En 30 segundos
Grant Sanderson's second conversation with Lex Fridman runs from a letter Feynman wrote to his dead wife to GPT-3 predicting a zombie apocalypse. Along the way he argues that the pleasure of a great lecture is a poor predictor of long-term learning, that humans are born thinking in logarithms and then trained out of it, and that the people who ask "who am I to explain this" are exactly the people who should hit publish. The through-line is not a theory of everything. It is the smaller, reachable path: reinvent a few core ideas yourself, tell the story only once you have an insight that can carry it, and spend your brain cycles on problems you can actually see resolved.
- 1Sanderson puts himself with the foxes, not the hedgehogs: he knows many fields at decent depth, and he does not yet know enough of any one of them to make a significant research contribution. What he can add, he says, is exposition — things that are known but have never been explained well.
- 2A lily pad that doubles daily covers the lake on day 50, half the lake on day 49, and about one percent of the lake around day 43 or 44. That last version, he argues, is the one that matches how exponential crises feel while you are still inside them.
- 3He would rather work alone on the object itself. It is much easier to tell yourself that a script is too long, too short, or that a visualization is terrible than it is to say the same thing to a collaborator, so throwing a draft away is cheap and asking someone else to throw theirs away is not.
- 4The most important lesson for anyone who publishes, he says, is that the commenting public is not representative of the actual public. People who never read YouTube comments should notice that people like them are not the ones leaving comments either.
- 5He wishes the people modest enough to ask "who am I to post this" were the ones actually posting. A lot of educational content, he says, is made by someone who started researching the topic two weeks ago, while the experts stay quiet.
- 6Shannon's noisy-channel proof says a *random* encoding is almost at the theoretical limit. It then took decades to find codes anyone could actually write down, because drawing a random element from a gigantic set is a different task from giving that element a short description.
Lee la transcripción completa por capítulos
The Feynman of the coffee-shop story was never "not a math person"
This is Grant Sanderson's second time on Lex Fridman's podcast. Millions of people know him as the mind behind 3Blue1Brown, the YouTube channel that tries to make mathematics feel inevitable rather than ornamental. Fridman opens on Richard Feynman, a subject they had run out of time on before. Sanderson admits it is almost cliché to admire Feynman — the Super Bowl of scientific taste — and then argues that the iconography sits in front of a different person.
The personal crack in the icon is a letter. During the Manhattan Project, Feynman's young wife died of polio; two years later he wrote to her anyway, saying how much he still loved her and that no other woman could measure up. The public Feynman of *Surely You're Joking* is a mildly sexist philanderer. The letter is someone else. Sanderson thinks the same split runs through the science. The stage Feynman slaps the table and refuses fancy formulas; the working Feynman is doing something deep, and densely mathematical.
He once sat in a café reading a book about Feynman when a woman glanced at the cover, said she loved him, and began explaining that Feynman was never really a math person. Sanderson still does not understand how that can be a public perception of any physicist. What he actually likes in Feynman's method is the habit of reinventing. Faced with a paper, Feynman would try to solve the problem himself, get some personal ownership, and only then look at what others had done. Sanderson says the topics he has learned best are the ones with some element of rediscovery. The cost is speed. That slowness, he thinks, is part of why he is not an active researcher. Choose a few core building blocks, though, and try them before you see the author's path, and you populate your brain with counterexamples and private data the textbook will not give you. "If you simply go through the proof," he says, those intuitions never grow.
He calls himself a fox who still does not know enough to contribute
Fridman presses the obvious follow-up. Sanderson swims at reasonable depth across so many topics; does he ever want to dive in and discover something new? One of his biggest undergraduate regrets, he says, is not having built better relationships with professors. Success in research depends on mentorship, on people handing you scaffolded problems. He reaches for the old hedgehog-and-fox split: the fox knows many things, the hedgehog knows one thing very deeply. Von Neumann was a fox; Einstein was closer to a hedgehog. Both kinds of mind move science.
