Why “probability of 0” does not mean “impossible” | Probabilities of probabilities, part 2
ฝัง
- เผยแพร่เมื่อ 28 ก.ย. 2024
- An introduction to probability density functions
Help fund future projects: / 3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: 3b1b.co/thanks
Curious about measure theory? This does require some background in real analysis, but if you want to dig in, here is a textbook by the always-great Terence Tao.
terrytao.files...
Also, for the real analysis buffs among you, there was one statement I made in this video that is a rather nice puzzle. Namely, if the probabilities for each value in a given range (of the real number line) are all non-zero, no matter how small, their sum will be infinite. This isn't immediately obvious, given that you can have convergent sums of countable infinitely many values, but if you're up for it see if you can prove that the sum of any uncountable infinite collection of positive values must blow up to infinity.
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
------------------
These animations are largely made using manim, a scrappy open source python library: github.com/3b1...
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
vincerubinetti...
Stream the music on Spotify:
open.spotify.c...
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with TH-cam, if you want to stay posted on new videos, subscribe: 3b1b.co/subscribe
Various social media stuffs:
Website: www.3blue1brow...
Twitter: / 3blue1brown
Reddit: / 3blue1brown
Instagram: / 3blue1brown_animations
Patreon: / 3blue1brown
Facebook: / 3blue1brown
If you're curious, I never ended up making the third part of this. Or rather, I made part of it and thought it wasn't very good. The plan is to put together something like a probability series this year, where the beta distribution will surely be one of the topics. Thank you for your patience!
And thank you so much for your hard work!
Thanks for the update. I will be waiting for it!
3 hours ago wow thx man
3h ago? Is this being recommended to everyone all of a sudden?
@@bacicinvatteneaca probably because someone recently donated a bunch of money in hopes of a part 3, so he felt some responsibility to clarify.
I have to imagine it's frustrating to follow this channel. I believe this is the third video in a row (excluding those on epidemics) that I ended by saying something like "we'll look at Bayesian updating in a continuous context in the next part". But whenever I think hard about the setup/prerequisite section of that video there's always something interesting enough to pull out to stand as its own video; there are just so many interesting topics here! Thanks for your patience, and hopefully, everyone gets that the goal here is to just hit as many fundamental ideas in probability as is reasonable.
Also, in parallel with making these probability videos, I'll be trying a very different sort of experiment on the channel soon...stay tuned.
It's fine because we still love your content
if by frustrating you mean awesome then yes yes it is
Even if we get left hanging sometimes, we still love to see all your videos and experiments :D
Bro, frustrating is not a word I'd use to describe anything about this channel except my inability to fully grasp everything
pls do a video on the difference between the questions that map and mle are answers to
Mr. BlueBlueBlueBrown,
Part three?
Sincerely,
Probability Stans Worldwide
never knew his name was (Blue^3)Brown
@@GammaFZ Now you know
Mr. Blue+Blue+Blue+Brown
Day 448: Still waiting.
What do we do to get part blue of this?
Mr. (Blue+Blue+Blue)(Brown)
"The probability of the dart hitting the board is 1". You obviously haven't seen me play darts.
Or the wall
Reinatr48 or the face
nice one!
Or the person.
Or yourself.
Crush: You have 0% chance of being with me!
Me: So you're telling me there's a chance?
no. there MIGHT be a chance, and NOT there IS. it’s a logical implication between the two statements (“0 probability” and “impossibility”), and there is a different relation between another two statements (“0 probability” and “possibility”). when you have impossibility, it must be an event with 0 probability. when you have an event with 0 probability, you might have possibility and impossibility as well. all of this is due to our mathematical toolset’s limitations (infinitesimals are treated as zero). that’s why there are extensions in mathematics which can handle these situations better (e.g. hyper-real numbers where infinitesimals are not zero anymore). but when we have this ambiguity due to this kind of limitation, a “meta-probability” level emerges, since you can have possibility or impossibility when you deal with an event with 0 probability. this is a meta-possibility.
ps.: well, by the end of my comment I realised that you were technically correct, since there is no difference between “existence of chance” and “possibility of chance”.
k0p1k4
alright slow down Socrates
@@_kopcsi_ _"ps.: well, by the end of my comment I realised that you were technically correct, since there is no difference between “existence of chance” and “possibility of chance”."_
This is so sad... Can we hit 1 million likes?
