Comments on: Update on the Giant-Killers http://asymptotia.com/2006/10/05/update-on-the-giant-killers/ Tue, 16 Mar 2010 08:46:51 +0000 http://wordpress.org/?v=2.7.1 hourly 1 By: Elliot http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-2806 Elliot Sat, 28 Oct 2006 23:50:02 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-2806 Red, My reason for the comment was twofold 1) I have worked on this problem on and off for nearly 35 years and have a pretty good insight into why the pattern "appears" random which directly relates to differences between addition and multiplication. and 2) this comment was made to me directly by a stunningly brilliant but no longer practicing mathematican who must remain anonymous at this time. He came up with this analysis after looking at the problem for about 10 minutes. If you have something related to this I would encourage you to write it up. My sense is that there is a deep connection between the non-commutative aspects of mixing these operations and the non-commutative aspects of "mixing" space and time. But that is at this point just a wild speculation on my part. Regards, Elliot Red,

My reason for the comment was twofold 1) I have worked on this problem on and off for nearly 35 years and have a pretty good insight into why the pattern “appears” random which directly relates to differences between addition and multiplication. and 2) this comment was made to me directly by a stunningly brilliant but no longer practicing mathematican who must remain anonymous at this time. He came up with this analysis after looking at the problem for about 10 minutes.

If you have something related to this I would encourage you to write it up. My sense is that there is a deep connection between the non-commutative aspects of mixing these operations and the non-commutative aspects of “mixing” space and time. But that is at this point just a wild speculation on my part.

Regards,

Elliot

]]> By: Red http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-2787 Red Sat, 28 Oct 2006 20:37:54 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-2787 Elliot stated: "The Collatz conjecture is connected to the deep differences between addition and multiplication." I find this to be a remarkable statement in itself because: (i) it shows insight into the actual 3x+1 problem (ii) I've not seen it expressed that way before Is this actually well known or just a guess? The reason I ask is that I have an explicit analysis of this aspect but I've never bothered to write it up more formally. Should I? I'm not claiming this constitutes a proof at all. My original motivation was a kind of "No Go" theorem for Wolfram's claim that "complex" patterns (and by extension, physical phenomena) arise from "simple" rules. He uses 3x+1 as an exampe in his NKS book. However, when examined more closely one sees that addition is responsible for an amazing kind of 'mix master' effect. Thus, the 3x+1 rule can hardly be called "simple", even though it looks simple. Red Elliot stated: “The Collatz conjecture is connected to the deep differences between addition and multiplication.”

I find this to be a remarkable statement in itself because:
(i) it shows insight into the actual 3x+1 problem
(ii) I’ve not seen it expressed that way before

Is this actually well known or just a guess? The reason I ask is that I have an explicit analysis of this aspect but I’ve never bothered to write it up more formally. Should I? I’m not claiming this constitutes a proof at all.

My original motivation was a kind of “No Go” theorem for Wolfram’s claim that “complex” patterns (and by extension, physical phenomena) arise from “simple” rules. He uses 3x+1 as an exampe in his NKS book. However, when examined more closely one sees that addition is responsible for an amazing kind of ‘mix master’ effect. Thus, the 3x+1 rule can hardly be called “simple”, even though it looks simple.

Red

]]> By: Elliot http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-1912 Elliot Mon, 09 Oct 2006 19:29:53 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-1912 Since Erdos said of the problem "mathematics is not ready for such problems", perhaps the person who solve it can claim an honorary low Erdos number. Since Erdos said of the problem “mathematics is not ready for such problems”, perhaps the person who solve it can claim an honorary low Erdos number.

]]> By: Elliot http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-1909 Elliot Mon, 09 Oct 2006 18:56:59 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-1909 Aaron, The Collatz conjecture is connected to the deep differences between addition and multiplication. While conjectures in integer arithmetic may be plentiful. The devilishly simple nature of this problem without current resolution makes it attractive in its own way. I agree that it probably won't make it on to the Clay prize list however. But whoever cracks it will at a minimum become a folk hero. Elliot Aaron,

The Collatz conjecture is connected to the deep differences between addition and multiplication.

While conjectures in integer arithmetic may be plentiful. The devilishly simple nature of this problem without current resolution makes it attractive in its own way.

I agree that it probably won’t make it on to the Clay prize list however. But whoever cracks it will at a minimum become a folk hero.

Elliot

]]> By: Giant Still Standing - Asymptotia http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-1768 Giant Still Standing - Asymptotia Sun, 08 Oct 2006 22:56:11 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-1768 [...] The giant still stands, at least for now. From the preprint site: This paper is being withdrawn by the author due a serious flaw. [...] [...] The giant still stands, at least for now. From the preprint site: This paper is being withdrawn by the author due a serious flaw. [...]

]]> By: Clifford http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-1765 Clifford Sun, 08 Oct 2006 22:36:17 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-1765 Wow! -cvj Wow!