Between the two, Sanderson sees himself as the fox. He will take on a whole bunch of subjects, and at the moment he does not know enough of any of them to make a significant contribution. He still sees value in a decently deep picture of a wide terrain. Analytic number theory and algebraic number theory already lean on different neighbors — complex analysis in one direction, algebraic geometry in the other. Drop a PhD student from one seminar into the other and they are as lost as Fridman or Sanderson would be. Walking the ridgeline between those hills has personal value even if it never becomes a theorem.
Fridman is more generous than Sanderson wants to be. The videos, the multidimensional visualizations, feel like research, like the edge where new ideas are made. Sanderson says that is more generous than is necessary, and he promises it is not false humility. When he researches a video he often learns ten times as much as the video can hold, and the on-screen slice then feels elementary. He thinks that may be a mathematics thing. In machine learning, two weeks can leave you feeling you have basically mastered a topic. In mathematics, everything is either trivial or impossible, and the line between the two is shockingly thin. A subject is impenetrable, then you get a feel for it, and suddenly the whole field looks trivial. Every researcher, he suspects, is standing on the far side of that hump.
The satisfaction of a great lecture is a poor predictor of long-term learning
People have described a Feynman effect. While you watch the lectures, or read them, everything makes such perfect sense that the hour feels like an entertainment session — intellectual satisfaction you cannot get anywhere else. A week later you cannot recall what gave you the insight. Retention from books and lectures is never quite what educators hope. Sanderson thinks his own videos risk the same bill. At best they are intellectual candy: a glimpse of feeling as if you understand. Unless you reinvent the idea, do problems, or use spaced repetition so the terms actually sit in memory, it will not stick.
So the very thing that is admirable about Feynman's lectures — how satisfying they are to consume — may also be the flaw educators should watch for. Satisfaction does not correlate with long-term learning. Fridman offers a modern substitute Feynman did not have: the viewer can tinker, drag a slider, change a variable, move along a surface. That is not quite doing it yourself, but it is closer. Sanderson is not fully sold. His videos have a play button and a pause button. He could ship a Jupyter notebook instead, and he says he should. Look at the analytics on interactive explainers, though, and only a small sliver uses them as a playground. Most people consume them as well-constructed literature and maybe tweak the example once.
A video can capture most of that benefit if the author plays in the sandbox first and then decides which narrative to spend. His epidemic video was built that way. Rather than script it ahead of time, he made an agent-based SIR playground, played in it, and then told five or six stories the model had actually shown him. Other people rebuilt it in JavaScript so visitors could test their own hypotheses. Sanderson thinks a meaningful part of the value is not the sliders. It is being the person who decides what is interesting to walk through. Five sliders and a blank sandbox can be daunting. A little guidance is often what sparks the curiosity that makes someone want to imagine more.
Topology is not the study of what you can do with clay
Some of Sanderson's videos pause and hand the viewer a piece of homework that looks like laziness and is trying to be a motive. In the Möbius-strip video, the hope is not that you merely see why the strip cannot sit entirely above the plane with its boundary on the plane without intersecting itself. The hope is that you feel that impossibility, want to formalize it, and in formalizing it start to invent a definition of orientable versus non-orientable. Once you have that motive, the otherwise arbitrary definitions at the front of a topology textbook start to make sense.
He does not want to say topology is taught wrong, but he does think it is popularized wrong. The standard line is that topologists care about surfaces you can bend and stretch but not cut or glue. Is that really what mathematicians are into? The short answer is not really. Nobody sat down wondering about the properties of clay, with arbitrary rules about cutting. What they had was a pile of mathematical objects that share a very general structure: geometry without exact distances, only a notion of closeness. Once you have those structures, mappings between them translate into non-trivial facts about other parts of math. That, he says, is almost never what gets popularized, and it is not emphasized well enough at the start of a class.
The student is left walking through mud between two bad poles. Either the subject is too squishy — coffee mugs and donuts — or it is too rigid too soon, an axiom system of open sets in which an open set is not the opposite of a closed set, and some sets are both. You stay confused about how any of that relates to Möbius strips. Fridman offers a bridge Sanderson likes: fixed-point theorems that sound like trivia (stir your coffee and some molecule ends up where it began) and then map onto Nash equilibria. Drawing that line takes a little technical work, and popular media usually shies away from it. Sanderson leaves the exchange feeling as if he needs to make more topology videos.
