particles. If we allow highly biased particles in our universe, then we are already half admitting that there was some kind of "help," beyond randomness assisting on the job of creating life and matter, making it somewhat easier and somewhat speedier to have these things.

I believe trouble comes when one tries to shut out any kind of bias. Particles that were not biased toward anything would never do a thing that was permanent. Particles of the universe seem biased already, just by the fact that we have something rather than nothing at all.

That is the trouble, I believe, with shutting bias out, or trying to--it is unrealistic, particles of the universe are already biased.

Without bias, not enough time has passed for this universe to be here, it seems to me. Totally without bias, I do not see how a universe of particles could get built or stay built, especially in a mere 13.72 billion years. The harder I look at it the more obvious it seems that there had to have been help from some kind of bias for it to get done in that amount of time across that amount of space.

Do you see how much more likely it is on a strictly probabalistic basis?

Is carbon really unbiased? I do not think so.

[desiresjab]

For that amount of organization (the universe and us) to get done across that amount of space and time (13.72 billion years), there had to have been bias, I believe.

Stated differently, as three facts: (1) Even the small corner of the universe we are familiar with is quite vast, but still finite; (2) 13.72 billion years is a puny amount of time; (3) we are quite complex. The three facts do not go together, but there they are, and here we are.

One must admit, 13.72 billion years is very little time for unbiased matter to get down to the randomly occurring business of creating life and consciousness in all its complexity, is all I am saying in this post and the last, I am not sure how well.

[desiresjab]

What more of Plotinus's creative contemplation can you say? I expect that is what God did. But we are still artificial, aren't we?

[desiresjab]

The way we are using the term unbiased, neon and argon would be unbiased particles. Unbiased particles have no proclivity to mix with anything. In reality, most of the elements of our chemistry are gregarious and biased against non-interaction, as we know from high school. Our philosophical contention is that if elements did not "like," to socialize, there certainly would not have been time for complex life to develop already. Particles come pre-made with the proclivity to socialize. They did not have to come that way. It did not have to be that way, but it is. By and large, particles are quite gregarious. Now how could anyone refer to that as unbiased?

I have to wonder what other proclivities particles might come with.

[desiresjab]

Self organization might be another proclivity of particles.

[desiresjab]

Whoops, wrong thread!

[YesNo]

I don't think particles are unbiased, that is totally random, either. There is an idea of something having a "disposition" to behave one way or the other. It is different than being deterministic.

I don't know much about Plotinus. I am reading some of him now at http://www.sacred-texts.com/cla/plotenn/index.htm There is also a survey article at SEP: https://plato.stanford.edu/entries/plotinus/ I found out about Plotinus (and Whitehead) by reading Shimon Malin's "Nature Loves to Hide". Malin is a physicist writing about the quantum collapse of the wave function. His book is one of the clearest I have read about quantum physics.

[desiresjab]

I can't get my head around random anymore, either.

Disposition is a very good word in this context. One might even put in a little work describing exactly what disposition entails. The universe and matter only have to possess disposition for randomness to be escorted from the cosmological party.

One cannot deny the value of the concept of randomness, however. It has proven of immense scientific value and will probably continue to do so. A more refined concept which has figured out how to acknowledge the influence of disposition would probably be part of the new paradigm.

[YesNo]

The main benefit of random seems to me to be for statistical work. I don't think reality has anything random in it. Much of what we don't know, like will the market go up or down on Monday, depends on a lot of choices people make, not something random. We just don't know and so think of it as random, or unknown but maybe predictable to some extent.

[desiresjab]

The dispositions of various types of matter towards one another could be much different, it seems. Most matter could have the disposition of noble gases, an unwillingness to mix.

But since the general disposition of matter is to mix, that already does not seem neutral to me. Neutrality is needed if one is going to tout matter and the creation of life as having happened at random. We should have known that easily. What took us so long? We would not be here to figure things out in a universe where matter was more noble. We should have cut to the chase. We are here; the universe is not noble; the universe cannot be neutral; the universe is already out of neutral and in gear.

[desiresjab]

I will try to investigate whether a created universe is more probable than an accidental one. Please bear in mind the subject is a difficult one for me where solid purchases are rare. Sometimes it consists merely of fleeting epiphanies so brief that details escape before words can cage them. If it sometimes seems as if I do not know what I am talking about, it is because I usually do not know. I have intuitions, which I am trying to organize usefully. On some days we will likely need our micrometers to search for any progress that might have been made.

Now it is true that most blades of grass and most trees and most flowers are not planned. But this is not "as," true if a partially obscured "disposition," is at work in grass and trees and flowers, and for that matter, stars.

One of the first things we need to do is dehumanize our terms. Disposition needs to become proclivity, propensity or potential. We do not at this time need to posit that matter has any kind of inherent consciousness. That would only give us something else to defend. If we arrive at it in our deductions and musings, that is another matter.

It is not a one post job. Let this far serve as an introduction. Now I have to walk up to the lookout with my binoculars.

