Why π^π^π^π could be an integer (for all we know!).
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3 жыл бұрынCheck out the Jane Street programs if you're considering a mathematics/finance/programming job:
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Here is Tim Gowers's reply to the original tweet:
/ 1346212151581700096
Start your Schanuel's Conjecture journey here:
mathworld.wolfram.com/Schanue...
3^3^3^3 on wolfram alpha:
www.wolframalpha.com/input/?i...
And for completeness, here is pi^pi^pi^pi:
www.wolframalpha.com/input/?i...
If you have opinions about my 2n conjecture, send an email to matt+puzzles@standupmaths.com
Here is my Numberphile video about types of numbers.
• All the Numbers - Numb...
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Editing by Alex Genn-Bash
Maths graphics by Sam Hartburn and Matt Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
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@boysenbeary 3 жыл бұрын
“We set pi equal to 3” Engineers: *applause*
@user_2793 3 жыл бұрын
What an original joke
@eatpant1412 3 жыл бұрын
As an enginer I feel insulted. I use 355/113
@petermarksteiner7754 3 жыл бұрын
pi is exactly 3, because the bible says so: 1 Kings 7,23
@chrismanuel9768 3 жыл бұрын
Pi is 3.14. I don't need more accuracy than that.
@nocturnhabeo 3 жыл бұрын
Pi is 3+1 for a bit of room.
@eccentriastes6273 3 жыл бұрын
The year is 3021. Computing power has finally advanced to the point that we can confirm that pi to the power of pi to the power of pi to the power of pi is not in fact an integer. The Intergalactic Society of Mathematics is hosting a party to celebrate. Suddenly, someone speaks up from the back of the room. "But what about pi to the power of pi to the power of pi to the power of pi _to the power of pi_ ? Is that an integer?" The room falls silent.
@palashverma3470 3 жыл бұрын
Wait another 1000 years of course
@mickelodiansurname9578 3 жыл бұрын
And this sir is why you are not invited to such a party!
@mixnewton5157 3 жыл бұрын
@@palashverma3470 pi^pi^pi^pi^pi far away bigger than pi^pi^pi^pi it has 10^10^18 digit "10 followed by billion billion zero" zeros linearly, wait 10^10^18 year, second or blanck time, won't make a difference
@JamesDavy2009 3 жыл бұрын
I doubt that π^^5 ϵ *Z*
@ribozyme2899 3 жыл бұрын
Actually, if pi^pi^pi^pi is an integer, then pi^pi^pi^pi^pi is pi to an integer power, which cannot be an integer. (cause pi is transcendental)
@4thalt Жыл бұрын
6:48 I love how Matt just casually referred to the two people as Emma and Timothy like if they were close friends
@gwynjudd Ай бұрын
Well Emma did feature in his "calculating pi by hand" video so they do know each other
@JeremyRight-zi4yp 8 ай бұрын
2:00 - calling them "irrationals" is indirect, since π or e are irrationals as well. Numbers like √2 are algebraic, an antonym to transcendental.
@enricocarrara8672 Ай бұрын
For what it's worth, integers are also rational
@kylewood4001 Ай бұрын
Technically, the algebraic numbers include some imaginary numbers too, since the criterion is simply being a root of a polynomial with rational coefficients
@terrariariley1643 Ай бұрын
Look up why pi is transcendental ,because it is
@ThomasWeinhart 14 күн бұрын
Three minutes in and already two math mistakes (transcendentals are irrationals and a^b^c=a^(b^c), not (a^b)^c, though he seems to be aware of the latter). It's not funny if he does not take his math seriously.
@OrangeDrink Күн бұрын
My hunch is 2n would be imaginative similarity 1 or 2 (infitesimals)to the solution a number so large that essentially would be equal to computing all digits of pi itself, and that solution would be at its closing point mabey single digits example 222222 off repeated in difference at its closest point so would not match exactly unless the solution to pi was found to end in a plus 1 or minus one at some point that could be applied to the solution of a the ratio that it represents for certain digits, example would be a hypothetical as in an infinite circle properties of polygons could be used as substitutions with plus or minus corrections to the solution and for a number that is not computable ever but a solution that never ends as well . Thanks for the brain food!
@parmparm9341 3 жыл бұрын
This reminds me of 8 year old me trying to repeatedly multiply 9999 to itself in my calculator. I too was limited by the technology of my time.
@wumbowumbo1688 2 жыл бұрын
SAME LOL 😂
@retvolution 2 жыл бұрын
Lmao same
@asheep7797 Жыл бұрын
Same too
@ianc8266 Жыл бұрын
You can remember more digits than that with "I need a drink, alcoholic of course, after the heavy lectures."
@Shreyy17 Жыл бұрын
What I did (although a decade later) was using all 12 digits of the calc by 999.... and then multiplying by itself lol
@spankasheep 3 жыл бұрын
"We set pi equal to 3” I felt a great disturbance in the force.
@ThomasSMuhn 3 жыл бұрын
Well, the Bible says that pi equals 3; and the Bible also says that the Bible is never wrong. QED.
@efulmer8675 3 жыл бұрын
How about when Indiana almost legally declared pi is equal to 3.2?
@ThomasSMuhn 3 жыл бұрын
@@efulmer8675 'Cause godless heathens they are down there?
@efulmer8675 3 жыл бұрын
@@ThomasSMuhn It was in the late 1800s and the Indiana State Legislature brought in a mathematician to help settle the issue. They settled the issue by throwing out the bill All-0. Still, it is a hilarious collision of math and reality.
@DonReba 3 жыл бұрын
I'm pretty sure this is only allowed under martial law.
@diegog1853 2 жыл бұрын
Great video. Although I expected some kind of argument for why we would expect this number to be an integer. But as I understand it, there is no reason to believe that it is anything in particular. We simply don't know. Although I am inclined to think it is probably not an integer, it is true that you can get integers or rational by operating irrationals and transcendentals in certain ways. But there is always, I think, a good explanation for it, it seems that you have to be deliberate about it. Kind of like when trying to convert rationals into integers, if you multiply randomly, you will fail in even a vast majority of cases, when multiplying by the inverse for instance, you succeed. But of course, I don't know much about it, it is just the impression I got from watching the video. Pretty interesting question.
@kambuntschki6314 23 күн бұрын
Tbh im kinda disappointed because the entire point of the video was just "yeah we just cant know"
@diegog1853 23 күн бұрын
@@kambuntschki6314 Yeah and now that I think about it, it really is a different thing to say: "we don't know what this number is" to say "this number *can* be any type of number". There are numbers that it obviously cannot be, like 0. So it might be the case that it is also impossible for it to be an integer, but we haven't develop that reasoning yet.
