5. How Did Human Beings Acquire the Ability to do Math?

[@daviddemar8749]

professor devlin-i loved this entire series I've rediscovered my love for math in my 50s after it was "robbed " from me in high school. this series has encouraged and inspired me to continue my adventures journey, especially my self-study Calculus project. I hope that I will be able to go further and deeper and inspire others to do the same!

[@cliffordmorris6091]

Why do I have to listen to crap adverts?

[@davidste60]

@@cliffordmorris6091 That is due to your not having a good adblocker.

[@marcosferrer8071]

Thats inspiring.

[@DarkMatterBacon0]

@@cliffordmorris6091 quit q44q5q6qq5qqqqqqqq4qqqqqqqqqqqqqqqqqqqqwqqqqqqqq4q6q4q5qqq5qqwq5questioning 5htp I think 🤔 😕 😅 😐 are a good questioning 😉 questioning 😉 🤔 😜 😄 😀 😅 😉 🤔 even quit we don't want 😉 😜 60s for you questioning questioning 😉 😜 😀 🙄 🤣 🤔 5htp what are quit quit 🙄 😉 😜 for a 6th period and 6th exam 🙄 😉 😜 😀 🤣 4th is good 👍 😉 🙄 5th is questioning quit 😉 equal 😉 🙄 😜 the wqtches will questioning whether 😉 🙄 is not the only 😉 🙄 😜 5htp that equipment has to use 🙄 😉 and how it 🙄 😉 and what you 6th about 5th is going 🙄 😉 and wqtches for me is a little 🙄 and quit 🙄 😉 😜 4q5565q5q4qqqqe6q5qqq5q6q5q5q6q655q5wqwqeq4q5q65qwq665eq65wqeeq66quit smoking 🚬 🚭 5th of this 🙄 5htp exam 🙄 😉 😜 😀 and 🙄 😉 😜 55q55q6qq6q6qwqeq6wqwqq5q55556q6q65q65q5e5qq53q5q6q5q5wq6qwqq5qe6q66555qeverything quit 5htp 4chan.org 5th equal in an 5th period with 6th equipment 5th wheel out in a 5qwqee56q3q556qqqq5wqqq5q555q6eqqqeq5qwq5qqq6qeqqq65qqqqq56wq6wqquestioning whether you quit 6th questioning you and your friends or not you 5htp q equal in 5th questioning quit 🤷 the fact questioning your feelings quit on a 5htp basis 5htp questioning why do they feel q5q6qeq5q56qq3qe55qq65qq5qeqqq6qqq5qqq65q6q5eqqwqeq5qq6qqqeqqqqqqwqqqq6qwq5qq5qqqq5qqqqqq6qq6wqqqqqqeqwqqqqqqqqwqqqq45q6qqq45q5qq5qqqq5q5qqq55wqq55q65q56555555qq4q5q565q5qqeqq5qqq6q5q5qq5q56qqq65qqwq5q655qqq5wq4qqqq6q556q56q56wqq65eq3qq5qqqq6qqqq556eqqqeqqq665q6qwqq66655qq55qqq6q55q5qq55q5q6qqqq5qq5qq5665w5qq55qqwqq556wq554eq666

[@DarkMatterBacon0]

5th and questioning 60s the quit quit 🙄 questioning 5htp and I hope 🙏 questioning quit the game 🎮 and questioning

[@esaedromicroflora1247]

thank you Stanford. Sharing the knowledge like you do should be ethically mandatory for any "university".

[@gustavohermandio1440]

ikr

[@rooms250]

Really should. My campus has an iron grip unfortunately 🤦🏻‍♀️

[@derekeimer7758]

Yeah, why should someone have to pay a "university" for higher learning? actually show up for classes?, sometimes for 4 YEARS!! ya gotta do all that studyin' an testin', just to get a piece of paper that supposedly proves how smart you are, so MAYBE you can get hired somewhere or something? How stupid, it should all be free like public education.... They don't need to pay for all those buildings, research facilities, labs, etc... all those professors that spent their lives learning what they know should just share it for free, why should we have to sacrifice so much time, effort, and finance, just to be smarter? Its just not ethically right to make me pay for knowledge from some "university"............... For my next trick... I will guess your age!!! Totally FREE!!!!

[@derekeimer7758]

Then again, Stanford probably SHOULD be free.....

[@davesomeone4059]

@@derekeimer7758 why not make everything free?

[@Octoped]

All through grade school or college did I ever hear a teacher discuss mathematics like this guy? No!!! Man would it have helped me! Thanks Professor.

[@henrygarciga]

I learned so much math when I started making cross-blown flutes. Thanks to a physics instructor who played organ, Don Hall (CSUS) introduced me to musical acoustics, and soon I developed formulas for major and minor scales, helping me overcome the math phobia that cursed my every exposure to undergraduate courses in math. Relating the everyday relevance of math in human activities makes it a more interesting way to teach it.

[@bookbeing]

Hope you are still creating flutes to play and hear today🌞

[@henrygarciga]

@@bookbeing --Passions never cease until the body quits . Get in touch and I will mail you a comp. flute in any key .

[@attilathehunnette]

How very interesting! I wanted to add acoustics as an elective in my senior year schedule, but the class was full. Your life sounds rich! I'm old now (play piano and flute) but my passion has always been in harmony, as it was in all of music theory. Knowledge of acoustics would have been icing on the cake. Perhaps I could find a course here on KZbin!! My best to you :)

[@henrygarciga]

@@attilathehunnette --Think of the more difficult scale to play on the flute and I'll make it for you . The whole tone scale never resolves to our ear. Whole and half diminished scales also challenging . I made a flute with a guitar tuning from Africa .

