"As with many mathematicians, literal numbers are not my strong suit" As an engineering undergrad who has trouble doing single digit multiplication without a calculator, I feel so seen
@@Vihart I once had an A-level (US roughly 'AP') mathematics practice exam handed back to me by my teacher, completely ungraded, with the instruction to find my mistake on page one. ... The question was a to expand the first three terms of a binomial expansion, and I solved for the x^0, x^1, and x^3 terms... Thus successfully failing at counting to two.
@@marsdeatcurrently doing as levels as a first year maths student and the amount of times I just blanky stare into space trying to do single digit multiplication or multiplying 2 and 3 instead of adding is embarrassing
I sometimes think of this kind of puzzle as a "what's in my pocket" problem, after the scene in The Hobbit where Bilbo accidentally stumps Gollum with the riddle "What have I got in my pocket?" Like you said, there's an infinite family of solutions to any next-in-the-sequence question even when presented more formally, so only the asker can possibly know the "real" answer with certainty. This can feel unfair or unsatisfying even when the answer is eventually revealed, so it's no wonder that a lack of a clear solution agitates people who have gotten themselves invested in solving it. It seems that a lot of mathy people recognize "what's in my pocket" problems and dislike them. On the other hand, basically all traditional riddles are "what's in my pocket" problems at heart -- the whole point is to communicate with the person posing the riddle and try to decipher how their brain works, usually through some cute wordplay-filled clues they've given you. Obviously a lot of people like these riddles! They show up so much in culture and myth. The problem, I think, is that this kind of riddle has different expectations around it than a math riddle. With math riddles, you can pose them Martin Gardner-style where you find a fun problem, publish it with all ambiguity stripped out, and then let people chew on it for a month because once they have the answer they can usually verify it themselves. With traditional riddles, the asker and solver need to be in active dialogue so that the solver can be told when they have the right answer. This puzzle in the video has numbers and symbols in it, so people expect a math riddle, but really it's a traditional riddle that's been chopped in half.
To put it more concisely. Imagine if the post "What has four legs in the morning, two legs in the afternoon, and three legs in the evening?" went viral. (Also imagine that literally every person on the planet doesn't know this one already.) I don't think you'd get people arguing that they know The One True Answer -- you only know you have The One True Answer if you tell it to the sphinx and she doesn't devour you. The social contract is just different around riddles like that.
Your explanation enabled me to understand this situation and I genuinely feel much better for that. So from someone you'll never meet, thank you for bringing me a little peace.
I forgot how much I adore your "start with teaching math, end with a gentle reminder that human beings are flawed but we always have the capacity to learn and be kind" style of videos. Also, as someone with anxiety specifically formed around the idea that I'm never logical/objective enough to be taken seriously, this is very comforting. Genuinely, thank you.
This channel installed a love of both math and visual art for me years ago, and it has drastically influenced my path in life. I always liked art but I felt terrible at it. When I started doodling with formulas inspired by your videos, I felt like I was starting to succeed. Now I’m an illustration and Animation major, and my first inspiring art teacher was a mathematician. It’s a deeply pleasant surprise to see another video from this channel:)
I can't believe I've been watching your videos for an entire decade, all the way from middle school through grad school, and you're still making content that I love and feels amazingly, amazingly important. Danke for tieing in that important lesson in the end, your videos are and always will be awesome
I love your videos. My dad showed me your spirals video almost 11 years ago and it blew my mind as a kid. I just showed it to my math class earlier today because I was teaching them about patterns. It had the same effect on them as it had on me. Thank you for having such a profound impact!
It has been almost 11 years, hasn't it? I wonder what percentage of people who weren't mathematicians before watching Vihart actually studied the stuff afterwards at some point.
The "Someone did this to us!! And you can't death of the author this math test at me!!" line reminds me why I blame my fluid dynamics phd on this channel... about a decade ago during undergrad a friend showed me a "imagine me and you're in math class" video about doodling. Thereafter 2 things happened: 1) I went from "hating math" to "liking math", and 2) all of my notebooks since have been covered in doodles. Seriously, I go through my NASA supplied notebooks at about 1.2x normal pace due to the doodling. It's actually a problem... the liking math part is nice though.
God, Vi, you continue to be one of the most important and original voices on RUclips. Thank you for this video. I can already see it going alongside "Twelve Threads" and "Suspend Your Disbelief" as one of my favorite video essays on online culture and politics. What you were talking about at the end there reminded me of the "irrationality of rationality," which is a concept I've been thinking about a lot lately since learning about it in another video about climate change. Like you said, our culture places a lot of importance on rationality (often in the guise of mathematic and scientific "truth") but the actual truth is that life is not a logic puzzle. The world is not a logic puzzle. And if we start to approach it like it is -- by, for example, over-relying on important-sounding statistics like GDP as an analog for happiness and societal progress -- we're going to make decisions that value this "rationality" (which, at the end of the day, is often just a cover for ideology and power) over the lived experience of actual human beings.
Why do you say that life/the world isn't a logic puzzle? I think that it is since fulfilling your desires is helped by knowing how your actions will shape the world, and predicting the future like that seems like an enormously complicated logic puzzle.
Well logic means it should work and be according to some rule. On the other side it should be esthetic , beautiful, tasty a bit random here and there, in one words it should be pleasing too. Now even art is following some six rules. So it is a logic puzzle, it is a bit more too with the addition of human creativity. I am sorry for my weak English, but I hope you got what I wanted to say.
@@TheLastScoot Well logic means it should work and be according to some rule. On the other side it should be esthetic , beautiful, tasty a bit random here and there, in one words it should be pleasing too. Now even art is following some six rules. So it is a logic puzzle, it is a bit more too with the addition of human creativity. I am sorry for my weak English, but I hope you got what I wanted to say.
I think that that kind of rationality is misnamed, though. May it be called something like “logicality” to reflect an already usable relationship between “deep” and “deepity”. True rationality doesn’t concern itself with following a strict set of a priori rules, it concerns itself with consistently keeping your beliefs in check with reality and consistently achieving your goals given the hand you’re dealt-what Eliezer Yudkowsky metaphorically (but also pretty truthfully bluntly) called “winning”. But yeah, this is not a popular kind of understanding of what “rationality” means. But this is IMO the spirit of what people wanted for it to be, they just were wronger than we can be currently. I wish the world at large would get fixed about what it actually means. But that’s hard to do… 😞
I watched this video while very tired so I know I missed a lot of what you were saying by the end, but I just wanted to say I really like the number whatever-it-was at the end. Doing something very simple (writing down all the integers up to a certain point following a simple pattern of going from the top of the page to the bottom with no separation between the numbers) and then later finding other patterns in it is just so cool, and also my brain started finding the patterns partway through, picking up on the lines created when there are a lot of 1s next to each other. Also pretty colors lol
The "bad number place" makes me imagine Ted Danson welcoming a number to the "good number place"; the idea of a number sitting in that office going "Fork fork fork, I'm totally irrational I shouldn't be here." is just gold.
Hey Vi, I started watching ur content when I was somewhere in middle school and watching you go from math nerd to professional researcher was really inspiring. I’m starting my first year of graduate school in physics and I think not a small part of that was from ur love of math. Nice to see you post again!
love how i always come to vi hart's channel hoping to spark the part of my brain that loves maths but doesn't understand it, and end up lost in the sauce of profundity about the universe and how we culturally attempt to interact with existence
I'm so glad you explained the 18 answer well enough for me to understand. I also ended up with a sequence of subtracting 18, 16, 14, 12... which I'm sure is somehow related to the same x(x+1) equation as it gives the same answer. It never occurred to me to use anything but "normal" math, and so yes, we do clearly get very stuck in our ways and beliefs.
There's a way to get the sequence via modulo but it definitely missed the point of the video, it was fun doing though! f(X) = floor((x+2)/5)2+x+1 g(X) = f(x) * f(x+1) f(0) = 1, g(0) = 1 * 2 f(1) = 2, g(1) = 2 * 3 f(2) = 3, g(2) = 3 * 6 f(3) = 6, g(3) = 6 * 7 f(4) = 7
i think you've put onto words exactly why these sorts of "math quiz" memes upset me so much because after the last one of these i saw get big, i quickly concluded that the person who made it did every single bit of it on purpose, as an act of sadism against people who will hurt from seeing droves of internet strangers confidently declare their (often inexperienced) assumptions to be the sole and superior objective truth but you've also tied the subject back to something much more broad, and made a much better analysis than my own frustrations ever did
It's been a while since I watched one of Vihart's videos. RUclips recommended this video, and at first I rolled my eyes at the clickbaity title. Then I saw Vihart made it, and decided to watch it, because her videos always give a great glimpse inside her brain, and I love hearing her describe her thought processes with things like this. You have such a cool mind Vihart and I love getting a little window into it! I answered 18, for the record, and you nailed down my exact reasoning.
Just wanted to say: seeing that this was a Vihart video specifically, I felt particularly obligated to 1) participate in trying to solve the puzzle, 2) watch for tricky stuff, and 3) question everything I was seeing. "Do these = signs mean what I think they mean? For that matter, what about these shapes that I think are arabic numerals?" You have a way of engaging my mind in a way others do not. Thought you might like to know that.
You are awesome! I started watching your videos on a khan academy app i had some years back, and you helped me like math :) ty so much for your content.
best part of a "math" "problem" puzzle... is getting to understand how that other person found a solution that is different to yours... once u see a pattern or a solution and it validates all lines... your brain locks... and no matter how hard u try... its impossible to see any other pattern or solution :D we should really allow others to have an opinion and listen to it with our ears and hearts open. to me thats the only way to evolve... different perspectives are always needed... be brave and speak up your mind... it could spark a new solution to someone else best case (: have a nice day everyone. 333 thanks to Vi for warming my existence with her always super curious triangles and getting me inspired to the maximum
That is a bit silly. Your first step should be, is this under-determined, determined or over-determined. Once you realize it is under-determined you can find a few good answers.
Only missed opportunity here was to have a functional programmer jump in and argue that the other programming approach isn't good programming or whatever
I’m saving this video in my “hope worldwide” playlist- usually reserved for music that inspires hope. But Vi, by the end of this video- ❤❤❤i just was in awe with what you did here. Love this and thank you ❤❤❤❤- rock
When I was a kid and SNL still had Pat sketches my mom explained that there was no right answer and that was the point. It was my first taste of "if dumb people can argue about this, I'm wasting my time." Game recognize game. Fantastic video. Please make more. They don't always have to be this good.
Thats such an interesting take on the morality of thinking you know something. I was just talking about something similar the other day and it always leads back to: how is it better to be right or wrong? What morality does it include? I will definitely think about this more, thanks for the great video!
It's a brain thing, we feel good when we're right and bad when we're wrong, our brain does that automatically. Fun part is that the brain doesn't actually care if it's right or wrong, just if we believe it to be right or wrong, so ambiguous questions don't have the same effect. With something arbitrary, like what political side is the best, right or left, both answers can make you feel either good or bad depending on what you believe. You can take this to much more extremes too, if you can convince your identity structure that murder is the right thing to do then you can feel good from murder. Your entire mind, your identity, your world view, it's all like this, completely arbitrary. Because at the end of the day morality is not a real thing, it's something we've made up from an assumption that our life, human life, or life in general, has inherit meaning or value, something we have zero evidence for. Ultimately good and evil, right or wrong, this all comes from the simple experience of an animal feeling either pain or pleasure. Pain and pleasure comes from two separate parts of the brain, and these parts are what is activated when we're either right or wrong. So our brain responds to being wrong in the exact same way it responds to being punched, and to being right the same way it would respond to being kissed. This is all because our experience of pain and pleasure comes from adding vs substracting. When something is added to us, be it food, oxygen, affection, admiration, or an idea/belief, it feels good. When something is substracted from us we experience pain. If oxygen or food is substracted, pain. If affection is substracted, pain. If a body part or person is substracted, pain. If an idea that we had made part of our identity, personally or culturally, is substracted, pain. So any opinion that goes directly counter to our own is treated by the brain as an attack, something being substracted from what we consider self, and it will tell us we're in danger activating the fight or flight response. When this happens on a large scale, an entire culture telling another culture they're wrong, then we get wars. On a smaller scale we get divorces and people arguing on the internet. tldr: humans are stupid animals.