Humans are born thinking in logarithms, then arithmetic trains it out
Fridman asks whether people can reason intuitively about exponential growth. Sanderson's answer is the reverse of the usual lament. He thinks exponential growth is extremely intuitive to humans, that we then train it out of ourselves, and that it can become intuitive again if you study a technical field. Anthropologists have asked people in societies without modern arithmetic what pile sits halfway between one rock and nine rocks. Schooling says five. The unschooled instinct is often three: one times three is three, three times three is nine. One friend versus a hundred friends has a social midpoint closer to ten than to fifty. We are born thinking logarithmically, and basic arithmetic forces us to think linearly instead.
That native sense, he suspects, only really holds for small numbers. Ask the same society what happens if you triple a pile of rocks seven times, and the answer will still surprise them. Computer scientists and physicists looking at early Covid numbers were the ones muttering that the curve was a clean exponential, because they had trained the large-number side back in. The old chessboard proverb is the same collapse in story form: one grain of rice on the first square, doubled on each of the next sixty-three, and by the end you need more rice than there is in the world. Sanderson's own intuition falls apart there. He would never have predicted it.
The cleaner test is the lily pad. It doubles every day and covers the whole lake on day 50. On which day does it cover half? Day 49. Fridman pauses and thinks that cannot be right, which is exactly the point: even when you know the rule, the fact still has to land. Sanderson makes it more visceral. Ask instead when the pad covers one percent of the lake. You need roughly six and a half doublings to climb past a hundred, so you are looking at day 43 or 44. You have already lived 44 of the 50 days, the water still looks almost empty, and then the lake is gone. That version, he says, is closer to how an epidemic feels in the early weeks, when the data still look mild.
Moore's Law looks like a lily pad and behaves like a four-minute mile
Fridman, noticing the SpaceX shirt, brings up Elon Musk's gospel of exponential thinking: the thing everyone believes is impossible becomes possible because the curve is exponential. Sanderson splits the claim. It can be inspiring to notice a pattern like Moore's Law that holds shockingly well and enables better lives. People who took Moore's Law seriously in the 1960s could already see that the giant batch-processed machines would shrink onto a desk, and some of them predicted smartphones long before the objects existed. Faith is not quite the right word. Understanding that the pattern was happening is.
What is more interesting, he says, is the mechanism. Exponential growth happens when the rate of change is proportional to the thing itself. Technology grows that way only if progress is proportional to what you already have — software that lets you write more software, an internet that makes it faster to learn and therefore faster to build. Investment can work the same way when a company knows how to turn resources into more resources. Musk's taste for vertical integration, in this telling, is a bet that you should own the pieces whose development enables the adjacent pieces. The useful question is not the shape of the curve. It is when the proportional-growth property holds, and therefore when it will break — as an epidemic does when it nears saturation.
Fridman then offers the better reading of Moore's Law, and Sanderson takes it. It may not be an example of something growing in proportion to itself at all. It may be a benchmark that was set out and that everyone has been pressured to meet, a pile of micro-inventions rather than a lily pad left to cover the lake. It is also the four-minute mile: once the thing is declared a law, and once it has held for a decade and then two and then three, it becomes an achievable target that finds the people who can hit it. There is no law of exponential growth in human innovation, Sanderson says, except perhaps the true proportional case — computers that make better physics possible, physics that makes better computers, wash, rinse, repeat.
The part of his life he most wants to change is the missing hallway collisions
Talk of the Manhattan Project and Bell Labs turns the conversation toward how Sanderson actually works. Those labs were famous for rooms full of brilliant people playing off one another. 3Blue1Brown is, by contrast, singular: you look at the teaching and you know it is Grant. Does it get lonely? "Honestly, that right there, I think, is the biggest part of my life that I would like to change." He looks at a Bell Labs situation and is jealous of it. Reading about Feynman, he sees that Feynman shared an office with Julian Schwinger and thinks: of course they did, that is how the ideas get made. They very likely worked separately. The magic is still the snack-run collision, the overheard conversation, the puzzle a colleague is sharing.