@frankmerrill2366 13 күн бұрын
If using pi to (say) 8 places gives a number nearly midway between two integers (such as 87.54), it's pretty safe to assume that the answer is not an integer. Most probably even using just four decimal places may confirm the pi-to-pi-to-pi-to-pi is not an integer if the value falls far away from an integer. However, if the calculation comes out with something like 88.9999999997 (rounded), additional digits of pi may be necessary. If using pi = 3.14159265, one need only try 3.14159266 as well, and if there's no integer in the middle of the two calculations, this calculation cannot be an integer.
@sk4lman 2 жыл бұрын
I remember the moment I realized what the word trigonometry meant..! I started looking at the word "polygon", meaning "several corners". I then thought of what a triangle would be called, "probably Tri-gon". Then it absolutely struck me, "Tri-gono-metry = The measurement of triangles"!
@soupisfornoobs4081 2 жыл бұрын
"several corners" is one way to translate it, but it's understood to mean "several angles" by greek people
@spiderjerusalem4009 Жыл бұрын
methylgon, ethylgon, propylgon, butylgon, amilgon, isopropylgon, isobutylgon, isoamilgon, sek-butylgon, tert-butylgon, sek-amilgon, tert-amilgon, etc, list goes on
@akale2620 11 ай бұрын
Didn't they teach you what it means in school when you started it
@lunlunnnnn 10 ай бұрын
@@akale2620at my school they didn't teach us the etymology of the word; only that it has to do with triangles and how to use it
@jebadavie 10 ай бұрын
@@lunlunnnnnagreed. Sadly most schools did this. They just start with example problems and jump into the work. I was decent at math but didn't realize until my 30s that exponents 2(square) and 3(cubed) were called that because they formed that geometric shape out of the base unit.
@vermiformappendix 3 жыл бұрын
My math teacher used to say, “if you don’t like natural logarithms just e-raise it. Then you don’t have to deal with it”
@troodon1096 3 жыл бұрын
That totally sounds like a joke a math teacher would tell.
@rysea9855 3 жыл бұрын
Kinda genius ngl
@Simon-nx1sc 3 жыл бұрын
@@troodon1096 Damnit, apparently, I'm destined to become a math teacher
@thelivingcube 3 жыл бұрын
heh
@math_the_why_behind 3 жыл бұрын
Haha!
@KevinJCoburn 3 жыл бұрын
I'm surprised that you didn't save this for March 14.
@coolfred9083 3 жыл бұрын
Hopefully that means there's something even cooler for then
@yuvalne 3 жыл бұрын
I mean, traditionally he's calculating pi in March 14
@DapSchaf 3 жыл бұрын
He was too hyped. Or there will be a super amazing video
@leadnitrate2194 3 жыл бұрын
March 14 is reserved for calculating pi using non-standard ways.
@matthewclements6603 3 жыл бұрын
March 14 is 14/03/21 in Britain.
@dusk_and_dawn2187 Жыл бұрын
This video was amazing. So many fascinating thoughts. Absolutely loved it!❤
@omaanshkaushal3522 Жыл бұрын
This was such a fun video to watch. Definitely one of my favorites from Matt.
@absupinhere 3 жыл бұрын
“Everyone remembers where they were when they noticed that” Ah, yes. This takes me back to two seconds ago.
@pXnTilde 3 жыл бұрын
It was my only takeaway from this video
@verrybrainie 3 жыл бұрын
So it is klickbate?
@columbus8myhw 3 жыл бұрын
And, similarly, "irrationals" are called that because they're not ratios
@rmsgrey 3 жыл бұрын
Today, Matt Parker called me a nobody. I don't remember when, nor where, I made the connection between ratios and fractions and "rational".
3 жыл бұрын
I can't help but notice in order to understand spanish math you need to study english. In Spanish rational numbers = 'números racionales' but ratio = 'fracción'. You can pretty much see there's no real connection between the two in spanish. Always wondered why they were called 'racionales' and 'irracionales'.
@flan1591 3 жыл бұрын
Never before have I seen someone have so much fun with a stock studio audience, and I love it so much
@longpham-sj5sv 3 жыл бұрын
you look sus ngl
@ScormGaming 3 жыл бұрын
@@longpham-sj5sv Now that was the comment I was looking for
@grahamsayle 3 жыл бұрын
When the pretender is mistrustful
@DeadPool-fx3sq 3 жыл бұрын
Unliked this comment due to the likes beong 456
@davidmenn8771 3 жыл бұрын
Icarly? Sam Puckett?
@KuhWristChin 2 жыл бұрын
Thank you for making complicated math concepts fun and entertaining. Peace and Love Matt
@EquuleusPictor 2 жыл бұрын
It's remarkable how modern mathematics can produce amazingly powerful and accurate results for physics, engineering, computing and essentiatially all fields of applied science, yet remarkly simple statements in number theory, combinatorics, transcendental number theory and other pure math branches are not only unproven but seem to be utterly unpproachable by every mean know to mathematicians today and many see no progress for decades, sometimes more ...
@hyperbaroque 2 жыл бұрын
I think it's because the material world is a bridge itself between solutions. Physical reality serves as an "elegant solution" that solves the identities of all transcendental numbers in one instant. By working with physical reality we get to experience the subtleties we are missing by using this bridgework without knowing all the underlying equations. Oh, did this bridge we made using the bridgework of physical reality twist itself apart in a mind-bending way? We study it and find an underlying equation involving harmonics, and work to contramand that equation as a point of ethics in bridge-building. (And so on.) So to paraphrase Newton and Hawking regarding "standing on shoulders", with physical reality we are standing on unknown shoulders of unknown giants. (And to finish the thought: mathematics is the blind study of the anatomy of those shoulders, in hopes of discovering something about those giants.)
@joleneonyoutube 5 ай бұрын
what an absolutely stunning comment and quote, I hadnt heard or seen that finished thought before, thank you for sharing@@hyperbaroque
@carlhopkinson Ай бұрын
Infinities are infinitely harder to deal with.
@Xenophilius 2 жыл бұрын
"Say what you want about 3, at least we know it exactly. It's equal... to 3." This is what we call high-quality educational content.
@tomc.5704 2 жыл бұрын
I'll gladly take his word for it, but I have never seen a proof
@afuzzycreature8387 2 жыл бұрын
to be fair, we have harvard grad students who will argue against this
@rosepinkskyblue 2 жыл бұрын
LMAO 🤣
@NerdTheBox 2 жыл бұрын
tetris person poggers
@spl420 Жыл бұрын
It's more than we know about 0.1+0.2
@blackpenredpen 3 жыл бұрын
As soon as I saw the title, I went to WolframAlpha, haha!