@@daniel4647 Genuine thanks, I learned a lot. Although I disagree with the TL;DR; for all we know, humans are the smartest animal there is. At least for now that is.
I don't care much about being right or wrong. But when I construct a proof for a system of equations and get something like 3*2 = 6 and then 6/3 = 2 I can check it, and I know the formalism that allows for the arithmetic to work, and I know that there's a real proof of why 1+1=2, So I know the proof is valid. Its self consistent and I feel so good about being "right". Do I care about morality or about my endorphins ? Perhaps my brain works like that, rational thinking give me endorphins, moral thinking doesn't.
@@daniel4647 " if you can convince your identity structure that murder is the right thing to do " I pretty much convinced myself that it is if it poses a threat against my existence. People fear AI because of that, well, isn't basically any human using that reasoning ? Which is why you don't make threats to others. I certainly don't do that. Diplomacy wins and we get a peaceful society as a result (of literal MAD). But I do know that some people will reason that violence is wrong even if someone threats your existence, they somehow convinced themselves that they can forgive their own killer, good for them, but I bet most people would protect their own existence because that's a natural thing to do. This is a strange form of reasoning, I can't clearly get into it, is it altruism ? is that how it works ? forgiving the other's misdoing, It give me some bad feelings. Perhaps because I know game theory, the world isn't a zero sum game.
ive been watching this channel since I was in primary school when I was like 7 years old or something. and it still makes me feel interested in maths when school tries hard to make that impossible. thank you, vi!!
I recognised your channel name from the beautiful toothpaste video all those years ago. I forget the details (it's 2am) but your art is so genuine - it sticks with you
I started watching this channel in 4th grade and now im graduating high school and still so engaged and getting so much out of every video. You make math so accessible and are probably one of the big reasons im pursuing math in college. I love how at its core, you always teach the wonder of math and the excitement that can be found in the universe, and you do you with such fluidity and talent that anyone watching will take away valuable information.
I like how the title implies only 8 people will understand this. I'm guessing that was intentional clickbait to circle back to the conclusion of this video, which was amazing. Wonderful job
Lol, I got 12 via x(x+1), assumed there were other simple functions that fit and tried to think of another, then got x^2+x for a split second before realizing it was the same function written a different way. So it cracked me up when you got to that part and I was just like, wellp, guess I'm predictable.
there are infinitely many polynomials that pass through those points, here are a few: x4−30x3+336x2−1649x+3024, 3 = 372 x6−30x5+336x4−1680x3+3360x2−1649x+3024, 3 = 3612 x7−30x6+335x5−1651x4+3054x3−334x2+1651x−3024, 3 = 9372 −x5+29x4−305x3+1316x2−1373x−3024, 3 = -1428 x6−29x5+304x4−1285x3+1040x2+4675x−3024, 3 = 3972 x7−34x6+449x5-2804.5x4+7449x3-352.5x2−27218x+16632, 3 = -7728 so yeah pretty much anything could be the answer lol
@@pinguino55h40 When there is an infinite family of solutions to 'best fit' data to a function, it is customary (in the fields of mathematics that work with such things), to ask if there is a *simplest* function that does so, by some definition. In this case, there are no order 0 or 1 polynomials that fit the data, and the (y = x^2 + x) function is the only order-2 polynomial that fits the data. So as the unique lowest-order solution, it gives us our 'answer', in the interpretation that there is such a thing as 'the answer' at all in a meaningful way. Since there are four data points, we know that the 'best fit' function should not have degree higher than 3; there will be an infinite family of degree 4 or higher functions that produce the given pairs, and that isn't useful. So our task is to see if there exists a unique function of degree three or lower that 'best fits' the data. That process spits out (y = x^2 + x) in this case. But of course, that is the 'it is customary in these fields' thing again - when coming from a particular direction, one carries with them all manner of conventions, methods, and perspectives that might or might not be relevant, depending on how a question is structured, which is ultimately the point. :)
@@pinguino55h40 Another comment pointed out we could use the polynomial f(x) = -(x^4)/360 + (x^3)/12 + 5(x^2)/72 + 67x/12 - 42/5 and we would get f(3) = 11. I’m waiting for the inevitable polynomials where someone finds f(3) to produce 90, 42, and 69 as possible answers. :-)
@@HeavyMetalMouse yeah I see that, however I guess what I was trying to illustrate is that these questions are so ambiguous because we don't have the full context, we don't know what the author meant. If this question was made by some drunk guy at the bar who does not have a degree in maths I doubt he would consider the 'best fit' standard definition you gave. But if this was made by some mathematician that studies this field then he is familiar with the conventions and he would probably mean that. Ultimately, for the general public we are left with a question with multiple valid answers since we don't know the full details of the problem. Even with not so complicated and specialized reasonings (such as those illustrated in the video) we get different answers such as 12 and 18, which is troubling. And even if we limit ourselves to our 'math brain' or 'programming brain', or any perspective we could look at it, there are still many more nuances within these fields than the question itself communicates, such as the fact that infinitely many polynomials pass through those points, or functions for that matter. The question itself also fails to teach those nuances which is why I think it is a poor attempt at teaching maths if this question is just thrown out there in a 10 second short or tiktok that just says 'guess the correct answers guysss!' and does not elaborate further. Instead we should explore all the possibilities to teach that in maths there is always more than meets the eye in the beginning and that is one of the reasons why maths is very rigorous and specific.
I definitely read it as a function-I remember similar “logic” puzzles in school. I think 12 was supposed to be the intention, but the execution was bad. Pretty much any “math problem” that has gone viral in some way has been this way.
i love how many comments there are on here saying that you helped them like math in middle school. me too. this is such a wonderful channel. thank you for addressing this meta controversy and talking about the cultural values behind it-you continue to help challenge my assumptions, whether it was that math was boring or that logic is that the end all be all to knowledge.
I never saw the connection between valuing logic and not-listening-to-others so clearly and broadly pointed out. Very useful concept. Thanks. And how you got to it through engagement with this problem is delightful. Again, thanks.
I think the point is actually mistaken though, at least the way it was presented here. Putting reason and rationality above all else is not a choice. It is the foundation of anything else you do and how you set your other priorities. You can choose to lie to someone to be kind instead of telling them the truth, but that requires you to use reason to decide that that is the "right" choice under your system of ethics, regardless of what your system of ethics is. This "problem" a good example of how reasonable people can disagree when working with different assumptions and that real life is under-determined and there is no "right" answer. However, regardless of the approach you use, you have to be using logic and reason to reach your conclusion, and you need logic and reason to be able to explain to yourself and to others what assumptions you are making. If you said you were using programming logic or you were using pure maths logic and you got the answer of 3-4i, then you made a mistake in applying your system. You are objectively wrong about the conclusion you made because the conclusion you reached based on your stated assumptions and methods was not consistent with the answer you came up with. The only way you can check if your conclusion is correct based on your methods and assumptions is reason and logic. That kind of mistake would usually be caused by something that in programming would be detected by a unit test. It is important to stress test your assumptions and methods to make sure that your conclusions that you expect match what you actually would like them to be. This is similar to a functional test in programming. You don't want your ethical system to tell you that the answer to the trolley problem is to run over one person and then back up and run over the five people on the other track, as an extreme example. But to do that you need reason and logic. Proof by contradiction is also another example of where reason and logic have to be placed on the first step of any attempt at ethics. If you are evaluating an ethical framework, when you reach a state of contradiction, you know that modifications must be made either to the assumptions or to the methods.
@@HesderOlehexactly my friend. Vihart's rant is not directed against people who value logic or rationality above other people's opinions, it is directed against people who value their own opinions above everyone else's and then say it is the only logical option. In fact, that kind of person is failing rationality 101, which is to always be acutely aware of the limitations of your own mind. I'm a little sad Vihart conflates the too, though.
Worth mentioning that the "this isn't written formally" thing can work both ways. A missing ellipsis wouldn't necessarily mean that you can't repeat the pattern until you reach 3. For a question trying to rely on the reader to fill in the gaps, it's not surprising that someone would see a gap there to fill even if treating this as a sequence.
@@gaymerjerry THANK YOU! I heard the 18 explanation and all I can think is "where is the 10 then?" If the sequence matters at the end it matters at the start!
@@Mr.HowardEatsPants What do you mean where is the 10? 3x10=30-(3x4)=18, the 10 is still there. That's how my brain did it anyway and I got both 18 and 12 depending on if I filled in the empty spots between 6 and 3 or not. Filling in the missing numbers in the sequence would just change it to 3x10=30-(3x6)=12, still has the 10. 9x10=90-(9x0)=90 8x10=80-(8x1)=72 7x10=70-(7x2)=56 6x10=60-(6x3)=42
@@daniel4647 interesting! There are multiple ways of arriving at the answers! 10*9=90 9*8=72 8*7=56 7*6=42 6*3=18 Where the 10 kinda comes out of nowhere Personally, my first solution was that the pattern was x=x(x+1) Which gives 3=3x4 or 3=12 Really interesting that using the form n=(n*10)-(i*n) also gives the answer of 18 (with i starting at 0 and increasing)
Happy to see a new video from you. I programmed for 33 years, and because we start with 9=90, it seems to me that it can't be a number *the previous number in the list, because there is no number previous to 9. I would not assume some additional variable that starts with any specific value. But that is just me. Of course, as a programmer, I also note that there is nothing here that actually says that the same process is applied to all the numbers
Despite programming for so long, you seem to have forgotten that recurrence relations like this will be programmed with a base case, which basically follows from the inductions proofs used to mathematically prove them. Not sure how you can forget something like that after 33 years. Whether you go recursively or top-down, it does not matter that there isn’t something before the 9.
@@DrakeSingularity I would never assume this function is recursive. There’s nothing that indicates it as such, so I would first try to find a solution that is a pure function, and n*(n+1) fits
@@DrakeSingularity recursion is bad in basically every way except for making the programmer look clever, it would not be my first assumption for any algorithm used outside of education.
@@teslatrooper I’m saying this is a recurrence relation. It does not have to be implemented with recursion but that is the simplest way to do so. Memoization is generally better
@@DrakeSingularity "you seem to have forgotten... Not sure how you can forget something like that after 33 years." Your post is needlessly rude. After watching a video about the pitfalls of using logic to feel superior, you chose to add additional context to a comment while casting doubt on the commenter's memory. Rude for no reason.
vihart was one of the first English channels i started watching back when I made this account. I've always since then enjoyed your content and can say, math has become more likeable thanks to you
i ran the algorithm solution and got 12 lol. i saw it as a running loop that was decreasing a value by a constantly changing amount, and i figured out what the 3rd to last step would be for 3=?. that kind of algorithmic movement and pattern matching in data is my bread and butter so that's where i went, but even after getting that answer, i followed it up with "i have little confidence this is the only solution or even best solution". i call that the engineer's solution haha
I hadn’t thought of logic puzzles like that before. I tend to think of them not as a way to boost your ego and prove you’re right, but instead in a “puzzles are a fun way to challenge yourself, test your skills, and learn new things” kind of way. But there are so many different ways to look at them and I think people enjoy them for a huge variety of reasons. Another one some might have is “life has so many factors out of your control. Here’s something concrete” kind of way. I definitely am a 12 kind of thinker, but having you explain the 18 answer was really eye opening! I hadn’t even considered the possibility of not filling in the blanks of the missing numbers! Thinking about all of the possible answers out there waiting to be explained reminds me of the triangle problem where you name how many triangles there are. You have to twist your brain to see not just the ones that are obvious to you, but also look with a different perspective to see the ones that are hiding from you.