He tries to stay connected to communities of people who think in similar ways, but it is not in the day-to-day, and he would like to fix that. The pandemic, Fridman notes, has taken away chance collisions. He had seen on his brother's work calendar a scheduled slot whose entire title was "No Specific Agenda" — a way to manufacture the happenstance conversations remote work had stolen. Sanderson likes the title. It is the adult version of going to a bar to meet strangers, or striking up a conversation on a train, which is harder when you are the kind of academic who avoids human contact unless it is forced.
Does he work alone through the paralysis — this is too long, this visualization is the wrong direction? He actually prefers the work itself to be solitary. That is a personality quirk. He would like to be in an environment with others, collaborative in the sense that ideas get exchanged. The self-doubt is another matter. It is much easier to say "this script is too long, this is too short, this visualization sucks" to yourself than to a collaborator. He knows he is not good at that conversation. Throwing away his own script because it is not working is easy. Telling someone else they should do the same is not.
A perfect productive day is hard to describe because the mode changes. Some days the job is the script, some days animation, some days something in the direction of software engineering on the animation library, some days a variant of research, some days the email backlog. The idea starts with research, then scripting, then programming. A problematic way to do it, he says, is to start the project and therefore start the research. Better to be ambient-learning a ton of things in the background, and only once you feel you have the understanding do you put it on the list of things that can be a video. Otherwise you end up roadblocked forever, or you simply will not have a good way of talking about it. He is not a systematic person in the Cal Newport sense. Those perfect-day schedules are more fun to write than to follow, and you always write them as the best version of yourself.
The commenting public is not the actual public
Early in the channel, Sanderson's mother used to text him running totals: the channel has had 990,000 views, then 991,000. He assumed she was reading the about page. She was not. She had been going through every video every day and adding the counts by hand, thinking she was providing global analytics that would otherwise be invisible. Fridman recognizes the addiction in his own father, newly tracking views on a conversation they had recorded together. Born of love, Sanderson says. The downside is what people do with comments.
The most important lesson for any content creator, he says, is that the commenting public is not representative of the actual public. Ask yourself how often you read comments on YouTube. Most people realize they never do. The people who realize they never do it should understand that people like them are not the ones leaving comments. In Sanderson's case, reading comments would make him think his content was better than it is, because people are super nice. Viewers who are bored, put off, or frustrated usually just leave. They are certainly not going to watch the whole video, much less articulate what they disliked. Well-intentioned negative feedback is hugely underrepresented. A lot of the people who had the reaction he actually wanted never wrote it down.
Fridman holds up Joe Rogan as someone who genuinely does not care about comments, not as a pose but as a way of staying in the room. The cost of listening to all the passionate, well-meaning people in a comment section, they agree, is also the cost of having your psychology slowly degraded by the internet's underlying toxicity. Better to engage with a handful of people deeply than with as many as possible in a shallow way. Sanderson's own rule is to check the previous day's comments when he posts, which he manages about ninety percent of the time, and then to fall into a two-week binge he cannot quite defend.
When the pandemic closed classrooms, he did something almost opposite his usual practice: a live series called Lockdown Math, on camera, unedited, biweekly. His ordinary production rate was too slow to help people who suddenly needed remote math. Live quizzes let him reshape the lesson from the chat. Online teaching, he says, is basically a form of live streaming now, and it would be healthy if teachers viewed it that way. A friend showed him the ropes. The useful trick is broadcasting software such as OBS rather than raw screen-share: preset scenes — face, paper, Desmos — and keyboard shortcuts to switch, the old "camera three" call turned into a solo operation. He wrote a blog post on the setup. The largest educational prize of the pandemic, he thinks, would be if it trained a bunch of teachers into content creators.
The people who ask "who am I to post this" are the ones who should post
He uses the phrase "commoditized explanation." A given Algebra 1 lesson is taught millions of times in parallel, year after year, which seems inefficient. What should exist is a small handful of explanations online, so that when someone needs that explanation they can go to it, and classroom time can be spent on the parts of teaching that are not explanation — which is most of it. The way to get there is for people who are already explaining to publish in a public forum, and to treat the recording as a piece that was always going to reach more people than this semester's students, not a Zoom call that happened to be saved.
