I feel bad for the Universe, being held to such unrealistic standards of beauty. Perfect orbits tend to be photoshopped, anyway.

2:41 I've seen many pictures of Einstein... but never him lounging shirtless on a lawn chair. Kudos.

Can we give some mad props to the animators of this show? Production quality of this is absolutely off the chain. How they can do this every week is beyond me.

I believe the intuition that is usually right isn't the one that goes "this feels right" but more often the one that goes "something is off"

I think Richard Feynman said it best "It doesn't matter how smart you are, It doesn't matter how beautiful your theory is, If it doesn't match up with observation and experiment... It's wrong"

I believe it was Asimov who said that most scientific discoveries begin "That's funny!" (meaning current understanding doesn't predict it) rather than "Eureka!"

I will refer to particle colliders as "summoning circles" from now on...

The fact that adding epicycles upon epicycles can represent any motion is *literally* true by Fourier theory :)

*Sabine Hossenfelder has entered the chat*

We tend to be a little careless with Occam's Razor, and on more than one occasion we've nicked the face of physics with it.

My romantic notions of physics being beautiful were washed away the first time I saw the full equations for the standard model. Now all I care about is if it works, if it happens to be beautiful too, awesome.

I've always preferred the translation of the razor as - "It is vain to do with more what can be done with less". Which is itself a elegantly parsimonious expression than embodies the idea perfectly.

lol the pic of shirtless Einstein made me laugh out loud. 2:43

I love all the comments about Sabine

9:45 Some would say there’s a beauty in the Wilhelm Scream. We’ve gotten a lot more out of it than we put in.

By modifying my assumptions about what I would learn from this episode, I was able to think of the perfect halloween costume: Dirac-ula.

Both you and Sabine make good points. Good thing Dirac didn't give up when he was looking at that awful mess. I guess I'd think of mathematical elegance as a strategy not a requirement for a theory.

"Let x = x" The most beautiful & elegant equation of all. If you could understand that one, you would already know what to do next.

Sabine Hossenfelder wrote a very interesting book on this topic!

Weird that we mention the 4 "beautiful" Maxwell's equations without talking about the fact that someone else had to simplify them from 20 to 4 using vector formalism. Not to forget that his personal explanations of how the formulas describe reality were stunningly convoluted (to put it nicely). This would have shown that the "reduction" of formulas is also somewhat "subjective" depending on the underlying formalism you are willing use, just like Einstein's equations...

As long as the Space Time t-shirts remain beautiful, I won't argue.

Me 5 mins into the vid: HES BACK IN SPACE

That circles inside circles thing reminded me of Fourier series

2:42 Sick Einstein pic! I don't think I've ever seen it! Thanks!

Einstein: draw me like one of your French girls.

2:42 it’s interesting how he chose this particular and random photo of Einstein shirtless.

Episode made specifically for Sabine

2:41 "Hey! cool T-Shirt man"

It seems like people often misinterpret what physicists and mathematicians mean by "mathematical beauty". It's not so much about "looking nice" as it is about explaining a lot of complexity with very few rules. In other words (edit: as Matt explains around 4:47) it's like Occam's razor: If you have to make many assumptions in order to explain some set of observations, it's less likely to be correct than if you can explain the same observations with fewer or simpler assumptions. In this case "fewer/simpler mathematical rules" and "fewer assumptions" are essentially synonymous. Also, mathematical beauty can mean tying together various disparate theories under a single framework. Some famous examples in theoretical physics are electroweak unification, which gives a single formula to explain both electromagnetism and the weak force (later also unified with the strong force in the Georgi-Glashow theory and others), and the 5 theories of string theory being tied together by M-theory. Even if string theory turns out to be wrong, it is an amazing testament to the power of mathematical beauty. Edit #2: See Sabine's response below. I trust that she knows what she's talking about and that the interviews she's conducted have been more illuminating than my experiences. Take my comment with a grain of salt, though I think there is still a debate to be had.

Good to see that PBS was able to discuss philosophy in physics, really pleasant going in subjective topics like this, thank you very much.

I feel like Matt Parker in his last video explained it well. Any math that looks pretty just means we hid the ugly someplace else.

Beauty is in the eye of the beholder. I wonder what kinds of notions of symmetry a fiddler crab civilization would come up with.

beauty and chaos are the same thing just with the magnifying glass at different settings.

