Leonard Mlodinow - Why the ‘Unreasonable Effectiveness’ of Mathematics?

What is it about #mathematics that it can describe so accurately the world around us? From quantum physics, the very smallest features and forces of the foundations of matter and energy, to cosmology, the very largest structures and forces of the beginning and evolution of the universe, mathematics is the language of description. Why does the physical world follow so faithfully equations of abstract symbols and variables?

Leonard Mlodinow is a theoretical physicist, screenwriter, and author. He is known in physics for his work on the large N expansion, a method of approximating the spectrum of atoms based on the consideration of an infinite-dimensional version of the problem, and for his work on the quantum theory of light inside dielectrics.


Closer to Truth presents the world’s greatest thinkers exploring humanity’s deepest questions. Discover fundamental issues of existence. Engage new and diverse ways of thinking. Appreciate intense debates. Share your own opinions. Seek your own answers.

[zenshade]

I positively love that he asks this extraordinary question to every intelligent human being he interviews. I think the very simple answer is not only that God (however you to interpret that word) is a mathematician but that he/she/it couldn't be anything else. How else can you specify a coherent universe of patterns and forms worth exploring? Without some basic rules, you'd just get a bunch of chaos you couldn't get a grasp on. From there, how best to explore this beautiful thing you've created? From the outside looking in, or would you additionally want eyes down on the lowest levels exploring every nook and cranny? AND HERE WE ARE.

[أَفَلَايَعْقِلُونَ-هر]

actually most of the people don't address the main problem Wigner talked about, which is the ability of the mathematician to come up with mathematical patterns to describe the world, without looking at the world and using only his mind.

[CaptainJeoy]

It's simple, Mathematics describes patterns, patterns are simple at the core of it, and our procedurally generated universe follows certain patterns that can be described by mathematics.

Maths is only an abstraction of what is already going on.

[zgobermn]

Wow, Mlodinov simply echoes Wigner himself and understands the issues as Wigner himself did. Hence this unreasonable effectiveness of mathematics is MIRACULOUS, and as Wigner added, a GIFT we should all be thankful for. But then these descriptions cry out for an explanation, at least offer a reasonable inference. So, brute fact-no reason? Coincidence (what a jackpot!)? Multiverse (extravagant violation of the law of parsimony!)? Or inferring a single, simple mathematical MIND doing the math behind the universe (Einstein's 'superior reasoning power')-or as Mlodinov said at the end of the clip, God. Now that's a pretty rational inference. Only those committed to the ideology of reductive naturalism will find that unacceptable, not on the basis of the data but on dogma.

[Drakmar.the.Cursed]

The fact that the principals mathematics explain indeed appear to exist is what I find awesome. Mathematics, by my personal definition, is simply the words and symbols we as humans use to comprehend and communicate these principles. Mathematics didn't already exist before us, the principals it describes however did and do. I suppose the answer lies in where the individual slices their loaf of bread so to say.

[jamesruscheinski]

Does the abstract use mathematics to bring about the physical?

[michaelrichardson]

Situations in which this is perfectly reasonable and what you would expect are utterly disturbing.
Imagine a video game where all the characters are self aware and believe they are real world entities rather than a simulation.

[chrisg]

Zero, the thing mathematicians put there to show there's nothing there. Infinity, the number that means numberless. Limit, the number that you never get to, so always lies beyond the limit. Math deploys absurdities, contradictions and paradoxes to explain and predict.

Mlodinow may have been right to tell us 2:53 that "built into mathematical language you have rules of logic and reasoning. . . the framework of mathematics restrains where we're going", but then it's where you're coming from which makes that journey a wild adventure.

The effective unreasonableness of mathematics, not just its unreasonable effectiveness.

[billnorris]

As Leonard noted, mathematics is simply a descriptor.. Humans didn't invent math, we DISCOVERED it.. Aliens would discover the SAME rules and laws, whether they are just COUNTING objects or utilizing algebraic equations, Mathematic descriptors should be universally recognized among ALL intelligent entities.. One man's opinion..