Fridman tells the story of Russ Tedrake, the MIT roboticist whose underactuated-robotics course is already online and popular, and who had started playing with Manim after their first conversation. Tedrake had asked what equipment to buy. Sanderson's honest answer is that he does not recommend his own setup: it is excessive and hard to work with. For narration he uses a USB microphone, a Blue Yeti; for streams, a lapel mic, probably a Røde. Early 3Blue1Brown videos are the proof that he was terrible at audio for a long time. Hearing your own voice makes it hard to tell whether the weirdness is unfamiliarity or an actual artifact. Lockdown Math used two to five cameras, one overhead on paper because he wanted the paper feel, plus a compressor between camera and computer. He does not regret doing it live. The content is less tight than a recorded-and-edited version, but the mistakes and the live interaction are the point. A future series like that, he thinks, would live on a different channel so 3Blue1Brown stays clean.
The deeper sadness is not gear. Fridman's father can explain plasma physics simply and almost none of that is on the internet. If every excellent teacher chose one topic this year and made the best short video they could, the internet would be replete. There is self-interest in it too. For a researcher it is an accessible *Nature*-letter version of a life's passion, seen by far more people than a paper. Those lectures are what tell early students what to be interested in. If you want better graduate students in eight years, Sanderson says, make the best video you can and wait. Vsauce can walk through the Banach–Tarski paradox in depth and reach an audience no network executive would have green-lit. You do not need permission. You will be surprised how many people will engage with something you thought was niche.
The real barrier is embarrassment. World experts feel the same impostor question Sanderson still feels every time he posts: who am I to talk about this, even on a topic he has studied for life. He honestly wishes more of the people with that modesty were the ones posting. A lot of educational content is made by someone who started researching two weeks ago and is on a schedule; the people with the self-awareness not to post are often the best positioned to give an honest explanation. That is why a channel like Numberphile has value — it traps a smart person and forces them to explain on a sheet of paper — but one channel does not scale. Educators have to take it into their own hands. The pandemic is already forcing the content online. Hit publish and see. YouTube might sit quiet for a while and still be there ten years later. Fridman's counter is Joe Rogan pulling a whole library off YouTube for Spotify, the first time it occurred to him that YouTube videos might not live forever. Sanderson can imagine a poorer Alphabet, fifty years on, deleting unwatched files — or a world that has simply stopped being habituated to the site. A content-addressed network would keep a file at the same address as long as anyone hosted it. If people are not in the habit of going there, the address does not matter. The thought still makes him sad, because the job as he sees it is a set of canonical videos you can always go back to.
The same matrix multiply, stacked, is what makes abstraction look like intelligence
Fridman turns to the neural-network series. What is the most beautiful aspect of the field, mathematically or in application? Sanderson goes to the layered structure. Qualitatively distinct things happen from one layer to the next, and they follow the same mathematical rule: a nonlinearity and a matrix multiplication. Chris Olah's visualizations of convolutional nets trained on ImageNet make it visible. Neurons closer to the input pick up texture and edges; further back you get eyes, then animals, then cat versus dog versus deer. A generalizable object runs through layers of abstraction, and those layers are in some sense what constitute intelligence. He calls it automated abstracting. That it can be so simply represented is part of the power. Modern deep-learning research, he jokes, often does a pile of ad hoc experiments, keeps what worked, and then retrospectively writes the math that says it always had to. He does not care how you got there once you have the elegant piece.
Fridman raises the usual puzzle: the loss surface is full of local minima, and a dumb gradient-descent algorithm still finds good solutions. Sanderson is only half surprised. The space is so high-dimensional — GPT-3, he notes, has 175 billion parameters — that of course interesting points exist. The more interesting question is how you get there efficiently. Gradient descent works well on neural networks, and not on an arbitrary parameterization of the same space, because the layered structure lets you decompose the derivative in a way that is computationally feasible. That is backpropagation. There are probably infinitely many good solutions, not best solutions. Stephen Wolfram's related observation is that if you look at the space of all computations, a surprising fraction do something interesting. Kolmogorov-complexity thinking says almost everything is interesting. The delicate question is the opposite one: what is describable with low information and still does something interesting.