I didnt expect how this ended but man I loved it! You put things that only exist as thoughts in my head so eloquently & in ways I only wish I could have escape my mind
Thank you. I get told off by my brother quite a bit for looking up information just to 'prove I'm right' and to 'make him feel stupid'. And I've thought a lot recently about when it matters who's right or wrong. Usually I'm not purposefully trying to make someone else feel bad for not knowing something, but being accurate in what you say is important to me, especially when someone tells me that I'm the person who has things turned around, and just... I guess I do lose sight of whether it matters or not who is right in my effort to be seen as someone who isn't stupid. Thank you for the reminder.
On the other hand, it is not an objectively bad thing to want to be accurate and meaningful in your communication. We don't need to abandon this instinct necessarily - we simply need to find a better way to frame it socially when presenting it. When a friend is supporting their position with bad information, even if their position is right or good, it can be a good thing to correct that bad information, so that they can use better, good information, to support their position - but if we present it as "You are wrong about this." then that won't come through and we'll just look like the arse again. :/ Presentation and context are important in delivering information, which is also easy to forget. - Sincerely, someone who also has a lot of problems with this stuff.
@@HeavyMetalMouse I think part of the problem is that we place ourselves in the position of being the arbiter of what information is "good" or "bad" rather than just validating a person's experience.
You always manage to put concepts into words that I can’t reach on my own. And if I can’t reach those words on my own, inside my own head, then I’ve just gained something quite valuable by listening to your point of view, thus reinforcing the main themes in this video. Thanks, Vi. I’m always glad to hear from you.
I love your content. I've been watching it for two years now and I'm seriously considering taking maths A-Level partially because of how interesting it is to me to see how your brain works a you figure out problems.
Your aside about "All Lives Matter" just about gave me whiplash. I've had very similar thoughts on the topic and it's nice to hear that I'm not alone there. Your point is wonderfully succinct.
I'm both amazed and slightly upset every time i find out i can absolutely do the pattern recognition and problem solving part of math, so some areas are randomly easy. But the way these things are taught in formal education are completely inaccessible to me. The second half of the video was incredible. Points like these make me think maybe academics from many centuries ago were right, and dividing sciences among each other and splitting off humanities was a mistake in some ways. In another life, I think you might have enjoyed studying linguistics, specifically pragmatics and discourse linguistics. That field seems scientific and sensible at first, putting clear definitions and labels on all the unspoken parts of how we communicate with language. And in the pursuit of accuracy, of definitions and regularities to record just how people manage to make meaning when there are infinite variables and subtext, linguists do such a good job of abstracting the concept of "language" and how meaning is made... into absolute meaninglessness.
I was thinking to myself a few days ago, that we never see well structured videos from the greats of the early days of RUclips, such as those made by Vi Hart, Vsauce, and all those, who over the years, faded away from their viral existence years ago, but remembered for their part in making the platform suvh a fun place to visit. Then, bam out of nowhere, Vi like she read my mind, puts up a new video. My favorite Vi Hart submission I can't say for certain, because choosing one downplays so many more, all of which were great fun to soak into ones mind. There are literally so darn many good ones, from the story of Mr ug on the mobius strip world, to tau day., and so many more, told in a manner that made the viewer no only be entertained but made to think and remember the content as well, and hopefully a decade further into the future we can look back and remember this submission as well as those created long ago. We missed you Vi, so don't be such a stranger in the future and make our days just a little less mundane. Peace.
It does sometimes go the other way too. Veritasium's channel has exploded in the past few years, and now he makes much longer documentary style videos. I always like to imagine the trade off as, in the place of Vsauce we have Veritasium now. Which honestly I'm completely ok with
@@NonTwinBrothers veritasium's videos are so long because he intentionally makes them very long by filling them with either obvious stuff or stuff that you would research faster on your own by simply using the internet.
I used to watch your videos "religiously" when I was working 12000kms away from home years ago. I was pleasantly surprised to see you back from hiatus. Whether that is a once off for another decade or not; thank you for this!
Than I am one of those 8. At least it think I understood it. By the way I am not from Argentina. I did like the presentation, but I wasn't expecting her to be so philosophical.
I will never get sick of watching "You thought you came here to ponder math and/or logic, but let's talk about YOU" Vihart videos. Or any Vihart videos, they're all fun to echo around in my brain, and to think about thinking.
I was hoping the number of zeroes in the title would come out to 0.00000001%, since that way it implies that only the person who initially created the "math test" would understand the true meaning.
It might be intentional. At first sight it might seem like it is representing only one person, but 0.000000001% of people is actually roughly 0.08 people (since 1% of people is roughly 80 million people), which also loops back to the way "math tests" are usually made: there's an obvious but incorrect answer, then the more complicated but maybe correct answer, sometimes the layers go even deeper, like that one test with the burgers, the fries and the cups. Also that addictive, little ego boost it gives you.
Turns out that watching you paint those numbers while simultaneously listening to what you had to say was way more difficult than what I would have expected it to be. Also, it seems to me that it's more of a logical puzzle than a math puzzle.
Valueing a person as a human being does not mean believing everything they say. Like imagine you had a close friend who was a flat earther. You care for them. You have parties together. You help them out. But any time they start talking about the shape of the earth, you politely tell them that you aren't interested in that particular discussion.
I didn't go into this in the video, but your flat earther is a good hypothetical to make this distinction: generally my position is that while of course you don't have to believe what someone else believes, it's usually best to assume that something they tell you about their own experience and own life is true. Like, if you party with your male flat earther friend, and the next day they tell you that they got jumped on their walk home from the club later that night, it would be weird not to believe them. "Believe women" is a slogan that acknowledges how commonly women experience that if they talk about their assault, people feel justified in not believing them or defaulting to suspicion until proven otherwise. Many women do not get care, or help, or invited to parties anymore, by the people in their lives that take the side of their abuser. I guess I could've put all this into the video and made it even longer, but probably more on theme to have 2-way communication in the comments, so thanks for writing in.
my personal answer when I saw this was pretty much "n" because I really struggle with ambiguous problems like this, especially where i knew the format was incorrect and there felt like not enough information and 0 actual instructions, so I personally could not fathom the pattern and the smug way someone asked me made me so incurious about the answer that I just said "the only winning move is not to play". I love that there are multiple answers and I feel so vindicated in being averse to the problem as presented because it definitely smelt to me like a disingenuous Math Problem constructed for the sake of getting people to argue about it. math and science arent binary disciplines- they're a method to describe our reality. there is very rarely 1 answer to any problem- and your work helps me stay curious about the math part, which has always been a source of huge insecurity for me as someone with hella ADHD and dyslexia.
Your approach is absolutely right. The first step in these types of problems, is checking for if it under-determined, over-determined or under-determined. Once you realize it is under-determined then you can take the path you took. I have ADHD and ASD, and this "problem" reminds me of the worst type of multiple choice questions that I have found to be more common in Australia than the USA or UK. It is the "choose the most correct answer", how am I supposed to enter your mind and decide which answer is "more correct" that another. If A and C are clearly wrong, but B and D are both true or possibly true, how am I supposed to know what the person who wrote the question thinks is "more" correct"? What I disagree with you about is that math is to describe our reality, I say that because math can also be used to describe other realities. Sometimes it turns out what we thought wasn't our reality is actually our reality, but you can also have consistent mathematics that clearly contradict anything possible in our universe. Science though I agree with your assessment. I also disagree with Vi's conclusion that logic and reason have to be ignored or set aside. Putting reason and rationality above all else is not a choice. It is the foundation of anything else you do and how you set your other priorities. You can choose to lie to someone to be kind instead of telling them the truth, but that requires you to use reason to decide that that is the "right" choice under your system of ethics, regardless of what your system of ethics is. This "problem" a good example of how reasonable people can disagree when working with different assumptions and that real life is under-determined and there is no "right" answer. However, regardless of the approach you use, you have to be using logic and reason to reach your conclusion, and you need logic and reason to be able to explain to yourself and to others what assumptions you are making. If you said you were using programming logic or you were using pure maths logic and you got the answer of 3-4i, then you made a mistake in applying your system. You are objectively wrong about the conclusion you made because the conclusion you reached based on your stated assumptions and methods was not consistent with the answer you came up with. The only way you can check if your conclusion is correct based on your methods and assumptions is reason and logic. That kind of mistake would usually be caused by something that in programming would be detected by a unit test. It is important to stress test your assumptions and methods to make sure that your conclusions that you expect match what you actually would like them to be. This is similar to a functional test in programming. You don't want your ethical system to tell you that the answer to the trolley problem is to run over one person and then back up and run over the five people on the other track, as an extreme example. But to do that you need reason and logic. Proof by contradiction is also another example of where reason and logic have to be placed on the first step of any attempt at ethics. If you are evaluating an ethical framework, when you reach a state of contradiction, you know that modifications must be made either to the assumptions or to the methods.
Actually you can just pick any real number for the answer and then construct a 4th-degree polynomial to match that answer. The polynomial will be f(x) = [(n-12)/360]*x^4 - [(n-12)/12]*x^3 + [(67n-732)/72]*x^2 - [(165n-2016)/36]*x + (42n-504)/5, where n is your desired f(3). At n=12, it indeed comes down to f(x) = x^2+x.
Moving from 'notation is subjective' to 'nothing is true' is... foolishness. Your first part is an excellent treatise on epistemology and human communication; the second is, sadly, a descent into sophistry.
Thank you. This is . . . beautiful. And probably also true. I think. (When I'm not distracted by your math and your numbers and your drawings. Gonna have to watch it again.) You make an 18 feel better and teach me compassion for self and others.
Before you explained your reasoning for 20, I actually came up with a way that it could work! Take the number above, and subtract it by 1. Take the current number, and add 1. You end up with 5 x 4, and the previous answers stay the same. This, of course, relies on an imaginary 10 above the 9, which doesn’t work because skipping 4 and 5 are crucial to getting 20 as an answer. 20 probably isn’t correct, then, but I see how someone could get it.
i have my final exams for my uni degree soon, so this was great timing to get my mathsy brain parts going! and your words at the end were great. thanks vi!
"Culture teaches people to value their own logic more than they value women as equal human beings", okay but my logic says that they do deserve equal rights.
I'm a software engineer and the only two answers I could think of were 18 and 30, 30 indicating a bug of some sort. I had no clue where you got 12 until you explained it.
I have to say I often have a hard time with this "being kind instead of right" stuff. There are some people I hold dear in my life that believe things I really cannot bring myself to believe. My instinct when I hear those ideas is to focus on facts and question what I hear. I think that's a good way to interface with questionable new ideas but my skepticism is also hurtful to my dear ones. What's the solution here?
Consider that you might have the wrong facts. I don't mean to hijack the thoughts in the video, but very often the logic people have is more or less sound. Just that they would really prefer a specific outcome to their logic, and it's possible to get by choosing facts you like. They can then just hyperfocus on their own logic and see it as perfectly sound. That's why it's important to listen to others. If yours and their experience and conclusions differ - is it really that their logic is flawed? Or perhaps your facts are wrong or chosen badly? This is especially important in situations where you can't possibly have all the facts (because you don't share the experience, for example in issues of discrimination) so as a bare minimum, you WILL have to accept their experience as a fact. They might be tricking you, but ultimately there is no other way, you can't just infer and override their experience. And that is the part that comes from being kind - being receptive to accepting these facts that can only come from the experiences of other people. And using them in your logic - rather than making up things every time you can't get a fact yourself.
@@Serutans Exactly, although I would use the word "assumptions" instead of facts. People's fundamental assumptions differ and that changes their conclusions, even if their logical deductions themselves are perfectly valid.
Often what you describe is Religion. Sure, it makes no sense to believe in gods, but if someone is not disrespectful of math and science, and they offer to pray for your sick loved one, being kind is to say thank you. What they mean is that they feel bad both for your loved one's sickness and for how it pains you. It is their way of hoping they'll make a quick recovery. Accept the offer of empathy. Gracefully ignore the superstition it is wrapped in; it matters to them. Respect that it matters to them.
