Sir Roger...

From ASMR (prior post) to an hour+ of Roger Penrose, courtesy of Numberphile:




More on the podcast and Penrose here, from AMS:
https://blogs.ams.org/beyondreviews/2020/08/29/roger-penrose-on-numberphile/

Mathematical Values

This week's Sunday reflection, courtesy of Roger Penrose:

"How, in fact, does one decide which things in mathematics are important and which are not? Ultimately, the criteria have to be aesthetic ones. There are other values in mathematics, such as depth, generality, and utility. But these are not so much ends in themselves. Their significance would seem to rest on the values of the other things to which they relate. The ultimate values seem simply to be aesthetic; that is, artistic values such as one has in music or painting or any other art form."

Real vs. Imaginary...

Sunday reflection:

“…the terminology is misleading, for it suggests that there is some greater ‘reality’ to these so-called real numbers than there is to the so-called imaginary numbers. This impression comes about, I suppose, because there is the feeling that distance measures are, in some sense ‘really’ such real-number quantities. But we do not know this. We know that these real numbers are indeed very good for describing distances and times, but we do not know that this description holds good at absolutely all scales of distance or time."We have no actual understanding of the nature of a physical continuum at a scale of, say, one googolith of a metre or of a second, for example. The so-called real numbers are mathematical constructions, which are, nevertheless immensely valuable for the formulation of the physical laws of classical physics.”

— Sir Roger Penrose in Fashion, Faith, and Fantasy

Sir Roger Penrose Expounds

A blurb today about a new book I’m less than 100 pages into…

“Fashion, Faith, and Fantasy in the new physics of the Universe” is the latest from renowned Sir Roger Penrose. This is another beautifully produced, beautifully laid-out and diagrammed book from Princeton University Press. Given the breadth of these 400+ pages and Roger’s age I can’t help but wonder if this may be the last major work from him for a general audience. For all those reasons (and hey, simply because it IS from Roger Penrose) I’m sure it is worth recommending it to all readers interested in modern physics/cosmology. Peter Woit wrote a favorable review here (which I’ll point you to, since I won’t write a review):

http://www.math.columbia.edu/~woit/wordpress/?p=8759

I imagine the catchy main title (“Fashion, Faith, and Fantasy”) is especially intended to attract a wide general audience. Make no mistake about it though, it is heavy reading for anyone lacking acquaintance with theoretical physics, focused on the standard theory, inflation, quantum mechanics, string theory, and Penrose’s own twistor theory. There is a fair amount of math in the volume as well, and in fact, for math fans, the 70-page “Mathematical Appendix” may even be the best part of the book.

I won’t attempt a full review though because so much of the physics is simply beyond my grasp. Despite having read many popular cosmology books in the last two decades, the whole field is less, not more, comprehensible to me over time. I well understand the frustration (and rise) of the many skeptics of modern physics in recent years (Penrose himself is skeptical of many aspects). I don’t know of any other field where the more I’ve read, the fuzzier and less-comprehensible it all seems (not to mention being vociferously-debated-over by those who DO understand it!).

But with that said, I am looking forward to slowly slogging my way through this volume and gleaning from it what I can; there is possibly no better or more original expositor than Penrose to draw from. If modern physics theory is of interest to you you certainly won’t want to ignore this book either, and the more you already understand, the brighter read it will be.

I do have one curiosity about the book that maybe some knowledgeable reader can comment on in a few sentences:

I no more comprehend the specifics of the Langland’s Program in mathematics than the advanced cosmological theories in physics, but am still interested to hear about progress in cutting-edge Langlands work that hopes to unify mathematics (and in so doing may offer some unification to physics as well). Given that Penrose is a mathematical physicist I hoped there might be an update on Langlands somewhere in these 400+ pages, but it appears absent (not included in the Index to the volume). Am I wrong to think Langlands should tie in to some of this very theoretical discussion, or is there some reason one would NOT expect to see it in such a volume — is it too early on in Langlands work to be tying it back to "fashionable" ;-) physics, or perhaps the opposite problem, and it is simply too advanced for inclusion in a general audience volume? Just curious, if someone can enlighten me; I was looking forward to seeing Penrose's take on it all (or maybe it's just an area he has not much dabbled in?).

Anyway, here's how Woit ends his review of Sir Roger's volume:

"The range of non-crackpot speculative ideas about fundamental physics that normally get much attention is unfortunately quite narrow. In this environment Penrose is a breath of fresh air, providing here a different point of view on several topics, backed by serious and detailed argument. In some ways this is a popular book, but in others it is something else, deserving the attention of experts in the subject. I can’t recommend it too highly to anyone with a serious interest in fundamental questions about physics."

p.s.... Penrose will be at the Museum of Math in NY this coming Wed. evening promoting his book.

"the wonders of the world of algebra"

Sir Roger... and algebra:

Currently lacking time for longer posts, so just another quotation today, this time from the eminent Roger Penrose remarking on his introduction to algebra as a youngster (taken from his Foreward to Mircea Pitici's "The Best Writing on Mathematics 2013"):

"My earliest encounter with algebra came about also at an early age, when, having long been intrigued by the identity 2 + 2 = 2 X 2, I had hit upon 1.5 + 3 = 1.5 X 3. Wondering whether there might be other examples, and using some geometrical consideration concerning squares and rectangles, or something -- I had never done any algebra -- I hit upon some rather too-elaborate formula for what I had guessed might be a general expression for the solution to this problem. Upon my showing this to my older brother Oliver, he immediately showed me how my formula could be reduced to 1/a + 1/b = 1, and he explained to me how this formula indeed provided the general solution to a + b = a X b.  I was amazed by this power of simple algebra to transform and simplify  expressions, and this basic demonstration opened my eyes to the wonders of the world of algebra."

Contemplating Godel

Roger Penrose interviewed on Kurt Godel here:

http://simplycharly.com/godel/roger_penrose_godel_interview.html

...and Gregory Chaitin here:

http://simplycharly.com/godel/gregory_chaitin_interview.htm

...and lastly Raymond Smullyan here:

http://simplycharly.com/godel/raymond_smullyan_godel_interview.html