Why is Mathematics True and Beautiful? | Episode 2201 | Closer To Truth
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- เผยแพร่เมื่อ 5 มิ.ย. 2024
- Does mathematics have two transcendent attributes: truth and beauty? What makes math true? What makes math beautiful? Are there different kinds of mathematical existence? How can math combine idealized perfection and explanatory simplicity?
Featuring interviews with Robbert Dijkgraaf, Edward Witten, Max Tegmark, Sabine Hossenfelder, and Jim Holt.
▶ Early-release episodes of Season 22 available now at our website: bit.ly/3QwMzIA
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Closer To Truth host Robert Lawrence Kuhn takes viewers on an intriguing global journey into cutting-edge labs, magnificent libraries, hidden gardens, and revered sanctuaries in order to discover state-of-the-art ideas and make them real and relevant.
▶ Free access to Closer to Truth's library of 5,000 videos: bit.ly/376lkKN
Closer To Truth, hosted by Robert Lawrence Kuhn and directed by Peter Getzels, 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.
...Because math is one of the Rosetta Stones that allows us to understand the Information that is fundamental to this Universe. That's why.
Allows US is the keyword
Not really. Math is a collaborative project to whose base is communicative understanding. Truth can be ugly and abhorrent. Remember thinking about his with Thomas Swift as I listened to this episode.
I am a mathematician and my personal motto is "Nulla Veritas Sine Arte". No truth without beauty. Spot on!
I can't believe how much new stuff you are still putting out after all these years. Thank you so much!!
And more to come! We're so glad to have you watching 💫
'Truth is beauty. Beauty truth.
That is all we know and all we need to know'
Keats
Breath is Truth. Beauty is acquired by a journey of moving closer to Truth. Amazing 👏
Coherence is the ground of existence. The brain started as a comfort finder and is in us becoming a coherence detector. Keep at it, Bobby!
I want Robert to stay young and live longer So He keep digging more This is exciting.
Thanks Robert!
An amazing episode. As an Engineer I love math and I get a lot of inspirations from these interviews. Thank you Robert
Math is an abstraction, not part of the physical world. But it helps us understand and describe the physical world.
It should be noted that math theorems, although true, don't necessarily describe our world if any of their axioms & assumptions aren't true of our world. Axioms & assumptions can't be proved mathematically; we build "rational confidence" in them by conducting experiments that attempt to falsify them. Rational confidence falls short of certainty because a future experiment might falsify, or because some other set(s) of axioms & assumptions might also be consistent with the experiments that have been done.
"Beauty" in math proves nothing. It's usually equivalent to "simplicity." The relevant heuristic is that if you need to bet on one of a set of competing theories, bet on the simplest. (This doesn't imply the bet will pay off.)
Nailed it _!_ Imo
Thank you for continuing to put these out - nothing helps the discourse more than open, free information accessible to all. Great video!
Beautiful episode Robert and team. This is such a satisfying episode having followed the PBS show and your transition to online. An engaging group of guests who I imagine many were avidly requesting. The editing is minimalist and completely fits the previous seasons while feeling fresh. Can’t wait for the next episode!!
If you want to watch the next two episodes before they're on our TH-cam channel, just register for a free membership at closertotruth.com! 💫
Thank you for this episode. Truly enjoyable.
Absolutely beautiful episode! Thank You!
Thanks much for the round of enlightening viewpoints. To me Mathematics is a free flight of human spirit, hence the need for abstract beauty. As for its endless usefulness, one may recall E P Wigner's remark on the mathematical language: "... a wonderful gift which we neither understand nor deserve". The topic has always attracted lots of attention, and this will continue generation after generation... (I do hope so!!!).
I'm brushing up on my knowledge of math.
Awesome Guests and Interview! bravo 👏
Today I found this channel, and today I fell in love with it! These are the questions I have been asking myself for years, thank you for discussing these topics!
Thanks for making this video.
Great video. Thank you so much. I almost understand 45%.
Great show as always! "Multiplicity in unity." Footnote to Plato, perhaps. Heaven knows where we get these intuitions! Even though I feel mathematics and beauty has some relationship, Sabine Hosselfelder makes a very good and thought-provoking argument. 👌
thank you, a truly amazing video
Love this approach. Very difficult topic. I like to think the answers lie in the unification of simplicity and complexity, where the two ends asymptotes meet somewhere in positive and negative infinity. I feel like when I try to imagine infinity, I’m knocking on the door of what is true, real forever and in that perfection, beautiful. That said, I feel my brain/mind will never be able to know infinity, only aspire to it like a compass direction.
That's my boy RLK! 📈📊🖋
Outstanding!