Well,there might be a chance of chance .
@Angel Yotov
No; being with me or not being with me is binary and not continuous so if being with me is 0% the only other possibility which is not being with me would be 100%. “There’s a 0% chance that there’s a 100% chance of you being with me” would be a better example.
When I was trying to learn linear algebra, you put out a series solving all my confusion. then when I got interested in neural networks you put out a series which made me dive deeper and end up trying to learn stats. then you put a series on stats.
Shayan Poordian Oh man, it went the exact same way for me. Started the engineering grad and the Calc/Algebra ones were fundamental to my success. Then the Diferential Equations series and now that I'm into data analysis, stats. God knows how much I love this channel :D
You're a lucky one. I still dream of that elliptic curves video
Grant Sanderson really is the gift that keeps on giving.
I kind of went from the other direction: From studying statistical science, I started branching off into more traditional mathematics, like linear algebra. His series on linear algebra is also what brought me to the channel. And I'm thrilled that he's branching into stats/probability/data science, because that's my wheelhouse.
@@Aldrnari His linear algebra series is quite helpful. His video on change of basis in particular is what made that concept _finally_ make sense to me. I really liked his analogy to two people choosing two different vectors as their basis and then making it into a puzzle of how to translate between the two different reference frames.
Just a former maths teacher talking into the internet void about probability:
To me it makes sense that the dart has a probability of 0 of hitting a specific point on the dart board. If you are aiming at a specific point, it means that you are betting on the fact that your accuracy will be on the level of atoms, and even smaller (because math has no Planck length). You literally are boasting infinite accuracy, which is impossible. That is why your probability of hitting that specific point is 0. But if you say "I am going to hit Bullseye". Then things change, now you are being reasonable. The bet is no longer on hitting the infinitely small point, but rather hitting an area which contains infinitely many of these infinitely small points. In some sense you have infinitely higher probability now since you have infinitely many small points. But of course in our real world we have the Planck length which means that we are never really talking about infinity, just very big or very small numbers. That also means that the probability is never truly 0, however it is extremely tiny. ^^
This comment deserves more likes. It made me understand the matter at hand even more. Props!
oh, so thats what he said? pretty obvious
Nice analogy
But I think you're somewhat conflating physics with math here
Well in fact we don't even know whether Planck length is the smallest unit of length. We *think* so. There is no proof of this.
what if we use a plank length dart ?
8:38 probability the dart hits somewhere on the board is 1
With my throwing arm, that's pretty generous...
me: (misses something literally next to me)
also me: I blame quantum physics and whatever things are unexplained.
My friend trying to comfort there is a chance of me getting a girlfriend.
Girlfriends are discrete objects, and in a discrete setting, a probability of zero still always means it is impossible.
Sorry bud
lol
@@cifar10 why'd you have to hurt us this way???
Don't worry man, girls love top-hatted gentlemen.
@@NovaWarrior77 as a girl I can confirm this
8:31 That reminds me of one of Zeno's paradoxes, where he says that one grain of mullet falling does not make a sound, but a thousand grains falling does make a sound, seemingly showing that many nothings somehow make something
Nice
Sometimes I wonder how Zeno managed to get through life, given how often he thought about the seeming impossibility of iterating a bunch of small things into one big thing.
@@NoriMori1992 Or he was just a troll
3b1b, How about taking consideration on making *"Essence of Number Theory"* ? Much respect!
I would love that tbh
That would be amazing, but is there much scope for visualization?
Yes great idea
That would be really cool
This is a great idea!! I intend on presenting myself to the math Spanish olympiad next year, and it would be really useful
I'd love to see the third video in this three part series when it is ready! You've done a great job setting the scene. If I had explanations and graphics like this on my statistics MSc it would have been much smoother!
1:31 that's some sneaky famous constants right there
Magnus Eide-Fredriksen Easter Eggs in a video released on Easter... who woulda thunk 😀
@@grammarnazi9456 *thunk*
Denislav Ivanov , if you don't like colloquialism, then why not also correct the use of *woulda* which is obviously actually *would'a*, a corruption of *would've*, a contraction of *would have*? Why would it be OK to corrupt one word but not the other?
