"You like math? Name every number then."

@hkayakh

3 жыл бұрын

-infinity to +infinity

@CaptHayfever

3 жыл бұрын

@@hkayakh: That's only the reals.

@hkayakh

3 жыл бұрын

@@CaptHayfever i is in there, if it weren't then it isn't

@maxonmendel5757

3 жыл бұрын

I wish I could upvote this twice.

@Ryanisthere

3 жыл бұрын

@@hkayakh imagine a square with the two points (∞, ∞i) and (-∞, -∞i) thats all the numbers well until we get into quaternions

It's reassuring to hear a mathematician say they read a math paper and couldn't comprehend it.

@sorenlily2280

5 жыл бұрын

It's absolutely true. It's like a native english speaker listening to a really heavy accent, like a heavy irish, or austrailian accent. If you've never really been exposed to that kind of accent before (that area of mathematics), you won't have a damn clue what they're saying, even though you're a native english speaker (mathematician). If you listen to some lighter accents, you can train your ear to eventually understand the heavy accent, but it's not easy. And unfortunately, even when you understand one heavy accent, it really doesn't help you with most other accents.

@heimdall1973

5 жыл бұрын

@@sorenlily2280 That sounds more like the language that lawyers speak and that you encounter in terms and conditions... Give me maths any day!

@redbeam_

5 жыл бұрын

I find it kind of scary...

@angelmendez-rivera351

4 жыл бұрын

Barrack Obama Vlogs Eh, no. Scientific papers are rigorously written. People are simply not properly educated to understand them.

@General12th

4 жыл бұрын

@@angelmendez-rivera351 In this case "people" includes professional mathematicians as well. Math is a subject with so much breadth _and_ depth that folks in one field can be newcomers in other fields.

0:15 There are only three whole numbers: 11, 17, and 3435.

@slamalamadingdangdongdiggy5268

4 жыл бұрын

That's why it's an Euler diagram

@bradbobov4815

4 жыл бұрын

Gives me chicken nuggets flashbacks

@sohenwei6937

4 жыл бұрын

Can someone please explain

@missrobinhoodie

4 жыл бұрын

Eꜰꜰi the numbers in the diagramm are examples of and not „all“ numbers of this category = Eulers diagramm

@nataliarodriguez3740

4 жыл бұрын

3

-We're going to do all the numbers -We're not going to do Complex numbers Oh

@coopergates9680

4 жыл бұрын

Quaternions.... octonions.... infinite cardinals and ordinals... Or versions such as p-adic and quote notation

@bogdandamaschin9381

4 жыл бұрын

Complex numbers do not exist technicaly speaking

@General12th

4 жыл бұрын

@@bogdandamaschin9381 All numbers are made up.

@noelkahn4212

4 жыл бұрын

@Cooper Gates technically the infinite cardinals, and ordinals aren't numbers that would be computable or normal I think

@EebstertheGreat

4 жыл бұрын

@@noelkahn4212 There is not the same notion of computability for cardinal numbers that there is for real numbers, but there is a similar notion for ordinals. Finite ordinals (natural numbers) are all "computable" in any sense, since you can compute them by just supplying all the digits. Uncountable ordinals are not computable. But it turns out that not all countable ordinals can be "computed" either, given the appropriate meaning of the word. Using a generalizaiton of Turing computability called hyperarithmetic, you can construct notations and prove theorems for all recursive ordinals. But you cannot do that for non-recursive ordinals, the first of which is called the Church-Kleene ordinal. Countable ordinals larger than this can be considered non-computable.

"An infinite series that gives you pie." -- Isn't that the Great British Bake-off ?

@serglian8558

5 жыл бұрын

yeah, I guess

@oldcowbb

4 жыл бұрын

it ended after they changed the host

@_Sara

4 жыл бұрын

No. -_- The name of the food and the name of the number are homophones. "Homophones" are words that have identical pronounciations but vary in spelling. "Pi" = the number and "pie" = the food.

@fghsgh

4 жыл бұрын

@@_Sara r/whooosh also, try not to annoy people by responding to their comments 6 months after they've written them EDIT 2 years later: sorry

@_Sara

4 жыл бұрын

@@fghsgh I am sorry I do not see every single KZread comment the exact moment they are posted. :)

So the majority of numbers are normal and noncomputable, but we don't know a single one? It's like... the mathematical version of dark matter. Dark mather.

@henrymick9648

5 жыл бұрын

Lol, you commented on the TwoSet Video aswell.

@superposition2644

5 жыл бұрын

It's kind of like that, except with no dark energy or mass or photons or space-time or transfinite ordinals.

@eventhorizon853

5 жыл бұрын

Pretty much, and just like the whole dark matter fiasco it looks more like a coping mechanism for our lack of understanding rather than a reasonable explanation.

@brcoutme

5 жыл бұрын

What they didn't show is what/if we know numbers are not normal numbers for the non-trival cases. That is to say, we don't know weather or not all transcendental numbers or computable numbers (that are outside of our transcendental numbers) are normal numbers. Rational (and thus, whole) numbers, are trivial to see that they are not normal numbers. (Thus, why Matt did not draw any intersection into them for his Normal numbers circle).

@brcoutme

5 жыл бұрын

@Ron Maimon I'm not going to lie most of that was over my head, but I did follow the bit about how to guarantee an uncomputable number is also a normal number by simply placing the digits of a known normal number into the digits of an uncomputable number (even though we can not actually compute it obviously). Not familiar with the Liouville numbers, but I'll take you word that it is a transcendental number that definitely isn't a normal number. I agree that the video would have been better giving these examples at least.