Shannon's noisy-channel coding theorem is his example. You want to send bits through a channel that flips some of them, and you want an encoding resilient to that noise. Shannon's non-constructive proof does not build a code. It says that if you chose a *random* encoding, it would be almost at the limit. That is a weird kind of existence proof, and it then took decades for anyone to find codes close to the limit. A random element of an ungodly huge set is a different object from an efficient description of that element. Implementing the random code would mean a gigantic lookup table, computationally infeasible. Tons of possible programs are interesting. The engineering question is when you can have a low-information description that remains interesting, and therefore a blueprint you can actually build.
Someone had emailed Sanderson a day or two earlier wanting to pair GPT-3 with Manim: a high-level description in, a mathematical animation out, "trying to put me out of a job." He would be surprised if that worked as stated. If you pick the right examples, though, generating something cool is already huge value. Writing is often getting a bunch of stuff on the page and deciding what to whittle; a generator with a human refiner is a powerful symbiosis. His favorite demo was Tim Blais of A Cappella Science seeding the pre-Covid model with a novel virus emerging in Wuhan. GPT-3, whose training cutoff was before the pandemic, wrote a month-by-month chronicle that turns into a zombie apocalypse — of course it would, given the internet — and the early paragraphs are shockingly reasonable before it runs away. The flip side is that it struggles with numerical patterns. Feed it Fibonacci and it loses the thread. Sanderson is not surprised. Seeing 1, 1, 2, 3, 5, 8, 13, you do not guess the next term by vibe. You hang several hypotheses at once — generated from previous terms, multiplied by a constant — and you test them. Pattern recognition is most of understanding, and GPT-3 is astonishing at it. What differentiates mathematics is that the pattern is not the end goal. It is a signpost. One of his earliest videos divides a circle with chords: 1, 2, 4, 8, 16 regions, and then 31. Almost a power of two, with a beautiful reason it is not. The difference between a student and a working mathematician is not how many patterns they have seen. It is whether, in the instant of seeing one, they ask whether the problem itself should have produced it. An algorithm that did that on purpose would be a little scientist.
Most math animations should not start in Manim — do as he says, not as he does
Manim, the Python library behind the channel, is out in the world, and Sanderson always feels guilty when it comes up. He thinks of it as a scrap-heap tool a math teacher put together, open-sourced because people asked, and then kept scraping together. A lot of what makes it hard to work with is a function of him not being a software engineer. He has spent some of the year making it better and more flexible. He would love to get his act together about integrating with what the community actually wants, and he admits he has been shamefully neglectful of that community. Put the guilt aside, and the first piece of advice is to make sure the thing you are animating should be done programmatically at all.
If you just need a graph with a little motion, use Desmos, Grapher, GeoGebra, Mathematica. You can get very far, and in a lot of ways it would make more sense for some of what he does. He keeps using Manim because he is in a cycle of improving it by making videos. "Do as I say, not as I do." The original motive was that functions have many representations other than graphs. Transformations can use movement over time to show the relationship between inputs and outputs, instead of an x-direction and a y-direction; vector fields are the same idea. He wanted something flexible enough that you did not feel trapped in a coordinate plane, and programmatic enough that loops, conditionals, and abstraction were available when the scene needed them — parameters, branching, arbitrarily increasing complexity. If you are just putting text on screen and sliding objects around, use Keynote. The craft is distilling what should be programmatic into Manim and sending the rest elsewhere.
Python is home. He loves that it is both object-oriented and functional, so you can whip something together in a functional style when that is the faster shape. The biggest disadvantage is that it is slow. Computationally intensive work either forces you to think about efficiency more than you should, or it just takes a long time. Old Manim was way slower than it needed to be because the backend rendering was, in his word, absurd. He has rewritten it so the hard work happens in shaders, GLSL on the GPU, fast enough that a 3D scene can be interactive while you code — orbit, hover, elements that follow the mouse. A viewer with only play and pause will never feel that. The developer does. When Python itself is still the bottleneck, it is because a lot of data is sitting in the object you want to animate.