"The ideals that have lighted my way, and time after time have given me new courage to face life cheerfully, have been Kindness, Beauty, and Truth." --Albert Einstein

One of the reasons that keeps a person glued to your videos is that 'The topics discussed, although being of interest to the viewer & available on other videos as well, its ur methodology of presentation & language👈👍🏼- an epitome of complexity, which arouses a sense of wonder & makes the whole concept that much more mysterious & awe inspiring.

Truth is beauty...and beauty is truth...sir!

someone's been watching sabine hossenfelder

Saw Matt in recent episode of How the Universe Works! Well done Matt

The simplest and most elegant explanation for all the laws of physics: THIS IS A DREAM

The lack of beauty in higher physics made me switch to math for my Phd after I did my Master in physics I still remember having to lern the Bethe-Weizsäcker formula for same exam 🤯

Finding beauty in physics is like finding the perfect cup of wine. When you solve that equation perfectly, you get the feeling....

Intuition is useful as long as you apply scientific rigor between intuitive leaps. Yeah, that feels right.

Matt glanced a bit over it, but stacking circular motion on top of circular motion can give you any movement pattern you like down to arbitrary precision. Today, we call this Fourier transformation.

PBS space time is the perfect channel to fall asleep. Everynight without fail it is the last piece of content I consume before gently closing my eyes listening to his sooth voice. If only my phone could autoswitch off at the video of the video , then life would be perfect. Thx ❤️

Beauty should never be the guiding force. It is only good as a confirmation, after it is proven to be good. As an engineer, I often have to go through several ugly and complicated solutions, until I get to the end result, which is simple and beautiful. If I skip those, because they are “ugly”, I would never find the correct solution. Beauty can only be evaluated in retrospect. A more beautiful theory is easier to teach, to use, and to build upon. Also, quite often, only the very best solution is beautiful. The second best solution is ugly, and complicated. But the second best is still useful and good enough. For example (assuming it doesn’t fail) the string theory might be an ugly and complicated theory, which describes the universe better than both relativity and quantum physics. And the theory one step beyond the string theory will be simple and beautiful. And we cannot skip the ugly one we have to work ourselves through it.

Like much else in physics, beauty is relative.

I personally would put it like this: when you discover that two phenomena are actually two sides of the same medal, you are grouping them together reducing the actors into play. This process leads you to less variables and shorter equations that explain a wider range of observations. Despite the GR is more complex than the Newtonian gravitational law, it is more "dense of explanations"

The universe is elegant and beautiful in it's simplicity and complexity. Each layer of beauty revealed by elegant theories and once we understand that layer to an extent, there is another layer ready to be discovered. It is amazing and awesome!

I was hoping for a mention of "truth/beauty" as the "alternative" names for the Top/Bottom quarks. I'm still confused as to how those were dropped, but we kept Strange/Charm instead of renaming them "sideways/centre" 😜

2:41 never saw THAT einstein pic before

Dude... this is one of my favorite episodes ever. I've had that sense of beauty (elegance) when working through physics / math problems myself. Very interesting to see how it played such a large role with the Greats!

Nice reference to the 2nd podcast on the theories of everything! I was so mind blown with that episode, and still trying to sort my thoughts after it.

Sabine Hossenfelder, Lee Smolin and Peter Woit gave that video a thumbs up.

Perfect thing to watch during lunch

Matt! This is one of the best video lessons you ever taught. It’s excellent!

13:45 such an excellent question and answer! Touched on both the explanation of the light being re emitted at several wavelengths as the electrons do smaller jumps back down, and also the fact that even if the light is perfectly re emitted at the original absorbed wavelength, you'll see less of it since it's scattered in different directions more than other wavelengths going through that cloud or obstacle.

Is it inconceivable to think that since Nature tends to “settle into” a “lowest energy state” (such as attractors and the slowing down of a swinging pendulum) that mathematical descriptions of natural phenomena should also tend to do the same thing (like what Einstein said about making things as simple as possible, but not any simpler)?

Maybe, a "beauty" formula means "easy to memorise" :D

As a student in Art History, I find this topic very interesting. The idea of beauty is in part inherent to our culture. The Renaissance period played a big role on how Occidental perceive beauty (and what it 'should be') , and symmetry was a big part of it. It would be interesting to do some research to find out other standards of beauty in other cultures. Cause yes, while completely subjective, our sense of beauty can lead us to solutions that help our mind to get toward the idea of what reality (objectivity) could be. But being stuck in one conception of beauty won't help much. I love the conclusion you did on your essay!