3:42 _Rap Lyrics_ Which? We don't know Pi to the e We don't know e to the e We don't know Pi to the Pi We don't know Right, these are all in the cusp!

@Razorcarl

4 жыл бұрын

Wow

@isaacmiles-watt2758

4 жыл бұрын

We know!

@GaryFerrao

4 жыл бұрын

4:19 there's st… there's a list; here's the only ones we know, and THAT'S IT. 4:25 Graham's number, in here. Googolplex, in here.

@thallduck

3 жыл бұрын

Looking for a math rap? Watch 3blue1brown's poem on e to the pi i

@spongebobbatteries

3 жыл бұрын

_bars_

I would love them to make a sequel to this, including the imaginary, hypercomplex numbers and hyperreals and asurreals etc.

I see Matt is trying to one up the other numberphile presenters by talking about *ALL THE NUMBERS*

@kapitantaryfa

5 жыл бұрын

he should put them in a magic square

@General12th

5 жыл бұрын

Then Tony will come back with a video about *ALL THE OTHER NUMBERS*

@standupmaths

5 жыл бұрын

Aceronian “ne up them? I’m trying to up them by an uncomputable amount.

@sevret313

5 жыл бұрын

All they need to do to up him again is to solve his mistakes in the Parker Square.

@rq4740

5 жыл бұрын

@standupmaths I’m afraid your letters have gone off eating each other again, Matt 😂

So "all the numbers", but not quite. So it's like a Parker Diagram then.

@TheMrvidfreak

5 жыл бұрын

For sure. Even the Parker Square, drawn on a non-cube for the occasion, can be seen present at the birth celebrations of another of its kind at 12:07.

@Filip6754

5 жыл бұрын

He hasn't begun with the naturals either.

@Ploppism

5 жыл бұрын

A Parker Circle?

@SassInYourClass

5 жыл бұрын

Chvocht - Also no direct mention of integers. He just kind of halfway acknowledges them exist without labeling them.

@davecrupel2817

5 жыл бұрын

I take it we're never letting Matt live this down...

I love how mathematicians discovered the rarest group of numbers and decided to call them 'normal numbers'.

@jasondeng7677

2 жыл бұрын

12:34 not really the rarest but yeah... still a strange name to choose for this kind of like obscure category

@user-ef8kc4rv7n

Жыл бұрын

They're not rare almost all numbers are normal. If you were to randomly pick a value from a distribution it would be normal with probability 1.

@d3xCl34n

Жыл бұрын

they describe the normal - 1 tree 2 monkeys 6 bananas (thats the logic).

@mihailmilev9909

Жыл бұрын

@@d3xCl34n *w h a t*

@mihailmilev9909

Жыл бұрын

@@d3xCl34n banana monkey brain neuron activation

"As mathematicians we're thinking we are getting somewhere, but up until now we have found none of the numbers."

I love how the code on the laptop animation actually does compute pi when you run it! Attention to detail!

@forstnamelorstname4169

4 жыл бұрын

So does the recipe.

@rocketlawnchair9352

4 жыл бұрын

And written in Python, making the whole thing a play-on-words. I love numberphile.

@fanq_

3 жыл бұрын

@@rocketlawnchair9352 python most likely because Matt knows and uses python to play around and research videos

@AssemblyWizard

3 жыл бұрын

5:05

@toniokettner4821

2 жыл бұрын

by just looking to the right you'll be surprised that the 3.14... gives exactly that away

this video should be called 'None of the Numbers'

@jimmythewig3354

5 жыл бұрын

Or Parker All of the Numbers...

@Tjalve70

5 жыл бұрын

Infinitely few of the numbers?

@ZeHoSmusician

5 жыл бұрын

Adding a quantum dimension to this topic: The video is of course titled "all the numbers"...but that's *if you don't watch it*. As soon you do, then the title changes to "none of the numbers"... :D

@neilgerace355

3 жыл бұрын

"Almost all" numbers are transcendental

@luantuan1653

3 жыл бұрын

'Some of the Numbers'

I just love everytime a different subject illustrates this saying: "The more you know, the more you know you dont know"

@dasguptaarup8684

3 жыл бұрын

you might say that is "clarity" : knowing what you don't know....

@slkjvlkfsvnlsdfhgdght5447

3 жыл бұрын

@@dasguptaarup8684 noice!

@user-kf9rf3zy6b

9 ай бұрын

This video is the humblest way of saying "I know that I know nothing"

@ronald3836

3 ай бұрын

I know.

5000 years ago: we need something to help count stuff! Let’s call it numbers! Now, in 2020: we don’t know most of the numbers!

@aldobernaltvbernal8745

4 жыл бұрын

but we don't lol

@KombatGod

4 жыл бұрын

I just discovered a new number! 1278603764680367894927767590382684995837376374858483735241790693752137800965358000000000000010000100100100006594762729191661916151881161681948583826261515618010100101000101110000001001111111106648493025858493028475749374748387384847641324422048487646483929201.003 Yes, it's a new number. It's nothing special but it was never said nor written down in the history of mankind.

@hyungilkoo9340

4 жыл бұрын

KrossoverGod why is there a r in it

@KombatGod

4 жыл бұрын

@@hyungilkoo9340 There's no r in it.

@hyungilkoo9340

4 жыл бұрын

KrossoverGod yes there is there’s also an e in it

"this is where numbers are, and we have none" is so funny to me

@ModernandVintageWatches

2 жыл бұрын

I am amazed with all the science channels, the breakthrough in physics, medicine etc are almost daily basis now

You should do a video about the 100 page proof in Principia Mathematika of how 1 + 1 = 2

@Blox117

5 жыл бұрын

damn thats a hard one

@Blox117

5 жыл бұрын

i only have proof for how 1=1

@DominiqEffect

5 жыл бұрын

@@Blox117 But not in Lie algebra groups.