@captainsnake8515 3 жыл бұрын
Blackpenredpen: “do not trust wolfram alpha, trust algebra” Also blackpenredpen:
@michaelwu9892 3 жыл бұрын
you are our favorite pokemon math youtuber
@rogo7330 3 жыл бұрын
You had to fight evil Not join it!
@cezarcatalin1406 3 жыл бұрын
Michael Wu COMRADE !
@nahometesfay1112 3 жыл бұрын
@@captainsnake8515 I trust wolfram alpha with my life Well really my school work, but that's pretty much my life right now. Yay college!
@gwillen 2 ай бұрын
This is amazing. I love that you led with Tim Gowers' response, to reassure all the mathematicians in the audience: this isn't as simple as it might look, keep watching! 😅
@encyclical 2 жыл бұрын
I’ve watched this video 3 or 4 times since it came out. Great quality and fun video
@CharlesJrPike 3 жыл бұрын
"How about we start by setting pi equal to 3..." What is this, stand-up engineering?
@sykes1024 3 жыл бұрын
Eh, even an engineer'd probably use 22/7. Setting pi to 3, is closer to what a theoretical astro physicist would do. Though, maybe they'd just set pi to 1.
@kindlin 3 жыл бұрын
@@sykes1024 I love the joke, but in actuality, Natural Units make perfect sense. We have set all of our units to be useable with day-to-day activities, like driving a car or baking a cake. If you set the units to be most useful for theoretical astrophysicists, then you get a lot of 1's, and all the equations become a lot easier to work with, on a theoretical basis. You only need to bring back in all the powers of c and h if you want to make an experimental prediction in numbers that make any sense to us hoomans.
@pdorism 3 жыл бұрын
As a physicist, I always have pi = e = 3. We don't use calculators, we just look at the first digit and the order of magnitude
@Aeronwor 3 жыл бұрын
that seems right, but you do need to include 30% safety factor and round up to the next standard size.
@davidmarshall2399 3 жыл бұрын
@@Aeronwor or use 4. Depends which side is conservative
@laikahusky6358 3 жыл бұрын
"For simplicity's sake, why don't we start with setting pi equal to 3." Engineers everywhere rejoiced
@peteranon8455 3 жыл бұрын
.... and cried....
@billwhoever2830 3 жыл бұрын
Trust me, I'm an engineer: π=3
@persilious81 3 жыл бұрын
@@billwhoever2830 But for some reason my wheels always fall off
@themushroom2130 3 жыл бұрын
@@persilious81 “I want a refund”
@michalnemecek3575 2 жыл бұрын
I'm not an engineer because I always use at least 3.14 (unless I'm using a calculator, which always uses about 3.14159265359)
@JohnSmith-ut5th 2 жыл бұрын
Actually, we can apply number theory to this, in particular, Fermat's Little Theorem. We have methods of calculating the nth digit of pi in binary without having to calculate all the previous digits. In the appropriately chosen modulus, this is all you need to determine if the number is integer or not.
@stargazer7644 Жыл бұрын
But we aren’t calculating pi here, we’re calculating pi to a power.
@sethkunert6234 4 ай бұрын
@@stargazer7644that is still an nth of pi
@WhiteGandalfs 27 күн бұрын
@@stargazer7644 We are looking after nothing else than: HAS pi something behind the comma or has it not? And for that, we are allowed to use modulus. modulus 1, to be specific. Which makes things drastically easy. And then concerning accuracy: We only need enough accuracy to get the first few (maybe just for satisfaction the first three or so) digits after the comma correctly, all others are just overhead. Hint: The digits will not be zero (or 9) behind the comma. If they were zero (or 9), we first would gather a bit more accuracy. Only if there after a lot more zeros would make their debut, would we need to invest in thoughts about proving anything. But since the digits behind the comma will for sure not be around zero, all other thoughts about proving integer-ness are invalid anyways.
@fewwiggle 24 күн бұрын
@@WhiteGandalfs "HAS pi something behind the comma or has it not?" Do you mean the decimal point? Regardless, the problem is π^π^π^π You need to know the EXACT value of MANY, MANY digits of π to know if the 'last' digit is an integer.
@hbxit1888 2 жыл бұрын
Last year when I viewed this video, I brushed off jane street like I do with any ad I see in any video. Today, Jane Street is my absolute dream job and I would absolutely do anything for a job there. It is truly an amazing company. Lesson here, ads are not always that terrible.
@gregoryburns4821 3 жыл бұрын
Matt, can you please get closed captioning? I really appreciate your presentations and cannot tell what you are saying. The deaf community would benefit so much!
@frankjosephjr3722 3 жыл бұрын
Captions take a few hours to show up on videos
@EcceJack 3 жыл бұрын
@@frankjosephjr3722 Does it? I've only ever uploaded videos (not on this account!) that didn't need an immediate release, and found I could easily add subtitles before "publishing" the video - and then they appeared immediately. I suppose it's possible that - if you're trying to upload immediately - these things take a while to process..?
@aaronjulien7331 3 жыл бұрын
@@frankjosephjr3722 yeah, atuo-generated ones
@dovecat 3 жыл бұрын
@@EcceJack they may be referring to the KZfaq auto generated captions
@MrZerRap 3 жыл бұрын
It Might be a good idea to allow for the comunnity to caption the videos, Matt! I'm willing to volunteer in doing Portuguese subtitles if you want!
@NightiNerd 3 жыл бұрын
Why don't we calculate it in base π? π in base π is just 10, an integer! The only problem is that the good old integers are now transcendental.
@stevanmiladinovic4007 2 жыл бұрын
Base-Pi that'd still be a ten-billion-digit number.
@yyattt 2 жыл бұрын
pi^pi^pi^pi = 10^10^10^10 base pi 10^10^10^10 is an integer therefore pi^pi^pi^pi is an integer if we work in base pi. QED
@NightiNerd 2 жыл бұрын
@snarl banarl Hmmm, that's true. Now I have another idea: π^π^π^π is 10 in base π^π^π^π. It's an integer! We leave the proof for other bases to the interested reader.
@electricengine8407 2 жыл бұрын
10 in base pi is NOT an integer
@arduous222 2 жыл бұрын
This is a galaxy brain meme lol
@KpxUrz5745 2 жыл бұрын
Enjoy this channel immensely. Most of us need tutoring when it comes to mathematics.
