Talk:Robert Berger (mathematician)

problems
Several problems here:

1. This brief article contradicts the more detailed article at Aperiodic tiling. This article implies that Berger used results from Penrose's work, but the Aperiodic Tiling article gives a completely different history (which is backed up by various articles I found on line). Essentially Dr Hao Wang posed the question if the tiling problem is computable: Berger first proved that the problem is not computable (which implies that there is an aperiodic solution) and then found the first aperiodic solution.

2. This background (which addresses the "too technical" flag) is well covered in Aperiodic tiling. So does it need repeating here?

3. I can't find anything on Robert Berger's life. He's not in the Mathematical Genealogy project - well only if he is the German Robert W Berger and the details don's seem to fit. He is not listed as a Ph D STudent of Dr Wang [http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=29869

Finally, he seems to have written only the one paper - at least in the area of tiling.

R. Berger, The undecidability of the domino problem, Mem. Amer. Math. Soc. 66, 1966.]

Did he go off to Wall Street rather than pursuing a career in academic mathematics?

Dr/Professor/Mr Berger - if you are reading this please correct me if I am wrong!!

Maybe we should merge? I'm flagging on The Maths articles needing attention to see what happens.

--Cje 09:17, 16 August 2005 (UTC)


 * I don't understand how exactly this article contradicts the information in Aperiodic tiling. Could you be more specific? Both say that Burger invented the "first aperiodic set of tiles consisting of 20,426 distinct tile shapes � in 1966", correct? Is it the qualifying phrase "by using the rules of Penrose tiling and the Golden Rule" that you find problematic? Is this because Penrose tiling hadn't yet been described in 1966?  Perhaps (and this is purely a guess), that the phrase is just describing the kind of tiling rules used, making no assertion as to chronology? Any any case I think the the phrase and link  Golden Rule is wrong. Perhaps Golden ratio was meant? As a specific answer to your question 2 above, whatever the correct history and background is, it should (IMHO) be added to this article. It is quite ok (and is actually a good thing) to have "repeating" content. Paul August &#9742; 20:35, August 16, 2005 (UTC)

Let me try and clarify!

It is the phrase "by using the rules of Penrose tiling" that I was objecting to. The natural reading of that phrase is that he used Penrose's technique. Well: 1) Penrose tiling had not been described in 1966. 2) As I understand it Berger's tiling is *not* an example of Penrose tiling, so one couldn't say "he used the method of Penrose tiling, though at the time the the method had not been named after Penrose"

I do take your point on repeating content in general. If we had bio information on Robert Berger then including a brief explanation of the significance of his work makes perfect sense. But a a bio article that says "a. the only thing we know about this guy is his work on X b. Here is a brief summary of X. c. See article on X for more on X" does seem to me to be "repeating" content for no good reason.

I do hope that someone knows the story here and can help out!

--Cje 07:21, 17 August 2005 (UTC)

Oh and I am bemused by the reference to the Golden Rule? Where does that fit in? --Cje 07:36, 17 August 2005 (UTC)


 * The version at Wang tile is correct and the phrase "... by using the rules of Penrose tiling and the Golden Rule" in this article is wrong (Grünbaum and Shephard, Tilings and Patterns, 1987). The same book says that Berger brought the number 20426 down to 104. No biographical details on Berger are mentioned. The library of Harvard (where I assume Berger did his PhD, given the cv in Wang Hao) lists Berger's year of birth as 1938. I agree with Cje that we do not have enough information to make an article. -- Jitse Niesen (talk) 14:12, 17 August 2005 (UTC)


 * You are right, Cje, Berger's work was entirely independent of Penrose's work. And I agree that the "Golden rule" reference is nonsense wrt Berger's work.  I just emailed someone I know who might have some information about Berger, and will edit the biography if I find out anything useful.
 * BTW, if I get a chance sometime next year, I intend to greatly improve the aperiodic tiling and symbolic dynamics pages. Since I wrote my diss on "generalized Penrose tilings", and for a time had a website describing my dissertation, I have lotsta nifty figures lying around I could upload (just put two little ones on my user page).---CH  (talk) 16:49, 22 August 2005 (UTC)


 * Branko Grunbaum got back to me faster than I'm getting back to you guys, wow! Alas, while he confirms that R. Berger's first name is Robert, he doesn't know any more.  He suggested someone check old membership lists of the AMS (someone with, er, an active membership can do that more easily than I). Barring that, I do have one other person I ask.  Let me know.---CH  (talk) 00:20, 23 August 2005 (UTC)

Berger's construction was essentially to model Turing machines using tiles. Penrose used an inflation/substitution technuique. The two techniques are entirely different. Mat Newman.


 * Everyone watching is long gone, but here a point: Mat Newman is correct, and Berger predates everyone; his construction, it must be said, does have a hierarchical structure, that was ultimately made more bare by Raphael Robinson in his own proof of the undecidability of the tiling problem. Penrose took this further, creating an explicit inflation/substitution structure. But it's there in Berger's work. Great to see something about current work from this wonderful mind who opened up such a fascinating avenue! C Goodman-Strauss (talk) 03:09, 9 December 2011 (UTC)

--Sergiolerner 04:35, 21 July 2006 (UTC)

I've read R. Berger Thesis and I've reproduce his results. As you have already said, Berger's does not rely on Penrose tilings. The paper itself is a bit tedious to read, but after you understand the basics you are lead into the mind of a brilliant man. The construction described on the paper is very creative. He made two discoveries: the first aperiodic structure on Wang tiles and a turing machine modeled over that structure. The skeleton of the aperiodic structure (named K)is recursive. May I modify Bergers biography according to the things discussed here? I can also add some images of his aperiodic tilings generated by computer.

SDL, Buenos Aires, Argentina.


 * I was in Cambridge a couple of weeks ago and stopped by the archives library at Harvard, but they aren't open weekends. :(  I think there was a copy on the stacks in one of the science libraries, but the reference librarian and I couldn't find it.  Must've been lost.  Oh well.  Lunch 01:49, 21 November 2006 (UTC)

Robert W Berger
I moved info about Robert W. Berger to a new page&mdash; G716  &lt;T·C&gt; 13:40, 27 September 2008 (UTC)