@yourlordandsaviouryeesusbe2998

5 жыл бұрын

@@DominiqEffect *confused*

@heimdall1973

5 жыл бұрын

@@Blox117 Let's see it

"countable infinity land" I prefer the observable universe of numbers 😂

@RandomAmbles

2 жыл бұрын

Weeeeeeell... quantum mechanics currently suggests that there are continuous properties in the actual universe, which is sick, just absolutely sick. Like rotational, translational and Lorentz symmetry are all supposed to be continuousish. I'm skeptical of this, frankly, but I need to be open to the possibility that the universe is not fundamentally discrete. Apparently Buckminster Fuller was considering how to construct systems of physics with discrete properties, but he's pretty much unreadable. It's an open question.

@bardofhighrenown

2 жыл бұрын

Hard disagree "Countable infinity-land" is the superior term.

@ModernandVintageWatches

2 жыл бұрын

I am amazed with all the science channels, the breakthrough in physics, medicine etc are almost daily basis now

My takeaway is that the real numbers are far more complicated than one might think. I certainly felt a level of comfort with them when I took my first real analysis course years ago - “they’re just non-terminating decimal expansions with no repetitions” - but even that alone is an extremely deep and complicated statement. People are fooled by the simple name “real numbers” that we sort of understand them, but we just don’t. As Matt said, most reals are “dark”, and also bizarrely, there are subsets of the reals that can’t be assigned a meaningful notion of “volume”. This leads to weirdness like Banach-Tarski.

@isavenewspapers8890

4 ай бұрын

"non-terminating decimal expansions with no repetitions" That sounds like a description of the irrational numbers.

@eguineldo

Ай бұрын

​@@isavenewspapers8890 Irrationals definitely are like that but there are rationalsk like 1/3 which have an infinite decimal expansion.

@isavenewspapers8890

Ай бұрын

@@eguineldo "with no repetitions"

@eguineldo

Ай бұрын

@@isavenewspapers8890 Apologies, I guess I didn't read your comment very thoroughly. Then I would agree

@isavenewspapers8890

Ай бұрын

@@eguineldo Nice. Technically, any terminating decimal expansion can also be made non-terminating; you just put infinitely many 0's at the end. You can even do some weird stuff like represent 1 as 0.999..., but let's not get too crazy here.

|*facepalms*| Mind blown in the first thirty seconds. Decades of math and science, a full understanding of what rational numbers are, and only when he says, "The rational numbers-those that are *ratios* ..." do I finally make the connection between those two words... Thanks, Matt!

@t.c.bramblett617

5 жыл бұрын

I remember when I made that connection too, it was one of the big epiphanies. lol as a non-math student or professional, I also got my mind blow quite late in life by Euler's formula, and I think the biggest mind blow moment I can remember regarding math was learning about Cantor's infinities

@ryanoutram7059

5 жыл бұрын

"Ratio" came first too! :)

@tcoren1

5 жыл бұрын

Barefoot the way I heard it, the ancient greek (or whoever), weren’t big fans of irrational numbers, and felt they didn’t make sense-they were “irrational”, and that’s were the term comes from

@t.c.bramblett617

5 жыл бұрын

@@tcoren1 Yeah the Greek term is "alogos" for irrational or unknowable. "ir/ratio" is Latin and was the translation used by later Renaissance mathematicians

@brooksolomon7663

5 жыл бұрын

Is the "golden ratio" rational or irrational? That was the first question that came to my right after he said that

e was the first number that arose "naturally" in math to be proven transcendental, but the actual first numbers were the Liouville numbers in 1844, deliberately constructed for the purpose of being transcendental.

@guillaumelagueyte1019

5 жыл бұрын

Artificial numbers heh

@vivekmathur3514

5 жыл бұрын

Ceski.

@alansmithee419

5 жыл бұрын

@@guillaumelagueyte1019 so... Numbers? Literally all numbers.

@Cythil

5 жыл бұрын

It is quite funny that we see numbers as "Artificial" or "Natural" when we just mean by that they where ether constructed specifically for the purpose of creating number that fits a category, or was number that we had constructed for a different purpose that was later found out to belong to one of the categories. Maybe not the best terminology but it sort of feels right anyway. ^_^

@EebstertheGreat

5 жыл бұрын

@@Cythil Pretty much. e is a useful constant in many ways, and its transcendence is the type of problem mathematicians were really interested in. Liouville defined his numbers just to demonstrate that transcendental numbers exist; they have no other known practical use. It's sort of like pointing out that 0.123456789101112131415... is normal. This is true, and it's trivial to show, but it isn't exactly a useful result in the study of normal numbers.

I just feel awe at the fact that we created math as a concept and now its something people are working their lives to unveil because we created something, a huge set of rules and interactions that have lied out a entire infinitely sized concept that has grown larger than what the creators understand of it. The concept of math growing larger than the people who created it, now that's something.

@mondkalb9813

2 жыл бұрын

Math + computers = even more awe. :D When I got my Amiga back in the late 80s, I started exploring fractals (mainly the Mandelbrot set) and continued so later on with better and better PCs. What then took hours or days to compute, you can do now nearly in real time on modern home computers. There are videos on Youbtube showing zooms into the set to unbelievable depths. What struck me with amazement: Even on small home computers, when you zoom in deep enough, the whole Mandelbrot set relatively grows bigger than the entire known universe pretty fast. With 100% certainty you are looking at details, that nobody else has ever seen (though, due to the nature of the set, they all look similar).