Interesting side note of history: Kepler felt into his own "beauty trap" when he found some coincidences in the ratios of the different radii of the planets. He spent years of his life to prove that the mathematical foundations of the solar system lies within the "hidden beauty" of the proportions of the five platonic solids (tetrahedron, cube, octahedron etc.)

Less complicated things might simply be more likely to occur.

Speaking of beauty, can you please tell me where all the music on the show comes from?

Hey Matt 👋 just wanted to see if you're doing okay. I feel like we take for granted how much effort you and the space time crew put into these beautiful episodes. Thank you all for giving your viewers the gift of knowledge in such a lovely package. I hope you all are safe, eating well and sleeping enough. Love you all 💖🥰

These video are like bed time story as a child..i dont understand a single thing..but it help me going to sleep knowing that some peoples are working hard for my lack of understanding. Thanks you.

About beauty. In art (music, painting) there has been a trend toward ever high levels of dissonance being appreciated as beautiful. Proust argued that it was the primary role of the artist to train a new audience to appreciate a new kind of beauty. Perhaps the same is true for math? Perhaps future physicists will appreciate a different style of elegance.

WHOA NOW THIS IS INTERESTING Upon first thought, one would say that our sense of beauty is simply the way it is due to our evolutionary history. But then, why would evolution result in a sense of beauty that, when applied to mathematics, just so happens to be extremely useful in describing/understanding the nature of reality, at a level far removed from the lives of our ancestors. This is also surprising because of the fact that, as mentioned, it's not just our sense of beauty that's employed to describe reality, but beauty applied to mathematics. Yet there doesn't seem to be a reason why our mathematical intuitions and our sense of beauty - two seemingly quite distinct features of an organism - would end up evolving 'in parallel' in such a manner so as to converge at a brain that's pretty good at describing reality. So, is there something more to the nature of evolution and its place in physical reality - and in particular - the evolution of brain-like stuff. I'm not saying that our brain and psychology isn't entirely the product of our evolutionary history, but is there a framework from which evolution can be viewed which makes the powers of physicists make more sense? (I don't know how/if consciousness comes into this picture.) P.S. This might all be BS

One of the most articulate, informational and nice channel (and person) on the tube :) Oh, yes, and Baumgartner painting restoration too :)

Not Physics related, but relating to the concept of beauty and its hard to define origins, I recommend the book "The Aesthetic Brain: How We Evolved to Desire Beauty and Enjoy Art" by Anjan Chatterjee. I found it a really interesting read.

This seems like it was made in response to last month's livestream

I always found solid mathematics something you had to actively try to pretty up, more often cold hard truth not something beautiful itself.

Another amazing video from my favorite YT channel. Thank you! I love that you're getting into philosophy of science - it's endlessly fascinating - and quite important, as these issues of "is 'beauty' leading us astray?" - "what's with the state of fundamental physics?" - and the lively discussions on your channel show. It might be interesting to note that there are quite elaborate research-programs in the epistemology and meta-theory of science - especially on issues like "what can we take science to actually tell us about the world?" - "what is evidence and what can it tell us about theories? Is Verification possible? Is Falsification possible? What are the problems with each? Is observation objective - or theory-laden?" - "how do empirical adequacy, parsimony and coherence interrelate to give explanatory power and epistemic probability to an account?". Also more specific questions like "What are the evaluation-criteria for interpretations of quantum-mechanics? - How do notions of probability work in them and are they coherent?", "What constraints are there of the ontology of theories of quantum gravity?" and so on. Programs like the structuralist meta-theory of empirical sciences by Suppes, Sneed, Suppe, Stegmüller, Moulines, Balzer et al. used set-theory, model-theory and propositional logic to describe the relation between theories and models - and to describe theory-change and inter-theoretic reduction. Other research-programs research the application of Bayesian Belief Revision theory to meta-theory of empirical sciences (science is widely held to proceed by abductive inference to the best explanation, which can be explicated in Bayesian terms - and thus, things like revising belief-networks based on new data can be modeled formally - this in turn can be applied to gain insights into how scientific accounts of phenomena change over time) - other programs research complexity-theoretical approaches (Schmidhuber, Hutter et al. - incidentally, Schmidhuber's lab was also the birthplace of LSTMs, for all you computational neuroscience nerds out there) Fascinating stuff - in general, it's well worth researching whether the tools of science can help us understand foundational and meta-level issues - and thankfully, there is lively and productive interdepartmental research between philosophers of science, mathematicians, computer scientists, physicists and behavioral scientists on these issues ... unfortunately, a lot of foundational research still gets defunded. Foundational issues - epistemic, methodological and ontological questions are important. The best physicists and mathematicians knew this as well - Descartes, Newton, Leibnitz, Helmholtz, Mach, Poincaré, Duhem, Einstein, Heisenberg, Planck, Schrödinger, Dirac, Weyl ... they were all thinking hard about such issues, and as methodical as they could.

