They were expecting there to be false positives, but not so many. It looks like we need a new and better telescope anyway since Kepler had a malfunction a couple of years ago. There are over 1000 that passed the test.
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They were expecting there to be false positives, but not so many. It looks like we need a new and better telescope anyway since Kepler had a malfunction a couple of years ago. There are over 1000 that passed the test.
Do you know if one is being built and if so when it will be ready?
The Spitzer is operating, but I have no idea what it does: http://www.spitzer.caltech.edu
http://jwst.nasa.gov/about.htmlThe James Webb Space Telescope is another, but due to be launched in late 2018. Uses Infra-red detection.
Here is a list of space telescopes. Some of them I hadn't heard of before. https://en.wikipedia.org/wiki/List_of_space_telescopes
That's a mind-blowing list. I had no idea...
I was enjoying your debate with desiresjab so now I will go quiet and study the list of telescopes to try to get a new perspective on telescopy.
I was wondering what Crawford claimed Hubble's constant was. At the end of the paper he has this (page 83, I reformatted the numeric values):Quote:
Originally Posted by desiresjab
Results for the topics of the Hubble redshift, X-ray background radiation, the cosmic background radiation and dark matter show strong support for curvature cosmology. In particular CC predicts that the Hubble constant is 64.4 +/- 0.2kms^-1 Mpc^-1 whereas the value estimated from the type 1a supernova data is 63.8 +/-0.5 kms^-1 Mpc^-1 and the result from the Coma cluster (Section 5.15) is 65.7 kms^-1 Mpc^-1.
The data from Planck (Feb 5, 2015) show the result as: http://arxiv.org/abs/1502.01589
These data are consistent with the six-parameter inflationary LCDM cosmology. From the Planck temperature and lensing data, for this cosmology we find a Hubble constant, H0= (67.8 +/- 0.9) km/s/Mpc, a matter density parameter Omega_m = 0.308 +/- 0.012 and a scalar spectral index with n_s = 0.968 +/- 0.006.
I don't know if the disagreement is critical to Crawford's theory. It looks like the Hubble constant derived from the Planck data assumes the lamda CDM standard model is true. Given this newer data I wonder what the Curvature Cosmology would derive the constant to be?
Good pick up. In the first instance, the diagreement is about 1% either way. 1% is pretty monsterous. Trying to adjust for interstellar dust and gravitational lensing, all the while screening out background "noise" of various types, one wonders why there is not even more discrepancy between the systems. It is playing soccer where the goal is hidden.Quote:
Originally Posted by YesNo
Somehow one doubts that all figures for each system were derived independently. I think that is mentioned in the paper. Ahem, doesn't one use the rival's best measurements as fuel to prime their own engines?
It is a multi-dimensional, multi-player chess game of unknown infinitude or finitude. A clear winner is not in sight, I believe. All players already have strengths and weaknesses in their formations.
Right about here, Yessy boy, is a big gate where most mathematicians say, wait a minute, I'm a poet.
Unless one goes in and crunches differential equations, goes in and manipulates in tensor calculus, goes in and calculates in multi-dimensional Lie matrices, all in a coordinated manner and to a purpose, with all constants and variables applied correctly, the force, angle or mass of every one of them understood in the overall context, one does not get much closer, but just crowds the gate, methinks. This requires a great deal of advanced physics, in addition to the advanced math.
I am happy to be a gate crowder. Like many, though, I still plot a way inside. I doubt I will ever get through that gate, but things nearly as strange have already happened in my intellectual life. At this gate are some very interesting discussions. This or that crowder might have enough information to quibble on arbitrary points, to the enlightenment of all. Many can ask interesting questions.
Spinoza ..thought determines action, desire determines thought, instinct determines desire...therefore there is no free will, seems distant and quaint to us now, but worth reciting as one pole of the argument in time.
I get caught in recreations of depth. There are the recreations of depth I have gotten to and the ones I hope to get to.
One recreation is unsolved problems in number theory. It is one field of mathematics where everyone is allowed to play. Anything advanced you know is just gravy, because there is analytical number theory, too (meaning using calculus in addition to algebra).
I write articles of discovery to myself all the time, to keep this a little bit about writing. For instance, I have an original proof of Fermat's little theorem. Someone else probably proved this simple theorem before me in this way, but the point is I didn't know about it and was able to do it myself. I demanded absolute lucidity and got it, a visulization of irreproachable, irrefutable clarity.
I demand this same clarity of quadratic reciprocity in modular arithmetic, but have not yet acheived it. I am close. I have what I would call a good understanding. I know the theorem from diverse angles, can follow standard proofs. I have a multi-layered point of view. The visulaization is beginning to stir. Do I have such a visualization within me, or will it remain a shadowy thing that seems to stir on the ground and never stands?