@ModernandVintageWatches

2 жыл бұрын

I am amazed with all the science channels, the breakthrough in physics, medicine etc are almost daily basis now

@auscaliber1

Жыл бұрын

There is a long standing philosophical debate about whether maths is invented/created or discovered. I don't think we created maths, we just created our own sets of language and symbols to interpret it.

@mevideym

Жыл бұрын

@@auscaliber1 But we assume axioms which we deem useful and then derive true statements using logic from them

@cara-setun

Жыл бұрын

We don’t create math anymore than I create a landslide by tossing a rock onto an unstable pile. I trigger things with an input, but the architecture was there the whole time.

Ah yes the normal numbers. Their only weakness is against fighting type numbers.

@AureliusR

6 ай бұрын

Don't forget ghost-type numbers too.

@somerandommusicianSRM

5 ай бұрын

Normal numbers got nothing on steel type numbers

In the article "Borel normality and algorithmic randomness" Calude proved that every Chaitin's constant is normal. So, exist a non computable number, which is normal.

@superposition2644

5 жыл бұрын

:O

@thefamousarthur

5 жыл бұрын

Random Decimals: 2.817316571046953926392639363856293619263625287483748846362515375828402010164936492638262748392

@thefamousarthur

5 жыл бұрын

And so on.

@randomdude9135

4 жыл бұрын

I didn't fully understand what computable and an noncomputable numbers are. Can some one clearly explain? :/

@WaffleAbuser

4 жыл бұрын

@@randomdude9135 If there exists an algorithm to compute a number's digits, then it is a computable number. If no algorithm can exist, it's uncomputable.

How can one not love Matt Parker?

@TheOneMaddin

5 жыл бұрын

At times, he is a little bit too unprecise. But thats the price for being popular anong non-mathematicians.

@cordlefhrichter1520

5 жыл бұрын

@@TheOneMaddin Imprecise*

@Triumvirate888

5 жыл бұрын

Matt Parker loves himself so much that the rest of us don't need to.

@jon2431

5 жыл бұрын

@@Triumvirate888 GOT EM 😂

@jon2431

5 жыл бұрын

Also, you okay buddy? Sounds like you think loving yourself is a bad thing.

It's amazing how we will only ever know 0% of all numbers no matter how hard we try.

@nathantempest9175

4 жыл бұрын

not exactly ) but an infinetely close number to it

@DemoniteBL

3 жыл бұрын

infinitesimal% of the numbers

@Cowtymsmiesznego

2 жыл бұрын

@@nathantempest9175 The only real number "infinitely close" to 0 is 0.

@Elrog3

Жыл бұрын

@@Cowtymsmiesznego Maybe he uses hyperreals.

@charliedegiulio9951

Жыл бұрын

We have discovered infitecimal% of them

There is actually a larger circle around the computable numbers called the set of definable numbers. Definable numbers contain all computables and is also countably infinite. The Chaitin constant is a definable non-computable.

@Liggliluff

2 жыл бұрын

Can you give an example of a non-definable number? ;)

@sabouedcleek611

2 жыл бұрын

@@Liggliluff Wait a minute...

@SG2048-meta

2 жыл бұрын

@@Liggliluff uh, the chance that the number of- oh I just defined that number, uh, the number of ways you can ea- ah just defined that as well aaaah

@trifonmag4205

Жыл бұрын

@@Liggliluff literally point at anywhere on a ruler, the chances of the specific point being undefinable are almost 100% (unless you point at an integer)

@tobiaswilhelmi4819

Жыл бұрын

​@@trifonmag4205 Are you actually talking about the number defined as "I'm pointing at it right now"?

We need a video on non-computable numbers! (please)

@gibrana9214

5 жыл бұрын

By uploading, through a computer, it would become... Computable?

@gold4963

5 жыл бұрын

Gibran A ...Mind-blown.

@Patrickhh69

5 жыл бұрын

For example: busy beaver numbers and Rayo number

@KafshakTashtak

5 жыл бұрын

Does not fempute, does not fempute.

@aaaa-hj9vv

5 жыл бұрын

@@Patrickhh69 The busy beaver function is uncomputable, but the numbers themselves are computable because all integers are computable. That is, we can't compute what the numbers actually are, but we know that no matter what they are, they are computable numbers.

I like that you put 22/7 which is of course Parker Pi :)

@massimookissed1023

5 жыл бұрын

355/113

@martinepstein9826

5 жыл бұрын

333/106 is Parker 355/113

@dlevi67

5 жыл бұрын

@@martinepstein9826 Spoken like a true numberphile.

@Tfin

5 жыл бұрын

22/7 has been pi longer than he's been alive. It was what we used in school before they taught us decimals.

@dlevi67

5 жыл бұрын

@@Tfin Unusual curriculum where they teach pupils fractions and long division before decimals...

This is just one of those videos you have to watch every year.

"Chaitin's constant" is non-computable, and is proven to be algorithmically random (see: Downey, Rodney G., Hirschfeldt, Denis R., Algorithmic Randomness and Complexity), thus it is normal. So, strictly speaking, we know quite a few non-computable normal numbers - that is, Chaitin's constants Omega(F) for prefix-free universal computable functions F.

@andrewgaul3001

3 жыл бұрын

if you say so🙃

@JGHFunRun

Жыл бұрын

sauce?