[@attilathehunnette]

@@henrygarciga An E B G D A E scale on a flute?? Wow! Love the half-step, whole-step idea too. A whole tone scale is reserved for aliens and ghosts, I think :)

[@happybee0622]

Thank you Dr. Devlin! Good to see you again! You are the best professor ever! I learned a lots from you.

[@phildavenport4150]

Some of us acquire very little competence in maths, cannot recognize genius, and must make do with understanding our world in other ways. Some others of us become extremely adept. The rest of us, which is most of us, have to make the best of the limited abilities we have. The biggest and most cruel trick played on those of us in the middle is the ability to detect brilliance in those few we are privileged to experience, knowing that we can aspire all we like, but will never attain the heights we so desperately want to attain. And this is not only maths - we all know how Salieri must have felt the first time that he witnessed the sheer genius of Mozart in action. Mind you, I'm not bitter...

[@cosmicHalArizona]

You do with what gifts your given compensate for your weaknesses

[@books4739]

I'm bitter as hell

[@leftyshawenuph4026]

Prior to the internet, only (from what I can tell about how many people are in the room) around 20 people would have heard this lecture, this one time. This video has (at this time) 200,000 views.

[@EighthHouseTarot]

(USE OF PARENTHESIS) ((TO MAKE YOUR POINT)) (SEEM EXTRA GOOD)

[@leftyshawenuph4026]

@@EighthHouseTarot I'm can't tell if you support my mastery of the written English language, or feel threatened by it (I'm going to go with the latter, after seeing how flummoxed you are by parentheses). So strange that that's that's the one thing you zeroed in on. Did my perfect usage of the parentheses distract you? How does one "make" his point "extra good"? I only ever learned how to: 1) Make statements that simply support my point and, 2) Prove my point. I am quite adept at both.

[@TonicTheSeshHog]

Almost half the amount of views in under a week, as its now at 297,000 views 😶

[@coachjoe3074]

Algorithm hitting hard. 310k, 8days after the OP

[@lococomrade3488]

@@TheFreemanuk Nope. The world has always been nutty and people always blame new technology. Look into the Luddites. Don't be one.

[@susanadiasjohnson457]

This professor explains things so effortlessly that one can understand it in one's sleep. Beautiflly done.

[@vonaudio5435]

Oddly enough, that’s how I actually discovered this talk. I went to sleep with KZbin running, and I woke up in the middle of his lecture! 😂

[@lethalbroccoli01]

@@vonaudio5435 i just put this on to fall asleep LMAO

[@fredericjeanbart9283]

I love to see intelligent people expose what they have in ther brain, thank you.

[@futurestar3348]

+Frédéric Jeanbart Too bad all my professors' do is read of their fucking power point slides, really grinds my gears.

[@gmat5586]

Wow, this is wuvley. What a bwain, amazing bwain.

[@ker0356]

@@gmat5586 💀

[@MissChrissyM1]

U mean…..in their BWAIN

[@douglasmemmo9288]

Ah, yes. Pseudofedenhanced intelligence laced bwain. Vewy enlightening, Indeed.

[@deeliciousplum]

This has been such an inspiring talk on quite a diversity of math topics. Thank you for sharing these.

[@dataflowgeometry]

Looking at how a squirrel is a natural acrobat (or a monkey), it suggests that the mammalian brain has a very sophisticated spatial / physics computer on board. So, spatial mathematics need not be 100% formally taught -- a great deal of its foundations are innate or imprinted via worldly experience. Spatial math is about extending natural intuitions into language, sketching, painting, sculpting, mapping, navigation, and in this century, computer graphics, robotics, space exploration and molecular design.

[@messier8769]

Hi

[@Minsoup4]

@@messier8769 sup

[@bahamut256]

I don't think that's quite right. The right side of the brain controls creativity and art. Mathematical endeavors are logical and are controlled by the left side. As someone who draws and paints frequently, I cannot draw if I cover my left eye, nor can I do maths or speak while drawing, as those are left brain functions. Quite a few systems for acrobatics and maneuverability are actually not necessarily based on brain power as well, your sense of balance, as well as those squirrels, are based on pressure sensitive hairs brushing against perilymph fluid inside the ear that provides orientation. This is why traumatic deafness and loss of balance are often simultaneous. So I disagree that there is a necessarily a complex spatial system on board, as we have evidence of simple systems in the body performing complex jobs.

[@dataflowgeometry]

@@bahamut256 Mathematics problem-solving (challenging ones, not gimmes) harnesses many different parts of the brain, and both hemispheres. These can bring in visualization, sketching, language & symbols, experiential memory, numeracy, models, manipulatives and computer graphics. Deductive logic is more on the left side, and creative, inductive "aha-moment" seeking more on the right side. Einstein used violin playing to expand and relax his mind when facing a gnarly problem.

[@daniela_to]

@@bahamut256 This left-right/logic/creativity dichotomy has long ago proven to be a gross oversimplification of how the brain works.

[@johnnyharry4859]

Thinking about math as a language, clearly will help take away the seeming intellectual intimidation of higher mathematics. We need only learn those languages. If we approach math in this way, I think it will awaken us to a surprising simplicity. I think getting Prof. Devlin's book "The Math Gene" will be a key for me, in learning how to speak this language. Getting to the very root of it - is where this revelation of simplicity will come. As a confessed mathematical moron its already given me hope. TYVM.

