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Topic: hilbert's third problem
Replies: 24   Last Post: Aug 16, 2013 3:33 AM

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GS Chandy

Posts: 8,307
From: Hyderabad, Mumbai/Bangalore, India
Registered: 9/29/05
Re: hilbert's third problem
Posted: Aug 4, 2013 4:44 AM
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Responding to Frank Zubek's boasts dt. Aug 4, 2013 1:33 AM (copy pasted below my signature for ready reference):

I did find Frank Zubek's boasts in his post to be 'interesting', at least. As to whether I find the boasts to be believable or not, let me state that I am open to being convinced about them, though in general I am averse to believing loud boasts, categorical commands (whether intended literally or metaphorically) such as:


(and the like).

I recall that - while I was at graduate school studying math (homological algebra) - we grad students used to have have much discussion about the "Hilbert Problems" and other such knotty matters. I now do not have ready access to many of my books and the like; I therefore googled for 'Hilbert Problems' and came up with a link to Hilbert's original paper, "Lecture delivered before the International Congress of Mathematicians at Paris in 1900" (file:///media/DATA/Documents2/New%20Sorted%20Date/Current/Math-teach%20-%20Mathematical%20Problems%20by%20David%20Hilbert.html) [Those were thrilling times indeed]!

Hilbert's 3rd Problem,which Mr Zubek boasts that he showed the "Synergeo guys" how to solve it (though Kirby and Buckminster Fuller didn't have the slightest clue about Mr Zubek's "blocks because the cleverness was lacking" [words to that effect]).

Hilbert's original statement of his 'Third Problem' goes like this:
> "3. The equality of two volumes of two tetrahedra of equal bases and equal altitudes

>"In two letters to Gerling, Gauss (5) expresses his regret that certain theorems of solid geometry depend upon the method of exhaustion, i. e., in modern phraseology, upon the axiom of continuity (or upon the axiom of Archimedes). Gauss mentions in particular the theorem of Euclid, that triangular pyramids of equal altitudes are to each other as their bases. Now the analogous problem in the plane has been solved.6 Gerling also succeeded in proving the equality of volume of symmetrical polyhedra by dividing them into congruent parts. Nevertheless, it seems to me probable that a general proof of this kind for the theorem of Euclid just mentioned is impossible, and it should be our task to give a rigorous proof of its impossibility. This would be obtained, as soon as we succeeded in specifying two tetrahedra of equal bases and equal altitudes which can in no way be split up into congruent tetrahedra, and which cannot be combined with congruent tetrahedra to form two polyhedra !
which themselves could be split up into congruent tetrahedra. (7) [The bracketed numbers are the references provided by Hilbert].

I have carefully looked at (but have not adequately *studied*) all the messages of the recent threads initiated by Mr Zubek and at threads initiated by others on issues he had raised - mainly his 'refutation' of Kirby and Buckminster Fuller):
- -- "cubes are unstable"
- -- "edge of a cube"
- -- "unit rad. spheres"
- -- "synergetics made by Z modules 4 years old Urner's lie"
- -- "how much sense this makes"
- -- "powering is cube shaped"
- -- "tet. calculations easier - Joe N"
- -- "zubek's catches"
- -- "REJECTED Re: tet. calculations easier - Joe N"
- -- "To Joe"
- -- "hilbert's third problem "
At one stage (long before I came up with the 'One Page Management System' [OPMS]]), I had spent a fair bit of time and effort studying the works of Buckminster Fuller, his geodesic domes (constructing a good number of them from small enough to hold in two hands right up to 'human habitation' size; and also his 'tensegrity structures', etc); Fuller's theories on 'Synergetics' and its relationships to 'systems in the real world'.

Buckminster Fuller and "Synergetics"
I have tried to study Buckminster Fuller's "Synergetics" (in part) - though I must confess that I've not fully understood it as I believe it deserves to be understood.

I have not yet been able to view 'Synergistics' 'through the prism' of OPMS, which is when I shall be able to understand it more fully than I do now.

There is (IMHO) a considerable value in 'Synergistics', and much to learn from it about Fuller's insights into how the real world operates. I do wish SOMEONE would take up the challenge to *unlock synergistics* for all of us! (see below).

Fuller's work is, in fact (IMHO), something that is waiting for some 'aficionado' to take up the huge challenge to make it accessible and available to the rest of us. I don't believe that Kirby Urner has quite succeeded in doing this. (I note that I have carefully read through [have not *studied*] many of Kirby Urner's posts here at Math-teach AND at various other locations at which Kirby posts - including some of his blogs, etc).

Frank Zubek posted Aug 4, 2013 1:33 AM
> It was me showing the synergeo guys how to accomplish
> Hilbert's third problem listed among unsolved
> problems
> with my set, and of course using my blocks, and for
> sure Kirby nor Fuller never could even have a
> faintest clue, yet the problem existed in his time
> but the cleverness was lacking.
> Now of course they can do it, after ME.
> I was also the first to show how to use any number of
> magnets that never repel, commonly used in polyhedra
> manufacturers, again it was not Fuller but me and now
> everyone is using my system.
> It was me who done the lowest common denominator for
> all the structures.
> It was me who discovered the most minimal blocks
> Fuller again had no clue, and any of the synergeo
> enthusiasts, and it was ME to show that two fused
> reg. tet. are NOT the minimal but the 1/8 octahedrons
> are.
> All done on a pocket calculator and a napkin, isn't
> that something.
> frank
> frank

IMHO, there *may* be (though I seriously doubt THIS) something of value in Mr Zubek's boasts. I'm afraid that, after carefully reading through all his posts here (and all the responses to those posts) I have understood little or nothing of it. This is possibly because of my own inadequacies, though I HAVE been able to understand some fairly complex and difficult stuff. At least part of the problem is that I am to a good extent turned off by Mr Zubek's boastful ways.

I observe in passing that it was only just a couple of years ago that Girgoriy Perelman had provided the final touches to the proof of the 'Poincare Conjecture' (which has some significant links to Hilbert's Eighth Problem and his Tenth Problem). I bring this up because Perelman, in solving the Poincare Conjecture actually won one of the several Clay Millennium Awards (of $ 1 million). On being awarded the Clay Award, Perelman refused it, and Wikipedia has the following interesting entry:

Poincare Conjecture: (
"...the Clay Mathematics Institute offered a $1,000,000 prize for the first correct solution of the Poincare Conjecture). Perelman's work survived review and was confirmed in 2006, leading to his being offered a Fields Medal, which he declined. Perelman was awarded the Millennium Prize on March 18, 2010.[2] On July 1, 2010, he turned down the prize saying that he believes his contribution in proving the Poincaré conjecture was no greater than that of Hamilton's (who first suggested using the Ricci flow for the solution).[3][4] The Poincaré conjecture is the only solved Millennium problem.
If I'm not mistaken, the concept of the 'Ricci Flow' was something that I believe was invented by Perelman himself!! And yet he refused the Clay Millennium Award!

In the face of such modesty from one of the true mathematical geniuses of our times, I do find it difficult to take the boastfulness of Frank Zubek, the certitudes of Wayne Bishop, Haim, and their cohorts and consorts.


Message was edited by: GS Chandy

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