@kano4ka 5 ай бұрын
I don't understand almost anything in English, but thanks to the pictures I get the gist. It's gorgeous, I'm thrilled, thank you very much!
@Milkymalk 3 жыл бұрын
Matt: "It is complex..." Me: "Okay, explain it." Matt: "...literally." Me: "Oh."
@BattousaiHBr 3 жыл бұрын
fear not, the complexity is merely _imaginary_
@Kanzu999 3 жыл бұрын
*Applause from crowd*
@michaelvstemerman 3 жыл бұрын
@@BattousaiHBr Quarternions be like:
@slkjvlkfsvnlsdfhgdght5447 3 жыл бұрын
@@BattousaiHBr boo! boo!
@kennarajora6532 3 жыл бұрын
@@BattousaiHBr only part of it is. The other is the real part.
@KirillTsukanov 3 жыл бұрын
√2 is the only irrational number in existence, now confirmed
@Luca_5425 3 жыл бұрын
I was surprised as well
@usernamenotfound80 3 жыл бұрын
π^π^π^π is rational. Proof: It isn't √2.
@cpotisch 3 жыл бұрын
@@Luca_5425 You know he was joking, right?
@Luca_5425 3 жыл бұрын
@@cpotisch of course
@Chisito23 3 жыл бұрын
@@usernamenotfound80 QED 😎👌
@mischa7406 Жыл бұрын
This video has the best intro. I often come back to this just for the first 10 seconds. And then stick around for the whole vid, obv
@mischa7406 Ай бұрын
Hey look its me again watching the first 10 seconds
@peepock7796 2 жыл бұрын
I think it would be better to refer to the “irrationals” from the beginning of the video as constructables or algebraic instead of irrational, because transcendental numbers are also irrational but they aren’t constructable nor algebraic.
@jacksonsmith2955 Жыл бұрын
Integers are rational numbers too. To be more precise he could have labeled the groups "integers", "non-integer rationals", and "non-transcendental irrationals" but he got the point across which is what really matters.
@WaterShowsProd 3 жыл бұрын
Don't give that virtual audience CG tomatoes, whatever you do.
@Eric_The_Cleric 3 жыл бұрын
Virtual audiences are vicious.
@johnchessant3012 3 жыл бұрын
Fun fact: Even though we don't know for sure if pi+e and pi*e are irrational, we know that at least one of them is. Otherwise, if pi+e and pi*e were both rational, then the solutions (namely pi and e) to the equation x^2 - (pi+e)x + pi*e = 0 would be quadratic irrationals, but we know this is not the case.
@kddanstars9288 3 жыл бұрын
What's your source
@CreeperDeLux 3 жыл бұрын
@@kddanstars9288 if you know the quadratic formula, you can see that he ia right
@daicon2k6 3 жыл бұрын
Yes, but the question at 12:20 wasn't whether pi+e and pi*e are irrational, but rather whether they are transcendental.
@ratlinggull2223 3 жыл бұрын
Pi+e = pie, but because pi is already pronounced pie, we prove that e=0.
@thassalantekreskel5742 3 жыл бұрын
@@ratlinggull2223 And in a cylinder with a radius Z and a height A, the volume equals Pi*Z*Z*A
@benjiboy1337 Жыл бұрын
I wonder if this could be approached geometrically. I'm not sure what it would mean to raise a unit circle to the power of a unit circle, but with such of a conceptual tool, maybe it would be easier to figure out if it's sensible for pi^^3 to be an integer or not. If a unit circle raised to a power of itself, however that conceptualization presents itself, in some way increases its approximate proximity to a shape of non-transcendental volume, then it's conceivable that pi up-up-arrow x is an integer for some value of x. If the complexity of the resulting shape increases, and does so again when again raised to the power of the unit circle, perhaps we could conclude that it is not sensible for any x to yield pi ^^ x = integer.
@usof75756 6 ай бұрын
This is all way beyond me but if I had to make something up I would guess that circle^circle would be a sphere. So taking that all the way to the end would be a 5d circle. Granted I have no idea what I'm talking about and there's no way it's that simple.
@benjiboy1337 6 ай бұрын
@@usof75756 I'm not actually sure what operation turns a unit circle into a unit sphere, but a unit circle raised to the power of a unit circle would be something like pi^2 unit circles, projected into four dimensions... I think. Since you're basically multiplying every point on the unit circle by another unit circle, the area should be (pi*r^2)^(pi*r^2), giving us pi^2*r^4. Plugging in 1 for r, we get just pi^2... so this might not be that useful of a line of inquiry after all. Using geometry for higher maths is mind bending, because we live in a 3-spatial one-temporal dimensional reference frame. There's some precedent for transcendental numbers to "cancel out" to an integer, though I only know of one actual case in Euler's formula. There's probably a Nobel or equivalent prize waiting for whoever discovers an equally beautiful formula in mathematics.
@idkmax5977 Жыл бұрын
4:44 Mathematics dictator
@idkmax5977 Жыл бұрын
😅😅😅
@RC32Smiths01 3 жыл бұрын
*Me putting the expression in a calculator to see if it's an integer before watching the video*
@misiekeloo6114 3 жыл бұрын
Error: Result is too big
@du42bz 3 жыл бұрын
I thought my phone crashed
@RC32Smiths01 3 жыл бұрын
@@misiekeloo6114 Indeed haha
@RC32Smiths01 3 жыл бұрын
@@du42bz same
@catfort.dragon 3 жыл бұрын
Google says it's undefined
@emileheskey2754 3 жыл бұрын
"Everyone remembers where they were, the first time they noticed that" Yeah, on the toilet about 10 seconds ago, what a beautiful moment that was
@rups251195 2 жыл бұрын
Same
@aidenbagshaw5573 2 жыл бұрын
“RATIOnal. Everyone remembers where they were when they first noticed that.” I was here, watching this video.
@bikramkalsi1 8 ай бұрын
you are doing gods work my friend
@Thror251 3 жыл бұрын
To calculate pi^pi^pi^pi more easily, mathematicians should just work in base pi....
@samuelthecamel 3 жыл бұрын
That's great until you try to see if the extremely large result in base pi is an integer
@EebstertheGreat 3 жыл бұрын
In base π, π^π (i.e. 10^10) is equal to 1012.031000012..., because π^π = π³ + π + 2 +3 π⁻² + π⁻³ + π⁻⁸ + 2 π⁻⁹ + · · · . So that's not really helpful.