[@raginald7mars408]

.. as a German Biologist - from my German High School on - I am fascinated with Pythagoras. For him- it was not about “mathematics” it was about access to Spirituality via clarity of Mind, The ability to Prove something. The Diagonal and the side are incommensurable in a square of 1. Mind Boggling - when you have one...

[@Reverend11dMEOW]

ALL Carpenters utilize Pythagoras, and they do not the background why "345" equates to using a 33 meter measuring tape during the "Make this rectangular structure (meaning making all the corners in affordable housing SQUARE by measuring from corner to opposite corner, then make this measurement Match the measurement of the remaining corner set, then the third person is triggered to 'Do It" when "NAIL IT" is heard, which will lock this level of abstraction into place labeled Square per Pythagoras, but it has to be Squared-Up Again when the subfloor is cut which the walls' Bottom Plate MUST Trust Implicitly as it is near-impossible square the bottom plate that consists of 2x4 (which everyone has exactly zero gripe when that inch and 5/8" result from losing as much water as possible in proper lumber kilns, or it will rot more often in humid environments and not be as strong in all since the water having vanished brings whole bunch of cellulose's empty cell's walls tight together). Carpenters use 3 4 5 EVERY TIME a 90-degree relationship is required somewhere one square side (using the identical factor all the way around) of four, the side it forms the right-angle with identical multiple of three, and VIOLA! whatever represents the hypotenuse get measured as the factor of 5.

[@phildavenport4150]

@@Reverend11dMEOW Wish I could play the viola.

[@Reverend11dMEOW]

@@phildavenport4150 I always spell "VOILA" as viola and nobody has busted me yet. ;-) Until now.

[@THESHOMROM]

I didn't understand or wasn't able to follow much of the lecture, but I came away knowing more and hungry for even more. This is a good exciting lecture from a good exciting, teacher. Math is only as exciting as the teachers are. Some mathematicians are excellent teachers, many aren't. They are good at solving problems but not good at explaining how they've come to the solution.

[@YourFriendlyGApilot]

I agree. Way too much rambling and side notes taking center stage obfuscating the main message.

[@stevenzapiler5806]

Math teaching is a good example of, yes, the importance of the passion of the teacher for the subject. That passion makes an impact on the students, because they learn to express their own passion as a way of being a learner.

[@alexi077]

19:17 indeed, maths is faster in your mother tongue if one is bilingual but, i speak 5 languages and i have caught myself many times using the language that i was speaking the most in the past half year. I am greek, my first language was russian and i have been living in germany my last 20 years but today, i counted in englisch because thats the language i used the most last 2 months!

[@ugiswrong]

How many years to learn Russian does it take

[@fernandough2117]

@@ugiswrong 9 months just to get started with the lessons in his case

[@alexi077]

@@ugiswrong that depends on the person... some, like me, are quick learners. I learn to speak languages in 3-9 months. My wife trys to learn greek since 4 years, lol. But i would guess, you can get the basics in 9 months.

[@davidrodgersNJ]

Necessity is the mother of invention. Agriculture requires geometry, calendars, accounting...

[@joe_hoeller_chicago]

“How to quantify a solution”, is a really interesting way of dissecting the thought process: To learn how to quantify is the challenge!

[@vicachcoup]

Great talk Thanks for persevering through that sore throat Sounded fine to the listener btw

[@ModMINI]

Watching this video, I would propose that before numbers came "targeting ability" - as for the throwing example, having discrete quanta of movement (numbers) and being able to throw an object, analyze the result and move "two notches to the left" to compensate for the margin of error. That would be a huge competitive advantage as compared to an animal that just kept doing the exact thing without capacity to calibrate.

[@GageHolt]

For sure. I would imagine that sort of thing would’ve been happening on a cellular level a long time ago. It amazes me how well my dog/cat display instances of critical thinking. I believe they could comprehend some pretty crazy stuff if only they had the tool to communicate it (language).

[@dataflowgeometry]

Numbers started with counting small numbers of discrete things (e.g., how many children are you raising? How many mouths to feed are you preparing food for?). These are innate perceptions to some degree, advanced through verbal language. As far as continuous quantity, all humans come innately wired up to perceive distance, and comparisons of distance (e.g., closer, farther, approach, retreat). Another innate quantity is perception of force or weight (e.g., experienced when lifting logs). Another is perception of heat and cold. One of the first breakthroughs was primitive instrumentation to measure quantitative things -- a stick or bone used to measure distances, a stones used to measure weight.

[@alvodin6197]

That doesn't make any sense. Many things could be an advantage, but you are not explaining anything. Maybe we need to move on from Freud and "survival of the fittest".. which isn't even what Darwin himself meant.

[@PeaceFinder12]

To summarize, there is a math gene because it offers evolutionary advantage. Animals have math capacity but it is smaller per say in most respects than a human. When developing complex language, a natural ability to do some types of math is generated. Math and language are both mental representations and models of the real world... (he didn't talk about this but with this we can start predicting possible futures based on the relationships we have acquired). Once we understand the world we can behave in such a way that it offers evolutionary advantage in terms of survival and reproduction. Math and social relationships are quite similar. Like a soap opera where we must realize the nature of people and their relationships to other people and how it all functions. Math does something similar but with the characters being numbers, unknowns, functions, etc. Our ability to do complex math must depend on our ability to figure out complex social situations/relationships. 51:41 The reason why people who are good at socializing are not very good at math .... or why people who are really good at math are not very good at socializing is because of what we devoted time to. Whether we put our mental effort to figure out numbers and our social life suffers vs figuring out social aspects and our ability to do math suffers. But the possibility to do either is there. Perhaps someone with a more efficient brain can do both. I wonder how many people in the audience can do both at a somewhat high level. :P There is more to the video but this was the most interesting to me.