π e δ φ
I don't get it? please explain. I don't see Pi, e, etc.
1:55 I think this 'paradox' is a good example of what infinitesimals can be useful to describe. A value which added together infinitely many times gives something finite. It's a concept that is hard to understand but is clearly a thing for these sorts of concepts. Not that it gives a useful value, but it's a useful concept to understand this.
I just re-watched the "divergence and curl" video and now I can't stop thinking about how the factory at 2:25 has positive div.
ah yes,the car field xD
Bruh
Vector car field
Hey Grant! This video is amazing. I was wondering if this series would ever come to and end with the third part with beta distributions? I am really curious. Thank you for your great work!
5:26 - And here I was looking for Acrobat Reader every time I saw a PDF?
Hahahah
Me too
Hahaha
Me too
(Partially in response to the pinned comment by OP)
Can we all stop and thank and/or applaud 3Blue1Brown for the lack of sponsored content? I really appreciate the integrity and the obvious desire to drive the channel in an "educational over commercial" direction. Regardless of anything else, it's a very entertaining channel and I, for one, greatly appreciate the purism and consistancy.
*Steps down off of my soapbox*
should i say : the probability to see part 3 tends to zero ?
When you started explaining about how we should view *h* as ranges, my mind immediately tried integrating the function P(P(h)).
I'm starting to get worried that I've been studying Calculus for way too long.
When will we get the next and final chapter to this awesome series? 🙃 keep coming back hoping to find it haha
I know. Just had the same thought myself!
If they can't be nonzero, and they can't be zero, we simply extend the problem to the surreals and make them equal to the infinitesimal times a scalar, so they all add up to one.
Yes! I love this way to explain/express this using surreal numbers! Thank you so much, I'm going to cite this example from now on when questioned on the "usefullness" of surreal numbers.
@Jake P Technically there are multiple different hyperreal number sets, of which the surreals are the largest (though the surreals are a proper class, not a set, but I'm getting off topic now). However, any of them should allow this. The differences between them don't really come up so long as you're using them for calculus.
@@modnarsarhp it does have a value, zero is the value
@@modnarsarhp no, I mean the value is zero, not some small nonzero number
@@tejing2001 Do you know of an example of a person calculating Bayesian probability using this approach? I'm very interested in it, but don't really know where to start.
Still waiting fo 3rd part(
man you know this video is incredibly useful for understanding maxwells speed distribution in KTG if you just relate it and that's the one thing I adore about this video thanks grant🙏
Have not seen it yet but I know this video is gonna be good "almost surely"!
Ah shoot you stole my joke.
"...Well even if that probability was minuscule, adding them all up to get the total probability of any one of these values will blow up to infinity."
Applies over the Reals (and thus over the rationals, etc). But it doesn't apply over the Surreal Numbers, or any other ordered field with infinitesimals like the Hyperreals. For example, {1, 2, 3, 4, ... |} * {0 | 1, 1/2, 1/4, 1/8, ...} = 1 (in any set theory which permits transfinite induction up to $S_{\omega^2}$).
Given the passing of Conway it might be nice to do a video on the Surreals. They're one of his lesser known but more interesting constructs, though the Hyperreals are a more popular way to get the same results (they're isomorphic to the Surreals if the Axiom of Global Choice is accepted). But I find the Surreals to have a far more intuitive construction than the Ultrapower Construction of the Hyperreals.
Edit: After finishing the video, of course model theory is brought up. That's very closely related to nonstandard analysis, which uses the hyperreal numbers.
where di he talk about model theory?
5:26 show this to someone without context
Crazy, I just took my econometrics final on exactly this topic: random variables, sample distribution, measure theory, and next time I check my TH-cam home page I see this video !
It's a pity that Part 3 is still missing. Recently, I've had to learn about beta distribution for my job so I watched videos from other channels and I think I've got it now. But I would still like to see how this channel will explain the topic, because I have learned so much from you in the past few years!
Just HOW DID THIS MAN LEARN MATHS, I'm literally dying to know, it's my ultimate dream to learn math concepts as he puts it in his videos, his videos and Khan academy's are what truely got me to love maths
You go to university?