-cvj

]]> By: Say Lee http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-1763 Say Lee Sun, 08 Oct 2006 21:09:06 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-1763 Actually I meant peek. Actually I meant peek.

]]> By: Say Lee http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-1762 Say Lee Sun, 08 Oct 2006 20:53:24 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-1762 I just checked the website of the preprint, thinking that I might want to take a peep as I'm in kind of fluid (water) mechanics business and this is what I saw: This paper is being withdrawn by the author due a serious flaw. So what's the deal? I just checked the website of the preprint, thinking that I might want to take a peep as I’m in kind of fluid (water) mechanics business and this is what I saw:

This paper is being withdrawn by the author due a serious flaw.

So what’s the deal?

]]> By: Clifford http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-1735 Clifford Sun, 08 Oct 2006 01:56:23 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-1735 It is rather fascinating though.... Thanks Chris W., and Aaron. -cvj It is rather fascinating though…. Thanks Chris W., and Aaron.

-cvj

]]> By: Aaron Bergman http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-1734 Aaron Bergman Sun, 08 Oct 2006 01:52:27 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-1734 Unless to Collatz conjecture is shown to be related to something deep, I can't imagine it ever becoming a Clay problem. Conjectures in integer arithmetic are a dime a dozen, really. Unless to Collatz conjecture is shown to be related to something deep, I can’t imagine it ever becoming a Clay problem. Conjectures in integer arithmetic are a dime a dozen, really.

]]> By: Chris W. http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-1733 Chris W. Sun, 08 Oct 2006 01:25:58 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-1733 Wikipedia has covered it in <a href="http://en.wikipedia.org/wiki/Collatz_conjecture" rel="nofollow">detail</a>. Wikipedia has covered it in detail.

]]> By: Clifford http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-1696 Clifford Sat, 07 Oct 2006 00:48:06 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-1696 Any info on it? I do not know this.... Might have a go at it on the bus.... ;-) -cvj Any info on it? I do not know this…. Might have a go at it on the bus…. ;-)

-cvj

]]> By: Elliot http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-1694 Elliot Sat, 07 Oct 2006 00:34:59 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-1694 I'm hoping that if a couple of the Clay problems are solved the "Collatz conjecture" will be added to the list. It is devastatingly simple to state but very difficult to prove. A number theory problem that will make you tear your hair out. Cheers Elliot I’m hoping that if a couple of the Clay problems are solved the “Collatz conjecture” will be added to the list. It is devastatingly simple to state but very difficult to prove. A number theory problem that will make you tear your hair out.

Cheers

Elliot

]]> By: Clifford http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-1687 Clifford Fri, 06 Oct 2006 22:57:27 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-1687 Oh... he did? Hey, someone tell them I can use the money...they should not keep it since it will only confuse the budget quite a bit. I'll set up a little institute here. I'll call it whatever they want me to call it. ;-) -cvj Oh… he did? Hey, someone tell them I can use the money…they should not keep it since it will only confuse the budget quite a bit. I’ll set up a little institute here. I’ll call it whatever they want me to call it. ;-)

-cvj

]]> By: Yacine D. http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-1685 Yacine D. Fri, 06 Oct 2006 22:47:42 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-1685 Note that the Clay institute actually did not have to dole out the previous million dollar as Perelman refused it. So I would rather say that their budget is quite positive these days ;) Note that the Clay institute actually did not have to dole out the previous million dollar as Perelman refused it. So I would rather say that their budget is quite positive these days ;)

]]> By: Chris W. http://asymptotia.com/2006/10/05/update-on-the-giant-killers/comment-page-1/#comment-1649 Chris W. Fri, 06 Oct 2006 04:34:08 +0000 http://asymptotia.com/2006/10/05/update-on-the-giant-killers/#comment-1649 Christina Sormani's <a href="http://comet.lehman.cuny.edu/sormani/others/SmithNavierStokes.html" rel="nofollow">summary</a> discusses Penny Smith's work on the Einstein field equation about as much as Navier-Stokes, since they are so interrelated. Note this: <blockquote>Smith's results in this direction provide a nice counterpoint to work of Klainerman and Rodnianski she admires. Her theorem requires smoother initial data than theirs but she obtains eternal solutions (solutions that exist for all time). In an abstract for one of her talks, Smith wrote that her methods also "suggest a new and stable numerical method for the Einstein Evolution Problem".</blockquote> Christina Sormani’s summary discusses Penny Smith’s work on the Einstein field equation about as much as Navier-Stokes, since they are so interrelated. Note this:

Smith’s results in this direction provide a nice counterpoint to work of Klainerman and Rodnianski she admires. Her theorem requires smoother initial data than theirs but she obtains eternal solutions (solutions that exist for all time). In an abstract for one of her talks, Smith wrote that her methods also “suggest a new and stable numerical method for the Einstein Evolution Problem”.

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