I started to love maths for the first time in my life.
maths ok nigel 😂
@@meesalikeu the crow cannot swin , the rabbit cannot fly , the fish cannot walk.
I’ve been a convinced mathematical Platonist for as long as I can remember. (And what *is* that amazing building in the opening scene?)
Great program. Thanks.
Interesting episode and next we’ll need a series on what we mean by true
Yeah... How about studying content worth our time & consideration. Why am I the only one who hears the music!
Periphyseon, by Eriugena, translation by O'Meara.
Plotinus Enneads, select works translated by Thomas Taylor and complete translation by Lyyod.
Plato complete works.
Proclus books.
Iamblichus books.
Syrianus books.
Bhagavad Gita
Upanishads translated by Nikhilananda 4 vol. set, and the 18 principal Upanishads translated by Radhakrisnan.
Upadesa sahashria by sankara, translated by jagadananda.
Vivekacudamani by sankara, translated by Madhavananda.
Philosophy as a rite of Rebith by Algis U.
Meister Eckhart complete works.
The Unknown God, by D. Carabine.
Mystical languages of unsaying, by M. Sells.
Plotinus: Road to Reality, by JM Rist.
Bible - KJV translation only. archaic is very important here with mysticism.
Jacob Bohme books - a German mystics
Emmanuel Swedenborg books - a scientist turned mystic and metaphysics.
Coomaraswamy books.
The presocratic Philosopher's - book.
Sweet touches of harmony - book; Pythagorean influence.
Lore and science in ancient pythagoreanism - book.
The Universal One, by Walter Russel.
The gods of field theory:
Henri Poincare
Tesla
Steinmetz
Maxwell
Dollard
Awesome.. LOVED all the nuances like the new opening commentary and the reimagined summation.
Wonderful conversation fantastic about Maths subject 😮
Referred to this channel by Dr. James D Tabor.
This is my 1st episode to ever watch
Thanks again Robert for the awesome content ❤
It never stops to amaze me that we are still moving along the lines drawn by Plato/Socrates more that 2K years ago.
It also also interesting that most of these highly intelligent and accomplished people equates beauty with simplicity.
I think Sabine is spot on btw.
Love it
Great camera shots
what's that structure called at the beginning please?
Phi is the beautiful concept describing paired items in parallel design. Its formula connects the square root of the first twin prime, 5, with its sequntial difference, 2. This same relationship holds for the first square prime, 11, and its sequential difference, 4. Again it holds for the first sexy prime, 29, and its sequential difference, 6. I have collected the first 150 of these instances which can show most of the patterns available to human perceptions. This is why math is beautiful. It is "true" because addition and multiplication can be adequately resolved.
@@vladimirrogozhin7797God is a human puppet out of work.
Very excited for this
Critical thinking can unlock the full potential of our minds. It's important to seek truths. 💭
1:31, not only I love your love of wisdom( philo-Sophia), but the captivating the lovely music you start with- that to my knowledge is made by your wife❤❤❤❤
It's remarkable and curious that, when discussing mathematics, no pure mathematician is present.
Dr. Hossenfelder proving again that she’s thinking light-years ahead of her colleagues. Way to go, Sabine!
There is also something curious about math that the equations apart from their meaning and what comes out from them also physically look rather beautiful, it might sound crazy but actually they gather beauty in all its varieties
The truth and beauty of math that the average mind does not understand and therefore appreciate, but instead fears and subsequently hates. Just ask them. On a personal note as a grad student (long ago) the "toughest" math course I faced was Topics in Mathematical Physics. Though it really wasn't tough as it was strange (taught by one of the early proponents of string theory - in fact, to give a hint he was the first to ponder the 26th dimension).
New season? Fuckin dooope
Witten is EXACTLY right - the beauty of mathematics is the same as the beauty of music. But I don’t think he would be too happy about the logical implication: mathematics is, like music, a beautiful construct, not a discovered truth. As soon as mathematics goes beyond the counting numbers it has to be defended by far-from-obvious ‘axioms’ or additional rules (starting with the prohibition of division by zero, followed by the axiom of infinity…) to enable the analytic extensions, etc.
The beauty of mathematics is nothing like the beauty of music, except that both “senses of beauty” are subjective individual experiences. Probably a better (but not perfect) example would have been to say, the beauty of math is like the beauty of chess. In that both stem from made up human rules, which when followed logically can lead to moments of beauty for those who have a deep understanding of them.
@@longcastle4863 I think every culture produces mathematics and music. I like the chess #3 analogy, but it’s not universal.