@@akaimizu9780 unfortunately yes I'm an engineering student studying communications engineering 3rd year and this guy explains math in a way no teacher or professor I've ever heard of did (nor in any other subject)
@@zizo-ve8ib take a probability and stochastic process course
@@kinghassy334 I did take such a course, though not complete, but problems started from correlations, auto correlation and cross correlation and such
@@zizo-ve8ib well you have to take into consideration that this isnt done in one sitting, its research materials multiple takes, writing and perfecting script.
its harder for teachers to have that kind of script when you are working with live audience that has questions. also its almost impossible (probability of 0) for someone to talk like this of the top of his head
In case you forget, we're still waiting for the next part :)))
Anyway, ty for great content
I see what you did there with the decimals at 1:47 :D
I need the part 3, excelent videos!
This series is great. (As are all your other videos). I am a big fan of your work. I am looking forward to the next part on probabilities of probabilities, especially on the beta distribution. No pressure, take your time :). But, as it has been several years now, do you intend on continuing this series at all, or is it stopped? Once again no pressure, just wondering because it looks like you have moved to something else (which is also great).
2:05 the way i see it, the probability of any of those values is not 0. It’s an infinitesimal (1/inf). Something that exists but with an infinitely small value is not the same as it not existing at all.
For example the probability of the value being 0.70001 is (1/inf), but the probability of the value being 2.0 is 0, because it can never ever be that value.
So if there’s an infinite number of possible values from 0.0 to 1.0, each at (1/inf), then you get
(inf x 1/inf) = 1
As i said, that’s just the way i see it, and it makes sense.
That doesn't work unfortunately. This is because between every two different numbers there an infinite amount of numbers, not just between 0.0 and 1.0. So for example if you split it in half then the amount of numbers between 0.0 and 0.5 is inf. Each of those number would have a chance of 1/inf so the chance of a random being between 0.0 and 0.5 would be inf * 1/inf = 1. The problem is that the same would hold for the numbers between 0.5 and 1.0. So you would have a chance of 1 of being below 0.5 but also a chance of 1 of being above 0.5. So as you can see it leads to a contradiction.
Generic Internetter Exactly! I agree with you 100% When he's adding the zeros he takes the sum to be zero as if we're adding finitely many of them but we have an infinite number of zeros to add and that means recourse must be had to the theory of infinitesimals
@@sjiht0019 Also note that a sum of infinitely many numbers is not necessarily infinity, but a sum of an *uncountable* number of positive numbers is infinity.
@@sjiht0019 You assume inf/2 = inf. This isn't true in non-standard analysis, which is the rigorous way of treating the infinitesimals the OP is getting at.
@@sjiht0019
Also, if it is the first number above 0, you would have to go through an infinite amount of 0.
For example
0.00... = 0
Waiting for part 3 and 4!!!🥰
5:16 - Nice Euclid’s Orchard :D
Urizen i always remember when my family went on road trips through long highways, there were tons of orchards. When the little sticks holding the saplings up moved past, it created a very similar effect. Cool to know that it has a name!
I am impatiently waiting for the rest videos.
Your job seems awesome. You get to make videos for others to learn while going really in depth and learning a lot. That’s the dream
I think about this as: when we use 1 dimension to denote the probability, as the probability gets smaller and smaller it becomes zero, but if we use 2 dimensions or more, the area becomes zero, yes, but we still have one dimension that's not zero, i.e. the height.
I guess that's why we look at the (radial) probability density of an electron around the nucleus
I finally know why, after 2 years of believing there's some high level science behind it, that's out of my reach! Thanks, thanks a lot 😭🙏🏻
These are awesome - is Part 3 ever gonna drop?!
since the release of this video, there's been a 0% chance of it being finished on a given second, so possibly not
You're awesome! Please let us have part 3 ❤
What is the probability to choose a random real number, for example 0 or 1?
Is it possible to choose a random real number (?) Two levels of difficulty:
1-in such a way that any number can theoretically be chosen?
2- with an equal probability for each real number?
This melts my mind.
