Is There A Mathemetician or Logician in the House?

[Taffi Abernathy]

I'm putting this out with the hope that someone can provide the simplest possible explanation (think Occam's razor) for the zeta function in the Riemann Hypothesis. I have gone over this several times and am having difficulty grasping the concept. I feel frustrated and confused because at this point, I believe I should at least have a perfunctory understanding - and I don't!. Thank you.

[Brunotheboxer]

Originally Posted by Taffi Abernathy

I'm putting this out with the hope that someone can provide the simplest possible explanation (think Occam's razor) for the zeta function in the Riemann Hypothesis. I have gone over this several times and am having difficulty grasping the concept. I feel frustrated and confused because at this point, I believe I should at least have a perfunctory understanding - and I don't!. Thank you.

http://www.donotrememberthisaddress....hypothesis.php

[Carolina]

Nice work, Bruno!

[Taffi Abernathy]

Thanks much, Bruno! Look what I found in the intellectual mecca of the free world. Of course, I can only be referring to you tube. Check this out . . . Perhaps I should now request a veterinarian who has access to horse tranquilizers. This guy sure could use some.

http://www.youtube.com/watch?v=g0Vv0VBC5TA

[Gedanken]

That's a pretty broad question, Faith. What aspect of the zeta fucntion are you trying to understand?

[Taffi Abernathy]

James,

My difficulty in formulating a more focused question is due to my inability to grasp these concepts. I did fine in statistics and don't know why I am unable to grasp this. My gaining an understanding is for my own personal enrichment and no matter how many times I've read this material, it goes right over my head. Since I don't need this information, I should arguably let go and accept that it is a source of frustratration. It nonetheless remains something I want to understand. But I also know we can't do well at everything.

[Gedanken]

I hear ya. I read it the equation a couple of times and went, "Yeah, so?". Looking at the applications of the function, one thing that does make sense is that it is used in things such as probability distributions, so that was my starting point. Without this, I figure I wouldn't have really cared enough to read on.

Anyway, as far as I understand it, in its purest form, the Reimann function (and other derirative functions such as the Euler product) doesn't accomodate for the existence of the number zero, at least not without involving easily provable conditions (trivial zeros). I'll admit that I'm not quite clear about why you'd go looking for non-trivial zeros because IMHO trivial zeros seem to do the trick, but what the hey, these guys have to justify their tenure, right?

Anyway, taking a bit of a leap of faith and assuming that non-trivial zeros are a non-trivial issue, introducing a real part of 0.5 to the zeta function as the constant in a line where all the critical zeros should lie. Throwing in the i makes things a bit of a pain - I never liked dealing with the square root of -1 when I was in high school and I still don't like it - because we can't represent it in a nice, easy linear manner.

The challenge seems to be that while we can apply the function and support Reimann's hypothesis about the real part being 0.5, nobody's actually been able to mathematically prove it, and that's the challenge that's got YouTube boy wetting himself.

Now if I can just figure out what the big deal is about non-trivial zeros, this would all make sense.

[Taffi Abernathy]

Nice translation, I wish it had come that easily to me. The poor fellow on youtube is probably on a lockdown unit at Bellview ingesting cocktails of Risperdal, Paxil and Zyprexa, since as life would have it, the hypothesis wasn't proven after all. This means, he exposed that meaty stomach of his for naught. For tonight, I better leave this hypothesis alone (as well as thoughts of that stomach) behind, but no doubt I'll be back to it tomorrow. My advice to you James, is not to ponder or try to make sense of non-trivial zeros, you will drive yourself beserk. Your help was this was appreciated.

[Gedanken]

Originally Posted by Taffi Abernathy

My advice to you James, is not to ponder or try to make sense of non-trivial zeros, you will drive yourself beserk.

Well, fortune smiles upon me, Faith - just as I posted, the Canon 5D that I ordered on Sunday arrived, so I've gotten distracted taking photos.

I'll go back to the non-trivial zeros at some point - it's got my curiosity piqued, and over the past few years my appreciation of the number zero has actually increased.