[YesNo]

I think the kalam cosmological argument that William Lane Craig promotes is a valid argument. This is a rational proof that the universe had a personal Creator. Where it can be challenged is in the second premise claiming that the universe had a beginning. If the universe actually had a beginning, that is, something like the Big Bang actually happened, then the kalam cosmological argument would be a proof for the existence of God. It is based on Al-Kindi and Al-Ghazali philosophies which are based on Plotinus and Plato.

[desiresjab]

Since I am trying to "prove," or disprove the existence of God myself, I am interested in any other proofs. Your references were not clear to me. Do you have a link?

My first effort will simply be to try and demonstrate that a created universe is more likely than a random one. By created, one is allowed to mean anything but random.

I just lost a long post I cannot seem to recover. Dang it! That is the advantage of little bits.

[desiresjab]

Any help at all in coming about or developing as it did precludes a random universe. For things to come about with no proclivity to come about, is absurd on the face of it. The less the proclivity exists for things to act in a certain way, the lower the probability of it happening.

Universal stuff with no proclivity to get together and make other things has a probability of creating the universe that asymptotically approaches zero. Proclivity, that built-in potential, is the reason we are here observing at all.

[desiresjab]

On the verge of horizons, we proceed.

We have seen that the connections between matter & matter are multifarious. Chemical combinations (for instance) are too numerous to be catalogued, and are in fact infinite.

With the right set of eyes nature is seen to be very busy at all times in most places. There is all kinds of commerce and trade in the chemical world (staying with the analogy) for instance. This commerce is normal and natural, not a special circumstance, as if things were made to work in combination.

Our universe seems set up for activity, just as a universe of noble gases would seem set up for inactivity.

We feel a "bias," in our set up towards activity and new combinations. We feel this same bias made the creation of life not only possible but a sure thing in our universe, given enough time. 14 billion years is not long enough to the intuition, however. Even more time should have been required to produce simple life and evolve it to complex life with minimal consciousness and then evolve that consciousness to the high self consciousness of man.

Not only is 14 billion years a short time in this context, but consider that the process of development was arrested and almost wiped out at least several times in mass extinctions. In other words, the process of getting to where we are now went super fast, almost copying cosmic inflation itself, and happened in spite of massive setbacks. Such success smacks of a proclivity for those things we are counting as a success.

[desiresjab]

An extraordinarily rare event? I don't think so. The world kept returning to life, rather nursing it back strong, after each mass extinction. The way stellar nebulae are natural nurseries for stars and other cosmic misfits, the world is a natural nursery (the only one we know of) for experiments in animation.

[desiresjab]

Once you heat up gases rich with incidental elements things start to happen. That is our universe. There are many heat sources. Gravity collects the gases and they heat up under the continued action of gravity and a few basic laws.

The honest investigator is not allowed to let it go with only a note that our universe seems hugely biased toward activity and creation, compared to other universes we can easily imagine, that is. This observation must be addressed. It must be dealt with.

It is significant that we have to admit to living in a biased universe. Our universe creates things all the time--even space, for new space is being created all the time for the first time as our universe expands. It is not expanding into what was formerly empty space, but what was formerly nameless nothingness. There was no space there. There was no there at all.

We have to ask ourselves why this is so. Do we actually live in a universe where runaway creation is the order of the day? If this is the case there is no reason to assume life is not merely the tip of the iceberg of the possible. In a universe geared for runaway creation, one should not be surprised if afterlife is part of the deal, too, since we already know life is, and life is pretty strange itself, everyone can probably admit.

The right conditions for life to kick up are scarce and scattered, but not nonexistent. It will not occur too early in the universe, for we will need some iron first, to be supplied by spent supernovae exploding and disseminating heavy stuff. After gravity collects the materials into a hot soup, the brew cooks and cools for a long while, the heavy stuff sinking to the center of the mass where it will become the magnetic iron core of a planet. Life as we know it must have a protective magnetic field, provided by its spinning molten core.

We have to suspect that our universe is open to other experiments in integration, not just on the chemical plane of our analogy, but also in areas where we are not equipped to observe the activity the way we have taught ourselves to observe chemical activity, and where we have no valid reasons for suspecting that kind of activity in the first place.

To some, our universe was made that way, and to others it just turned out that way. The common point is that it is that way.

Just because we have shifted the mantle of creator from the shoulders of a mysterious being to the universe itself, does not mean we have escaped the hard questions.

We have to ask ourselves if it was a random accident that the universe turned out this way, or was it purposeful?

The universe has become a great creator. Did it create itself? Can something which does not exist yet create itself anyway? Why does the universe have those biases we can easily observe it to have?

We should rule out anything creating itself before it even exists. The universe did not create itself. Doesn't that feel better?

Whatever created the universe created it with certain biases. Were these biases purposeful, or were they accidents. Were they inevitable? Why?

As we can see, there is no escape just because we now might now admit certain proclivities in matter to be responsible for life. We are clearly obligated to shift our attention to the proclivities and explain them as well as we can under our paradigm of randomness, or admit the universe had a separate creator who handed over the mundane duties of creation to the universe itself.

[YesNo]

I don't see how it could create itself. I think the cause of the creation was some agent not an event. That is there was a purpose involved.