RLK is a guy with grace. He seeks truth and invites a bunch of people for the journey. And he spends a tremendous effort to make the journey, pleasant. I enjoy the interviews. They make me think in new ways. Beginning at 5'30" RLK posits two existences each according to mathematical laws and principles: 1 the real world and 2 possible worlds. However, he does include the option 0, no existence, a world also possible me mathematical laws and principles, a mathematical world with no elements and no relations. That is the world where RLK and every other "beable" of this universe will eventually go to. Lukasiewicz; logic contained three values existence, non-existence and possibility. Mathematics is the possibility. It exists only partially and is being discovered by the human mind in a frictionless world organized by reason as expressed in journals, conferences, and libraries available to all of those curios to read its news. Unfortunately, the discovery is threatened by the tumultuous world of human desires, organized by passion, oblivious to reason. The meaning of the universe is being sculpted by the theorems of mathematics, but nothing guarantees is completion.
Which came first mathematics of consciousness? Well which was defined first?
Consciousness came first.
I've always respected extremely intelligent people who are able to remain sane while pursuing the unanswerable. I've known a few in my life and, most if not all, loose their minds at a fairly young age.
I like all sciences(just was inguinal hernia surgery)👍. Now I can do situps, running, gym etc. again.
If Mathematics is the ultimate truth we have not any unsolved problems.
No cancer and fusion energy. Numbers are just tools. But good tools.
Correct, "Math" is a Tool, not an end in itself. I you are a "math intuitive", it may be an end in itself, for those very few who are, but for the rest of us just a tool. Kuhn only hopes to link it (and most everything else...) to some Deity who whipped it all up in 6 Days (Took Sunday off...).
👍Excellent, lots too think about👍
I still remember when she played ridicule debating with Bernardo Kastrup! Did anybody else see that debate?
I saw that. I think when SH insisted on the reality of the collapse of the wave function BK should have pointed out that belief in the actuality of the function is an absolutely clear example of the belief in unobservable theoretical constructs, i.e. the exact target of his criticism.
As someone who in previous years was tasked to make the math bend as far as it could before it broke, I cannot speak to either its beauty or its truth.
Thats obvious! How could you?
Interesting point of view... will or can you elaborate on your role? *edit punctuation
@@David.C.Velasquez when he is doing that its not ether one.
this hole thing is really open ended if you think about it
What struck me most about this episode was Dr. Hassenfelder’s argument that “beauty,” as defined by mathematicians, is a fairly thin soup that reflects more the aesthetic of mathematicians than it does any law or clue that beautiful equations are likely also to be true.
Mathematicians seem to equate “beauty” in a mathematical proof with a simplicity, symmetry, and elegance that inspires awe because it uses these qualities to describe an otherwise complex and messy reality. While that definition may appeal to those who like order and clarity in their lives, it would likely sound trite or vapid to a great painter or novelist or dramatist or pottery maker. In those fields, what is considered beautiful is that which possesses all the qualities mentioned above, plus a flaw of some kind that renders the entire composition imperfect or even tragic. That is, human. The humanity of a subject may lie in a face that is almost perfect, if it weren’t so sad, for example.
Nature also tends to render forms that are not beautiful in the sense that mathematicians tie beauty to standards of simplicity and clarity. There are no perfect forms in nature. The imperfection creates the possibility of infinite variety, however, such that there have never been, and never will be, two snowflakes exactly the same. Nor two of anything else, for that matter, exactly the same.
The awe that arises in the artist in the face of imperfect, broken, flawed, infinitely unique reality is what the artist would describe as the experience of beauty. The task of the artist is to render that imperfection, that sense of tragedy, as elegantly as possible. That’s how we got Melville’s white whale and Picasso’s “Guernica.”
1/137 and all electrons are exactly the same.
Which place is this at the beginning?
I think it's better to think of truth in a broader context. To most people, truth means "it does what it says on the box." It's a symmetry between language and meaning.
Mathematical truths are especially concerned with these kinds of symmetries, expressing them in a precise language where the descriptions and meanings have exact definitions.
Scientific truths are concerned with a different symmetry - the one between theory and observation, in a way that mathematics isn't. Because science is constrained in a way that mathematics isn't, mathematics has potential for both infinite precision, and infinite inaccuracy!
On the other hand, quantum mechanics isn't going to produce answers to questions of professional ethics any time soon. For this kind of truth, the vagaries of natural language must be entertained out of necessity. The vague truths that people are primarily concerned with is closely related to the question of trust. It's a symmetry between promise and fulfillment.
To say something is true is to say it's symmetric. If some symmetry between symbol and meaning isn't assumed, there isn't even any basis for language. Truth, then, must be an assumption taken before mathematics can be spoken, or understood.