[@anotherpointofview222]

51:41 his old school use of a snot rag.

[@DarkEclipz]

This series of videos really gave a good insight about math for me. I am not really interested in memorizing all the 'formulas', but much more in the why. Why do all there formulas work? And those who saw the patterns, what where they thinking at that moment? Although I have been studying mathematics for a really short time, the questions of why these formulas work is what is really empowering my journey (and passion) about my new hobby (mathematics). Thank you for these insightful thoughts!

[@SR-er6hx]

Mind to share answers?

[@tawermeister99]

The thing your talking about. The ‘why’ is called mathematical proof. If you think of theorems or functions as the ‘how’ a sort of nice shortcut to do work in maths. The proof is why those theorems etc can accomplish their purpose.

[@DarkEclipz]

@@tawermeister99 After 5 more years of studying, beautifully said! :)

[@cheedozer7391]

@@DarkEclipz How's the journey going?

[@maxdakka7973]

I used to read Keith Devlin's blog on the train to and from work a long time ago and was surprised I recognized his face here. This man wrote no less than 3 blog articles disabusing grade school math teachers of their misunderstanding and misteaching of simple multiplication. Have any of you ever thought about what multiplication means at the most fundamental, atomic, primal level?

[@JuusoAlasuutari]

In my experience, the best way to learn is to not strive towards learning itself, but to place concrete goals which require you to do learning. Think of what you want to achieve or create, then find out what you need to learn, and proceed in that manner. For instance, if you want to learn programming, then think of what _kind_ of program you'd like to create, and learn the kind of programming that lets you achieve that.

[@fernandough2117]

Word

[@robertlambert4514]

1:38:56 I love the way he talks about the avalanche of knowledge that will come about solving one of these problems. "If I had the money, which i don't because I haven't solved one of these problems."(sic) is just hilarious to me because of the casual no bullshit way he delivered it not waiting for a laugh of any kind. That puts the final nail into his work being labours of love and thirst for knowledge to have and share, above the monetary value recieved for them in my mind.

[@kennethsnyder9236]

I wonder how many Robert Lambert’s there are “U-TUBING”? I can sware that your name has crossed paths with my interests. Conservative, Science, Space and Debating, etc….

[@gk-qf9hv]

No the level of abstraction is not the only difference between math and soap opera. Human beings spend many YEARS learning about the relations between human! Rarely more than few minutes at a time on Math.

[@mrnobody2873]

I'm watching this 10 years after it was recorded. I can't help wondering if he ever started a lecture on Infinity and if so, is he still doing it?😎

[@bookzdotmedia]

Lol

[@carl-henrikkristoffersen2313]

Waiting for an infinite amount of time is part of the lecture.

[@tegan71969]

He seemed very forgetful here. Not being able to remember his own book title (and a few other things during the lecture), was a key indicator of possible pre Alzheimers. Perhaps that's why the Infinity lecture never happened?

[@ranyork7626]

Simple, if hes not, he didnt.

[@mrnobody2873]

@@tegan71969 with ADHD, I’ve been unable to recall common words at various times throughout my life that I shouldn’t ever expect to lose, like “bird.”

[@donnacsuti4980]

The fact is animals like cats and dogs and have multiple babies (for example say 5) can count and must be able to add and subtract. They know when one or more are missing. They also count human family members. Simple math is needed for survival and must be built in, in our and their brains.

[@anotherpointofview222]

True @DonaCsuti but cats and dogs can't get you to invest substantial sums of money for them to teach it to you.

[@alexthedog]

the deeliciousplum 6 years ago This has been such an inspiring talk on quite a diversity of math topics. Thank you for sharing these.

[@alexthedog]

Daniel Smock 12 minutes ago esaedro microflora 1 day ago thank you Stanford. Sharing the knowledge like you do should be ethically mandatory for any "university".

[@WealthandReligion]

This was put out before the information purge. Cherish it while it lasts.

[@davesomeone4059]

KZbin takes 9 years to figure out I wanted to see this. Some humans are better at math than others it seems.

[@alexthedog]

esaedro microflora 1 day ago thank you Stanford. Sharing the knowledge like you do should be ethically mandatory for any "university".

[@dpraptorP]

Animals and even insects inherit incredible abilities. I find it perfectly plausible that we pass on genes for many things, like music, math, painting even alcoholism. Pretty much all things that you specialized in could be written in the genes, its when DNA is combined and the crossover with the other parent selects one or the other gene for that. Sometimes you get lucky and get the smart gene. Like Mozart did!