It is my highest immediate goal in math, I frankly admit. Until I can see right through it the way I can see right through Fermat's little theorem in a visualization, I will never be through with it. It is as central to number theory as the Pythagorean theorem is to geometry and trig, but a lot more difficult. Even Euler was not up to hashing out all its difficulties, which is really saying something, since this guy in math is up there with Bach and Monet, if you will. Only the foremost of all mathematicians Gauss was able to bring this problem to rest, proving it eight different ways in his lifetime. Gauss made a little mini-career of crushing problems that had crushed the greatest mathematicians before him, sometimes for thousands of years. Gauss is what Ramanujan would have been, lucky enough to be born right in time and space. Those two were born to it, we know for certain. We know Mozart was born into music, and most likely for it, though one feels a mathematical rearing instead of a musical one in the case of mozart might have produced a superb mathematician rather than a superb musician and composer. He displayed exactly the same ability to "calculate" in his head, composing multiple pieces in various mediums before bothering to write them down.
Shakespeare is the tough one. Was the universally consensus greatest poet/dramatist of all time born to it? That does not mean he did not have to work ceaselessly at his art.
About Spinoza's determinism it seems that instinct only provides constraints and dispositions rather than determining anything. For example, sexual desire is like a carrot disposing us to say yes to pleasure rather than forcing us to do so.
Do you have a link to your proof of Fermat's little theorem? I would be interested in reading it.
There are people who can visualize numbers. I remember seeing someone who could recite pi to many decimal places by visualizing what the number should be. I will see if I can find that youtube video again.
Edit: Danial Tammet comes to mind as a savant with abilities to calculate and visualize numbers. There is also Jason Padgett: http://www.livescience.com/45349-bra...th-genius.html
Tammet must have irregularities in his corpus colosum, which separates the brain's two hemispheres. Some people have an unnatural correspondence between the two hemispheres, synesthetes being notable.Quote:
Originally Posted by YesNo
Tammet is a savant, not a genius in the traditional sense. No one has figured out a way to make his astounding abilities work for humanity in a large way. If we ourselves were a bit smarter--say two hundred years smarter--I think it a fair assumption that Tammet would have much more to tell us. How do you talk to a dolphin, though? We are not yet smart enough to do that in their own language, either. Fran Peak, on the other hand, was a classic idiot savant. For all his abilities you could not get much out of him because he does not comprehend or apprehend the world in conventional terms whatsoever.
Do you know the brain preserves in an identifiable marking on the frontal lobe the learning of a stringed instrument early in life? Einstein had this marking from early violin lessons. It looks something like a horseshoe, and I myself will have it from learning guitar early. If you learned a stringed instrument early in life, you will have this marking!
Now get ready for something eerie. If you learned piano instead of a stringed instrument, the same marking is there all right, but on the other hemisphere. I do not know what happens if you learned both simultaneously, or what kind of marking there is for wind instruments or other groups. Piano is actually classified as a percussive instrument, I believe. Somehow I doubt a snare drummer has the same marking, but who knows?
Okay, a(p-1)=1 (mod p) is the standard form of Fermat's little theorem, and the equals sign is a congruence symbol, which is three parallel lines instead of two. Congruence means two numbers belong to the same congruence class.
Roughly, you can say two numbers are congruent if they give the same remainder when divided by another particular number, usually called p because it is a prime. Instead of mod, think of the word divisor, for that is exactly what a modulus is.
A more beautiful and insightful form comes from the preceding step in the usual modern proof, and is ap=a (mod p). Take a picture of that. This is a very intriguing congruence. You can always think of what is in front of the mod symbol as the remainder in a division which has already taken place, or that is going to take place. In our case it was when ap was divided by p. This left a remainder of a, which is enough to hear heavenly choirs sing as one instinctively asks why?
Now a does not have to be prime, but for illustrative purposes, choosing from among the smallest primes has obvious advantages. The theorem says it is only true when p, the exponent, is a prime, though, and a is not a multiple or a factor of p. This is called being relatively prime. But two primes are always relatively prime to each other. Another reason to choose them.
To envision what ap=a (divisor p) means, lay down three tiles of length 5. Next to them, lay down tiles of length 3. Proceed until you have laid down six of the 3 length tiles. If you had stopped at five of the latter, the two strips of tiles would be of equal length, but as it now stands we have one tile of length 3 sticking out. Because we are dealing with two primes, we could have done our operations in either order. In other words, in our example either 3 or 5 can serve as the modulus (divisor), as you choose, and it does not matter which tiles we lay down first or think of as the divisor. We could have a 5 "sticking out" if we had gone the other way, is the only difference, and it makes no difference.
