Within a short while I will see the final piece. I don't need them now.
Within a short while I will see the final piece. I don't need them now.
Does anyone participate in grid computing volunteer projects by letting those projects use their computer's resources in the background?
I understand some of them allow one to participate in searches for extraterrestrial life or pulsars or even special prime numbers. Here is the site: http://boinc.berkeley.edu/download.php
My blog: https://frankhubeny.blog/
I think that is to give access to your computer for them to use it while you sleep or are away.
Yes, they would use it for some project you signed up for. It could be something related to cosmology (like gravitational waves) as well as astronomy or health or even mathematics (finding primes).
I haven't signed up for it, but I do have an old computer that I might as well clean up and turn on for them to use.
It is sort of like a large communal gaming system that might have some use-value besides the game itself.
My blog: https://frankhubeny.blog/
I started up the old laptop, downloaded the BOINC software, installed it as administrator, signed up for PrimeGrid and the computer is now happily busy again. Well, I don't know if it is happy about that, but I am glad to put it to use.
My blog: https://frankhubeny.blog/
I started reading Jimena Canales, "The Physicist and the Philosopher: Einstein, Bergson, and the debate that changed our understanding of time".
I am hoping it will help me understand the cultural context in which we view cosmology today. The debate mentioned in the book occurred on April 6, 1922, and apparently has cultural influence to the present day. I hadn't heard of it before, but we don't have to be aware of the influences we have, especially those we take for granted.
My blog: https://frankhubeny.blog/
My conclusion is that Eisenstein already knew what he was after. He was after a way of arriving back at Euler's criterion through his lattice point rectangle representation, which he managed to do. He shows that the number of even lattice points in ABC has the same character as the total points in CZY which is no different from AYX. Then it is seen that WAY is also equal to the unmarked triangle in his diagram that sits under CZY.
He shows that his exponent u+v is equal to (p-1/2) (q-1/2). Very good. The deed is done.
However, it does not show or explain the mechanics of why moduli behave toward each other according to species, landing or not landing in one another's quadratic residue sets. You cannot get those mechanics from this proof. It is the wrong kind of proof for that, it does not delve there. Viewing those mechanics may require learning some new mathematics. I am far more interested in the mechanics than the proof itself, it turns out. I need to see different proofs to determine which one explains the mechanics I am after.
The same mechanism seen in Eisenstein's proof that clearly explains the behavior of 4n+3 primes and pinpoints the reason for it does not explain the quadratic behavior of moduli in general. Without foreknowledge I believe there is no way Eisenstein could have worked backwards from his diagram to explain that quadratic reciprocity was merely Euler's criterion.
There is only so much one can get from any one proof. Then one has to look elsewhere for other interesting ideas.
I put together a Google sheet trying to test your conjecture that the number of lattice points in the two triangles for twin primes are equal. It looks like it works for twin primes less than 100. That is all the further I tested it.
Another topic that has caught my attention are the lengths of prime gaps. For twin primes the length would be 2, however, the gap could be arbitrarily large.
My blog: https://frankhubeny.blog/
There is any gap as long as you please if you go far enough out the number line. That has been proven. That proof must be a hard nut.Originally Posted by YesNo
Yes. The proof that the gap can be arbitrarily large is well known. That there are infinitely many twin primes has not been solved. That's the hard problem. Here is a status from a Wikipedia article: https://en.wikipedia.org/wiki/Twin_prime
On April 17, 2013, Yitang Zhang announced a proof that for some integer N that is less than 70 million, there are infinitely many pairs of primes that differ by N.[1][2] Zhang's paper was accepted by Annals of Mathematics in early May 2013.[3] Terence Tao subsequently proposed a Polymath Project collaborative effort to optimize Zhang’s bound.[4] As of April 14, 2014, one year after Zhang's announcement, according to the Polymath project wiki, the bound has been reduced to 246.
So there are infinitely many gaps of size as small as 246. One just has to get that down to 2.
My blog: https://frankhubeny.blog/
The computer crashed a few times, but I finally realized I should run it at 50% capacity rather than 100% capacity to give it a chance to cool off. Also I put it on top of small objects so that the heat can move away faster. But I got my first badge for running 10,000 points worth of stuff.
My blog: https://frankhubeny.blog/
Just trying to help with the posts. I am new at this forum and I myself lost some texts because this forum has a time out problem. Now, if it is a small post like this one I keep saving and editing it on the edit pad. If it is a long post like yours I write it on Word and then paste it on the forum page.
Last edited by Danik 2016; 03-06-2016 at 10:07 PM.
"I seemed to have sensed also from an early age that some of my experiences as a reader would change me more as a person than would many an event in the world where I sat and read. "
Gerald Murnane, Tamarisk Row
My problems disappeared, perhaps yours will too.
After reading a couple chapters in this, I realize that Einstein was involved in two conflicts. One of them was with Bohr over quantum physics and the other was with Bergson over the reality of time. In both, Einstein won the reputation prize since he is remembered better than Bohr and Bergson, but he lost the quantum physics debate to Bohr and, as I am beginning to see, he likely also lost the time debate to Bergson. However, with Bergson, I don't understand the issues at stake as well. They involve time dilation and the reality of various measurements, but that is as far as I've got. This question relates to a cosmology thread in that it questions the "reality" of "space-time".
My blog: https://frankhubeny.blog/
I am over half way through Canales' history of the debate between Bergson and Einstein.
I realize I would likely be on Bergson's side. By putting time and space together into "space-time" Einstein created a deterministic block universe where nothing new could happen. This doesn't fit reality as I experience it. So, being pragmatic, I assume there's something wrong with it.
Also it looks like Poincare and Lorentz, who came up with the measurable effects of relativity theory before Einstein did might have better ways of interpreting it, but I am still trying to figure out what those different interpretations are.
At a high level, the difference between Bergman and Einstein is obvious. Einstein gets a mathematical theory (from Lorentz) and then assumes that his preferred model is reality rather than just a way to model reality. Time is linked to space, because it is convenient for the mathematics to manipulate it that way. It is sort of like following Galileo and saying the Sun really is the center of the universe regardless of our current view that that is no more true than saying the Earth is the center of the universe. On the other hand Bergson is interested in presenting the lived experience of time which is not deterministic.
Canales did a good job of bringing in the various people who participated in this debate in the 20th century. I didn't realize how connected all of these ideas were.
My blog: https://frankhubeny.blog/
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