@vigilantcosmicpenguin8721 3 жыл бұрын
cursed
@Syuvinya 3 жыл бұрын
@@EebstertheGreat This is a big brain moment
@briant7265 3 жыл бұрын
@@samuelthecamel It WOULD be an integer, of course. The problem would be that all of the numbers that are currently nice, simple integers would become transcendental. Counting would become impossible.
@lerntuspel6256 3 жыл бұрын
I know what pi to the pi to the pi to the pi is. Its "Error: Overflow"
@antoniocoulton5017 3 жыл бұрын
Don't be silly, it is very obviously equal to "MATH error"
@sadkritx6200 3 жыл бұрын
@@antoniocoulton5017 math error on casio calculators. Don't know what others say though
@tiem217 3 жыл бұрын
@@sadkritx6200 TI says Error: Overflow
@tobiasbrohl5958 3 жыл бұрын
it's "overflow - huge result is out of SpeedCrunch's number range"
@giovanicampos4120 3 жыл бұрын
Yeah I did it in my calculator and get math error
@regimeoftruth 2 жыл бұрын
A proof that there are no integers in the sequence π, π^π, π^π^π, … would certainly be interesting. A proof that there are integers might be even more interesting.
@samueljehanno 5 ай бұрын
This is interesting !
@CafeMuyCaliente 5 ай бұрын
And if all pi^^n wont be integers, what about pi^^pi ?
@samueljehanno 4 ай бұрын
@@CafeMuyCaliente interesting
@dylonlarue8350 2 жыл бұрын
Still in the adverts but I can tell I’m gonna love this channel.
@phitsf5475 3 жыл бұрын
"Pie to the pie to the pie to the pie" My doctor didn't like this diet plan
@hello_iam_potato 3 жыл бұрын
Underrated
@michaelsmith4904 3 жыл бұрын
I remember a song some years back that went something like "moe to the e to the.." or something like that, and was thinking that if we knew the value of "moe" we could calculate the value of the equation.
@azlandpilotcar4450 3 жыл бұрын
We say n^2 is n squared, ^3 is cubed, and ^4 is hypercubed. I think this might be pi hyperpied.
@gurrrn1102 3 жыл бұрын
Also pie to the pie to the pie to the pie sounds like a rapper saying pie pie pie pie
@hello_iam_potato 3 жыл бұрын
@@gurrrn1102 sick rhyme
@aykborstelmann8623 3 жыл бұрын
"We set pi to 3" Astrophysicists: Wait what, thought the approximation was 10?
@pankajbhambhani2268 3 жыл бұрын
My reaction exactly. Surely we can approximate pi^pi^pi^pi to within a few orders of magnitude?
@CarbonRollerCaco 3 жыл бұрын
Why do they of all people use 10, anyway? Everyone knows base 10's just a cultural bias inspired by our hands. And 3×3 squares, but those aren't that much more relevant to physics.
@pankajbhambhani2268 3 жыл бұрын
@@CarbonRollerCaco I guess because base 10 is the standard in scientific notation. If a star has mass x * 10^y, astronomers usually can't precisely measure x, so they don't care about. They only care about y, the order of magnitude, which they can estimate properly.
@user-mv2nn6rw2w 3 жыл бұрын
@@CarbonRollerCaco Because other people use 10. No number is better than another in a vacuum. Same reason why you use lightyear instead of inches to talk about astronomy, despite the calculation to change basis is trivially easy.
@CarbonRollerCaco 3 жыл бұрын
@@pankajbhambhani2268 It's still ironic that scientific notation, which is supposed to be unbiased, uses a scientifically wonky base informed by culture only because of evolutionary happenstance. But it is understandable in a sense as they need to quickly relate things to what's already convenient, even if it's an anachronism. Even still, it sounds wrong as THE base for magnitude.
@i_am_lambda 2 жыл бұрын
Still the best opening to any KZfaq video
@zachhoy 8 ай бұрын
I love the 2010 powerpoint themes used in your titles! haha jk love everything but that stood out for a comment for me for some reason
@Fun_maths 3 жыл бұрын
I like how he wrote that 11^6/13 is rational as a callback to a video he did about why an advanced casio calculator said that 11^6/13=156158413*pi/3600
@ZevEisenberg 3 жыл бұрын
-1/12 was also a callback to a Numberphile video
@meltingkeith7046 3 жыл бұрын
@@ZevEisenberg don't know if I'd call the -1/12 a callback or just generally a controversial result in mathematics in general and hence worth putting in
@trogdorstrngbd 3 жыл бұрын
@@meltingkeith7046 The result itself isn't controversial. The sloppy/misleading presentation of it to the general populace was.
@Garbaz 3 жыл бұрын
Well spotted, didn't notice that one!
@onradioactivewaves 3 жыл бұрын
@@ZevEisenberg that was actually - 1/( 4 π)
@PanduPoluan 3 жыл бұрын
Let me tell you: PyPy to the PyPI results in a lot of incompatible libraries. (Thankfully, the most important ones are compatible.)
@ratlinggull2223 3 жыл бұрын
my mind became numb py
@jacquesstoop2587 3 жыл бұрын
*Sigh py*
@PanduPoluan 3 жыл бұрын
@@jacquesstoop2587 Daaaaamn I was racking my brain trying to pun SciPy 😆
@kakyoindonut3213 3 жыл бұрын
damn, is this Py Game or something?
@Orincaby 2 жыл бұрын
@@kakyoindonut3213 don't worry it's just a joke from the programmer's PyPline
@mahmoudalbahar1641 2 жыл бұрын
Many thanks for this good video.
@BegsToDiffer 9 ай бұрын
This is excellent stuff!
@jerwahjwcc 3 жыл бұрын
Worried that the pandemic is finally getting to Matt and he's building an army of imaginary audience friends
@danielhenderson9719 3 жыл бұрын
Don’t worry. He’s not building them. He’s already built them.
@simonecatenacci726 3 жыл бұрын
There is no problem, as long as he multiplies the imaginary audience by itself, he will get a real audience
@syllogism5843 3 жыл бұрын
@@simonecatenacci726 Although it will be negative, so not much applause alas
@AmaroqStarwind 3 жыл бұрын
I think you mean Lateral.
@ailaG 3 жыл бұрын
His audience is quite complex.
@DannyGottawa 3 жыл бұрын
"What kind of clickbait is this???" A seriously nerdy kind
@perplexedon9834 Жыл бұрын
It be pretty wild if any power tower turned out to be an integer. It'd mean that using higher order inverse tetration you could define pi in terms of integers. This would be categorically like pi turning out to be sqrt3. It can be defined using finite algebra (though extended from what we usually arbitrarily limit ourselves to.