[@nelsongonzalez4533]

Without language and the ability to communicate properly, you wouldn't be able to stand in front of the class... teaching about numbers and mathematics and conveying valuable information 😜🙄🤓

[@francoisverkoczy5659]

Yes but without the math, you couldn't formulate numerical structure, or ordinate senses, to come up with the language!!! So math must come first, period. (Pardon the pun)😊

[@ShamelessHorse]

This got me thinking about numbers, how they appear in nature and how we use them, this lead me to the following conclusion. Numbers, as we have defined them, are our way of dealing with the immesurable nature of reality. We deal with this by admitting our weakness and abstracting the problem. We can talk about the number 1, but we cannot point to the exact spot on the number line where the value 1 is located. So what is 1? It is an abstract pointer to this theoretical location on the number line that we don't know the exact location of, we can define it as being "the number closer to the value of 1 than any other value". Why is this a useful definition instead of just saying 1=1? Because it shows that we can never pinpoint the exact location of 1 on the number line, and also it subtly implies recursion, it is hinting for us to keep looking for values closer to one. So what are we really saying when we say something like 1 + 2 = 3? We are _not_ hopping along the number line and reaching the goal of 3, remember we don't know where 3 is either. No, what we are saying with this equation (and this is actually a really clever bit of abstraction when you ponder on it) is that the pointer that represents the location of 1, added to the pointer that represents the location of 2, is equal to the pointer that represents the location of 3. You see, we have not had to touch the number line or worry about our inaccuracies with these values. In this way we can describe the number 3 with no less accuracy than 1 or 2, indeed all numbers can be described with equal accuracy because our calculations are operating on abstract values.

[@glutinousmaximus]

ShamelessHorse That's very good. But you still have to worry about inaccuracies since you are necessarily using an abstract model. In this case, positing that you can precisely reproduce the distance between pointer 1, pointer 2 and pointer 3. You must also posit a perfect line AND a perfect physical correspondence between the 3 pointers. This will not precisely translate to the real world. Leaving Set theory aside; lets say 1 apple + 1 apple = 2 apples. Sounds good. But the two apples MUST be precisely equal in all respects; even to the identical arrangement of the atoms, and the positions, charge and spin of the particles involved. This will never happen. Even so, _humans_ will agree that you finish up with 2 apples..! Peruse Kurt Godel and the Incompleteness Theorum if you have not seen it before. Cheers! .

[@glutinousmaximus]

Adam Mangler _Quick joke:_ Teacher: "Johnny, what is five added to five?" (Johnny considers for a few seconds) "Ten Miss" Teacher: "That's pretty good Johnny" Johnny: "Good Miss? It's bleeding perfect..!"

[@ensign_poo]

Thank you for the thoughtful advice. I was not trying to convey that I was disinterested in learning. I was trying to point out that this particular platform isn't as welcoming as it should be. I've sat in at a couple of study sessions with Math students insofar that they attempt to teach me what they are learning. Win/win. I get rudimentary knowledge and they get to understand it better by teaching it. Also, I've been learning about types of numbers: hexagonal, triangular, happy, etc.

[@kevincasson9848]

Love this man! Coukd listen to him 24/7

[@gogobram]

It's not about vocabulary, it's about images. Making process is a matter of evaluation, which requires comparing things. To compare different models and solutions, it certainly helps to compose and de-compose solutions. And that soon involves labeling concepts, which seems to require vocabulary, but it does not. The moment you want to streamline external and internal communication, you need to map concepts and labels to vocabulary. And from that point on, it's just more efficient to use that vocabulary also in the internal thinking process. So, I do agree that vocabulary will ultimately follow and becomes a part of our thinking process. However, only in a far evolved state I think. It's not a strict requirement though, and many people use "feelings" and "images" to evaluate problems. There's a ton of concepts that don't have words or vocabulary, but which we use on a daily basis nevertheless. That shows that it's not required to have a language in order to think mathematically. e.g. the vocabulary to describe the texture of metal and that of a stone, Even though we would both clumsily call them "hard", "smooth" and "cold", there is a huge difference. We do have a visual image of both of them, which is stored inside our brain. And that image is more powerful than words. Simply put, we all know that a single picture can tell more than a 1000 words. Because of that, I would say, that a bigger leap in our thinking is the ability to store images and to recall them. Either in our own memory, or by drawing them down. And our ability to make mathematical drawings of our ideas. Children are taught at school how to read and write and strongly tested on their ability to remember what they've read. Only very few times are children actually tested on their ability to decompose and remember images. However, those children are the ones that clearly stand out in the mathematics classes. Not through words, but through images and techniques that don't even have vocabulary. e.g. what is this called ? x +1 = y - 2x 3x + 1 = y Is there a single word to label this ? It doesn't seem to need one. It's a visual thing.

[@lisasternenkind6467]

Keith Devlin is such a sympathetic man and mathematician. Ever since I can think back, I imagine numbers in a very physical way. I am able to write down an image how they relate to another. Whenever I count or do mathematics, this image comes up. Also every number has a form and a color and also some kind of physical stability value, like a 5 is a complete circle, which is blue and very stable, or a ten is a red rectangle housing 2 blue circles and is extremely stable, or 20 consists of 2 such rectangles, whereas the 7 and all prime numbers are of some kind of yellow hue ans sort of physically instable. I also view the numbers 1 to 9 as sort of introduction of numbers and the 0 in this concept is only a fading point. The higher numbers are, the stronger is their color value. The funny thing is, that I grew up bilingual. I went to a Germen school first, and then I went to an overseaseas American school from 5th to 8th grade, and finaly to a school in Austria, where the language again was German. I always wondered why I would do easy additions und subtractions in German, multiplying and dividing and other mathematics in English, and higher mathematics in German. Now I finally got the answer. EDIT: I am NOT a mathematician, yet the first profession I learned was software programmer and I constructed many data banks, from the start to finally usage of the data. I then learned another profession, because this wasn't interesting anymore when I fully knew how to do that. I would have been able to earn lots of money, but to be bored is like being brain dead. I still love to learn, so if things get boring, my brain needs new input.