[desiresjab]

I don't see how it could create itself. I think the cause of the creation was some agent not an event. That is there was a purpose involved.

It would have to precede itself to create itself, a clear impossibility to our minds.

However, if the Hubbleverse is not all there is to the universe, the universe could be infinitely old already. If an eternity has already passed--correct me if I am wrong--but isn't that the same as saying that everything that could ever possibly happen has to have happened already, and we can only be living through a repeated portion?

Is that a logical problem if we consider the universe to be infinite in age? An uncreated, non-deterministic yet non-random universe could not produce an event that had not already happened. I think that is one ineluctable reality of an infinitely old universe.

Well, there is nothing in me which demands that events surrounding me--nor even my own experiences-- be new. Given long enough, events and experiences would repeat for a spell and maybe even forever, like the team of monkeys expected to type Hamlet. But if things repeat, isn't that determinism again, rearing its ugly head once more? There is this uncomfortable logical quandary when we consider the universe to be infinitely old without a beginning. I am not sure I can get out of it.

But wait! I just realized nothing in me demands or requires Free Will, either. I like the sound of it all right. That is why I did not want to give it up. But it is not as if my philosophy must have it or I cannot be satisfied.

I still like the idea that we possess a simulated Free Will asymptotically close to the real thing.

I suspect there are many shades of consciousness. What are some physical phenomena which might be conscious activity rather than the mechanical or random processes we think they are?

[YesNo]

I tend to think there are only two general kinds of causation--event causation and agent causation. If an agent does it there was some freedom involved. I don't think there is any really random stuff happening, not even quantum collapses.

[desiresjab]

Sometimes we have to separate concepts in our minds to see what we have so far, cease our backward extrapolating for a moment and appraise. We think of perspective and of angles subtended. At the beach what angle should a gull subtend a certain distance from some observer? We know an answer only if we assume the observer is human. No one said the observer could not be an eagle, whose vision can operate at magnification power 3, meaning of course, a larger angle subtended at the same distance.

Now think about the question (How conscious is it?). At what distance in time were primate ancestors conscious enough to be human? Is the answer only when they could ask this question? Not they, just one man or woman. If one man asks that question, all men everywhere become immediately human, even those in the middle of murdering someone who finish.

Seeing is to vision as thought is to consciousness. Many species appear to worry, but only humans worry about an afterlife.

How large should a star appear? No size at all. How large should anything be at any particular distance? No size at all, is the correct answer. Can you apply this answer to the concept of consciousness?

[desiresjab]

There are people who believe explicitly in God, at least they claim they do. To them there is no sloppy overflow in God's natural universe. God does not do anything approximately, but everything precisely, they believe. Everything God does and has created is real. Creation is part of the definition of real after all, when you think about it.

If God has a purpose in everything, what is the purpose of optical illusion? Why was a choice made to give us senses that are often unreliable? Surely, God could have done it differently if that being has only a portion of the control over the universe attributed to him by his faithful. To say that God works in mysterious ways, is the ultimate cop-out and an explanation of nothing. It explains that you do not have an answer, or anything close to one.

For years I have suspected that Buddha got very close to the truth with his notion of Maya. It seems to me now that there is a lot more to optical illusion than the little bit one finds in entertaining books on the subject. Formal optical illusions presented in books cannot be controlled or prevented when we follow directions and look at the right spot, etc.

Does God really have some interest in fooling and testing people. That idea seems awfully old fashioned to me. In my early life there was an aunt who insisted that even dinosaur bones were something put there to tempt man from God's words.

I do not know if God has an interest in testing us, but from all the evidence, it seems said entity does have an interest in fooling us, otherwise why give us senses that cannot be relied upon consistently?

If there is a God, what then is the purpose of optical illusion? I suspect that a great deal of what we experience is an illusion of one variety or another, just not the kind slick and obvious enough to include in a coffee table book on illusions and paradoxes. But what is the purpose, then? What is a human supposed to take from a world whose content is so steeped in illusion? What is the lesson? Why illusion instead of direct truth, if you were God?

[desiresjab]

I can compare reality to a card trick, i.e. an illusion. The hidden top card is called reality. However, you can see I am going to cheat. The edge of the second card is showing, and that is the one I intend to turn over. If you had not seen that small edge protruding, you would have been cheated without a clue and never been any the wiser. But you did see that edge. Sometimes in real life we see that small edge too. We can tell then that what we are seeing is an illusion. Without that edge we would be none the wiser, and most of the time we see nothing but what we sincerely believe to faithfully represent reality.

We see no small edges protruding, so we assume we are viewing reality and not an illusion. That seems after all like a poor reason for judging something real. Did you ever have the feeling that illusion is operating all around you constantly and you are unfortunately ill-equipped to prove it?

Go to any popular internet site of illusions. They show you how to recognize an illusion--as far as possible, that is. They show you the edge, then you can understand the trick. What about all the times we do not see an edge at all but are still viewing an illusion? Did you ever have the feeling these are very common events and not rare?

[svejorange]

Cosmology is deep and wide topic, thank you for waking it up!