3·3·3·3·3/5 is the division we have going on, by the way.
The points along the number line which have 3 and 5 (a and p) as a common factor can be marked mentally. Why ap always leaves an a sticking out (the remainder) when divided by p, is the question illustrated above with tiles, but not yet proven. To prove that ap always leaves an a sticking out, try:
Factoring 35-3, as a concrete example. The first one, 3(34-1), is easy enough. But as you continue to factor, fractions come into play. 3·3(33-1/3) (mod 5) , means the logic of the proof relies on modular inverses and a few other tricky concepts. I leave the final steps as an exercise.
(Hint): The object is to show that the expression 35-3, more generally known as ap-a, belongs to the zero class. No more is necessary.
P.S. Going with the visualization for a proof turns a simple proof into one more difficult, but we had to stay with the illustration because it makes the concept so clear.
P.S.S. I made a mistake with the factorization and corrected it. I marked that part in red. Formerly, I had 9 as the denominator of the fraction. That would occur on the next factorization. I have also included the mod operator there, to make things even more clear.
What does my last post have to do with cosmology? Well, plenty, perhaps.
Earlier in the discussion we sort of determined that as far as man's imagination goes, even God is limited in the kind of universe which that entity could create. Specifically, that entity could not create a universe where two is not the sucessor of one. If we settle for that, and I have, then just how far does that idea extend into mathematics? Does it mean God would also be incapable of creating a universe where Fermat's little theorem is not true?
Huge question. I don't know how to answer it.
It is an astounding thought. God could only make universes which obey our mathematics. God cannot make a physical universe which does not obey some mathematics, cannot make a universe where alternative algebraic structures are not possible, could not make a universe where any of the notions of our mathematics are false, other than twiddling with basic axioms as we ourselves have already done.
Well, someone must have a thought on that. A God constrained by mathematics. Actually, that is, constrained by the leap from mathematics to matter. Or is it just mathematics that constrains God? That one is tough. Help me out, somebody.
I didn't know about these markings, but it supports the idea of neuroplasticity which is part of a recent kind of evidence of how the mind affects the brain rather than the other way around.Quote:
Originally Posted by desiresjab
Here is a link to a variety of proofs: https://en.wikipedia.org/wiki/Proofs...little_theoremQuote:
Originally Posted by desiresjab
I am familiar with the ones for modular arithmetic and the proof using the binomial theorem. I was unaware of Golomb's combinatorial proof: http://www.cimat.mx/~mmoreno/teachin...Little_Thm.pdf. One thing Golomb asks which is important for these proofs to make sure they are correct is where do they use the hypothesis that p is prime since the result is not in general true for all integers.
I am still trying to understand your proof about tiling as well as the dynamical system proof mentioned in the link of proofs above.
I subscribe to Robert Prechter's Elliott Wave reports. This seems to me to be a similar view of how markets behave. They are not the result of rational activity on the part of market participants but rather "social mood" which is a sort of unconscious herding even when people are apparently making individual decisions to take on risk by buying equities and bonds. What causes social mood? It would be based on Fibonacci (mathematical) constraints on impulsive and corrective waves and not fundamental events.Quote:
Originally Posted by desiresjab
I find this a little too deterministic at times and there must be multiple herds in place since for each buyer following some herd there is a seller following another herd and apparently Prechter thinks he can think outside this herding box. But it seems to work and I keep wondering what herd I am in. What I like about it is the idea that we are constrained by systems (or consciousness) above our own rather than by something unconscious below us. It is similar to Niles Eldredge's punctuated equilibria where the biological species are considered to be real and above our individual existences providing us with additional constraints such as pair bonding.
Unlike your perspective about God's constraints, these are systems providing dynamic constraints. I suspect God is also constrained as to how hydrogen behaves, but I don't know that it matters if consciousness is fundamental.
Fortunately, these thoughts are interesting in themselves, for I don't see how they connect with what I said about Godly constraints. No matter.Quote:
Originally Posted by YesNo
We might be able to apply a certain stimulus to a mosquito or a dolphin, and cause a certain behavior in them. We might make them herd, for instance. We said something, we just don't know exactly what it is, we only know it causes this behavior.
The people can be gathered by a signal to the town square. A variety of meanings could be attached to their coming there, and we do not know which is correct necessarily, just as in the case with animal communications. It takes an even more well designed experiment to know what we ourselves have said in their terms. At face value, we do not know if the people showed up in the square to pray, for a town meeting, to dance, for an emergency announcement or for something else. We gave the signal, but what does it mean to those who responded?