This was beautifully said. Well done!

Beauty is inherent in the object, firstly, and then it enters in the eye of the beholder. It's strange to me that modernists fight so strongly against this this simple cause and effect.

I like the fact that your take is much more nuanced and informed than Sabine Hossenfelder's one

Thankyou Glad your trip was great.

Thank you for the enlightenment, this video truly exposes not only the physics of real/desired explanations from the great scientists, but an understanding from the perspective of "non physic" individuals looking to gain a more true understanding.

"what is the meaning of life" & "beautiful laws" feel like asking questions like "how do you earth?". It just makes me ask, what do you mean? Is "earth" a verb n opposite of "unearth" or what? Meaning of life in what? It's asking like "what's the height" but not specifying height of what.

“Beauty” in the form of ‘symmetry’ is obviously a useful guide as it will reduce the entropy of one’s theory, which in-turn generalized the theory and provides the ability to do more work. However this is entirely contingent on the theory’s context. It is either stand-alone, or it is embedded in a larger theory, or it is adjacent to another. So depending on the case, further symmetrizing one’s theory might further remove it from associated theories. Likewise, if you are trying to tie two theories together, and one is accepted but incomplete (as all theories must be) then the interface of connectivity will be an awkward one, until they can be reformed with respect to one another’s associated domain of application. Additionally, all this says nothing about ‘how the world works’ per say, but instead speaks only of means to produce information conserving (nothing but the axioms and boundary conditions) models of our world. Currently we have lots of theories beautiful in their own right and lots of conjoined theories which are less attractive; and that should come as no surprise, since the TOE notwithstanding, all we have are jigsaw pieces, which can only be as symmetric as they are isolated - indeed, it can be said that the distinction of theories in the first place is nothing more than an account of their mutual asymmetries.

Beautiful work my friend.

I have to say this is an ambitious episode. It is not full of hard or catchy science, but it takes on a philosophical topic that is very difficult to communicate well. Props to Matt and everyone involved here.

Question: what does beautiful mean? Symmetry?

Speaking of beauty... I would like an episode dedicated to E8 Theory and how it may or may not be wrong

Truth is never absolute. That is where the word "Perspective" comes to play. 'Truths are relative to various perspectives and angles of observing things.'

I really have to compliment you on the quality of the presentation. Who ever composed the moving starscape in the background, the sound of motion while shifting focus, and the lighting that placed you in the foreground created a much better presence than earlier videos. To the point where my 4K monitor was fully engaged and portrayed you as a live stream, not a flat recorded video. Kudos to your videographer, that one is a keeper. Use that one again. Pardon me while I re-watch the video. :)

I like Eric Weintein's take on where to put physics money. Take all the money. Build the collider, and build all the medium experiments, AND all the small experiments. Let's crack this reality wide open! Well, maybe not literally. Careful with the vacuum decay experiments...

So I read the 'Lost in Math' of Sabine Hossenfelder and it has me worried. Edit: So I butchered her name. :D

Great video, thank you!

Thank you for this!

Thank god I am an atheist

It seems quite obvious to me that the most elegant and mathematically beautiful models are _always_ the correct ones. Now, I'm not saying that the most elegant and mathematically beautiful models are necessarily the best at describing the behavior of the physical universe. I'm just saying that if they aren't, it's because the physical universe is behaving incorrectly. *Mathematician, signing out.*

I put a comment on one of their recent videos about collider technologies asking how they felt about what Sabine Hossenfelder says about 'beauty' in physics. Very nice to have a video response!

Absolutely beautiful video!

*Sabine Hossenfelder has entered the chat* 😉

"first" is the simplest, most beautiful comment. It is, however, usually incorrect.

Complicated proofs, complicated formula, complicated equations are BEAUTIFUL!

Beautiful episode.

Was literally just thinking about this. Insane

Let’s assume that in the next couple of years we unify quantum gravity and find a set of beautiful mathematical equations that explain everything. Do physicists, then, retire?

The beauty of of this video and presenter indicate that PBS SpaceTime is AWESOME. I will conduct scientific research to help bridge this leap in intuition by re-watching an appropriate sample size of their past and future videos in an attempt to confirm.

Beautiful video .interesting stuff. Thank you 🌹