@trifonmag4205

Жыл бұрын

@@JGHFunRun ketchup

Numberphile: "ALL The Numbers!" Me: *heavy breathing* (Gets un-countably infinitely excited)

@whatisthis2809

5 жыл бұрын

Ω level of excited?

@brumbysdalby27

5 жыл бұрын

Hey v sauce Michael here

I found hundreds of uncomputable numbers in my calculus homework

@saetainlatin

5 жыл бұрын

just wait when you get to differential equations, no numbers whatsoever, just uncomputable letters and variables

@dlevi67

5 жыл бұрын

@@saetainlatin Abstract algebra I find much worse. Differential equations I can somehow "understand" geometrically (not always, and not always easily), but a variety? Or a vector space?

@LuigiElettrico

5 жыл бұрын

Uncomputable teacher xD

@jakedones2099

5 жыл бұрын

@@dlevi67 I agree with you

@lyrimetacurl0

5 жыл бұрын

@@saetainlatin Then wait till you get to partial differential equations

I love the little details here. Like how the drawn circles are slightly larger in the upper left area and more compressed in the lower right and the animation matches it. Also can we talk about how the camera man has continuously gotten smarter as these videos go on. His questions keep getting more and more clever.

This is my favorite numberphile video. Keep coming back to this.

When I was 5 years old I started writing numbers on a paper. (1 2 3 4 etc). When I got done with one paper I'd tape another piece of paper to the bottom and continue. Eventually I had a 20 foot long roll of paper that all the way up to 1200. I then made a few other, shorter rolls. They somehow morphed into a character called "The Numbers" and his friends, and I used to write stories about them including a time where they had to escape vicious evil pianos. Fun times.

@tonio103683

5 жыл бұрын

Reminds me of Philemon. Cool story.

@bb2fiddler

5 жыл бұрын

I want to read some, link plz

@PhilBagels

5 жыл бұрын

When I was about 10 or 11, I wrote out a Pascal's Triangle, and taped additional pieces of paper to the bottom of it so I could keep adding more rows. It never got to 20 feet long, but it was probably over 4 feet long.

@jamesWilliams-py5zy

5 жыл бұрын

R/thathappened

@iqbaltrojan

5 жыл бұрын

awesome!

I love that he snickered during the -1/12 :^)

@kaviramyead7987

5 жыл бұрын

If you don't get it google zeta function regularization.

Matt Parker managed to spoil even our understanding of numbers! Thank you very much.

“Grease a circular tin.” I love it!

it was proven that chaitin's constants are normal in 1994

@cj719521

5 жыл бұрын

Citation needed

@BattousaiHBr

5 жыл бұрын

@@cj719521 wikipedia 4Head

@gabrielfrey3004

5 жыл бұрын

Yes. Chaitin’s constant is normal Even if it was not normal, it would probably be possible to create a non computable normal number based on the Chaitin’s constant and the Champernowne constant, for example by alternating set of bits from these two numbers

@gabrielfrey3004

5 жыл бұрын

Yevhenii Diomidov Yes, I was thinking of using the Champerowne constant construction and just adding some digits from a non computable number (or some of the non computable rules used to define a non computable number)

@steffahn

5 жыл бұрын

To add on to the "this is the only properly empty section" claim at 11:56, for which of course your comment already says it's false, we additionally have - at least according to Wikipedia (article on "normal number"s) - that "there [...] exists no algebraic number that has been proven to be normal in any base". So if Wikipedia is correct there, that's a different "properly empty section" in the sense of the video.

Thank you SO MUCH for stretching my brain like this!! I am not a mathematician, nor will I ever be one, but I swear my quality of life is noticeably improved every time you guys blow my mind like this! I’m gonna have to go lay down for a bit and sort of digest this stuff. Thanks again!!

@Woogieboog

2 ай бұрын

LOL @ lay down for a bit and digest this stuff.

This is one of my favorite videos about math. It is so mysterious and I end up with questions. I wonder if it might be easier to check if an irrational or transcendental number is normal by changing the base of the number system. We use base 10. If we use base 2, we just have to deal with 0s and 1s.

12:13 "this is completely empty" as in "we don't know any numbers that go in here", not as in "we know that zero numbers go in here".

@heimdall1973

5 жыл бұрын

The animation was wrong though. As it zoomed out and the "normal" circle gets relatively larger, the line should straighten and curve the other way, making it so the normal numbers are outside the circle and the circles would then indicate bubbles that are virtually nothing but we don't know anything from outside those bubbles.

@factsverse9957

4 жыл бұрын

@@heimdall1973 but it gets the point across, it's not an intended pun because it's technically wrong.

@Cowtymsmiesznego

2 жыл бұрын

In fact, as he explained later - almost all numbers DO go in there

Can we get Algebraic Parker Number?

@FawwazSyarif

5 жыл бұрын

I can't believe I met you here!

@cristianstancu6700

5 жыл бұрын

Almost but not quite

@darealpoopster

5 жыл бұрын

Fauzan D. Rywannis Probabilistically it’s 0

@tryAGAIN87

5 жыл бұрын

I thought the Parker square was already algebraic, although not consistent with magic squares lol. Does that then mean the Parker square is a non-computable magic square?

0:40 "Circular Thingys" 10/10 best description

@sugarandbones6272

3 жыл бұрын

it's so much better when you realize that particular diagram is neither a venn diagram nor euler diagram

I love how the cameraman is just as clueless as everyone else, it kind of acts to give the viewers some chance to comprehend the math via him asking the questions we were all thinking.

3:18 I never knew 1873 was transcendental

God, Matt Parker is truly the best.

@GrandMoffTarkinsTeaDispenser

5 жыл бұрын

He is isn't he? Man is full of joy and brightens my day to see this video, thank you Matt.

