Max Tegmark - Why the ‘Unreasonable Effectiveness’ of Mathematics?

In 1960, the physicist Eugene Wigner published an article, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," which has attracted great interest and controversy. Is math’s effectiveness, especially in physics, indeed “unreasonable,” a mystery with no rational explanation? Or is such effectiveness more apparent than real, a kind of selection bias: you see what you look for, or you only pay attention when it works? Does mathematics convey deeper meaning?



Max Tegmark is Professor of Physics at Massachusetts Institute of Technology. He holds a BS in Physics and a BA in Economics from the Royal Institute of Technology in Sweden. He also earned a MA and PhD in physics from University of California, Berkeley.


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.

[yusefaziz]

I love the diversity of subjects in science you talk about. Definitely top 5 on my YouTube Channel list!!!

[thereligionofrationality]

One of the reasons I love this channel is that that it ALWAYS provokes ironic questions in me. (Not sarcastic, just slightly ironic)! Today's is, "Why is language so unreasonably effective at allowing animals to describe the world to each other?"

[mikedziuba]

I'd say there is a good reason why mathematics is so effective at describing the world in a precise and an accurate way. And this reason is that basic concepts in mathematics are based on physical reality. Two plus two equals four isn't just a mathematical idea. This is something you can deduce from testing and observing in the world and in the universe.

And the rest of mathematics is an extension of these basics concepts through deductive logic. Deductive logic makes sure that if your starting premises are true, then any deductive conclusions you make also have to be true, no matter matter how many deductive steps you take, provided that you haven't made even one mistake in all of your steps.

So, the effectiveness of mathematics is perfectly reasonable, and it can't be in any other way. Because the only way mathematics can end up being false and ineffective is through mistakes in its logic.

[ReynaSingh]

Math just like any language is representational of reality. We can keep adjusting our model but the map is not the territory

[Gotenham]

Dang this video quality is much better!

[FR-yrlo]

When you confuse reality and the DESCRIPTION of PERCEIVED patterns of the behavior of this reality. Which, ultimately, is consciousness/experiences.

[gulllars]

A clever candidate for a deeper truth on how math underlies everything is an even more fundamental approach that space and everything in it is not distinct mathematical things but emerging from computation on a hypergraph. Or rather multicomputation on a hypergraph with all possible rulesets computation can be done, which weirdly gives rise to both relativity and quantum-effects, and has the interesting property that unlike math, there is no way to get the result other than running the computation. You can find math to describe emergent pockets of reducibility, but most of computational space is irreducible. If anyone comes across this and are interested, what I'm referring to is the Wolfram physics project. There is a series of very interesting podcasts with Lex Fridman and Stephen Wolfram where they dive into this that is well worth the watch if this is an area of interest.

[spiralsun]

I think everything is writing like a novel and mathematical ideas are counting words and punctuation. Specifying the construction of the meaning like in a computer: but it takes a person looking at the mathematical constructions for them to mean anything.

[KpxUrz]

A wonderful intelligent discussion of physics and related deep topics. Thanks for a great video.

[scoreprinceton]

The universe might be an expression of relationships and mathematics being the language of relationships might be a natural ally to each other.

[Pleasebeopenminded]

It is because the universe exists as a mathematical object. Just as the Mandelbrot set gives rise to an infinite amount of fractals, there is a master equation that gives rise to all possible universes and all possible equations. This might be what people refer to as "the logos."

[wayneasiam]

Love your videos, and Max is always a treat for us viewers. Maybe Mathematics is a Primordial Wave Collapse Function... Amy mathematical equation or theory, or even whimsical mathematical thought can be divided in half forever, never having a soluble answer...hmmm?

[mikebaker]

If the opening two minutes was about language instead of math:

Long ago we had this word "attraction" that was originally abstract and about human behavior and we applied it to express and describe how magnetism works... and how amazing is it that we can now use it to describe how atoms hold their shape and galaxies interact?!?

Yes.... because that is how finding new applications of previous principles works. What am I missing?

[richardventus]

I don’t think this episode goes far enough to explain how simplicity can generate infinite complexity.  Of course, I’m thinking of fractals of which the Mandelbrot set is an example.  I believe that scientific evidence suggests that the universe is fractal rather than quantum in nature. For example, looking at the boundaries of the Mandelbrot set we know that there are an infinite number of similar 'looks' and complexities regardless of how closely we look - even if we look trillions of times more closely. Perhaps 'locality' and 'non-locality' are the axes to plot the fractal of the universe on an Argand diagram?  This could also be a substitute for the 'multiverse' theory so that every possible outcome of the wavefunction collapse plays out in all the other 'fractal scales' all at once - and we only observe the result that is at our fractal scale. By mathematics we can now envisage that the Big Bang seeded a fractal structure to the universe so that other universes could lie within each other at differing fractal scales.  Indeed, an infinite number of fractal scale universes could lie within every one of our fundamental particles!  Furthermore, could dark matter be the evidence for the ‘information energy’ of the sum of an infinite number of fractal scales which we are not aware of? It was only in the 70’s that we discovered fractals by mathematics, but perhaps in this case the results really do give a hint to reality rather than reality leading to the discoveries of mathematics .

[superjaykramer]

Max you're the man...Full stop the smartest logical human being full stop.

[benjamin_markus]

Why this is an interesting question to so many just eludes me. Why _wouldn't_ maths be effective in describing relations between quantities, probabilites, trajectories, etc when it was precisely the purpose it was developed for, or least the starting point for the various branches that developed in it? The ones who make a big fuss about it seem to be ignorant of the deeply interconnected history of (what we now call) physics and mathematics since the very early ages of human thought.

[pretzelogic]

I wish he said something about why the math of Super Symmetry is so useful with zero physical support for complementary particles ever being found. (If my limited understanding has not made this a stupid question).

[Pheer]

I read somewhere that most mathematicians subscribe to this platonist view, and believe in a sort of "heaven, " a third realm beyond the material world and the world of mental forms, where pure abstract concepts like math exist. Really interesting idea - perhaps it's naive but I have to say, while I'm agnostic generally, I'm more seriously considering ideas like deism or the necessity of some kind of unmoved mover that created and/or sustains the universe.

[melgross]

It’s interesting, but I’m not convinced. I’ve gone back and forth on this issue over the decades. Just because math can describe most everything we know about the universe doesn’t mean the universe is math. What about human languages? Math is actually part of that. But there are many different ones, and many more that have disappeared. What about Pi? They just calculated it to over 60 trillion digits, but still no understanding why it’s so irrationally, and apparently random. There’s no math that’s able to explain that, yet it’s a very basic relationship.

[mukeshvats]

I believe Knowledge changes the view, Am I Right, if Yes, then, Next thing, Knowledge which you possess, is it reliable/ true, to make further decision/ conclusion, Again, Am I Right, if Yes, then, You got my point, 100Nu.