[@sharryfeng4967]

Interesting topic. Until I reached retirement age then be able to think things over! During the golden age, life was too busy to seek out all the things that were created at the beginning! Thanks for the lessons!

[@dakrontu]

Complex sequences of movements are made up of simpler sequences. So the cerebellum, which translates an intent to a sequence of actions, has a recursive ability. And one kind of sequence of actions is the uttering of a sentence. Likewise the recipient hears what is said and re-constructs the tree that the speaker's cerebellum serialised. So these are innate abilities and must tie in with the ability to comprehend structures written down as mathematical equations and also allow the same structure to be serialised in other forms.

[@mahoshing5248]

The thinking brain was inculcated into the human experience as part of their in breading and development. You preface your presentation by saying as far as we know, is a healthy place to start.

[@robertlivenmore1786]

I see early humans as easily able to 'calculate' amount of fish caught necessary to feed a family. This is an analog process and is a precursor digital calculation (numbers).

[@PeaceFinder12]

Yeah, he didn't give many examples as to why generating exact numbers is useful in an evolutionary sense. Your example makes sense though. Definitely when it comes to money and trading exact numbers play a huge role.

[@ConversationswiththeAI]

Turns out his Infinity lecture never started and he is still doing it today...

[@szymonbaranowski8184]

People who built pyramids knew math very well... it was as formal math as it can get... a guy from Greece calculated earth radius traveling to Egypt and using just a piece of rope and stick... machines make humans ret arded - thats a fact. The more work you relegate to machines the less you do it yourself and the worse you get at it as a result of it.

[@callmemom6936]

I have to remind my husband to be patient with our children when it comes to travel. They learned to rely completely on a GPS to guide them and it is nothing but a crutch. We grew up relying on maps, memories and landmarks. If I drive somewhere once, I never need to ask again. I even learned to drive and navigate in another country without a GPS. The reason I share this is once we rely on technology, we release those gifts and abilities. As humans we are seeking comfort and ease and it conflicts with our true nature. We absolutely need to challenge our minds and bodies to live based on our true human potential. We were once so connected with this universe there was not a need to even define mathematics. It was a simply a part of the connection humans experienced with nature and the entire universe. It did not need to be explained. It was as natural as breathing. The obstacles/barriers we’ve created have destroyed that divine, pure synergistic connection with the universe and have brought us to where we are today. Have we truly evolved or are we slowly eroding.

[@tobsvonmittelstraum2300]

I am seeing myself leaning more and more towards the platonist position right now :)

[@archaicsage4803]

Monastic Metaphysics is the truth of reality based on Field Unification.

[@Louis-zp8bt]

Seventeen years old and I am still dumbfounded on how I got 30 minutes into this lecture. This topic is beyond interesting, and Devlin seems like a brilliant man to have come up with this theory.

[@sryburn641]

Stanford rocks!!! Nuff said.

[@Halderchess]

Thanks for the great lecture sir.

[@Louis-zp8bt]

The soap opera relationship with math makes perfect sense. It's all coming to me now.

[@HF-jc9xl]

The Hebrew Language - is a Numerical Code. Each letter/ word has number example Mother 40 - Father 2 -Child 42

[@TeaParty1776]

One Objectivist says that early herders needed a method to know that all of their animals survived predators so they compared their number to a number of stones.

[@johnsomebody1753]

1. Less than 3 mins into this he asked, ,"How did the brain acquire that ability ?". It may seem pedantic to some, but the importance of the difference remains. Brain didn't acquire that ability. Mind did. Brains don't just do maths, as though that's their purpose. 2. The ability to construct and follow, a causal effect, and", etc. But before that, comes observance and cognition. Starting a cognitive journey, veering a couple of degrees off course from what is being studied, and continuing to add assumptions, (and as I now expect, from many speakers, hyperbole), rather than observance, surely has to result in losing the path to discovery of what is, doesn't it ?

[@robbiedevine8518]

I wonder if he or others ever correlated the need for complex thought to other huge factors 10,000 years ago, such as rapid sea level rise at the end of the Younger Dryas. Unprecedented change would have been occurring, and those that could organize and move entire civilizations inland would have an advantage. This might have woken up or otherwise repurposed those latent circuits in our brains

[@davidwilkie9551]

Quanta=> Resonance=> Reflection=> Echo=> Memory=> Mimicry => Representational Languages, facets of duality.(?) First comes the interest in exploration, then the value of a discovery,..for persons raised on pre 1900s literature. Anyone practical and curious who is still impervious to the writing style of the adventure narrative, after the mass produced books from printing presses, would not like the modern world. Risk aversion rules, and if a question is interesting enough, the proposed methods to find solutions can be more useful than a "proof". This is a great lecture.

[@nathanmussiett3757]

When he started off saying he was giving a lecture while on cough syrup and sudafed I knew that it was going to be more interesting than I expected

[@sandrawoodworth8391]

Wonderful presentation. Thank you

[@mathization]

I made an ebook to defy the dumbdown times, pls help others, and prevent them from being criminals, but helpful to society. Up to you if you care, and silence is malicious apathy.

[@flektoprime]

Comment #1 - its been 5-9 kY since the calendar (reasonable for the agricultural neolithic), and that is geometry (and celestial pattern recognition).

[@alexthedog]

THESHOMROM 9 months ago (edited) I didn't understand or wasn't able to follow much of the lecture, but I came away knowing more and hungry for even more. This is a good exciting lecture from a good exciting, teacher. Math is only as exciting as the teachers are. Some mathematicians are excellent teachers, many aren't. They are good at solving problems but not good at explaining how they've come to the solution.