My advice would be to 1) believe people about their own _experiences,_ especially their own internal experiences (e.g. "I get harassed on the street regularly" or "loud noises are painful for me") 2) without being rude to people in the moment, independently verify the _facts_ they present you that aren't about their own experiences (e.g. if they tell you "democracies have fewer wars than autocracies", you don't have to contradict them in the moment, but you don't have to believe it without looking it up for yourself) 3) question the _narratives_ they're presenting you with, and be kind but firm about your right to make up your own mind. A concept that's helped me a lot is the idea of "mental sovereignty": you get to be in charge of what you believe, and if other people are trying to make you feel like you're a bad person in one way or another for believing that you are in charge of what goes on inside your head, it is okay to push back on that. (There are of course all sorts of ways it might be hurtful to _voice_ your beliefs in one or another particular context, but you are legitimately, really, and truly in charge of the inside of your head, and no one can or should take that away from you.) Honestly, I don't think I can really get behind the "truth vs kindness" binary ViHart is setting up here (so you can take my advice with that caveat, if you want). I used to have some beliefs that, to the extent that I acted on them, caused me to be devastatingly unkind to people. And the reason I held those beliefs was because I was in social environments where truth-seeking was actively discouraged and seen as a sign of being a bad person. Even evaluating the idea "are these beliefs based in reality, or were they made up to try to control people like me?" was seen as only something an "unfaithful" person would do. So I've come to really value the right to seek truth quite dearly, and feel that seeing truth as opposed to kindness is a great way to have less of both in your life.
@@lexk4423 Thanks for sharing. You speak wisdom. On the subject of people trying to make you feel bad for thinking for yourself; I have very slowly learnt that they are the very bad people that they're trying to make you sound like. Not beyond salvation, but they're certainly not a mind I enjoy exposing mine to.
the pattern I saw in the numbers was that the right side of numbers grew by previous growth +2. or add 2 to the growth from previous number. For example the difference between the top two numbers was 18. the difference between the number beneath and the second one was 16. than 14 and so on.
this is how i was taught about quadratic sequences, a constant increase in growth after some playing around with coefficients you can arrive at x^2 + x + 0 although the problem is given in a strange way
I agree with pretty much everything said in this video. No, I'm not gonna follow that statement up with an "except". The video didn't do where I expected it to, but where it went instead was way more important than the relatively minor gripe I thought you were going to address. My prediction, (in a video about predicting patterns), about where you're going was that you point was going to be that those math puzzles on many parts of social media are like playing thermonuclear war or tic-tac-toe in the movie WarGames (1983): The only winning move is not to play. That is, when you see one of those *intentionally* ambiguous supposed "logic puzzles" posted by a Facebook page that has nothing to do with logic or math puzzles, and the only reason you saw it in your feed is because one of your Facebook friends, (who also likely didn't care at all about whatever that page was *really* promoting), had commented with their "correct" answer, it's important to understand that the only reason that whoever posted the question to start with was to drive engagement on the post to up their page's visibility, and nothing drives engagement like people disagreeing and getting to tell others that they are wrong, or that they missed some detail. (No, *you're* a run-on sentence!) That's why we had that trend of low effort posts with those sort of kinda equation systems using clip-art images instead of letters for their variables. But where if you look *closely* you would see that some of the clip art had been subtly altered to have a different number of things, or include a clock that's pointing to a different time. Or those "Which cup will fill up first?" puzzles where the answer depended on if you thought a solid line through a 2D-representation of pipes and cups meant that the pipe was blocked or not. The only winning move is to not take the bait, ie don't make a comment. Because that's the way to stop your (and your friends') timelines to fill up with that sort of spam. Well, that and taking a moment to click "Show me less like this"/"Hide this page". Those posts have almost completely vanished from my timelines now. I'm not sure if this is because Facebook changed something to make these posts less viral, if me ranting about them (outside of those posts themselves) made my friends stop commenting on them, or if most Internet users collectively decided that we no longer cared about them. My guess would be that Facebook changed something, because the other alternatives require that several humans changed their behavior to the better, and that sadly sounds less likely. Of course, if you're following pages/channels/forums that are *about* logic, math, and/or puzzles, then cutting them some slack for having some puzzles that you personally don't find very interesting makes more sense. Especially if they somehow manage to made content that's both profound *and* entertaining out of those puzzles. But what are the odds of that?
Vi, you should do a video about the “randomness” or not of the little sheet of paper you stick behind the sheet of your notepad to keep the ink from messing up the next page. It LOOKS random but it came from your intentional writing of ink and yet it might be random because the holes in the notebook paper weren’t put there in any way that you or anyone else intended.
I don't want to be that guy who stirs up the comments section by pointing out mistakes in your video or issues with your logic... But... ......... When colouring all the 1's in at the end, you missed the second 1 of 141 and proceeded to colour it in black. And this really upset me.
ahhh I tried so hard to get them all, because I know things like that bother some people. If I could do it again, I'd do it differently, but alas---some mistakes are permanent.
holy shit this video knocked my socks off. also a longtime viewer, means a lot to see you again after some time. your video about being famous on the internet really struck me when it came out, and so did this one. i spend a lot of time thinking about social dynamics and it was incredible to go into this expecting an easygoing math puzzle explanation but getting articulations speaking directly to my heart about the whys behind the ways i see people interacting recently. thanks for your thoughtful commentaries as always, hope you're doing well.
the presentation of the problem doesnt really lead it to being something worth thinking about once you have an answer, its very low stakes and it doesnt take too long to get to 12
I was hoping you wouldn't point out the fact that there are an infinite number of functions that work so I could look all smug in the comments, but alas, you beat me to it.
Vihart... I think your escape from logic here is... not successful. Like the whole reason we know black lives matter is because black people are alive and conscious and human, things which we know *from logic,* therefore I would say, valuing "black lives more than logic" is not really possible at all because, how exactly do you make a value judgement without logical reasoning? One logical principle is the law of identity, the idea that things are themselves... In order to value black lives don't we first have to be certain that when we are valuing them that means something specific? Logic is really really fundamental to everything we do. To criticize some people as simply valuing logic over 'black lives' is not a particularly coherent statement
I'm glad that it makes logical sense to you to value black lives, no criticism there. I know I didn't go into the history of how logic and intellectualism has been used to justify things like slavery and genocide, so I wouldn't expect everyone to have the context behind my reference. There's some really dark stuff that still persists in various forms to this day.
@@Vihart I will admit... There is without doubt a point to be made here. I think certain kinds of "logic" are less "logic" and more "class-oriented dogmatism," a term I just made up to mean more or less, people saying things that sound plausible to their demographic which also *just happen* to uphold existing power structures... And so I do see it as a legitimate point to point out hey, if your "logic" is just your own assumptions which you do not even allow to be touched by your **empathy** (to me empathy should be part of any one's "logical value judgements") then yeah that is awful. And the anti-BLM people (and other reactionary conservative groups you alluded to) are definitely far more comfy with their convenient logic which just so happens to justify everything them and their demographic *wants* to believe without letting it be "soiled" by the demands of basic empathy.
My first thought was instantly thus; 9 * 10 is 90 8 * 9 is 72 7 * 8 is 56 6 * 7 is 42 And given its imformallity i too assumed each were seperate statments, and so after 5 is multipled by 6, then 4 by 5, then 3 by 4 which is 12. Still dont see that darned 18 tho
if you multiply 9 and 8 you get 72, 8 and 7 you get 56, 7 and 6 you get 42, so if you follow the logic that you multiply a number by the number on top of it, you would get 6×3 which would mean 3 =18
I knew, logically, that Vi would blow the lid off this thing, and I am delighted to announce I was completely 100% and entirely correct. I regret to announce, however, that my chair lacks arms.
You've been found out, hooligan! I'm revoking your armchair club membership. We'll be by tomorrow to seize your entry card & cast you several subtly derisive raised eyebrows.
@@kristajones7202 Yes I realize that this was the intent, but it isn’t actually true. The legibility is greatly reduced by using sharpies, especially in ratio to the size of the writing. for such small print, a pen with thinner line depth would be more legible and still show up on paper, not to mention improve the viewing experience. This would be enough of a reason, without adding the uncomfortable fact of paper bleed through, and much paper waste, add to that the experiential component of being very stinky pens. If you are going to write in sharpie, it would be more legible in a font size closer to 2”.
as an avid Stack Exchange user, my strategy to all math problems is just to say the wrong answer and wait for someone else to pop in and correct me.
the only reason im transitioning is just to make this strategy even more effective.
@@puppable using transphobia for efficiency gains is very funny
old joke, try to be more original, or should i say duplicated joke.
That is wrong! ;-)
Cunningham's law -
The best way to get an answer on the internet is not to ask, but to say the wrong answer.
"As with many mathematicians, literal numbers are not my strong suit"
As an engineering undergrad who has trouble doing single digit multiplication without a calculator, I feel so seen
Yeah, I still don't have those memorized in my consciousness. Brains are weird.
@@Vihart I once had an A-level (US roughly 'AP') mathematics practice exam handed back to me by my teacher, completely ungraded, with the instruction to find my mistake on page one.
... The question was a to expand the first three terms of a binomial expansion, and I solved for the x^0, x^1, and x^3 terms... Thus successfully failing at counting to two.
Pitagorical table my beloved
@@marsdeatcurrently doing as levels as a first year maths student and the amount of times I just blanky stare into space trying to do single digit multiplication or multiplying 2 and 3 instead of adding is embarrassing
"Your calculator history is more embarrassing than your browser history
Skeletor will return next week with more disturbing facts"
I sometimes think of this kind of puzzle as a "what's in my pocket" problem, after the scene in The Hobbit where Bilbo accidentally stumps Gollum with the riddle "What have I got in my pocket?" Like you said, there's an infinite family of solutions to any next-in-the-sequence question even when presented more formally, so only the asker can possibly know the "real" answer with certainty. This can feel unfair or unsatisfying even when the answer is eventually revealed, so it's no wonder that a lack of a clear solution agitates people who have gotten themselves invested in solving it. It seems that a lot of mathy people recognize "what's in my pocket" problems and dislike them.
On the other hand, basically all traditional riddles are "what's in my pocket" problems at heart -- the whole point is to communicate with the person posing the riddle and try to decipher how their brain works, usually through some cute wordplay-filled clues they've given you. Obviously a lot of people like these riddles! They show up so much in culture and myth. The problem, I think, is that this kind of riddle has different expectations around it than a math riddle. With math riddles, you can pose them Martin Gardner-style where you find a fun problem, publish it with all ambiguity stripped out, and then let people chew on it for a month because once they have the answer they can usually verify it themselves. With traditional riddles, the asker and solver need to be in active dialogue so that the solver can be told when they have the right answer. This puzzle in the video has numbers and symbols in it, so people expect a math riddle, but really it's a traditional riddle that's been chopped in half.
To put it more concisely. Imagine if the post "What has four legs in the morning, two legs in the afternoon, and three legs in the evening?" went viral. (Also imagine that literally every person on the planet doesn't know this one already.) I don't think you'd get people arguing that they know The One True Answer -- you only know you have The One True Answer if you tell it to the sphinx and she doesn't devour you. The social contract is just different around riddles like that.
That's a great idiom for labeling these types of questions. And a really interesting comparison to raise. Good stuff
Nasty little BAGGINSES!
People that use the word "cute" to describe something thats not "cute" at all, yea, i understand how their brain works ...
Your explanation enabled me to understand this situation and I genuinely feel much better for that. So from someone you'll never meet, thank you for bringing me a little peace.
I forgot how much I adore your "start with teaching math, end with a gentle reminder that human beings are flawed but we always have the capacity to learn and be kind" style of videos. Also, as someone with anxiety specifically formed around the idea that I'm never logical/objective enough to be taken seriously, this is very comforting. Genuinely, thank you.