This is a good opportunity to use 3b1b's videos to calculate the probability of us 100% getting a part 3 to this video
I think it may be easier for people to understand if they consider what it even means to specify the number of interest. This comes down to significant figures. When one says 70% probability, what really is meant is 70% +/- 0.5%, or 70.0 +/- 0.05%, or 70.00 +/- 0.005%. At some point there is a limited degree of precision expected, because they probably aren't asking for the difference in likelihood of the probability being 70.0000000000% versus 70.0000000001%. Thus when it is asked what the probability of the probability being 70% is, what is really being asked is what the probability of the probability being within some expected tolerance of 70%, which ties directly into the concept of integrating over a probability density function.
You know, it really seems to me like this should be taught *starting* with PDFs. Then you introduce discrete probabilities as just slicing up the PDF into a set of ranges, and you're done. Just seems to make more intuitive sense that way - it's strongly intuitive visually how you're making that step from continuous to discrete.
The first minute of this video explained the Hilbert hotel paradox for me.
math is not too difficult, teaching math is a different story (very HARD) thanks to you. 3b1b
lol I understood nothing but he has a calming voice so it's all good
the car factory's name changed, lol. I prolly only noticed because my brain was like, "okay, I won't be able to follow along the actual content so maybe I find something else that doesn't blow my mind." 😂
All of this goes to say 0*infinity can equal anything, and is intuitively the reason that limits in form 0/0 or 0*infinity are indeterminate, and you can get cases where 0*inf = 0, 0*inf = any positive real number, and 0*inf = infinity.
How long did it take you to animate all those little arrows at 5:14-5:16. Such a small detail but I appreciate it lol. I mean I can’t imagine what kinda work gets put into these videos but then to just take to time to sprinkle in nice little details like that. Its more than we deserve...
Next episode; "Accuracies of accuracies"
The paradox introduced can be thought of by thinking of an exact value as an *infinitesimally small* slice. It's not simply 0, which would result in adding up a bunch of zeros to get nothing, and it's not a conventional "non-zero number" which would result in an infinite area. As it turns out, adding up an infinite amount of infinitely small pieces (which is commonly estimated in calculus) can sum up to a finite number.
My probability of getting a girlfriend is zero....
So I still have a chance
that's a discrete scenario my friend, so i guess you don't have a chance :)
th-cam.com/video/ZA4JkHKZM50/w-d-xo.html&lc=UgzPdzTFR_flYoo0fXZ4AaABAg
see this man's reply
You still have a chance, but only if she has measure zero
"so you're telling me there's a chance"
No, because you getting a girlfriend is not one possible future out of all possible futures, but an uncountable set of possible futures, whose probability is still zero. The probability of every future in which you don't have a girlfriend is zero, but one of them will occur.
Except a probability of zero DOES mean "impossible".
That's the whole definition.
Making your bars infinitely narrow doesn't give them a probability of zero.
It reduces your ranges to something meaningless.
A line is simply something different from a surface.
Me before exam: Finally, prepared probability for maths exam.
Same me after watching this video: pencho, kuch nhi aata probability ka
You didn't put in mind that when you flip a coin, it can land vertically :D
Yeah but that will never happen
...
Wait
Yesnt going to happen man
"Possiblity is better tied to proabability density rather than probability" sentence with high impact.
It’s so sad there is no part 3 yet :(
Love your videos, you've saved me many a time! Would really appreciate part 3 about now, if you can!
3Blue1Brown: 2:16
Zeno: Write that down!
You make my head exploding 🤯
1:52 ...I'm pretty sure using the Σ notation to denote summation over an uncountably infinite set is illegal D:
Yuuuup, this rubbed me the wrong way too. Using logic similar to what is employed here it's easy to make a 1 = 0 proof.
What but they use it all the time in high school
perfect video to watch for students starting to learn integration
Haha, tiny brown pi at 8:26 symbolizing you.
Of course, then we have pi at 0:17
A lot of problems in maths seem to come about from entertaining infinitely divisible reality, which is neatly dealt with in reality by having a smallest size of reality.
I think the probability of p(0.7) being 0 is just misleading.
When you demonstrate the bar distribution, it is clear that the probability (in a uniform distribution example) would be 1 / x, where x is the number of divisions. As x gets bigger, the probability gets smaller. One is tempted to quickly say that as x becomes infinity, the probability becomes 0, BUT that's where the intuition problem begins.