Case in point: we were doing some organisational culture surveys for a scientific research institution early last year, and their results didn't come back great. Anyway, this one nuclear scientist wrote to me saying that he had recalculated the scale scores from the raw data (they had been rescaled from a 1-5 scale to a 0-100 scale), and that all of the scales were 5 points lower than what they should have been.

I immediately wrote back saying that he had almost gotten it right, but he had forgotten to factor in the lack of a zero in the original 1-5 scale. Had he subtracted 1 from the scores before rescaling them to 100, he would have found that the scores were spot-on. I closed the email to him with a the old Huxley quote: "There is nothing so tragic as the collision between a beautiful theoryu and a single inconvenient fact".

[Taffi Abernathy]

"Twas ever thus: Enjoy your new camera, it arrived just in time to take pictures of your beautiful new house.

[JJ Irani]

WOW!! Hated math and never understood the zeta function......but give me Catherine ZETA Jones........now that's a different game of calculus!!

[Taffi Abernathy]

Originally Posted by JJ Irani

WOW!! Hated math and never understood the zeta function......but give me Catherine ZETA Jones........now that's a different game of calculus!!

I was half asleep and made the mistake of checking into the forum right before bed. I read this post and now I'm wide awake from laughing.

[unclesallie]

well, JJ, your wish is my command! and i agree, BTW, i don't understand a word of this, and if there were U Tube replays of the Frisco Kid where the Indian Chief says, "I don't understand a word he's said"(referring to a very young Harrison Ford character)....and if this post confuses anyone, think of how I feel after reading about theoretical mathematics.......

[Jimbits76]

Originally Posted by JJ Irani

WOW!! Hated math and never understood the zeta function......but give me Catherine ZETA Jones........now that's a different game of calculus!!

Carry the two JJ. Carry the two!!!!!!!!!!!!!!!!!!!!!!!!!!!

J

[DoxaDavid]

Originally Posted by Jimbits76

Carry the two JJ. Carry the two!!!!!!!!!!!!!!!!!!!!!!!!!!!

J

I'm Sure if JJ takes off his shoes it would help in getting past the number 10..

[2careless]

Of all the Clay Institute Millenium problems, the only that piques my interest is the P=NP problem. I did try tackle that one when I was young and bored without any success.
I might try pick it up since now I'm old and boring.

[Gentleman8]

Originally Posted by Gedanken

Anyway, taking a bit of a leap of Faith

This is interesting:
http://www.telegraph.co.uk/news/ukne...ed-1m-sum.html

[Launch Mini]

Originally Posted by Gentleman8

This is interesting:
http://www.telegraph.co.uk/news/ukne...ed-1m-sum.html

If you prove it wrong, then that person must have the correct answers, so in a circle it goes.

[Launch Mini]

I had am amazing math teacher in Grade 12. We did all this crap, but he actually made it interesting ( hard to believe). I forget most of it now.
Some of the things he "taught" us ( well made us figure out for ourselves with a bit of guidance), were Probability of Poker Games ( this was fun as we would change the normal "ordering of winning hands" based on the recalculated odds of the hands(so in some games a hand with not even a pair would beat a full house) and play poker during classes) and how to solve the Rubik's cube.
Ah the good old days.

[Mike B]

Wow , I was reading this thread, and I have absolutely no clue about what's being talked about lol. I only went up to Algebra 2, and some advanced statistics classes in college lol

[Taffi Abernathy]

The Riemann zeta function
The Riemann zeta function is given for complex s with real part greater than 1 by


Euler showed that it is given by the Euler product


where the infinite product extends over all prime numbers p, and again converges for complex s with real part greater than 1. The convergence of the Euler product shows that ζ(s) has no zeros in this region, as none of the factors have zeros.

The Riemann hypothesis discusses zeros outside the region of convergence of this series, so it needs to be analytically continued to all complex s. This can be done by expressing it in terms of the Dirichlet eta function as follows. If s has positive real part, then the zeta function satisfies


where the series on the right converges whenever s has positive real part (though if the real part is less than 1 the convergence is excruciatingly slow). Thus, this alternative series extends the zeta function from Re(s) > 1 to the larger domain Re(s) > 0.