Actually, Kurt Godel showed that there are truths in mathematics that cannot be proved nor disproved based on the axioms. The only solution is to invent additional axioms. However that leads to new truths that also cannot be proved nor disproved !
Mathematics supports postulations of a multiverse. Does that make it true?
Most likely. Even things like Neptune, Black holes, Gravitational waves, lensing were all predicted through maths.
Math's truths are a tiny part of the Total Truth.
So belief is truth? Whatever if indoctrination was not true religion would not even exist…would take one generation it would be gone
what was muted on 5:14, before “mathematics”?
.....also relates to "this question if" Mathematics is being invented or discovered....
Man this is the perfect thing to watch when waiting on a 45-minute food order
This podcast is incomplete without sir Roger Penrose...
OK, I'll explain it. Math is true because it is trivially true, it all follows by logic from initial postulates and definitions. Math is beautiful to some, and not to others, just like I am beautiful to some people, and not to others...no one knows why we find things beautiful...it is dependent on the individual finding it beautiful. Hope this clears it up. Thenkyu.
That one can get more than what one puts in is a superfluous expression and adds nothing to the search for fundamental truth. If you have X² in an equation and you input 2 as the value of X, why should it be of any surprise when you get 4 as your output? To test the fundamental viability of the aforementioned statement, please input zero (0) as the value of your variable X to see whether your output will be more than your input.
Differentiating between 'emulation' of reality and 'simulation' of reality is the de facto issue.
Many scientists have lost sight of the importance of that distinction, of finding/discovering the emulator, rather than creating an approximation/simulator.
The only way to tell the difference is with a tolerance of 0 error.
But how do you ever get such a tolerance, with imprecise models that can never know if they have actually included 'all' the variables and/or, equipment that can never be deemed absolutely precise, with reference to both the timing/latency of events and/or ever more abstract inferred measurement, rather than direct measurement.
Mathematic is a Consequence of our Eternal Consciousnes-
and Life-structure.
Logic is 'Mathematic in Colors',
when a Life-student learned that Logic is Love,
He left the studies, Not yet ready for this.
Intelligence, means Logic and Order,
the Perspective-Princip, is all relations relationship,
Intelligence + Perspective-Princip = Mathematic.
Highly probable that Dijkgraaf had John Conway and the monster group when he mentioned mathematicians talking about possible worlds like a naturalist would talk about features of this universe.
I thought Dijkgraph's name was "Digraph," which would be pretty cool too
Please have on Robert Lawrence Kuhn and merge your theme songs for one episode it's heartbreaking
world is fire & water & earth is flower then life bang
1:20 Bingo! The illusion of ‘certainty’ and ability to control (albeit only as ‘understanding’) what humans cannot control. Though I’m sympathetic, given how difficult it is to manage existential anxiety, taking refuge in any gaga land won’t solve anything. On the contrary; being so lost in it, divorced from reality, has led to a sort of lofty stupidity.
The "getting more out than you put in" bit is suspicious. Notice the equations look simple but they are only part of the story. The mechanisms the equations are built on is what contains the missing complexity and therefore beauty. The Mandelbrot doesn't emerge if you only use real numbers and those simple mechanics, only with complex numbers which are mechanically more complex.
Beauty is in the eye of the beholder....or more recently..."THE OBSERVER"!!🤔🤓
We wrote a language to describe, why be amazed it does?
Please help resolve an argument between my roomate and me: this is the first new complete episode of the classic show in a long time (season 22.)
But are the interviews also brand new or are they recycled/re-edited segments of existing footage?
(I think the former since I do not remember the specific conversations. But my roomate disagrees, pointing out that by now all of these guests have been on several times, and while the motif of the season is new, all of these talking points have been touched on in the past. In addition, especially on TH-cam, they almost always repost old clips. Finally, both Robert and the guests do not look too old.)
Regardless I am thankful and looking forward to a full new season of "TOS...😜."
Hi there, this is a brand new episode we've never aired on our channels before. This season started airing on PBS just this year.
Nature is definitely deeply logical.
Why is mathematics true and beautiful written in words 😮
Thanks. I go back to Plato. Whether we're discovering or inventing is arguable. The real crux of the question is: WHAT are we discovering or inventing? It's no good to say they're 'mathematical objects'. What does that even mean? If you & I had no idea what a baseball game was (or humans, or English), we could still watch a game of it. We'd go thru 3 stages. 1) What's going on here? 2) Starting to get the hang of it, & making some guesses as to what happens next. And 3) Speculating as to what would happen if some specific unusual circumstance arose. This is just like science. The important thing is that we are not inventing or discovering 'mathematical entities'. We are figuring out the rules of the game. In physics, the game is the universe, & it does make some sense to assume it's self consistent. If we call that 'beauty' then fine. But we should avoid putting to much of our own aesthetic expectations onto it, as they can lead us astray. tavi.