@joryjones6808

5 жыл бұрын

Aidan Worthington nice Feynman pic but mine’s better.

@folksyoxytocin

5 жыл бұрын

@@joryjones6808 Thanks bby. But mine is the best

@henryordish

5 жыл бұрын

u missed a comma after "Parker"

"We gonna talk about ALL the numbers!!!!" (except the negatives) In other words, all the parker numbers

@helloofthebeach

3 жыл бұрын

Negative numbers have committed the unforgivable crime of being boring.

@adamrezabek9469

3 жыл бұрын

@@helloofthebeach but without them, we have no fun with complex numbers

I like the " so its tike the least efficent way to do this" reaction -> His mimik and voice for " it is"

I think it would be interesting to do a video on non-computable numbers. Seems like a fascinating concept that we know examples of something so seemingly impossible

9:28 "That's an N, it's just climbing under the A" a.k.a. _Parker spelling_

When Parker said this is beyond me... wow :D

Still my most beloved Numberphile video. I've watched it so many times now, it flashes me every single time. Whenever I feel tempted to believe that we may have maths figured out for the most part, I watch this video. And bam, I'm back at square zero. Really an intellectual shower if you think about it, for getting rid of primate-brain hubris.

@semicolumnn

2 жыл бұрын

I know that the fact that we have none of them is scary but they’re just arbitrary numbers in R, which means they obey theorems and rules of the real numbers, and are just limits of Cauchy sequences like 3 and -1/12

@ModernandVintageWatches

2 жыл бұрын

I am amazed with all the science channels, the breakthrough in physics, medicine etc are almost daily basis now

"up until now we have found none of the numbers" - Absolutely love that line!

For me, everything outside of the "Rational numbers" circle might as well be labelled "Here be dragons" :)

@Cookiefz

5 жыл бұрын

What's wrong with dedekind-completeness and algebraic closure?

@dlevi67

5 жыл бұрын

Don't have irrational fears. It's not even complex stuff.

@Vietcongster

5 жыл бұрын

Beyond the computable numbers should be labeled "Here be Lovecraftian Elder Gods"

@dlevi67

5 жыл бұрын

@@Vietcongster Appropriately surreal...

@trondordoesstuff

5 жыл бұрын

@@Vietcongster Beyond computable numbers and in normal numbers should be labeled "Here be".... I actually don't know.

PLEASE DO A VIDEO ON UNCOMPUTABLE NUMBERS!!!

@heimdall1973

5 жыл бұрын

I might give it a go when I'm not too busy. As long as there's some interest. There's not loads to say about them, but there is something. Shall I give it a go?

@robertdarcy6210

5 жыл бұрын

@@heimdall1973 yes

@heimdall1973

5 жыл бұрын

@@robertdarcy6210 I'll have to work out how to do video editing to animate the numbers and curves as is done in this video. Mathematically I already know some things I'd like to mention and how I'd like to present it... So... I can record myself talking and writing. But during some of the video, I would like to keep the sound and replace the picture of me with an animation - that I don't know yet how to do. I'll check what the built-in video editing software on my laptop can do...

@felixmerz6229

5 жыл бұрын

ThreeBlueOneBrown animates his videos using a python module he wrote and it's on github. If you're into programming, it's probably the most useful tool for that purpose.

@heimdall1973

5 жыл бұрын

@@felixmerz6229 Thanks. I'll look into it. I never tried python before but it looks simple enough.

ahem, _observe_ from random import choice while 1: print('0.'+''.join(choice("0123456789") for i in range(∞)))

one thing is being a phisycist or a chemyst looking at what has everyone in your field has discovered and wonder how much is yet to be found. other thing completely diferent is to look at your field of study knowing *exactly* what everyone don't know and don't even understand. This is a a whole other level of a beast.

Perhaps I have been watching too much Great British Baking Show, but I quite liked the Pi Recipe at 6:05

Thank you for refuting the *assumed* normalcy of π; that ALWAYS bothers me!

Just saying, watching Turing and Champernowne both mentioned in the same video is quite satisfactory

I like the choice of the rational numbers, 22/7 being an approximation for pi and -1/12 being the result of summing 1 + 2 + .. + n. Maybe 7/2 & 1/17 also have special properties, but I'm not aware of these.

If Pi turned out to be "Normal" then would you be able to find Pi within itself? Would Pi be a fractal?

@Kycilak

5 жыл бұрын

As a layman I'd say no because π would have to be recursive.

@yourlordandsaviouryeesusbe2998

5 жыл бұрын

@@Kycilak But how can it be recursive if the digits of π itself never repeat and are infinitely many...

@Kycilak

5 жыл бұрын

@@yourlordandsaviouryeesusbe2998 That was my point. More formally I would construct proof by contradiction. Say whole π can be found in its fractional part after some finite number n of digits from decimal point. That means that somewhere in its fractional part it continues with the same digits with which it starts. In order to contain itself whole would mean that after another n+1 digits from decimal point it would start again this sequence and so on. That would mean that digits of π are recurring which would make π rational. We have proofs that π is not rational so we have come to contradiction. Hence our assumption must be wrong and π is not contained whole in its fractional part. QED I hope I have not made any mistakes. Feel free to correct me. As I said I am but a layman.

@heimdall1973

5 жыл бұрын

What you *can* say about pi (if it's normal) is that however big (finite) chunk of pi's digit sequence you take, it will be contained elsewhere within the sequence again and again. For example, the first billion digits will be repeated infinitely many times. So will the first quadrillion digits. Or the first Graham's number of digits... Of course, not periodically.