In the strip 0 < Re(s) < 1 the zeta function satisfies the functional equation


One may then define ζ(s) for all remaining nonzero complex numbers s by assuming that this equation holds outside the strip as well, and letting ζ(s) equal the right-hand side of the equation whenever s has non-positive real part. If s is a negative even integer then ζ(s) = 0 because the factor sin(πs/2) vanishes; these are the trivial zeros of the zeta function. (If s is a positive even integer this argument does not apply because the zeros of sin are cancelled by the poles of the gamma function.) The value ζ(0) = -1/2 is not determined by the functional equation, but is the limiting value of ζ(s) as s approaches zero. The functional equation also implies that the zeta function has no zeros other than the trivial zeros with negative real part, so all non-trivial zeros lie in the critical strip where s has real part between 0 and 1.

—Riemann's statement of the Riemann hypothesis, from (Riemann 1859). (He was discussing a version of the zeta function, modified so that its roots are real rather than on the critical line.)

For your reading pleasure . . .
It looks like a review of statistics is in order before attempting to understand this.

[2careless]

Stats doesn't touch number theory, therefore it's no use for Riemann hypothesis. This whole stuff is more pure math and has nearly no applied usage, imho.
If we're talking about singular value decomposition, which has a lot more applied usage e.g. in psychometrics and information retrieval analysis, I'm all ears.

[Jimbits76]

Man I wish I were smart.

I'd love to be intelligent. Most lads grow up wanting to be a footballer or rock star.

I grew up wanting to be a quantam physicist or mathematical theorist.

Unfortunately I wasn't gifted with the correct raw materials!

Instead I can just about tie my shoelaces and hum a tune at the same time.

I feel sad!

J

[Gedanken]

Originally Posted by 2careless

Stats doesn't touch number theory, therefore it's no use for Riemann hypothesis. This whole stuff is more pure math and has nearly no applied usage, imho.
If we're talking about singular value decomposition, which has a lot more applied usage e.g. in psychometrics and information retrieval analysis, I'm all ears.

Dunno about that, Kai. Riemann's work does have some influence on probability distributions, so it could well have a major impact on stats.

[2careless]

Possibly for Riemann's work, but I really can't corelate Riemann's Hypothesis has applied usage, other than prime number generation, which may have implications on cryptology.

[Taffi Abernathy]

Originally Posted by Jimbits76

Man I wish I were smart.

I'd love to be intelligent. Most lads grow up wanting to be a footballer or rock star.

I grew up wanting to be a quantam physicist or mathematical theorist.

Unfortunately I wasn't gifted with the correct raw materials!

Instead I can just about tie my shoelaces and hum a tune at the same time.

I feel sad!

J

Jim,

You're wishing for something you already possess. For instance, you have sharp wit, a sign of high intelligence as well as sensitivity, an indicator of social intelligence. There are different types of intelligence and most people have their areas where they excel, but I'm sure very, very few excel across every dimension. My strengths are more strongly dominated by language/verbal/writing than geared towards mathematics, which is why I am struggling to understand this information. Believe me when I tell you that a quantum physicist and a math theorist have their areas of deficiency too. You are fine as you are - at least that's my opinion. Faith

[Jimbits76]

Originally Posted by Taffi Abernathy

Jim,

You're wishing for something you already possess. For instance, you have sharp wit, a sign of high intelligence as well as sensitivity, an indicator of social intelligence. There are different types of intelligence and most people have their areas where they excel, but I'm sure very, very few excel across every dimension. My strengths are more strongly dominated by language/verbal/writing than geared towards mathematics, which is why I am struggling to understand this information. Believe me when I tell you that a quantum physicist and a math theorist have their areas of deficiency too. You are fine as you are - at least that's my opinion. Faith

Thanks Faith...do I get a diploma to go with that shining reference



J