This channel installed a love of both math and visual art for me years ago, and it has drastically influenced my path in life. I always liked art but I felt terrible at it. When I started doodling with formulas inspired by your videos, I felt like I was starting to succeed. Now I’m an illustration and Animation major, and my first inspiring art teacher was a mathematician.
It’s a deeply pleasant surprise to see another video from this channel:)
That is such a beautiful story, I hope you're still in a good place and doing what you love.
I can't believe I've been watching your videos for an entire decade, all the way from middle school through grad school, and you're still making content that I love and feels amazingly, amazingly important. Danke for tieing in that important lesson in the end, your videos are and always will be awesome
Likewise
Hey, me too :)
My kids actually discovered this channel! They were in elementary school and now are in high school.
@@aekelly Now how cool is that!
@@andrewbarsky4556 That's really exciting, best of luck to you!
I love your videos. My dad showed me your spirals video almost 11 years ago and it blew my mind as a kid. I just showed it to my math class earlier today because I was teaching them about patterns. It had the same effect on them as it had on me. Thank you for having such a profound impact!
I was feeling down, and your comment made me smile. Such a sweet story. :)
It has been almost 11 years, hasn't it? I wonder what percentage of people who weren't mathematicians before watching Vihart actually studied the stuff afterwards at some point.
The "Someone did this to us!! And you can't death of the author this math test at me!!" line reminds me why I blame my fluid dynamics phd on this channel... about a decade ago during undergrad a friend showed me a "imagine me and you're in math class" video about doodling. Thereafter 2 things happened: 1) I went from "hating math" to "liking math", and 2) all of my notebooks since have been covered in doodles. Seriously, I go through my NASA supplied notebooks at about 1.2x normal pace due to the doodling. It's actually a problem... the liking math part is nice though.
Awesome! As a US taxpayer I hereby approve a 1.2% increase in NASA's notebook budget to support such activities.
Ohh yeah, vihart is definitely part of the reason I’m now studying computer science
@@Vihart Wait, are you starting a new Math Test?!
1.2x normal pace = 1.2% budget increase
1.3x normal pace = ?
I imagine that NASA notebooks are just like regular notebooks but with more...space
@@Sairin13 I'm so angry that that is the perfect pun for this situation. Like, there's nothing better. How dare you. Thank you for making me laugh
God, Vi, you continue to be one of the most important and original voices on RUclips. Thank you for this video. I can already see it going alongside "Twelve Threads" and "Suspend Your Disbelief" as one of my favorite video essays on online culture and politics.
What you were talking about at the end there reminded me of the "irrationality of rationality," which is a concept I've been thinking about a lot lately since learning about it in another video about climate change. Like you said, our culture places a lot of importance on rationality (often in the guise of mathematic and scientific "truth") but the actual truth is that life is not a logic puzzle. The world is not a logic puzzle. And if we start to approach it like it is -- by, for example, over-relying on important-sounding statistics like GDP as an analog for happiness and societal progress -- we're going to make decisions that value this "rationality" (which, at the end of the day, is often just a cover for ideology and power) over the lived experience of actual human beings.
I don't think I've heard that precise phrasing before, thank you!
Why do you say that life/the world isn't a logic puzzle?
I think that it is since fulfilling your desires is helped by knowing how your actions will shape the world, and predicting the future like that seems like an enormously complicated logic puzzle.
Well logic means it should work and be according to some rule. On the other side it should be esthetic , beautiful, tasty a bit random here and there, in one words it should be pleasing too. Now even art is following some six rules. So it is a logic puzzle, it is a bit more too with the addition of human creativity. I am sorry for my weak English, but I hope you got what I wanted to say.
@@TheLastScoot Well logic means it should work and be according to some rule. On the other side it should be esthetic , beautiful, tasty a bit random here and there, in one words it should be pleasing too. Now even art is following some six rules. So it is a logic puzzle, it is a bit more too with the addition of human creativity. I am sorry for my weak English, but I hope you got what I wanted to say.
I think that that kind of rationality is misnamed, though. May it be called something like “logicality” to reflect an already usable relationship between “deep” and “deepity”.
True rationality doesn’t concern itself with following a strict set of a priori rules, it concerns itself with consistently keeping your beliefs in check with reality and consistently achieving your goals given the hand you’re dealt-what Eliezer Yudkowsky metaphorically (but also pretty truthfully bluntly) called “winning”. But yeah, this is not a popular kind of understanding of what “rationality” means. But this is IMO the spirit of what people wanted for it to be, they just were wronger than we can be currently. I wish the world at large would get fixed about what it actually means. But that’s hard to do… 😞
I watched this video while very tired so I know I missed a lot of what you were saying by the end, but I just wanted to say I really like the number whatever-it-was at the end. Doing something very simple (writing down all the integers up to a certain point following a simple pattern of going from the top of the page to the bottom with no separation between the numbers) and then later finding other patterns in it is just so cool, and also my brain started finding the patterns partway through, picking up on the lines created when there are a lot of 1s next to each other. Also pretty colors lol
Same lol. Watched this before bed and got distracted from the final commentary by fun patterns
The pattern at the end has totally done my head in. I'm still waiting for the explanation, the punch-line, ages after the video is over. Arghhhhhhhhh
The "bad number place" makes me imagine Ted Danson welcoming a number to the "good number place"; the idea of a number sitting in that office going "Fork fork fork, I'm totally irrational I shouldn't be here." is just gold.
spoiler
.
cant wait for the reveal that no number has gotten into the hood number place in centuries
2 belongs in good number space for sure.
+
I guess that makes 6 the Tahani of numbers.
Hey Vi, I started watching ur content when I was somewhere in middle school and watching you go from math nerd to professional researcher was really inspiring. I’m starting my first year of graduate school in physics and I think not a small part of that was from ur love of math. Nice to see you post again!
Good job, have fun adding to the pool of human knowledge!
love how i always come to vi hart's channel hoping to spark the part of my brain that loves maths but doesn't understand it, and end up lost in the sauce of profundity about the universe and how we culturally attempt to interact with existence
I'm so glad you explained the 18 answer well enough for me to understand. I also ended up with a sequence of subtracting 18, 16, 14, 12... which I'm sure is somehow related to the same x(x+1) equation as it gives the same answer. It never occurred to me to use anything but "normal" math, and so yes, we do clearly get very stuck in our ways and beliefs.
Yeah I got the same pattern
There's a way to get the sequence via modulo but it definitely missed the point of the video, it was fun doing though!
f(X) = floor((x+2)/5)2+x+1
g(X) = f(x) * f(x+1)
f(0) = 1, g(0) = 1 * 2
f(1) = 2, g(1) = 2 * 3
f(2) = 3, g(2) = 3 * 6
f(3) = 6, g(3) = 6 * 7
f(4) = 7
i think you've put onto words exactly why these sorts of "math quiz" memes upset me so much
because after the last one of these i saw get big, i quickly concluded that the person who made it did every single bit of it on purpose, as an act of sadism against people who will hurt from seeing droves of internet strangers confidently declare their (often inexperienced) assumptions to be the sole and superior objective truth
but you've also tied the subject back to something much more broad, and made a much better analysis than my own frustrations ever did
It's been a while since I watched one of Vihart's videos. RUclips recommended this video, and at first I rolled my eyes at the clickbaity title. Then I saw Vihart made it, and decided to watch it, because her videos always give a great glimpse inside her brain, and I love hearing her describe her thought processes with things like this. You have such a cool mind Vihart and I love getting a little window into it! I answered 18, for the record, and you nailed down my exact reasoning.
Same reaction I had. I answered 12, but I can see why some people would answer 18. Maybe everyone's answer is right?
Thank you for clicking my clickbait, and glad you enjoyed!
Wait, which reasoning? What is your answer for 2 at the end?
@@jacobcain9008 It was implied but not actually demonstrated that you can fit a polynomial to any answer, x(x +1) for 12 is just the simplest.
Just wanted to say: seeing that this was a Vihart video specifically, I felt particularly obligated to 1) participate in trying to solve the puzzle, 2) watch for tricky stuff, and 3) question everything I was seeing. "Do these = signs mean what I think they mean? For that matter, what about these shapes that I think are arabic numerals?" You have a way of engaging my mind in a way others do not. Thought you might like to know that.
Going this deep into a math question that really has no clear answer is not the content we wanted, but the content we needed.
@@TheRatsintheWalls The armchair crowd says, "Good! You *should* want what you need."
(At least) that's (one way) how you get from "is" to "ought".
@@michaelmicek That's more like armchair psychology rather than moral philosophy.
I'm sending this to my dad who got me started on Khan Academy 12 years ago. Thank you Vi, you're changing lives.
You are awesome! I started watching your videos on a khan academy app i had some years back, and you helped me like math :) ty so much for your content.
best part of a "math" "problem" puzzle... is getting to understand how that other person found a solution that is different to yours... once u see a pattern or a solution and it validates all lines... your brain locks... and no matter how hard u try... its impossible to see any other pattern or solution :D we should really allow others to have an opinion and listen to it with our ears and hearts open. to me thats the only way to evolve... different perspectives are always needed... be brave and speak up your mind... it could spark a new solution to someone else best case (:
have a nice day everyone.
333 thanks to Vi for warming my existence with her always super curious triangles and getting me inspired to the maximum
That is a bit silly. Your first step should be, is this under-determined, determined or over-determined. Once you realize it is under-determined you can find a few good answers.
I was able to hear Yanny And Laurel, but the dress has always been white and gold.
I have missed you dearly
Same
agreed
Omg same I feel like I've been waiting for them to post forever
π=•υ•
SAME🎉
Only missed opportunity here was to have a functional programmer jump in and argue that the other programming approach isn't good programming or whatever
don't worry they're on it in the comments
I’m saving this video in my “hope worldwide” playlist- usually reserved for music that inspires hope. But Vi, by the end of this video- ❤❤❤i just was in awe with what you did here. Love this and thank you ❤❤❤❤- rock
Problem: your title says that only 1/10 of a person will understand the video (out of the entire human population)
Guess we need to start making more humans
When I was a kid and SNL still had Pat sketches my mom explained that there was no right answer and that was the point. It was my first taste of "if dumb people can argue about this, I'm wasting my time." Game recognize game. Fantastic video. Please make more. They don't always have to be this good.
Thats such an interesting take on the morality of thinking you know something. I was just talking about something similar the other day and it always leads back to: how is it better to be right or wrong? What morality does it include? I will definitely think about this more, thanks for the great video!
Select your thoughts to be as accurate a reflection of the world as possible. Morality should be in how you choose to act on that information.
It's a brain thing, we feel good when we're right and bad when we're wrong, our brain does that automatically. Fun part is that the brain doesn't actually care if it's right or wrong, just if we believe it to be right or wrong, so ambiguous questions don't have the same effect. With something arbitrary, like what political side is the best, right or left, both answers can make you feel either good or bad depending on what you believe. You can take this to much more extremes too, if you can convince your identity structure that murder is the right thing to do then you can feel good from murder. Your entire mind, your identity, your world view, it's all like this, completely arbitrary. Because at the end of the day morality is not a real thing, it's something we've made up from an assumption that our life, human life, or life in general, has inherit meaning or value, something we have zero evidence for. Ultimately good and evil, right or wrong, this all comes from the simple experience of an animal feeling either pain or pleasure. Pain and pleasure comes from two separate parts of the brain, and these parts are what is activated when we're either right or wrong. So our brain responds to being wrong in the exact same way it responds to being punched, and to being right the same way it would respond to being kissed. This is all because our experience of pain and pleasure comes from adding vs substracting. When something is added to us, be it food, oxygen, affection, admiration, or an idea/belief, it feels good. When something is substracted from us we experience pain. If oxygen or food is substracted, pain. If affection is substracted, pain. If a body part or person is substracted, pain. If an idea that we had made part of our identity, personally or culturally, is substracted, pain. So any opinion that goes directly counter to our own is treated by the brain as an attack, something being substracted from what we consider self, and it will tell us we're in danger activating the fight or flight response. When this happens on a large scale, an entire culture telling another culture they're wrong, then we get wars. On a smaller scale we get divorces and people arguing on the internet.
tldr: humans are stupid animals.