@babilon6097 9 ай бұрын
But we can already define it using integers. Matt does it every year for 14th of March (which people using skewed date notation call a pi day).
@Errenium 8 ай бұрын
@@babilon6097get back to me on april 31st /lh
@perplexedon9834 8 ай бұрын
@@babilon6097you're right, I meant a finite algebraic expression, like how the golden ratio can be.
@typicwhisper6569 6 ай бұрын
@perplexedon9834 Tetration and its inverse are transcendental functions, so it could never be a finite algebraic expression.
@samueljehanno 5 ай бұрын
But why couldn't it be finite algebraic expression ?@@typicwhisper6569
@XeiDaMoKaFE Жыл бұрын
7:50 wrong 3 is infinite
@FourthDerivative 2 жыл бұрын
I can never hear "three to the three to the three" without having bad flashbacks to Graham's Number
@LittleEinsteinAdi 2 жыл бұрын
yea
@NoriMori1992 2 жыл бұрын
Same.
@woollycomet 2 жыл бұрын
Haha so trueee
@1mol831 Жыл бұрын
If we can find a phenomenon in nature... ... That we can do with ... via the use of sciences?
@IBlewUpYourHouse 3 жыл бұрын
"We know 3, beacuse it is equal to 3" Yes the floor here is made of floor
@RWZiggy 3 жыл бұрын
But 3 + 3 equals 7, for large values of 3.
@timothymclean 3 жыл бұрын
But we're talking about 3, not 4.
@shreebatsachaturvedi5376 3 жыл бұрын
@@RWZiggy However, it is also worth noting that the limit of 3 as 3 approaches 0 is 4.
@LA-MJ 3 жыл бұрын
Hi, Vsauce here...
@underrated1524 3 жыл бұрын
floor(3) = 3
@draisens 9 ай бұрын
the insertion of studio audience for example is simply revolutionary.
@kekoasilva1501 2 жыл бұрын
This is the mathematical content I’ve been waiting for
@outsidestuff5283 3 жыл бұрын
Matt: lets set Pi equal to 3 Everyone: boooooo Engineers: this is my time to shine...
@semiclassical7620 3 жыл бұрын
Pfft, pi=3 is crude. Now pi^2=10, that’s where the money is! (More like 9.9 but that’s not as catchy)
@floop_the_pigs2840 3 жыл бұрын
3=e=π=√g (on earth)
@georgelionon9050 3 жыл бұрын
Pi is 22/7... that's probably good enough for anything a normal person does.
@floop_the_pigs2840 3 жыл бұрын
@@georgelionon9050 honestly yeah
@Runoratsu 3 жыл бұрын
Astrophysicists: Pi = 1 is close enough.
@neilruston8796 2 жыл бұрын
I'm surprised there was no mention of the fact that e^(i.pi) = -1 Transcendental AND imaginary numbers combined to produce an integer.
@urnoob5528 Жыл бұрын
Well try to plot a complex power without formula U cant Complex power is defined by infinite series Complex number and cos, sin is easy to plot But u cant plot a complex power without converting to cos and sin It is unintuitive, someone just wanted to give it a definition and so they did by infinite series If u want to prove me wrong otherwise, try to plot 7^(3+i8) without converting it or anything
@2eanimation Жыл бұрын
@@urnoob5528 "It is unintuitive" So are PDEs, that doesn't make them wrong. "someone just wanted to give it a definition and so they did by infinite series" Everything related to e^x(or better say, the exponential function, without knowing that exp(1) = e) can be derived from its power series alone. Or (I) exp(a + b) = exp(a)exp(b) and (II) 1 + x inf] (1 + x/n)^n Or continuous growth Or y = y' Or... If the power series is a perfectly fine way to define exp(x), exp(i) is perfectly fine as well. Let's not forget about the useful math thanks to exp(i). Laplace/Fourier transform comes to mind ;) "But u cant plot a complex power without converting to cos and sin" 7^(3 + i8) = 7^3 * e^(i8ln(7)). Vector with length 7^3, x-axis and vector enclose 8ln(7) rads, that is (360 * 8ln(7) / 2π)° ~= 891.94° ^= 171.94° (mod 360). Look mom, without trigs! "without converting it or anything" try to plot x^2 * y'' + x * y' + 4 * y = 0, y(-1) = 3, y'(0) = 0 wItHoUt CoNvErTiNg It Or AnYtHiNg
@aguyontheinternet8436 Жыл бұрын
Well _I_ think he should have mentioned e^(i*τ)=1 instead, which is the far superior formula
@mikeoxmall69420 Жыл бұрын
God is the greatest troll ever😂
@fahrenheit2101 Жыл бұрын
@@aguyontheinternet8436 ew no
@smmizanurrahman71 9 ай бұрын
This was such a fun video
@seanmurphy8435 3 жыл бұрын
e^(i*pi) is an integer. I'm surprised you didn't mention it. Great video!
@bman5257 2 жыл бұрын
i is imaginary though. I think he purposefully kept the categories in real numbers.
@JackiTheOne 2 жыл бұрын
i is not a transcendental number tho
@AuroraNora3 2 жыл бұрын
@@JackiTheOne i*π is transcendental
@YTEdy 2 жыл бұрын
But it's a different pi. It's not the number pi it's an arc of pi radians, or 180 degrees or 1/2 circle, both of those definitions are no longer transcendental.
@mr.cheese5697 2 жыл бұрын
Nice, don't touch the like, please
@christopherquigley5468 3 жыл бұрын
I feel like everyone is thinking in circles here.
@calebclunie4001 3 жыл бұрын
On a pie chart, it might be assumed, but on a donut chart, one might come across phi. I tried bringing this up, but I was told to "shut my blooming phi HOLE!"
@vblaas246 3 жыл бұрын
@@calebclunie4001 Thanks, now I'm imagining a fractal donut of a donut... define the emerging donut. And the ratio of the radii. Someone calculate?
@zbnmth 3 жыл бұрын
semicircles...
@Dowlphin 3 жыл бұрын
Don't be a square.
@Dowlphin 3 жыл бұрын
@@vblaas246 That sounds totally radiical!
@PooperScooperTrooper Жыл бұрын
I love how Douglas Adams' 42 always gets a reference 🙂
@SupremeSkeptic 9 ай бұрын
What an elightening video... I am, now, more convinced than ever that e^e^e^e^e^e = Elephant (for all we know!).