The "beauty" of mathematics and its truth have to do with the passage of time.
We only know about the past because it is encoded in the present. The way how the past is encoded in the present must be such that we could easily decode it. That means some very efficient algorithms, which we perceive as physics laws. They must be very symmetric and laconic in order to work. We perceive that as "beauty". That's what the source of our mathematics is. We discover it, not invent.
The laws how the past is encoded in the present allow us to perceive the passage of time and causality. The cusuality makes sense of the events, which create time.
These are my favourite videos to watch
I like to think mathematical modelling is akin to clay sculptors.
The only difference between the two is the medium used, and the foundational depth to its existance.
Perhaps then they should both be considered artforms, and as such, beauty becomes a necessary term.
The truth then, a faithful reproduction of the reality that they try to model.
I enjoy these interviews from the past, but it would be nice to see more new stuff. Your show was unlike anything else in the united states. It seems that only in England they have television programs about philosophy and science and religion, while here on The Learning Channel we have shows with names like How Fat Can You Get are Honey Boo Boo Boo
Robert is approaching 80…
Hi there, this is actually a new episode. It just aired on PBS this year and this is the first run on our channels.
Read Penelope Maddy and Robert Knapp.
💯
We can never absolutly precise its impossible. We can generalize an approximation and probability only.
Tools of approximation we use on this paradoxical world does put math on par with how we allocate one for one symbols and correlate ultimate knowing with cycular reasoning.
We can take known standards allocate symbols but when we reduce it we quickly learn we cant be precise
Mathematicians are very convinced that mathematics is beautiful.
They have proven it …
3:05 ^
❤
Someone tune that piano!!
"As simple as possible but not simpler." Yeah, I think I'll go with Einstein also.😊
Folks are confusing Truth with Simplicity and Beauty with Complexity.
Good evening,
Thank you for this interesting video on lovely argument: mathematics..!!
• all scientists agreed our universe is unique and fine tuned with fundamental constants.
• Also they are agreed our universe following the mathematics language.
• this video dedicated to the mathematics and mathematics everywhere: in the universe, nature..
• Now let us read what is written in the Holy Quran 1445 years about mathematics:
• " The sun and the moon [move] by precise calculation " Surah Al-Rahman 5..!!
• "precise calculation " = our universe is fine tuned and following the mathematics language.
Glory be to Allah Almighty..!!
Thank you again for this fantastic contribution..!!
These concepts should be taught at the very beginnings of learning. A first grader would understand the imaginary truths under woven in an axiom if explained thoroughly enough. Why the symbols of math themselves would seem more real to them. Why are our elementary schools teaching the true basics of math?
correction: "Why aren't our elementary schools."
Is Max being interviewed in an old power plant? Huge wheels? Old steam plant? Anyone know?
Ohh nooo !!! Houston we got a serious problem !!! What the heck for Pete's sake ???
The assumption that all of quantum mechanics must add up to Newtonian physics- which adds up to relativity- seems to me to be purely logical and based on the observations we've made around us. Complexity tends to emerge from adding up simplicity. When we see a complex biological structure, we know it didn't just appear this way- it evolved form much simpler, less dramatic changes that just kept adding up over immense amounts of time. And usually when I hear someone complaining about how the mainstream follows this or that mathematics and they're so close minded and blah, blah, blah- it's because this person has a new math or theory that's not getting the attention or credit they feel it deserves. Sabine loves being a contrarian- and she makes sometimes very silly and dangerous assertions- like asserting there is no real mental health crisis in the US. Which is a silly thing to assert- and if you don't believe me- go to any major city's emergency room on a Saturday night. Or go to their local jail and count the ppl you find who have obvious mental health issues.
I think there is one place where mathematics and physics converge - fundamental constants. These constants are examples of inevitabilities I believe for any universe and yes, they are the context which deprives God of the ability to be all-mighty.
Personally, I think the only reason mathematical physics theories are so successful is because measuring apparatuses speak numbers.
When one infinity is NOT equal to another infinity, your concept of infinity is fatally flawed.
Is mathematics invented or discovered? Is a song, a poem, or a novel written or discovered? It wasn't there before it was written. Was it there to be written?
If to think is a miracle life has meaning
...........otherwise
Ah, now eventually you do plan to have mathematicians on your, on your mathematics podcast, right? Hello?
[he taps the camera lens and breathes on it]
Hello? Yes?