@@daniel4647 Genuine thanks, I learned a lot.
Although I disagree with the TL;DR; for all we know, humans are the smartest animal there is. At least for now that is.
I don't care much about being right or wrong.
But when I construct a proof for a system of equations and get something like
3*2 = 6
and then
6/3 = 2
I can check it, and I know the formalism that allows for the arithmetic to work, and I know that there's a real proof of why 1+1=2, So I know the proof is valid.
Its self consistent and I feel so good about being "right".
Do I care about morality or about my endorphins ? Perhaps my brain works like that, rational thinking give me endorphins, moral thinking doesn't.
@@daniel4647 " if you can convince your identity structure that murder is the right thing to do "
I pretty much convinced myself that it is if it poses a threat against my existence. People fear AI because of that, well, isn't basically any human using that reasoning ?
Which is why you don't make threats to others. I certainly don't do that.
Diplomacy wins and we get a peaceful society as a result (of literal MAD).
But I do know that some people will reason that violence is wrong even if someone threats your existence, they somehow convinced themselves that they can forgive their own killer, good for them, but I bet most people would protect their own existence because that's a natural thing to do. This is a strange form of reasoning, I can't clearly get into it, is it altruism ? is that how it works ? forgiving the other's misdoing, It give me some bad feelings.
Perhaps because I know game theory, the world isn't a zero sum game.
ive been watching this channel since I was in primary school when I was like 7 years old or something. and it still makes me feel interested in maths when school tries hard to make that impossible. thank you, vi!!
I recognised your channel name from the beautiful toothpaste video all those years ago. I forget the details (it's 2am) but your art is so genuine - it sticks with you
I started watching this channel in 4th grade and now im graduating high school and still so engaged and getting so much out of every video. You make math so accessible and are probably one of the big reasons im pursuing math in college. I love how at its core, you always teach the wonder of math and the excitement that can be found in the universe, and you do you with such fluidity and talent that anyone watching will take away valuable information.
I like how the title implies only 8 people will understand this. I'm guessing that was intentional clickbait to circle back to the conclusion of this video, which was amazing. Wonderful job
haha you made me go do the math - I may have screwed up because I came up with "one in one hundred billion"
Lol, I got 12 via x(x+1), assumed there were other simple functions that fit and tried to think of another, then got x^2+x for a split second before realizing it was the same function written a different way. So it cracked me up when you got to that part and I was just like, wellp, guess I'm predictable.
me too in that order
there are infinitely many polynomials that pass through those points, here are a few:
x4−30x3+336x2−1649x+3024, 3 = 372
x6−30x5+336x4−1680x3+3360x2−1649x+3024, 3 = 3612
x7−30x6+335x5−1651x4+3054x3−334x2+1651x−3024, 3 = 9372
−x5+29x4−305x3+1316x2−1373x−3024, 3 = -1428
x6−29x5+304x4−1285x3+1040x2+4675x−3024, 3 = 3972
x7−34x6+449x5-2804.5x4+7449x3-352.5x2−27218x+16632, 3 = -7728
so yeah pretty much anything could be the answer lol
@@pinguino55h40 When there is an infinite family of solutions to 'best fit' data to a function, it is customary (in the fields of mathematics that work with such things), to ask if there is a *simplest* function that does so, by some definition. In this case, there are no order 0 or 1 polynomials that fit the data, and the (y = x^2 + x) function is the only order-2 polynomial that fits the data. So as the unique lowest-order solution, it gives us our 'answer', in the interpretation that there is such a thing as 'the answer' at all in a meaningful way.
Since there are four data points, we know that the 'best fit' function should not have degree higher than 3; there will be an infinite family of degree 4 or higher functions that produce the given pairs, and that isn't useful. So our task is to see if there exists a unique function of degree three or lower that 'best fits' the data. That process spits out (y = x^2 + x) in this case.
But of course, that is the 'it is customary in these fields' thing again - when coming from a particular direction, one carries with them all manner of conventions, methods, and perspectives that might or might not be relevant, depending on how a question is structured, which is ultimately the point. :)
@@pinguino55h40 Another comment pointed out we could use the polynomial f(x) = -(x^4)/360 + (x^3)/12 + 5(x^2)/72 + 67x/12 - 42/5 and we would get f(3) = 11.
I’m waiting for the inevitable polynomials where someone finds f(3) to produce 90, 42, and 69 as possible answers. :-)
@@HeavyMetalMouse yeah I see that, however I guess what I was trying to illustrate is that these questions are so ambiguous because we don't have the full context, we don't know what the author meant. If this question was made by some drunk guy at the bar who does not have a degree in maths I doubt he would consider the 'best fit' standard definition you gave. But if this was made by some mathematician that studies this field then he is familiar with the conventions and he would probably mean that. Ultimately, for the general public we are left with a question with multiple valid answers since we don't know the full details of the problem. Even with not so complicated and specialized reasonings (such as those illustrated in the video) we get different answers such as 12 and 18, which is troubling. And even if we limit ourselves to our 'math brain' or 'programming brain', or any perspective we could look at it, there are still many more nuances within these fields than the question itself communicates, such as the fact that infinitely many polynomials pass through those points, or functions for that matter. The question itself also fails to teach those nuances which is why I think it is a poor attempt at teaching maths if this question is just thrown out there in a 10 second short or tiktok that just says 'guess the correct answers guysss!' and does not elaborate further. Instead we should explore all the possibilities to teach that in maths there is always more than meets the eye in the beginning and that is one of the reasons why maths is very rigorous and specific.
I definitely read it as a function-I remember similar “logic” puzzles in school. I think 12 was supposed to be the intention, but the execution was bad.
Pretty much any “math problem” that has gone viral in some way has been this way.
i love how many comments there are on here saying that you helped them like math in middle school. me too. this is such a wonderful channel. thank you for addressing this meta controversy and talking about the cultural values behind it-you continue to help challenge my assumptions, whether it was that math was boring or that logic is that the end all be all to knowledge.
How do you doodle without making any mistakes?
I think it is because she is dissociated in time space and sound haha
I never saw the connection between valuing logic and not-listening-to-others so clearly and broadly pointed out. Very useful concept. Thanks. And how you got to it through engagement with this problem is delightful. Again, thanks.
I think the point is actually mistaken though, at least the way it was presented here.
Putting reason and rationality above all else is not a choice. It is the foundation of anything else you do and how you set your other priorities. You can choose to lie to someone to be kind instead of telling them the truth, but that requires you to use reason to decide that that is the "right" choice under your system of ethics, regardless of what your system of ethics is.
This "problem" a good example of how reasonable people can disagree when working with different assumptions and that real life is under-determined and there is no "right" answer. However, regardless of the approach you use, you have to be using logic and reason to reach your conclusion, and you need logic and reason to be able to explain to yourself and to others what assumptions you are making.
If you said you were using programming logic or you were using pure maths logic and you got the answer of 3-4i, then you made a mistake in applying your system. You are objectively wrong about the conclusion you made because the conclusion you reached based on your stated assumptions and methods was not consistent with the answer you came up with. The only way you can check if your conclusion is correct based on your methods and assumptions is reason and logic. That kind of mistake would usually be caused by something that in programming would be detected by a unit test.
It is important to stress test your assumptions and methods to make sure that your conclusions that you expect match what you actually would like them to be. This is similar to a functional test in programming. You don't want your ethical system to tell you that the answer to the trolley problem is to run over one person and then back up and run over the five people on the other track, as an extreme example. But to do that you need reason and logic.
Proof by contradiction is also another example of where reason and logic have to be placed on the first step of any attempt at ethics. If you are evaluating an ethical framework, when you reach a state of contradiction, you know that modifications must be made either to the assumptions or to the methods.
@@HesderOlehexactly my friend. Vihart's rant is not directed against people who value logic or rationality above other people's opinions, it is directed against people who value their own opinions above everyone else's and then say it is the only logical option. In fact, that kind of person is failing rationality 101, which is to always be acutely aware of the limitations of your own mind. I'm a little sad Vihart conflates the too, though.
Worth mentioning that the "this isn't written formally" thing can work both ways. A missing ellipsis wouldn't necessarily mean that you can't repeat the pattern until you reach 3. For a question trying to rely on the reader to fill in the gaps, it's not surprising that someone would see a gap there to fill even if treating this as a sequence.
and then theres the question of if we assume 3=18 then why did we assume we can start with 10 as a previous input for 9=90
@@gaymerjerry THANK YOU! I heard the 18 explanation and all I can think is "where is the 10 then?" If the sequence matters at the end it matters at the start!
@@Mr.HowardEatsPants What do you mean where is the 10? 3x10=30-(3x4)=18, the 10 is still there. That's how my brain did it anyway and I got both 18 and 12 depending on if I filled in the empty spots between 6 and 3 or not. Filling in the missing numbers in the sequence would just change it to 3x10=30-(3x6)=12, still has the 10.
9x10=90-(9x0)=90
8x10=80-(8x1)=72
7x10=70-(7x2)=56
6x10=60-(6x3)=42
@@daniel4647 interesting! There are multiple ways of arriving at the answers!
10*9=90
9*8=72
8*7=56
7*6=42
6*3=18
Where the 10 kinda comes out of nowhere
Personally, my first solution was that the pattern was
x=x(x+1)
Which gives
3=3x4 or 3=12
Really interesting that using the form
n=(n*10)-(i*n) also gives the answer of 18 (with i starting at 0 and increasing)
@@Ghi102 The 10 sort of has to come “out of nowhere” or else there’s no solution. It’s just a random set of numbers with equal signs
Happy to see a new video from you. I programmed for 33 years, and because we start with 9=90, it seems to me that it can't be a number *the previous number in the list, because there is no number previous to 9. I would not assume some additional variable that starts with any specific value. But that is just me. Of course, as a programmer, I also note that there is nothing here that actually says that the same process is applied to all the numbers
Despite programming for so long, you seem to have forgotten that recurrence relations like this will be programmed with a base case, which basically follows from the inductions proofs used to mathematically prove them. Not sure how you can forget something like that after 33 years. Whether you go recursively or top-down, it does not matter that there isn’t something before the 9.
@@DrakeSingularity I would never assume this function is recursive. There’s nothing that indicates it as such, so I would first try to find a solution that is a pure function, and n*(n+1) fits
@@DrakeSingularity recursion is bad in basically every way except for making the programmer look clever, it would not be my first assumption for any algorithm used outside of education.
@@teslatrooper I’m saying this is a recurrence relation. It does not have to be implemented with recursion but that is the simplest way to do so. Memoization is generally better
@@DrakeSingularity "you seem to have forgotten... Not sure how you can forget something like that after 33 years." Your post is needlessly rude. After watching a video about the pitfalls of using logic to feel superior, you chose to add additional context to a comment while casting doubt on the commenter's memory. Rude for no reason.
Your videos are SO GOOD!! This is so interesting and really made me think. Also, love the beautiful design with the numbers at the end! Thank you!
vihart was one of the first English channels i started watching back when I made this account. I've always since then enjoyed your content and can say, math has become more likeable thanks to you
One of the things I really enjoy about your videos is that you include so much more than just math.
i ran the algorithm solution and got 12 lol. i saw it as a running loop that was decreasing a value by a constantly changing amount, and i figured out what the 3rd to last step would be for 3=?. that kind of algorithmic movement and pattern matching in data is my bread and butter so that's where i went, but even after getting that answer, i followed it up with "i have little confidence this is the only solution or even best solution". i call that the engineer's solution haha
I appreciate how your videos will pop in to my feed once or twice a year, and it's still just as joyous as the last time.
I hadn’t thought of logic puzzles like that before.
I tend to think of them not as a way to boost your ego and prove you’re right, but instead in a “puzzles are a fun way to challenge yourself, test your skills, and learn new things” kind of way. But there are so many different ways to look at them and I think people enjoy them for a huge variety of reasons. Another one some might have is “life has so many factors out of your control. Here’s something concrete” kind of way.
