Pythagoras versus the Mad Tailor: an essay on the unreasonable effectiveness of mathematics by Rick Searle

Dear Rick,

Great essay! I liked very much your tailor analogy, and your well-written arguments for a weak version of the Mathematical Universe Hypothesis.

Good luck in the contest,

Mohammed

Hi Rick--

I enjoyed your essay very much. Great title and concept. I had not heard the story of the honeybee. In the small world department, we both relied on science fiction authors to make points (you, Lem; me, Zelazny).

I was intrigued by your Weak MUH argument. I like the way that you set it out and, most important, detailed ways in which the hypothesis might fail. That's fantastic--the true sign of a first-class critical thinker!

Best regards and good luck,

Bill.

Rick,

If we successfully model a Theory of Everything, does this mean a strong MUH and thus that the universe is a mathematical structure? Would we say the the universe is knowable then? Does a weak version of Max Tegmark's MUH suspend the belief that nature itself is fundamentally mathematical until one model is established?

I am not a mathematician, so I find such questions unfathomable.

You essay is a great discussion and prompts many questions.

Jim

Rick,

I always enjoy your writing, and I think this is a top notch essay even though we have different interpretations of Tegmark's program.

I think weakening the MUH will kill it -- for the reason that the weaker version depends on the same "equally likely" hypothesis on which a probabilistically random world depends. Tegmark is quite straightforward in admitting that if the universe is random at foundation, MUH is refuted.

My argument for the MUH is based on classical probability. Given a binary choice, MUH is probably true.

Thanks for the good read, and best wishes in the competition. I hope you get a chance to drop by my forum.

Best,

Tom

Hi Rick,

Thanks. I thought I had rated your essay when I commented -- apparently not (forgive my senior moment :-) ). Done now, with my best.

This is certainly worth commenting on: "As for randomness if in either or both a weak or (strong) version of the MUH are true wouldn't randomness disappear once we abandon the notion of time? That is, if the probabilities have 'already' been 'decided' and our perception of randomness is merely subjective and based on our subjective experience of moving through time combined with our inability to see the structure as a whole."(?)

In my view, while randomness would disappear, classical binary probability would not. That's one of my main points -- that decidability with a time parameter implies a pairwise stochastic function (See Hess-Philipp 2002). That is, past and future simultaneously correlated events imply that the MUH is true with a probability of unity. That's why I think it cannot be weakened, unless one abandons classical probability along with randomness, which would obviate the hypothesis altogether.

All best,

Tom

By all means, Rick, read Prof. Hess's book. It isn't without controversy; however, I'm in full accord with the premise.

Thanks again, and all best,

Tom

Dear Rick,

I really like this essay, it is both well-argued and well-written :) I (or Pragmatic Physicist respectively) also approve of the pragmatism to get something useful out of the mathematical universe.

-- Sophia

Dear Rick,

I enjoyed reading your essay. I like your weak MUH, that "We live in a mathematical structure that is fully homeomorphic with a language of mathematics that retains this mathematics' Platonic features i.e. it is timeless and reversibility." And I also like that you made it testable, so that our confidence in it may decrease or increase under some conditions. Very well written and well argued!

Best wishes,

Cristi

Hello Rick,

Your essay was able to capture very well the theme of this year's essay. And nice to read.

If I may take you up on some aspects...

"One way that has been proposed that would overcome this problem is simply to do away with the map/territory distinction entirely in favor of the ultimate reality of the map itself. This is the case with Max Tegmark and his Mathematical Universe Hypothesis (MUH). In a way the MUH poses an even bigger big question; namely is mathematics itself the ultimate reality?"

If this proposal is favoured, then it should also be permissible to call it a Physical Universe Hypothesis or would it not? That is, mathematics is physics and physics is mathematics and therefore ultimate reality should EQUIVALENTLY be both physical and mathematical? This leads me to the next aspect,

Pythagorean idea that mathematics was the language of nature. Pythagoras, of course, inspired Plato who gave us the idea that the kinds of mathematical truths the Greeks were uncovering were both discovered and timeless. Plato also gave us the idea that these "forms" were the fundamental aspect of existence, and something more real than the world we experienced through our senses.

Geometry is fundamental to reality. I don't know if you are aware of the dialectical struggle that took place between the Pythagoreans, Proclus, Aristotle and Plato on how to define and describe the fundamental unit of geometry, the point. While the Pythagoreans, Proclus and partly Aristotle admitted that the point must be of some but very small dimension to be real, Plato suggested that the point was a zero-dimensional object, yet was still real. In Plato's words, "the point is not a geometrical fiction". You can check Metaphysics and Physics by Aristotle for reference. You can also check the references in my FQXi 2013 Essay.

Why I mention this is because of your recall of Plato's idea that these "forms", the 'point' included are the fundamental aspect of existence, and something more real... Is the 'point' real? Is the 'point', a fundamental aspect of existence? Which is the more likely to be real and a fundamental aspect of existence, that which is of zero dimension or that which is of some very, very small but non-zero dimension?

Then concerning your frequent, reference to Platonic features of 'timeless' and 'reversibility', can you educate me?

Can what is timeless be reversible, since reversible means something that can change, and what can change appears not to be a timeless feature.

I explore again in continuation of my previous 2013 effort in this year's essay, the spell as I would like to call it, cast upon our mathematica and physica, by another Greek, Parmenides, who happened to be teacher to the more famous Zeno. Parmenides, asked, "How can what IS perish?" That is, existing mathematical objects, be it of the Platonic or other variety cannot perish but must be eternally existing. Now, IF, and a big IF, our cosmology s correct and there was a Big bang and there will be a Big Crunch, whereby the Universe will perish, will a Mathematical Universe survive this outcome? If not, then we can agree that Mathematical Universe is actually the ultimate reality, as you quote Tegmark to have said. If Mathematical Universe survives, then it cannot be the ultimate reality that we behold in physics but something else, since reality has perished and still Mathematical Universe remains alive so to speak. For them to be one and the same, they must live and perish together.

My essay this year may be long and winding and not quite as straight to the point as I would have wished, but the meat of it is that what exists is not timeless but can perish.

Indeed, I made a proposal you can criticize for my benefit, that "the non-zero dimensional point does not have an eternal existence, but can appear and disappear spontaneously, or when induced to do so."

Best regards,

Akinbo

Rick,

Time grows short, so I am revisiting essays I've read (3/23) to assure I've rated them. I find that I have not rated yours, so I will rectify. I hope you get a chance to look at mine: http://fqxi.org/community/forum/topic/2345.

Jim

Dear Rick,

I share your argumentation about the objectivity of the Platonic world and your conclusion that the

"actual history of physics itself should put to rest the argument that mathematics is a mere invention of the human mind which we impose upon nature. Mathematics is truth not trick".

In this respect, you may see in our essay the arguments similar to yours. I think though that answering the question

"how, among such a huge number of mathematical structures are we able to find the one that is actually ours?"

you lost an important fact that the laws of nature are expressed by rather simple equations. This fact is used in our refutation of Tegmark's "mathematical democracy".

Regards,

Alexey.