In reality, since as x gets bigger, the probability gets smaller, that means that no matter how big x is, the probability will never be 0. This is obvious since if your 0 means 'nothing' then by increasing x you would obtain a probability smaller than nothing which is not possible. In other words, 0 is not "nothing" in this context, but rather, an infinitely small number (to match x, an infinitely big one).
Once you have that realization, you can tell that the sum of the individual probabilities is not 0 * inf, but simply (1/inf)*inf. Usually this type of operation has no defined answer, but since we know our "0" came from that very same number of divisions, it is clear the answer is 1
Wow part 3 is really cool
I cried when I switched my major to stats and went to class and it was all calculus..
bruh
A problem with the logic in 2:00, the sum of infinite amount of numbers is NOT always Infinite, and in some cases it can be calculated, for example the sum of an infinite geometric serie can be determined.
The point of the dart is not an infinitesimal point. It has an area no matter how small. And so the question of the probability of a dart hitting any "point" on the board should be what is the probability of the dart point's area being contained in the area on the dart board.
My boy Dream be like:
Petition to get the 3rd part of this series from Grant!
I wish at some point you would made some videos on Lebesgue Integration since it keeps being mentioned.
There is a huge difference between "equals zero" and "approaches zero". You might want to be more careful about which you mean at many of the points you used them.
has the third video comes out?
Nope not yet, still waiting
@@maxvanderveer4195 oh I hope it will comes out soon
A very similar issue comes up in quantum mechanics. Like with energy density and the ultraviolet catastrophe
where is the next part of video
Really
tell us if you found it please
The easiest way I can rationalise this in my head is as follows: The odds of h being exactly equal to any given value are infinitely small (0). However, there are infinite potential values of h. We are used to being able to total the probabilities of some real number of potential outcomes to 1, but we don't have a real number of possible outcomes.
Essentially, we are asking what zero multiplied by infinity equals, and that's an illogical question.
0*∞=n
∴ ∞ = n/0, which is illogical
almost struck a reward worthy topic
I just hope your prediction of 10M cases by Apr 22nd doesn't come true.
The number of recorded cases stopped following an exponential a couple weeks ago.
@@3blue1brown but test capacity stopped increasing a while ago too. Going by established death rates and infection to death delays, there's probably at least 5 million infected in the USA
The infinitely precise dart can hit (0.000001 , 0.23) because (0.000001 , 0.23) is an element of the set of points the dart can hit, and the derivative is the instantaneous rate of change.
dude thank u for these videos you have covered so damn much
I absolutely love your videos
Isn't the probability technically a limit approaching zero rather than actually literally being equal to zero? I might be misunderstanding but it would make a lot more sense if the probability is never technically zero, just close enough that mathematically it's effectively zero
So the way I think of it is each of those values is not P(0), but the smallest positive value above 0, which is infinitely small, and therefore converges to 0. It's technically not 0, but we have no way of writing its ACTUAL value, since its value is infinitely small.
You just discovered hyperreal, congratulations
In usually real number, infinitely small doesn't and can't exist, which is why 9.9999.... equals 10, there's no infinitely small 0.000....1
So, is the probability that an event is a possible event with zero probability still zero? If so, then not only do such events exist, but also the event that an event is such an event is itself such an event. Or for that matter, what about the probability that a possible event has zero probability, or the probability that a zero-probability event is possible? Are those two probabilities also zero?
Great Videos! I really appreciate watching them!
Any truly random draw from a continuous probability function is a transcendental number.
If the probability truly is zero, then barring a fault in the model it is impossible. In your case, the probability isn't zero - it's simply been rounded to zero because the actual probability is some small decimal number which is annoying to write down. Hence, probability of 0 means impossible assuming that the probability is *actually* 0.
1:37 Those are some nice decimal places you have there. I recognized pi, obviously, followed by e and then later phi; but that third one was strange. 4.6692? What kind of a number was that? That’d have to be the square root of like 19, which is a weird number. Curious, I looked it up, and - with no context - the Wikipedia page for the Feigenbaum constants came up. Wikipedia pages on higher math are completely unreadable, of course, so I looked it up on TH-cam and found a Numberphile video on it, because Numberphile has a video on every single number, and - because of a tiny little Easter egg in a video that I was rewatching for the second time - accidentally learned about a completely unrelated branch of mathematics and an incredibly strange phenomenon that arose therein.