@a_cats 3 жыл бұрын
The fact that he pauses just before saying each number makes me think he's actually calculating them all in his head
@peNdantry 3 жыл бұрын
You've fallen into his trap -- that's what Matt *wants* you to think ;)
@graemetang4173 2 жыл бұрын
7:00 Timothy was so concerned with whether or not he could break the 31.4 trillion digit record for pi that he never stopped to wonder if he SHOULD... guess we now just need to wait for a hero to get to 314 trillion
@vin_fm2354 2 жыл бұрын
When COVID happens people get bored
@METALSCAVENGER78 2 жыл бұрын
It is broken again.Now, it's 62.8 trillion digits.Exciting times
@greatorionbelt 2 жыл бұрын
@@METALSCAVENGER78 thats twice pi
@kijete Жыл бұрын
@@greatorionbelt tau
@David-gu8hv Жыл бұрын
:)
@altf3yt Ай бұрын
11^6/13 as a rational is a nice touch at 1:43
@user-fb2qr4ru6i Жыл бұрын
Eu gosto disso! Boa explicação detalhada!
@BlackDeath2812 3 жыл бұрын
1:53 I remember where I was when I noticed that. I was sat in my chair watching a video about how pi^pi^pi^pi could be an integer
@Youaveragecountryhumansfan 4 ай бұрын
Same! What are the odds?!
@Treviisolion 2 жыл бұрын
I was somewhat curious. Using some log calculations, the whole digit part (or the whole number I guess should pi^pi^pi^pi be an integer) would require ~245 petabytes of information. Surprisingly, while no computer has that kind of storage capacity, quite a few cloud storage have quite a bit more than that amount. So we may not be able to process that number, but we could store it if some alien gave that number to us.
@RGC_animation 2 жыл бұрын
Thrust me, in 20-30 years, most big cloud server would have that amount of storage.
@triciaf61 2 жыл бұрын
@@RGC_animation thrust you? oh my.
@joshuathomasmacalintalsoli6307 2 жыл бұрын
@@RGC_animation Moore's law just proves so
@danieljensen2626 2 жыл бұрын
My impression from what Matt was saying was we probably could calculate it if we dedicated all of Earth's computing resources to it for long enough (but like less than a human lifetime). But that's not exactly a reasonable thing to do.
@techrev9999 2 жыл бұрын
Today I learned that cloud storage is some sort of magical entity that is not a computer. Interesting. Do you have more hocus pocus to share.
@bobeyay 9 ай бұрын
1:42 I was todays years old, when I finally learned about why it is called rational numbers
@MichaelMoore99 2 жыл бұрын
Yes, I love the final "digts" of powers of 3, too. ;-)
@klikkolee 3 жыл бұрын
I was under the impression that "irrational" included "transcendental", and that things like root-2 were more specifically "algebraic".
@aidanhennessey5586 3 жыл бұрын
Your impression is corrext
@harrisonbaguley5691 3 жыл бұрын
transcendental numbers are by definition irrational, since they can't be expressed in a ratio. i'm assuming this video separated transcendentals from other irrational numbers to simplify the difference between numbers like root 2 and pi
@willgaj 3 жыл бұрын
I'm glad it's not just me 😅
@trogdorstrngbd 3 жыл бұрын
Everyone needs to upvote this comment! Matt has repeatedly made this mistake (I'm pretty sure he does it out of convenience) and needs to stop. It's mostly OK when he says it verbally in the presence of an accurate graphic depicting the number set relationships, but otherwise it's just wrong.
@theWebWizrd 3 жыл бұрын
Yup, I reacted to this as well when he essentially claimed pi is not an irrational number.
@rmschad5234 2 жыл бұрын
Matt: "What type of click bait is this?" Me (who clicked the video): "The good type, obviously."
@echoawoo7195 Жыл бұрын
Fun fact ! The short way to describe this (which unfortunately doesn't have accepted notation) is to say pi tetrated 4, sometimes you can use ^^ to indicate power towers instead, so it would be pi^^4 but many syntax structures use that for exponents instead so its not universal.
@takemyhand1988 6 ай бұрын
⁴^π
@samueljehanno 5 ай бұрын
Yeah sure
@andreamarino95 Ай бұрын
Very nice video. A small consideration about the number of necessary digits to compute a power. Take an approximation q of pi with n digits after 3. Every number with the same n digit approx can be written as q+10^(-n)s for s in (0,1). Then (q+10^(-n)s)^L =q^L(1+10^(-n)s/q)^L is between q^L(1+10^(-n)s/q) = q^L + 10^(-n)s q^(L-1) and q^L(1+10^(-n)s L/q) = q^L + 10^(-n)s q^(L-1)L That is, the percentual error is quite well understood (proportional to the original one and multiplied by a factor between 1/q and L/q), but the absolute error is proportional to q^(L-1). I found that counterintuitive at the beginning because I expected the error in the n digit to produce an error in the n*L digit, but it's actually the opposite: in the process of elevating to a power the error gets bigger and bigger, up to the point it can eat all the precision you had (almost)!! I guess this gives an idea of why computing powers with high precision is hard.
@anthonyisom7468 3 жыл бұрын
0:09 : "An integer?" *Someone puts a hat on it* "Perry the integer?!"
@tomcat1184 3 жыл бұрын
this is not for normies ,... only few people would understand
@kroolini3678 3 жыл бұрын
@@tomcat1184 one of the most normie memes around
@kroolini3678 3 жыл бұрын
@@brahadkokad5424 you’re 10
@yuvi6034 3 жыл бұрын
Nice one
@moparacker 3 жыл бұрын
Wouldn't "π + e" just be "pie"?
@catfort.dragon 3 жыл бұрын
But is pie an integer or not?
@TheNameOfJesus 3 жыл бұрын
That sounds rational to me.
@JayOhm 3 жыл бұрын
Since when "ab" can mean "a+b"? So "pie" is actually π×e
@psy0rz 3 жыл бұрын
Give this man a nobel price!
@mtgradwell 3 жыл бұрын
@@JayOhm No, that's pixie minus i.
@rainerbuechse6923 2 жыл бұрын
Great stuff!
@judedavis92 2 жыл бұрын
“I’m gonna do what’s called an engineer move” *Sets Pi equal to 3*
@psychopompous489 2 жыл бұрын
*Sets 3 equal to 3*
@e.s.6275 Жыл бұрын
Nope we engineers don't do that, ever.
@ffggddss 3 жыл бұрын
Arithmetic alert! At 8+ min, while you're showing powers of 3 (mod 1000), 3⁹ (mod 1000) is shown as 618, which is clearly impossible (it has to be an odd number!). The actual value is 683 (3⁹ = 19683). 3²⁷ (mod 1000) is, however, correctly shown as 987. Still a great video! Fred
@devd_rx 2 жыл бұрын
Yeah i was like how the heck 8 showed up
@M0jibake Жыл бұрын
And also "digits" is spelled "digts"!