@Kycilak

5 жыл бұрын

@@heimdall1973 I agree, all finite sequences would be in there somewhere.

Let's just admire the genius of the recipe at 6:04 😁

Could have also added definable numbers: numbers that can be defined in a formal language (so any number you can in any way define uniquely). These numbers form a countable infinity (as all formal sentences are finite strings of a finite set of symbols), so almost all numbers are undefinable, i.e. such that you cannot even specify any one of them.

@gofrisuto

4 ай бұрын

What do you mean we can't define it? Un undefined number is undefined because it doesn't have a name yet, however using set theory, all numbers can be defined.

really appreciate the content! i have a lot of passion for math and when i’m home sick (which happens a lot because of my weak immune system) this fills the hole that my alg 2 class does

@tommypensyl5891

2 жыл бұрын

I think we can still easily make an artificial normal, uncomputable number, by defining a new number to be the interlacing of the digits of an uncomputable number with the sequence of whole numbers.

Get it, 1873, 1882 and 1934 are transcendental.

@dlevi67

5 жыл бұрын

Also 139, 1826, 1837, 1852.

On the Wikipedia entry for Chaitin’s constant it says that it is indeed normal, contradicting what Matt said. What is it then?

@piguyalamode164

5 жыл бұрын

That probably means that people think its normal, but we don't know, unless it has a citation.

@logicalmusicman5081

5 жыл бұрын

It means that like the Hitch Hiker's Guide to the Galaxy, Wikipedia is often incorrect but is the most used encyclopedia because it is cheap (free).

@pi314159265358978

5 жыл бұрын

​@@piguyalamode164 It seems that there is a proof in "Borel Normality and Algorithmic Randomness" by Cristian Calude, 1994.

@Theo0x89

5 жыл бұрын

[citation needed]

@pietervannes4476

5 жыл бұрын

@@pi314159265358978 Always fun to see youtubers you know in comment sections of something completely different

6:20 By “most” he means “100%”. The ones inside that outermost circle make up the remaining 0%.

@Owen_loves_Butters

Жыл бұрын

But that 0% is actually not 0, but an infinitesimal.

There's also the "nameable/unnameable" reals. For some logical system (I hear the kids are all into ZFC these days), the set of all finite strings of symbols in in that system that define a unique real number is only countably infinite, thus we can only uniquely define a countable subset of the real numbers. The rest are "unnameable" numbers. This set is so weird that, by defininition, cannot ever find a specific example.

@NYKevin100

Жыл бұрын

Strictly speaking, you have to be very careful about how you reason about such things, or else you run into fun problems like Richard's paradox. Ideally, you want to characterize this in terms of model theory, but that requires a lot of rigor.

"e" wasn't the first number proven to be transcendental! The first number proven to be transcendental was an "artificial one" (as Matt would call it) called "Liouville's number".

@angelmendez-rivera351

5 жыл бұрын

TheWinter e is the first non-artificial number to be proven to be transcendental, is what he meant, and this much is true.

7:35 When even Matt doesn't understand it, how can we simple mortals understand it? But great video to show us a glimpse of it.

This video puts things to a whole new level

Thank you so much for blowing my mind. I love you.

This was a Parker Square of a video for not including the negatives

@andymcl92

5 жыл бұрын

They were just on the back of the page

@salehuddinabdulmanan6799

5 жыл бұрын

B to the inbox folder and I b b 9b0 to ppp the. To the b in o to to p 0bb HV 9

@salehuddinabdulmanan6799

5 жыл бұрын

J HV GCB

@salehuddinabdulmanan6799

5 жыл бұрын

To h0OhOhOhho0bhp0vp. To

@BattousaiHBr

5 жыл бұрын

nor the complex

Matt, I love you and all your Maths knowledge, but you apparently need to go read "Borel Normality and Algorithmic Randomness" by Cristian Calude, 1994. There is a proof contained within for Chaitin's constant being normal.

I would like to point out that the HUngarian guys' name, who contributed to the Copeland-Erdős constant, was indeed Erdős, and not Erdos or Erdós, or something lik that, because those names connot exist in our language. Respectfully.

This is probably my favorite Numberphile video

@ModernandVintageWatches

2 жыл бұрын

I am amazed with all the science channels, the breakthrough in physics, medicine etc are almost daily basis now

12:35 I was curious about what the statement "Most numbers are normal" means, and initially thought it meant that normal numbers are uncountable, but non-normal numbers are countable. But according to wikipedia, both sets are uncountable; in this case, "most numbers" means something different, to do with something called Lebesgue measure.

@pdawg216

5 жыл бұрын

Intuitively, you can think of that as if you picked a random number, the probability that it is normal is 1. Or, if you know about integrals, if you define a function which is 1 on the normal numbers, and 0 on the non-normal Numbers, and integrate that from 0 to 1, you get 1.

@henrikbrautmeier6534

5 жыл бұрын

Tbh i thought most numberfile viewer have a mathematic background. Everyday, one can learn something new

@GravelLeft

5 жыл бұрын

@@pdawg216 Wow, that's weird. It's as if you start with a function which is 1 for every real number, then the integral from 0 to 1 will be one, representing the area of a 1x1 square, then when you go to the integral of the function you described, it's as if you're removing an infinitesimal sliver of area from the square for each non-normal number, which there are uncountably infinitely many of. But the area still remains 1.