[@JulianMakes]

Please do a course on infinity! I did look but i can’t see one yet. Thank you

[@ej-fo8pd]

Pleasant teacher.

[@martianwarlordtv]

animals with locomotion can turn sensitivity to external landscapes and sequential cuing of action patterns into a survival advantage. direct and indirectly linked multicellular life forms can turn communication into survival advantage. throw in competitive pressure and natural selection over several billion years and voila.

[@Immortalprodigy1]

I agree, that definetely something I have started trying and I works for me really well :)

[@garycogswell5499]

Fear seems to be a common thread in our evolution. If a predator was coming up behind me, I'd like someone to at least point and yell.

[@Epoch11]

Where is the infinity lectures that were to come? Love to hear those.

[@Epoch11]

Mark G where are.....damn it.......

[@DarkMoonDroid]

@@Epoch11 LOL Same.

[@mr.winter3174]

Great lecture. I was just wondering if "sense of cause and effect" is really an ingredient for the specific mathematical ability. To me it always seemed that (at least) basic mathematical thinking introduces itself without the notion of time which is needed for causality (I guess). Thinking mathematically gives you insights into instantaneous relations of abstract entities, doesn't it? I mean: somehow paradoxes produce some kind of mathematical abstract time, right? When a timeless contradiction results in altering states of answers for example I would assume. Anyone stumbled across that too at 13:10? Just thinking out loud here.

[@AbleLawrence]

Too much dragging. I also can’t relate to soaps. I think myth making, the divine opera is more abstract and profound.

[@stevemiller8895]

What was the name of your book ? "I can't get off crack", but I can still do my math!

[@roberthamann7449]

Interesting program...and now I know why I have always been 'bad' in Math.

[@naimulhaq9626]

Humans are not the only ones to acquire the ability to do maths, all other animals can also. Some even have idea about the optimum number that will permit them to survive and avoid extinction !

[@jaywulf]

The funniest thing about this excellent lecture is the fact that a Maths Professor thinks 1 Mil is a lot of money!

[@homesculptor]

The cavepersons where sitting around a lightning strike next to a dead wooly mammoth that was medium rare. This was the only food for miles. One fat caveperson was still eating the next morning and very little of the mammoth was left. One caveperson clubbed the fat one to death, and then divided equal shares of the rest of the mammoth meat, and the rest of them went into a cave and lit candles from the tallow and drew pictures of equal amounts of animals needed to feed equally the hungry group. I didn't have time to follow this through, but that is my guess.

[@alexthedog]

Dataflow Geometry 6 months ago Looking at how a squirrel is a natural acrobat (or a monkey), it suggests that the mammalian brain has a very sophisticated spatial / physics computer on board. So, spatial mathematics need not be 100% formally taught -- a great deal of its foundations are innate or imprinted via worldly experience. Spatial math is about extending natural intuitions into language, sketching, painting, sculpting, mapping, navigation, and in this century, computer graphics, robotics, space exploration and molecular design.

[@Bryzle1]

Absent minded professor….has a beautiful mind.

[@bh-regime]

"Psshhh out it comes", lol. He is right about one thing, numbers and language are inextricable tied together. The idea however that ancient man learned to count through abstraction and some kind of numbers sense or algorithms. Ancient man was not a metaphysician, he learn to count through "digital" reckoning, the finger and toes being demonstrators of the phenomenal origin of numbers.

[@derekstone1553]

I’m suddenly seeing how the universe is Mary, crazy, & language & everything else in my mind

[@vanessajazp6341]

We “acquired” the ability to do math in the same way we “acquired” any other language - because we evolved, and we needed to measure things as we continued to progress.

[@helenmary9416]

but for some it is helpful to learn about what/how/maybe time unfolded and math expanded.

[@fernandough2117]

Lol. The good old scare quote. Acquire is an accurate word so no need to go pseudo rhetorical on it.

[@fraterehf8788]

Watching this video about how humans discovered how to do math, so I can repeat the event so I can pass my math classes.

[@MBro88]

Thanks. Maybe small companies (teams) of mathematicians with the identity working together could tackle a Millennium problem. Team takes credit?

[@SKMikeMurphySJ]

Makes Jordan Peterson look like a grade schoolteacher!

[@bogamcs]

Just listened to it again to find out what the title of the soap opera was he mentioned :D

[@bogamcs]

Just for the record, it's Mary Hartman, Mary Hartman

[@salmanuel4053]

So professorial is Keith Devlin, he speaks with abounding admiration for the luminaries of the field; I simply must read one of his books.

[@anotherpointofview222]

How or when did man acquire the capability called language is more the question for me? Applying values to symbolic representations like applying meaning to symbolic representations. ..is a variation on the same theme. But what good or what need would there be for these people who get paid to teach us their thoughts when possibly if applied properly our minds would come up with just as valid thoughts of our own. But then how would people determine the validity of their thoughts if there wasn't a hierarchy of learning.

[@griffruby8756]

P vs. NP: We are often told to "expect the unexpected." But this is a ridiculous and basically impossible demand, an "NP-Complete" problem, just like the traveling salesman problem. However, there is a way to approximate it "fairly closely." Imagine having a way to find a solution for the traveling salesman problem in polynomial time which, though most probably not the very most shortest or fastest solution, is at least one that will be very close to it, say 98%. When it comes to expecting the unexpected, a very good approximation (polynomial time) exists in "expecting the absurd." I used this as an engineering programmer in order to make software which quickly and properly acquired a reputation for being "extremely reliable." Anyone familiar with software knows that software bugs are inevitable, glitches always possible. But never with mine. If I could have expected the unexpected, it would have been perfectly and flawlesslesly reliable. But what I did was merely expecting the absurd which approximated expecting the unexpected so closely that no defect in any of my programs was ever found. Very helpful in processing and displaying radar and telemetry information in real-time for VAFB.