[caricue]

I guess it's good that Dr Kuhn seeks out many opinions since virtually all the questions he asks can only be answered by an opinion (unless he got to do the interview he wants the most - God). My opinion, for what it's worth, is that math seems effective because it is formulated with the answer already known, and if a new observation or experimental result should contradict it, the math will simply be modified until it is unreasonably effective once again.

[lrvogt]

Our math fails at the moment of the big bang so there is one example. I like Sabine Hossenfelder's comment that maybe things can be described with relatively simple formulas because we're looking at relatively simple things.

[enfomy]

Someone would have to explain how an illogical world could have existed for me to think a logical and mathematically describable world is unreasonable. My understanding is that everything and nothing would have to exist and not exist simultaneously, or something like that, for an illogical world to exist. The existence of anything other than that would disprove a purely chaotic world. Not to mention any claim to any type of truth about the world implies a kind of logic to it. I can’t even think of a simple answer for the unreasonable effectiveness of mathematics. It’s like asking why the unreasonable effectiveness of language, or grammar, or art, or circles. There’s many reasons why these things are effective, but are they unreasonably effective? Well, they have why’s.

[slappop]

The answer is an anthropic one: if reality wasn't consistent (i.e. the same cause always goes to the same effect and so reality is describable by a logical, mathematical model), we couldn't exist as biological machines. Maybe there are universes not described by mathematics, but no one lives there.

[xspotbox]

So we have quantum building blocks that are all exact copies of same kind, we have light conveying information at straight path and fixed speed, and everything can be perfectly balanced, those are the basic constituents of functional number theory that allow mathematics to exist. Except all those concepts are just constructs, electrons are all the same, but have no shape and defined location, light is traveling straight, but in a curved space, speed of light is a constant, but propagate at different rates in materials, perfect balance can't exist because nothing is divisible exactly at half and can't be because everything is connected and in constant motion. This would mean mathematics emerge only in restrains of our dimension, where things are well tuned with our biological senses.It doesn't mean there is no number theory deep down and in a holistic dimension, it's just representations of numbers are different, logical order still exist, so they must be convertible into our dimension.
Essence of the world could explain effectiveness of logical relations and structures, but not why are we aware of it. World could exist according to biological laws of evolution also, things pop up into existence and evolve into something else, than dissolve and transform into something completely different, like one form of chaos flow into another kind of unstable nonsense, just because it can.
This chaotic and relativistic nature of the world enable us to do more mathematics than we can see in our environment, we can invent new concepts and force elements to do extended mathematics that do not exist in natural world. Number theory is natural foundation of reality, mathematics is not, it's invented by evolution of mind. Why do we think of forms same as mathematical constructs, those things are very different, but there must be a reason why we mix them together in a single construct. It's because we can observe past and contemplate about the future, if we could sense only what is now, rules would still apply, but no mathematics could exist since there would be no way to follow how some system evolved. Light, relativity and time are somehow merged into a single principle, this is telling me not all reality could be described by mathematics. No wonder logos was such a big deal for ancient philosophers, mathematics is a veil constructed over true underlying nature of reality. Think about that, entire logical structure of the universe could fall apart, could unwind just the same as it was added together, but universe itself would still exist. What set mathematical monster in motion billions of years ago, this is a better question.

[DeusExAstra]

"Who says nature should be logical?"... logic does

[sergeynovikov]

it's a poor argument to refer to aliens when talking about mathematics. we cant see any aliens in our universe - our planet is a single one with life on it. and this can be a fundamental consequence from the laws of physics (formulated in a math form) which our universe obeys.

[sibeguy]

Most of modern cosmology is built on mathematics which is overly complicated and not grounded in reality...I call it Mathterbation!

What if the universe is rooted in much simpler set of concepts...Quality, Connection and Process. I recommend checking out the work of Arthur M Young in his books The Reflexive Universe and The Theory of Process.

[fatihokhider]

Dr Keun pls note that math is simple because it is based on ONE & platonic figures & shapes are points or lines...this might be encoding a unitary language of ONE ..so it is Allah's way to show his onness...!

[joedavis]

Wonderhussy Adventures has way more truth and wholesomeness in it t h a n this show does. Honestly it does.

[mustafaelbahi]

michio kaku said that God is a mathematician