@SuperYoonHo 2 жыл бұрын
nice work
@dushyanthabandarapalipana5492 2 жыл бұрын
Thanks!
@AnnoyingMoose 3 жыл бұрын
Who else here is not subscribed to this channel but is so much of a nerd that the KZfaq algorithm showed this video at the top of your recommendations?
@fulltimeslackerii8229 3 жыл бұрын
Name agrees with this comment
@scene2much 3 жыл бұрын
What episode did you lose your S-Card to ? (if you can even....)
@mikeychrisanthus9948 3 жыл бұрын
I got a recommendation for his ellipse perimeter video a few months ago. The only thing “nerdy” at the time I was subscribed to (and still am) is cracking the cryptic which has these two guys who work through very complex and interesting sudoku puzzles and such. I don’t quite know why I was recommended Matt Parker at the time, but I won’t complain, he’s great.
@masvindu 3 жыл бұрын
"They are any number that can be written as a ratio, in fact, it's in the name" That should have come naturally to me...... I mean rationally...
@happygimp0 3 жыл бұрын
i/2 is a ratio but not a rational number.
@blauesserpiroyal2887 3 жыл бұрын
@@happygimp0 rational numbers are ratios of integers
@combogalis 4 ай бұрын
wow you're right, pi IS about 3 using that from now on ty
@hamzapetridis206 7 ай бұрын
I love the fact that this video ha 2,7 million views & 83k likes. Great job !
@mattsnyder4754 3 жыл бұрын
This is like trying to rebuild after a hurricane by sending three more hurricanes through
@Kishmond 3 жыл бұрын
With an infinite number of hurricanes eventually everything will be blown back into place.
@xavariusquest4603 3 жыл бұрын
Yes...chimps given enough time and a keyboard will mash out the collected works of Shakespeare.
@bennyblubman9476 3 жыл бұрын
Yea it's just like evolution, you can get something complex and structured from pure chaos
@rcsibiu 3 жыл бұрын
yeah....send more hurricanes hoping that they ALL could eventually fix those buildings and revive those killed people .....absolutely stunning :))
@rstriker21 3 жыл бұрын
@@rcsibiu if the difference between life and death is just having your atoms in the right places, the chances of a hurricane reviving someone is technically more than 0 lol
@Wrenosaur_ 3 жыл бұрын
pi^pi^pi = Dream's luck when speedrunning.
@God-gi9iu 3 жыл бұрын
Mmm
@God-gi9iu 3 жыл бұрын
Ee
@flameseeker4058 2 жыл бұрын
about that
@insertnamehere4775 2 жыл бұрын
That's only like over 30 my guy Nvm it's xE+18
@incription 2 жыл бұрын
@dang bro it aged very well
@PC_Simo Жыл бұрын
”Let’s set π equal to 3.” I sense some Graham’s Numbery stuff approaching 😨.
@supercrafter7586 Күн бұрын
I saw the thumbnail, was going to go just compute it and just before I opened my calculator realized how huge it is
@balsoft01 2 жыл бұрын
Correction: Irrationals include transcendental numbers. "Things that are a solution to a nice polynomial equation" are called algebraic numbers (2:05)
@infinemyself5604 2 жыл бұрын
Algebraic numbers also include rational numbers. And rational numbers include integers.. so really right things to say would have been "integers", "non-integer rationals", "algebraic irrationals" and "transcendentals" But this is just too crowded, don't ya think?
@ElvisTranscriber2 2 жыл бұрын
@@infinemyself5604 no two-word terms, if they are more specific and avoids wrongly excluding a number from a group it actually belongs to is justified 😀
@chaosredefined3834 2 жыл бұрын
But this now leads to an interesting question. The proof that he gave that irrational ^ irrational = rational worked because sqrt(2)^sqrt(2) is either rational or irrational, and either way, we got an irrational ^ irrational = rational. However, are there two algebraic irrational numbers, a and b, such that a^b = rational.
@tantarudragos 2 жыл бұрын
@@chaosredefined3834 sqrt(2) is an algebraic irrational
@chaosredefined3834 2 жыл бұрын
@@tantarudragos This is true. But sqrt(2)^sqrt(2) is not. So, he ends up with a is transcendental, b is algebraic, and got a^b is rational.
@d0themath284 3 жыл бұрын
"we set pi equal to 3" Pappa flammy has entered the chat
@GaussianEntity 3 жыл бұрын
"We're doing calculations tho" Flammy has left the chat
@markuse.828 8 ай бұрын
Wouldn’t there be a way using p-adic numbers? Assuming we have a p-adic representation of pi or something sufficiently accurate?
@markuse.828 8 ай бұрын
Also I don’t think that ln(2) is a transcendent number. It solves the equation exp(x) = 2.
@fahrenheit2101 7 ай бұрын
Ln 2 is certainly transcendental A transcendental number is any real number that isnt a member of the set of algebraic numbers. An algebraic number x is the solution to some non-zero polynomial equation in x with integer coefficients. While ln 2 does satisfy your "simple" equation, it's not a polynomial, so ln 2 doesnt meet the requirements to be algebraic. You might say that polynomials are a weird arbitrary cutoff point. But one could easily take this further and say that we should also include trig equations, and suddenly pi becomes "algebraic" as a solution to sin(x) = 0 And we could define further functions to be more inclusive if we wanted to, and often do. But for the purposes of defining "algebraic" numbers as they are, polynomials are a fair cutoff point. As for p-adics, I don't know nearly enough about them to know if they show promise in dealing with such problems.
@LiborTinka 9 ай бұрын
I like the entertainment style - in an intellectual way. No cheap clickbait.
@thegiantmimir4664 3 жыл бұрын
When I saw integers, rationals, irrational, and transcendental numbers in a 2x2 grid with the idea that transcendental numbers were badly behaved, I immediately thought that we were assigning D&D alignments to types of numbers. Integers are Lawful Good, Rationals are Lawful Evil, Root 2 is Chaotic Good (the Robin Hood of numbers, if you will), and Pi is Chaotic Evil. When it made a certain sense to my brain, I went and had a lie down.
@bansheedearg Жыл бұрын
And then things got real complex. Real. Complex.
@MikaelaBlake 3 жыл бұрын
This is why I have a love/hate relationship with Maths. Something like this fascinates me to no end and I love it because I believe it is the language of the Universe, but at the same time it gives me a headache and I hate it. But I love it.
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