[@NaneuxPeeBrane]

I enjoyed this lecture.

[@CarterColeisInfamous]

1:26:19 "closed form"?

[@akhil999in]

basic thing is ability of abstract thinking. language and mathematics are logical consequences of abstract thinking.

[@jinmuluo1684]

I have found that someone good at mathmatics also speak very quickly, Both Dr Devlin and Dr Tao.

[@cynthiakraft9268]

He's teaching how math alright getting us To count how many times he said the$ word book but break it down to how many times he talked about his n how many times he talked about the other people

[@akhil999in]

abstract thinking associates properties ( or attributes ) to objects.

[@Misiok89]

2:00 stone age brain doing maths... it would be interesting to really try to see understanding of math in apes, delphins, crows and octopus to determine how far a non-mathematical creature is able to understand math. How to teach them and to check theirs limits. Probably by rewards... Would it be simmilar to teach child with disability? When i was teaching student (elementary school) with disability it was hard for me to make them curious. It was for me some kind of barier. They was not interested in most things that i was trying to do with them. Understanding causality is not impossible for annimals. Basic understanding logic exist even for dogs. They expect. It means that they do some logical "calculations". We just get from them very poor feedback. We are weak in understanding if they fully understand us. I had this problem many times while teaching at school... They was looking so smart, but they do not get the essence of the problem.

[@ochiorbus]

I think it's natural to do that by rewards. We learned to count by using candies: the teacher added 2 candies with 3 candies and that gave 5 candies and it counted all 5 of them. So, the brain understands that is is useful for him to learn to count. I think that happened also in our evolution. If I remember correctly there are animals that know to do basic math operations, like ravens/crows.

[@Misiok89]

@@ochiorbus We do not know how far reach potential math understending among animals. We do not know how to teach animals and how to get feedback. We do not know how to get proper feedback from kids. Animals cannot ask us. It is hard for them to ask. It is hard to be curios when you do not understand basics. It is easy to get discouraged and stop to trying. I saw that in school how kids get blockade. It is easy to generalize and expect such a reaction from animals

[@TeaParty1776]

Animals know individual things as individual things. Man knows individuals as units and compares units to a standard. Animals associate, not count, maybe 3-7 individuals. Man, w/units, has no limit to the individuals he can count. Infinity is a repeatable math sequence, a method of organizing units of concretes, not a real thing. Intro. To Objectivist Epistemology-Ayn Rand Leap Of Logic-David Harriman; science as the conceptual induction of units of concretes. Math Is About the World-Robert Knapp Several philosophy of math lectures-Pat Corvini ,Ayn Rand Institute/eStore/Science

[@Misiok89]

@@TeaParty1776 I didn't think to look at sets as a foundation of arithmetic unique to humans. Does the dog generalize dry food in the bowl? Can he see and understand the quantity? is it a collection for him? I caught myself that it is hard to me to imagine quantity of a 1000 i know that 100000 is close to numer of seconds in a day... But this number is just abstract for my imagination. I know procedure, but after some quantity there is only understanding of procedure. It is like doing calculus without getting intuition and understanding - for some it is just procedure that you forget few years after graduation.

[@TeaParty1776]

@@Misiok89 ?

[@davedillon1372]

It was necessary to stop the fighting over the abacus

[@riglisdimitri]

How about All where given by Other entities, Mr. Professor?

[@helicalactual]

What about the doroShango bone that was found in the Congo 60,000 years ago

[@ensign_poo]

Just like how I can learn about Maths by utilizing different platforms such as university students, the internet, and discourse with those who are more knowledgeable than I, perhaps you might try rock-climbing in order to have a picnic with a lover, or maybe even go paint-balling with friends. That way, you get your physical exercise without setting foot in a gym. In other words, there are many different ways to achieve our individual goals.

[@sharonjuniorchess]

What is a number? If we don't define our terms then we end up mixing meanings. There are different types of numbers and number systems.

[@theforbiddenman4823]

I STILL GOT A STONE AGE BRAIN - LOVE HATE WITH MATH`S - I JUST WISH I HAD A TEACHER LIKE THIS -

[@cinder544]

so, how did it begin? (can you tell it in less than 4x3 seconds?)

[@tobsvonmittelstraum2300]

You are right, they will only develop differing logic and math if they are fed differing information. Given that chimps may have a different kind of conciousness, it is very possible that they are fed unattainble knowledge; especially in the paradigm of idealism and relativism amongst. A chimp could experience everything as part of giant whole, without any boundary between you and I. This would make the terms "I" and "you" nonsensical, and plausibly undermine the law of identity.

[@Zackindy0846]

at 12 noon traveling +60 miles per hour is 60 miles = 1 hour of driving in one direction (right); 2 hours in the future is +2, At 2 pm you will be 120 miles to the right of the starting point. Answer +2(+60) = 60 + 60 = 120 miles -60 miles per hour is 60 miles = 1 hour driving in other direction (left). -2 hours is two hours in the past. At 12 noon you are asking about where you were at 10 am. Answer -2(-60) = +120 miles to the right from your current location.