Fridman asks about the walrus operator, the `:=` syntax added in Python 3.8, because the toxicity of that debate was part of what led Guido van Rossum to step down as benevolent dictator for life. Sanderson's knee-jerk is that he does not care that much either way. It seemed as if it would make code harder to read, and then so did list comprehensions until you were used to them. Use it or don't, and everyone should calm down about the spaces-versus-tabs fights. Fridman reads the episode as a case for leadership in open source: great leaders make a decision while disagreement is still alive. Wait too long for consensus and you get congressional paralysis. Sanderson is willing to call it admirable if Guido heard the disagreement, disagreed with the disagreement, and moved forward anyway. The world does not go anywhere if every divisive choice waits until the division is gone.
A theory of everything is too big a bite — spend your cycles on problems you can see resolved
Fridman asks about the 2020 season of theories of everything: Eric Weinstein's geometric unity, Stephen Wolfram's hypergraph physics project, the usual path through string theory. Sanderson is blunt about popular science. People are more interested in theories of everything than they should be. Whether you are trying to make sense of Einstein's lectures, Wolfram's project, or Edward Witten on string theory, you are not actually going to understand the substance of what they are saying. Some physicists will. You will not. Far more productive, he says, is to let yourself get really interested in phenomena that are still deep and that you have a chance of understanding. Before coming to the recording he had watched a Steve Mould video on why sugar polarizes light. Follow circularly polarized light far enough and you get a pretty good appreciation of two-state quantum systems — a place that reading about why quantum field theory is hard to reconcile with general relativity will never take you. Audiences should be less interested in theories of everything than they are; popularizers should be less emphatic. It is also nearly impossible to make a 3Blue1Brown video on a theory of everything. You cannot honestly pack it into twenty minutes.
The same rule applies to famous unsolved problems. If he made a video on Fermat's Last Theorem, he would not try to explain Wiles's proof. He would talk about the case n equals 3, which is still barely accessible. The core ideas send you into a number field that lives in the complex plane as a hexagonal lattice, and you start asking about factoring in that lattice. He has talked about lattice arithmetic in other videos; a viewer can actually get there. The things that make the general theorem hard are much deeper. Before you can understand why the general case is as hard as it is, you have to walk through the reachable cases. Any other attempt would be shallow, and a waste of the viewer's time.
As a kid he was sucked in by the twin-prime conjecture because he could understand the statement, and he had a dream of being the one to prove it. New math got viewed through that lens: maybe this applies. You mature, he says, to the point of realizing you should spend your brain cycles on problems you will see resolved, so you grow into the feeling of resolution, rather than on something that is not going to pan out in your hands. James Maynard is the positive example: a young, creative mathematician who pushes in the direction of twin primes without hitting them head-on, taking questions that are hard for similar reasons and making them tractable. Popular physics, Sanderson thinks, should encourage that habit through the physics of simple everyday phenomena, which can get quite deep. He gets messages asking him to explain Weinstein or Wolfram. He does not understand them, and more importantly they are too big a bite.
Fridman's last question is the meaning of life. Sanderson does not think life has a meaning, and he does not understand the question. Meaning, as he uses the word, is ascribed to things created with purpose — the label on a water bottle, one consciousness trying to get an idea into another. Most things do not have that property. Asking for the meaning of life is a little like asking "what is the height?" Height of what? You cannot ask for meaning without an intending consciousness, which is his way of revealing he is not very religious. He suspects people are actually asking what the guiding light should be when they make decisions day by day. If that is the question, his answer is interactions with other people, especially like-minded people, and bringing others joy. Something you create connects with someone, and the reverse. That is the state we use "meaning" to name: filled with happiness and energy to make more. Would a life alone on a desert island be meaningless? "I think we're all alone together." Fridman closes with Feynman's flower. An artist friend holds up a bloom and says the scientist takes it apart and makes it dull. Feynman thinks the friend is nutty. The beauty the artist sees is available to him too, and he also sees the cells, the processes, the fact that the color evolved to attract insects, which means insects see color, which raises the question of whether aesthetic sense exists in lower forms. Scientific knowledge only adds to the excitement, the mystery, and the awe. It only adds. He does not understand how it subtracts.
Más de este canal
3:36:56EN
5:15:51EN
3:12:58EN
3:46:18EN
3:51:47EN
2:53:42EN