I love the internet, and I love your videos
I love MItchell Feigenbaum. I think you'll like the book "Chaos" by James Gleick that covers the story of Chaos Theory (and related stuff, like non-linearity) very well. I have to say though, it's meant for the layman, so it does not go in-depth on any of the topics. It's more of a 'review' of the scientific community at the time, and the challenges of the emerging change brought by the idea of Chaos Theory (and those who thought about those ideas).
@@davids.4431 wait there's literally a theory called Chaos Theory??
@@luigiboy72 though the name is a bit misleading nowadays, it started off as the study of disordered and seemingly random behavior (be it of the weather or of certain equations), so they deemed it appropriate to call it chaos back then. Suffice to say that the badassery of studying 'chaos theory' was very welcomed by scientists in 1970, especially after a decade of fighting for it to be 'officially' recognized. Anyway, I highly recommend the book I mentioned if it has piqued your interest!
It's literally impossible for Numberphile to have a video on every single number.
@@jb888888888we need a video on probably of numberfile not having a video on every number xD
I like how whenever he says something, the little student pi's go like: *hmmmmm*
xPureOblivion "It's big brain time"
@@fatihaksu1830 ?
xPureOblivion that is also what I took from this
@@fatihaksu1830 u
we are the little πs
9 month later still waiting for part 3, it is okay take your time.
ME TOOO!!!!
@@Complexitivity +10. i'm in raptures as to how this all ends
One year and 5 days now. Still waiting.
@@a.fleischbender7681 god damn it how do we get his attention, i wanna watch all 3 in order again
In Latin it is called "coitus interruptus"
One of my favorite math jokes, relevant here:
A mathematician is a little drunk, and nudges the guy next to him at the bar and says, "Hey, think of a number. Any number at all." The guy says, "*Any* number?" "Yeah, any number."
"Okay, I got one," the guy says. "Is it rational?" the mathematician asks?
"Ummmm...yes..."
"HOW UNLIKELY!!!"
That's a good one
I'm big dumbness and I no get
@@justsomeguywithhalfamustac6837 i feel you dude,didnt get it either
@@henriquerock703 yes
@@justsomeguywithhalfamustac6837 , there are infinite numbers. In the infinite set of numbers, an overwhelming majority are irrational, so much so that, if something were to pick any number at random from the infinite set of all numbers, the probability of picking a rational number is 0.
A good way to illustrate that the probability of picking a rational number is 0 is to just imagine that you are creating the number you pick one digit at a time with each of the possibilities (0-9) being equally likely. So, to get a rational number, when you are picking the digits that go after the decimal point, you would basically have to get an infinite amount of zeroes in a row.
"Boy, this looks like Integral Calculus..."
...
"Oh"
Mindraker1 lol
1:31 If the numbers after 7 seem familiar, they are:
0
1
π
e
The Feigenbaum Constant
φ
After I saw π and e knew the other 2 were not random, thank you friend
Well, considering the date of upload, it's nice to find a couple of Easter eggs in this video :)
Good to see the Feigenbaum Constant is now considered somewhat of a famous number among math fans along with pi, e and the golden ratio. Veritasium might have something to do with it...))
@@dexter2392 I like to think of it as a tribute to Mitchell Feigenbaum who sadly died last year in June
it's sad how fiegenbaum doesn't have a universally known symbol yet
This series really makes probability and its probabilities click for me. Hopefully the long awaited part 3 will be uploaded soon :)
@@mEhLord19 brother it's 2$
@@Daniel-cc6gs rich
@@Daniel-cc6gs in my country 2 dollars will feed my family for a day. That a lot of money and take several days of work to get.
@@orvinal2883 where are you from?
@@Daniel-cc6gs Milwaukee
Interesting approach. So far, when I've seen PDFs in the wild, I've interpreted them with a PDF viewer. No longer!
I knew I was doing it wrong the entire time!
Asking the important questions right here
Adobe Reader works pretty good.
You should not have seen any of them in the wild in the first place. Printing out PDFs is just so 90s ...
Silly little distractions every time I had to write PDF on my work.. Cursed ambiguities