I definitely am a 12 kind of thinker, but having you explain the 18 answer was really eye opening! I hadn’t even considered the possibility of not filling in the blanks of the missing numbers!
Thinking about all of the possible answers out there waiting to be explained reminds me of the triangle problem where you name how many triangles there are. You have to twist your brain to see not just the ones that are obvious to you, but also look with a different perspective to see the ones that are hiding from you.
Upvoted for explaining to me that you've baited my clicks. 15 minutes into the video. Thankyou.
It’s a like a holiday when you upload, keep up the good work! 🎉🍾
I didnt expect how this ended but man I loved it! You put things that only exist as thoughts in my head so eloquently & in ways I only wish I could have escape my mind
Thank you. I get told off by my brother quite a bit for looking up information just to 'prove I'm right' and to 'make him feel stupid'. And I've thought a lot recently about when it matters who's right or wrong.
Usually I'm not purposefully trying to make someone else feel bad for not knowing something, but being accurate in what you say is important to me, especially when someone tells me that I'm the person who has things turned around, and just... I guess I do lose sight of whether it matters or not who is right in my effort to be seen as someone who isn't stupid.
Thank you for the reminder.
Good on you. That is a hard thing to admit and work through
On the other hand, it is not an objectively bad thing to want to be accurate and meaningful in your communication. We don't need to abandon this instinct necessarily - we simply need to find a better way to frame it socially when presenting it. When a friend is supporting their position with bad information, even if their position is right or good, it can be a good thing to correct that bad information, so that they can use better, good information, to support their position - but if we present it as "You are wrong about this." then that won't come through and we'll just look like the arse again. :/ Presentation and context are important in delivering information, which is also easy to forget.
- Sincerely, someone who also has a lot of problems with this stuff.
@@HeavyMetalMouse I think part of the problem is that we place ourselves in the position of being the arbiter of what information is "good" or "bad" rather than just validating a person's experience.
You always manage to put concepts into words that I can’t reach on my own. And if I can’t reach those words on my own, inside my own head, then I’ve just gained something quite valuable by listening to your point of view, thus reinforcing the main themes in this video. Thanks, Vi. I’m always glad to hear from you.
I love your content. I've been watching it for two years now and I'm seriously considering taking maths A-Level partially because of how interesting it is to me to see how your brain works a you figure out problems.
In the words of Captain Disillusion, I choose to follow my heart and use my head for everything else
Captain disillusion shout out in a Vihart video. It just makes sense.
Your handwriting is admirable. (Also, thank for interrogating my biases.)
this is me taking the whole test time trying to solve a problem that was simply printed incorrectly 😅
Your aside about "All Lives Matter" just about gave me whiplash. I've had very similar thoughts on the topic and it's nice to hear that I'm not alone there. Your point is wonderfully succinct.
I'm both amazed and slightly upset every time i find out i can absolutely do the pattern recognition and problem solving part of math, so some areas are randomly easy. But the way these things are taught in formal education are completely inaccessible to me.
The second half of the video was incredible. Points like these make me think maybe academics from many centuries ago were right, and dividing sciences among each other and splitting off humanities was a mistake in some ways.
In another life, I think you might have enjoyed studying linguistics, specifically pragmatics and discourse linguistics. That field seems scientific and sensible at first, putting clear definitions and labels on all the unspoken parts of how we communicate with language. And in the pursuit of accuracy, of definitions and regularities to record just how people manage to make meaning when there are infinite variables and subtext, linguists do such a good job of abstracting the concept of "language" and how meaning is made... into absolute meaninglessness.
I was thinking to myself a few days ago, that we never see well structured videos from the greats of the early days of RUclips, such as those made by Vi Hart, Vsauce, and all those, who over the years, faded away from their viral existence years ago, but remembered for their part in making the platform suvh a fun place to visit. Then, bam out of nowhere, Vi like she read my mind, puts up a new video.
My favorite Vi Hart submission I can't say for certain, because choosing one downplays so many more, all of which were great fun to soak into ones mind. There are literally so darn many good ones, from the story of Mr ug on the mobius strip world, to tau day., and so many more, told in a manner that made the viewer no only be entertained but made to think and remember the content as well, and hopefully a decade further into the future we can look back and remember this submission as well as those created long ago. We missed you Vi, so don't be such a stranger in the future and make our days just a little less mundane. Peace.
It does sometimes go the other way too.
Veritasium's channel has exploded in the past few years, and now he makes much longer documentary style videos. I always like to imagine the trade off as, in the place of Vsauce we have Veritasium now. Which honestly I'm completely ok with
@@NonTwinBrothers veritasium's videos are so long because he intentionally makes them very long by filling them with either obvious stuff or stuff that you would research faster on your own by simply using the internet.
I used to watch your videos "religiously" when I was working 12000kms away from home years ago. I was pleasantly surprised to see you back from hiatus. Whether that is a once off for another decade or not; thank you for this!
The title is indeed true I didn't understand a word you were saying
if only 0.000000001% of the population understand this, only about 8 people understand it
Than I am one of those 8. At least it think I understood it. By the way I am not from Argentina. I did like the presentation, but I wasn't expecting her to be so philosophical.
I will never get sick of watching "You thought you came here to ponder math and/or logic, but let's talk about YOU" Vihart videos. Or any Vihart videos, they're all fun to echo around in my brain, and to think about thinking.
I was hoping the number of zeroes in the title would come out to 0.00000001%, since that way it implies that only the person who initially created the "math test" would understand the true meaning.
It might be intentional. At first sight it might seem like it is representing only one person, but 0.000000001% of people is actually roughly 0.08 people (since 1% of people is roughly 80 million people), which also loops back to the way "math tests" are usually made: there's an obvious but incorrect answer, then the more complicated but maybe correct answer, sometimes the layers go even deeper, like that one test with the burgers, the fries and the cups. Also that addictive, little ego boost it gives you.
*Plot Twist:* The original author wrote f(3) = 90 but lost the formula. /s
Turns out that watching you paint those numbers while simultaneously listening to what you had to say was way more difficult than what I would have expected it to be.
Also, it seems to me that it's more of a logical puzzle than a math puzzle.
Valueing a person as a human being does not mean believing everything they say. Like imagine you had a close friend who was a flat earther. You care for them. You have parties together. You help them out. But any time they start talking about the shape of the earth, you politely tell them that you aren't interested in that particular discussion.
I didn't go into this in the video, but your flat earther is a good hypothetical to make this distinction: generally my position is that while of course you don't have to believe what someone else believes, it's usually best to assume that something they tell you about their own experience and own life is true. Like, if you party with your male flat earther friend, and the next day they tell you that they got jumped on their walk home from the club later that night, it would be weird not to believe them.
"Believe women" is a slogan that acknowledges how commonly women experience that if they talk about their assault, people feel justified in not believing them or defaulting to suspicion until proven otherwise. Many women do not get care, or help, or invited to parties anymore, by the people in their lives that take the side of their abuser. I guess I could've put all this into the video and made it even longer, but probably more on theme to have 2-way communication in the comments, so thanks for writing in.
Thank you Vihart.
I think you just helped vocalize something I consciously haven't been able to make into words.
I originally thought the solution was 12. But after watching this, I like the answer "blue" more.
my personal answer when I saw this was pretty much "n" because I really struggle with ambiguous problems like this, especially where i knew the format was incorrect and there felt like not enough information and 0 actual instructions, so I personally could not fathom the pattern and the smug way someone asked me made me so incurious about the answer that I just said "the only winning move is not to play".
I love that there are multiple answers and I feel so vindicated in being averse to the problem as presented because it definitely smelt to me like a disingenuous Math Problem constructed for the sake of getting people to argue about it. math and science arent binary disciplines- they're a method to describe our reality. there is very rarely 1 answer to any problem- and your work helps me stay curious about the math part, which has always been a source of huge insecurity for me as someone with hella ADHD and dyslexia.
Your approach is absolutely right. The first step in these types of problems, is checking for if it under-determined, over-determined or under-determined. Once you realize it is under-determined then you can take the path you took. I have ADHD and ASD, and this "problem" reminds me of the worst type of multiple choice questions that I have found to be more common in Australia than the USA or UK. It is the "choose the most correct answer", how am I supposed to enter your mind and decide which answer is "more correct" that another. If A and C are clearly wrong, but B and D are both true or possibly true, how am I supposed to know what the person who wrote the question thinks is "more" correct"?
What I disagree with you about is that math is to describe our reality, I say that because math can also be used to describe other realities. Sometimes it turns out what we thought wasn't our reality is actually our reality, but you can also have consistent mathematics that clearly contradict anything possible in our universe. Science though I agree with your assessment.
I also disagree with Vi's conclusion that logic and reason have to be ignored or set aside.
Putting reason and rationality above all else is not a choice. It is the foundation of anything else you do and how you set your other priorities. You can choose to lie to someone to be kind instead of telling them the truth, but that requires you to use reason to decide that that is the "right" choice under your system of ethics, regardless of what your system of ethics is.
This "problem" a good example of how reasonable people can disagree when working with different assumptions and that real life is under-determined and there is no "right" answer. However, regardless of the approach you use, you have to be using logic and reason to reach your conclusion, and you need logic and reason to be able to explain to yourself and to others what assumptions you are making.
If you said you were using programming logic or you were using pure maths logic and you got the answer of 3-4i, then you made a mistake in applying your system. You are objectively wrong about the conclusion you made because the conclusion you reached based on your stated assumptions and methods was not consistent with the answer you came up with. The only way you can check if your conclusion is correct based on your methods and assumptions is reason and logic. That kind of mistake would usually be caused by something that in programming would be detected by a unit test.
It is important to stress test your assumptions and methods to make sure that your conclusions that you expect match what you actually would like them to be. This is similar to a functional test in programming. You don't want your ethical system to tell you that the answer to the trolley problem is to run over one person and then back up and run over the five people on the other track, as an extreme example. But to do that you need reason and logic.
Proof by contradiction is also another example of where reason and logic have to be placed on the first step of any attempt at ethics. If you are evaluating an ethical framework, when you reach a state of contradiction, you know that modifications must be made either to the assumptions or to the methods.
Wow I felt like my mind was see-through when they made the “probably JavaScript” joke.
Your name is literally C
This was your destiny
Lovely to see you 🙂. Your thoughts on all this stuff are always intriguing. Fwiw… I got 18; yes, I’m a programmer.
The conclusion was not one that I expected but I love the point you make here!
I can't believe I'm just now finding this channel. I consider myself pretty open-minded but every video here opens it further. Thank you
I was literally just browsing ebay and someone was selling one of the notebooks used in your videos
Actually you can just pick any real number for the answer and then construct a 4th-degree polynomial to match that answer.
The polynomial will be
f(x) = [(n-12)/360]*x^4 - [(n-12)/12]*x^3 + [(67n-732)/72]*x^2 - [(165n-2016)/36]*x + (42n-504)/5,
where n is your desired f(3).
At n=12, it indeed comes down to f(x) = x^2+x.
Moving from 'notation is subjective' to 'nothing is true' is... foolishness. Your first part is an excellent treatise on epistemology and human communication; the second is, sadly, a descent into sophistry.
Rewatch the video. She doesn't argue that nothing is true.
Thank you. This is . . . beautiful. And probably also true. I think. (When I'm not distracted by your math and your numbers and your drawings. Gonna have to watch it again.) You make an 18 feel better and teach me compassion for self and others.
Before you explained your reasoning for 20, I actually came up with a way that it could work! Take the number above, and subtract it by 1. Take the current number, and add 1. You end up with 5 x 4, and the previous answers stay the same. This, of course, relies on an imaginary 10 above the 9, which doesn’t work because skipping 4 and 5 are crucial to getting 20 as an answer. 20 probably isn’t correct, then, but I see how someone could get it.
i have my final exams for my uni degree soon, so this was great timing to get my mathsy brain parts going! and your words at the end were great. thanks vi!