@haniyasu8236

5 жыл бұрын

The integral idea works, but you don't need it. Another way of thinking about it is that if you take all the real numbers from 0 to 1 and try to cover it with open intervals such that no normal number is left out, the total length of those intervals will never be less than 1. The key thing to note is that if you try to do this with other sets of numbers (like the rational or even algebraic numbers) , you can actually cover all of the them with open sets of any total length. For rational and algebraic numbers, this is easily provable by using the fact that they are countable. However, there are uncountable sets of numbers where you can do this as well (like the cantor set), so hence why the converse about normal numbers is significant.

@paoloborello2530

5 жыл бұрын

@@pdawg216 I'm not sure that function can be integrated with a Riemann integral

It's amazing. Basically every number is an infinite series of digits that follow no underlying rule

@Sonny_McMacsson

4 жыл бұрын

Rule #1: Follow no rules

"Champernowne's constant is one of the few numbers we know is normal" he says, writing it outside the "normal numbers" circle (and for that matter outside the computable one, too), making this in fact a Parker diagram

Spectacular - well done!

@ModernandVintageWatches

2 жыл бұрын

I am amazed with all the science channels, the breakthrough in physics, medicine etc are almost daily basis now

Wouldn't you be able to weave Chaitin's number with Champerowne's number? Alternating between writing out n and the n-th Chaitin digit? That would be an uncomputable normal number. Edit: Sorry that may not be a normal number. Maybe if you increase the occurrences of Champerowne's number at later places in the digit expansion, in order to give it infinitely more weight in the limit? So you'd wait longer and longer amounts of time until adding the next Chaitin's digit. Just an idea though. Edit 2: Wikipedia says that Chaitin's number is normal. Now I'm just confused.

@angelmendez-rivera351

5 жыл бұрын

nivolord Matt Parker is wrong. Chaitin's constant is in fact normal. This is a well-known fact in mathematical computer science.

@nivolord

5 жыл бұрын

@@angelmendez-rivera351 Ah, thank you! Seemed odd there wasn't an example of such a number.

9:23 That was a real Parker Square of an 'n' :D

Thank you. Great you add subtitles. I link to your video in my Number theory page on my site.

A slight correction; e was not the first number proven to be transcendental. It was Liouville's number in 1851. It is 0.1100010000000000000000010... (the nth digit is 1 if n=k! where k = 1, 2, 3, ... and 0 otherwise, so there is a 1 in the 1st, 2nd, 6th, 24th, etc. digit to the right of the decimal point). But it is true that other than numbers specifically constructed to be transcendental (like Liouville's number) e was the first number to be proven transcendental.

Actually e wasn't the first to be proved transcendental, some weird decimals were.

@prakashlikhitkar

5 жыл бұрын

Those weird decimals are called Liouville numbers.

@UltraCboy

5 жыл бұрын

Like the first normal numbers, the first transcendental numbers were specifically designed to be transcendental.

@alephnull4044

5 жыл бұрын

@@prakashlikhitkar Yep

@hedger0w

5 жыл бұрын

Dark numbers and weird decimals, I think I had enough internet for today. And its Monday. I might be able to watch video about infinity alone on Monday but this is too much.

@serraramayfield9230

5 жыл бұрын

The username makes this better

3:23 1873 is a transcendental number

@Owen_loves_Butters

9 ай бұрын

No

I love this channel so hard. ❤

@numberphile

4 жыл бұрын

Thanks

Still one of my favourite videos on this channel! :)

@ModernandVintageWatches

2 жыл бұрын

I am amazed with all the science channels, the breakthrough in physics, medicine etc are almost daily basis now

..and outside all those groups? The Parker Numbers.

@mathgeniuszach

4 жыл бұрын

A perfect example of how I can take a joke too literally... XD

So basically, there's an infinitesimally small ammount of things which make sense and we can grasp, and an uncountable f**kton of infinitely large lovecraftian horrors

I'd like to introduce the Pitman constant... It's like Champernown's constant except, instead of starting with the beginning of the number line, my constant starts with the end and goes back. It has the unique quality of being the only number with an infinite number of digits which we know the last uncountable number of digits for.

One thing I like is that although the set of computable numbers is countably infinite, the set itself is not computable _i.e._ there does not exist a finite algorithmic procedure for generating the set of computable numbers.

@ModernandVintageWatches

2 жыл бұрын

I am amazed with all the science channels, the breakthrough in physics, medicine etc are almost daily basis now

No normal uncomputable is non empty, actually it is very easy to come up with one : Let n be the number defined as such : at step i write the i-th digit of the chaitin number, then write the i-th natural number you've not yet written. This number is normal (by construction) and uncomputable.

@ChibiRuah

5 жыл бұрын

That was what I was wondering too

@Wargon2013

5 жыл бұрын

How is it uncomputable if you can define an algorithm to produce it?

@fnors2

5 жыл бұрын

"computable" informally (really informally) means that you can find an algorithm to aproximate the number to 'n' decimals then halt in finite time. The algorithm you gave can be used to approximate the number by stopping at 'n' decimals. So it is a computable number, since Chaitin number is computable.

@ramdamdam1402

5 жыл бұрын

@@Wargon2013 it is uncomputable because if an algorithm existed to produce this number, one could deduce an algorithm to write Chaitin constant.

@ramdamdam1402

5 жыл бұрын

@@fnors2 no because Chaitin is uncomputable. I don't give a method to write it ( because it doesn't exist), i just say write the i-th decimal of Chaitin.

Not that it really matters, but his name is written as Erdős, which translates to Foresty or Woody if anyone's interested :)

Clearly recommended on my feed to scramble my brain. Cheers....

3:13 The Liouville Constant, the sum of 10^(-n!) for n running from 1 to infinity, was already in 1851 constructed and proven to be a transcendental number.