"Culture teaches people to value their own logic more than they value women as equal human beings", okay but my logic says that they do deserve equal rights.
human rights were founded on some kind of logic also
we are not looking a neapolitan ice cream
A new Vihart video always makes the day better.
figured it out under a minute, this is really cool u deserve more subscribers
there is roughly a .03% chance one of the 8 people who will understand this video watched it as of may 2 2024 (277174 views)
I'm a software engineer and the only two answers I could think of were 18 and 30, 30 indicating a bug of some sort. I had no clue where you got 12 until you explained it.
I have to say I often have a hard time with this "being kind instead of right" stuff. There are some people I hold dear in my life that believe things I really cannot bring myself to believe. My instinct when I hear those ideas is to focus on facts and question what I hear. I think that's a good way to interface with questionable new ideas but my skepticism is also hurtful to my dear ones. What's the solution here?
Consider that you might have the wrong facts. I don't mean to hijack the thoughts in the video, but very often the logic people have is more or less sound. Just that they would really prefer a specific outcome to their logic, and it's possible to get by choosing facts you like. They can then just hyperfocus on their own logic and see it as perfectly sound.
That's why it's important to listen to others. If yours and their experience and conclusions differ - is it really that their logic is flawed? Or perhaps your facts are wrong or chosen badly? This is especially important in situations where you can't possibly have all the facts (because you don't share the experience, for example in issues of discrimination) so as a bare minimum, you WILL have to accept their experience as a fact. They might be tricking you, but ultimately there is no other way, you can't just infer and override their experience.
And that is the part that comes from being kind - being receptive to accepting these facts that can only come from the experiences of other people. And using them in your logic - rather than making up things every time you can't get a fact yourself.
@@Serutans Exactly, although I would use the word "assumptions" instead of facts. People's fundamental assumptions differ and that changes their conclusions, even if their logical deductions themselves are perfectly valid.
Often what you describe is Religion.
Sure, it makes no sense to believe in gods, but if someone is not disrespectful of math and science, and they offer to pray for your sick loved one, being kind is to say thank you.
What they mean is that they feel bad both for your loved one's sickness and for how it pains you. It is their way of hoping they'll make a quick recovery.
Accept the offer of empathy. Gracefully ignore the superstition it is wrapped in; it matters to them. Respect that it matters to them.
My advice would be to 1) believe people about their own _experiences,_ especially their own internal experiences (e.g. "I get harassed on the street regularly" or "loud noises are painful for me") 2) without being rude to people in the moment, independently verify the _facts_ they present you that aren't about their own experiences (e.g. if they tell you "democracies have fewer wars than autocracies", you don't have to contradict them in the moment, but you don't have to believe it without looking it up for yourself) 3) question the _narratives_ they're presenting you with, and be kind but firm about your right to make up your own mind. A concept that's helped me a lot is the idea of "mental sovereignty": you get to be in charge of what you believe, and if other people are trying to make you feel like you're a bad person in one way or another for believing that you are in charge of what goes on inside your head, it is okay to push back on that. (There are of course all sorts of ways it might be hurtful to _voice_ your beliefs in one or another particular context, but you are legitimately, really, and truly in charge of the inside of your head, and no one can or should take that away from you.)
Honestly, I don't think I can really get behind the "truth vs kindness" binary ViHart is setting up here (so you can take my advice with that caveat, if you want). I used to have some beliefs that, to the extent that I acted on them, caused me to be devastatingly unkind to people. And the reason I held those beliefs was because I was in social environments where truth-seeking was actively discouraged and seen as a sign of being a bad person. Even evaluating the idea "are these beliefs based in reality, or were they made up to try to control people like me?" was seen as only something an "unfaithful" person would do. So I've come to really value the right to seek truth quite dearly, and feel that seeing truth as opposed to kindness is a great way to have less of both in your life.
@@lexk4423 Thanks for sharing. You speak wisdom.
On the subject of people trying to make you feel bad for thinking for yourself; I have very slowly learnt that they are the very bad people that they're trying to make you sound like.
Not beyond salvation, but they're certainly not a mind I enjoy exposing mine to.
the pattern I saw in the numbers was that the right side of numbers grew by previous growth +2. or add 2 to the growth from previous number. For example the difference between the top two numbers was 18. the difference between the number beneath and the second one was 16. than 14 and so on.
yeah this is what I saw, the result being 3=22
this is how i was taught about quadratic sequences, a constant increase in growth
after some playing around with coefficients you can arrive at x^2 + x + 0
although the problem is given in a strange way
I agree with pretty much everything said in this video.
No, I'm not gonna follow that statement up with an "except". The video didn't do where I expected it to, but where it went instead was way more important than the relatively minor gripe I thought you were going to address.
My prediction, (in a video about predicting patterns), about where you're going was that you point was going to be that those math puzzles on many parts of social media are like playing thermonuclear war or tic-tac-toe in the movie WarGames (1983): The only winning move is not to play. That is, when you see one of those *intentionally* ambiguous supposed "logic puzzles" posted by a Facebook page that has nothing to do with logic or math puzzles, and the only reason you saw it in your feed is because one of your Facebook friends, (who also likely didn't care at all about whatever that page was *really* promoting), had commented with their "correct" answer, it's important to understand that the only reason that whoever posted the question to start with was to drive engagement on the post to up their page's visibility, and nothing drives engagement like people disagreeing and getting to tell others that they are wrong, or that they missed some detail. (No, *you're* a run-on sentence!)
That's why we had that trend of low effort posts with those sort of kinda equation systems using clip-art images instead of letters for their variables. But where if you look *closely* you would see that some of the clip art had been subtly altered to have a different number of things, or include a clock that's pointing to a different time. Or those "Which cup will fill up first?" puzzles where the answer depended on if you thought a solid line through a 2D-representation of pipes and cups meant that the pipe was blocked or not.
The only winning move is to not take the bait, ie don't make a comment. Because that's the way to stop your (and your friends') timelines to fill up with that sort of spam. Well, that and taking a moment to click "Show me less like this"/"Hide this page". Those posts have almost completely vanished from my timelines now. I'm not sure if this is because Facebook changed something to make these posts less viral, if me ranting about them (outside of those posts themselves) made my friends stop commenting on them, or if most Internet users collectively decided that we no longer cared about them. My guess would be that Facebook changed something, because the other alternatives require that several humans changed their behavior to the better, and that sadly sounds less likely.
Of course, if you're following pages/channels/forums that are *about* logic, math, and/or puzzles, then cutting them some slack for having some puzzles that you personally don't find very interesting makes more sense. Especially if they somehow manage to made content that's both profound *and* entertaining out of those puzzles.
But what are the odds of that?
Vi, you should do a video about the “randomness” or not of the little sheet of paper you stick behind the sheet of your notepad to keep the ink from messing up the next page.
It LOOKS random but it came from your intentional writing of ink and yet it might be random because the holes in the notebook paper weren’t put there in any way that you or anyone else intended.
tell me why these videos always have me HOOKED
I don't want to be that guy who stirs up the comments section by pointing out mistakes in your video or issues with your logic...
But...
.........
When colouring all the 1's in at the end, you missed the second 1 of 141 and proceeded to colour it in black.
And this really upset me.
ahhh I tried so hard to get them all, because I know things like that bother some people. If I could do it again, I'd do it differently, but alas---some mistakes are permanent.
@@Vihart Fix the mistake and reupload the video. Problem fixed!
brb going to go make a hexaflexaperplexingmathtestagon
Okay this is so fucking funny
holy shit this video knocked my socks off. also a longtime viewer, means a lot to see you again after some time. your video about being famous on the internet really struck me when it came out, and so did this one. i spend a lot of time thinking about social dynamics and it was incredible to go into this expecting an easygoing math puzzle explanation but getting articulations speaking directly to my heart about the whys behind the ways i see people interacting recently. thanks for your thoughtful commentaries as always, hope you're doing well.
Missed your channel. Watched it when I was in primary school and now I'm a senior in highschool.
Guys, c’mon, we all know from childhood that 3=the magic number.
I'm so 12-brained I couldn't for the life of me figure out how to arrive at any other answer lol.
Same
the presentation of the problem doesnt really lead it to being something worth thinking about once you have an answer, its very low stakes and it doesnt take too long to get to 12
I was hoping you wouldn't point out the fact that there are an infinite number of functions that work so I could look all smug in the comments, but alas, you beat me to it.
Yo I just realised I've been watching your videos for 11 years now, started off with squiggle inception and heaflexagons. Insane!
This video is awesome and I have no more words for it.
Vihart... I think your escape from logic here is... not successful.
Like the whole reason we know black lives matter is because black people are alive and conscious and human, things which we know *from logic,* therefore I would say, valuing "black lives more than logic" is not really possible at all because, how exactly do you make a value judgement without logical reasoning?
One logical principle is the law of identity, the idea that things are themselves...
In order to value black lives don't we first have to be certain that when we are valuing them that means something specific?
Logic is really really fundamental to everything we do.
To criticize some people as simply valuing logic over 'black lives' is not a particularly coherent statement
I'm glad that it makes logical sense to you to value black lives, no criticism there. I know I didn't go into the history of how logic and intellectualism has been used to justify things like slavery and genocide, so I wouldn't expect everyone to have the context behind my reference. There's some really dark stuff that still persists in various forms to this day.
@@Vihart I will admit...
There is without doubt a point to be made here.
I think certain kinds of "logic" are less "logic" and more "class-oriented dogmatism," a term I just made up to mean more or less, people saying things that sound plausible to their demographic which also *just happen* to uphold existing power structures...
And so I do see it as a legitimate point to point out hey, if your "logic" is just your own assumptions which you do not even allow to be touched by your **empathy** (to me empathy should be part of any one's "logical value judgements") then yeah that is awful.
And the anti-BLM people (and other reactionary conservative groups you alluded to) are definitely far more comfy with their convenient logic which just so happens to justify everything them and their demographic *wants* to believe without letting it be "soiled" by the demands of basic empathy.
My first thought was instantly thus;
9 * 10 is 90
8 * 9 is 72
7 * 8 is 56
6 * 7 is 42
And given its imformallity i too assumed each were seperate statments, and so after 5 is multipled by 6, then 4 by 5, then 3 by 4 which is 12.
Still dont see that darned 18 tho
if you have two lists of numbers (10,9,8,7,6) and (9,8,7,6,3) do you see the 18 now?😉
but then i'm showing my ⛰🚴⛈🐒🤟 and 🏕🗺🛌🐬❓ bias🤣
@@orchestratedpassage9468 ah i see it :p
Mb mb
@@orchestratedpassage9468 I still don't get it :c
if you multiply 9 and 8 you get 72, 8 and 7 you get 56, 7 and 6 you get 42, so if you follow the logic that you multiply a number by the number on top of it, you would get 6×3 which would mean 3 =18
I knew, logically, that Vi would blow the lid off this thing, and I am delighted to announce I was completely 100% and entirely correct. I regret to announce, however, that my chair lacks arms.
You've been found out, hooligan! I'm revoking your armchair club membership. We'll be by tomorrow to seize your entry card & cast you several subtly derisive raised eyebrows.
@@ItsAsparageese i can give you my card but i is on the complex number system and yours truly is but a simple person.
this was all very interesting, but I cannot get over being bothered by the usage of sharpies instead of pens.
Sharpies show up better on "film"
@@kristajones7202 Yes I realize that this was the intent, but it isn’t actually true. The legibility is greatly reduced by using sharpies, especially in ratio to the size of the writing. for such small print, a pen with thinner line depth would be more legible and still show up on paper, not to mention improve the viewing experience. This would be enough of a reason, without adding the uncomfortable fact of paper bleed through, and much paper waste, add to that the experiential component of being very stinky pens. If you are going to write in sharpie, it would be more legible in a font size closer to 2”.
Thanks for validating 18, I imagined it as regarding upper examples leading the ones below. Very interesting to hear the multitude of other views