Find your own ABC Conjecture Triple
ฝัง
- เผยแพร่เมื่อ 21 พ.ค. 2024
- Find your own ABC triple: abc.tngtech.com
Details about Jane Street + University of Oxford’s Black Academic Futures Scholarships: www.maths.ox.ac.uk/study-here/...
Huge thanks to Sebastian Stamminger and Daniel Pape from TNG for all of their help.
TNG: www.tngtech.com
Big Techday: www.tngtech.com/tng-ueber-uns...
Here is James Grime talking ABC. • abc Conjecture - Numbe...
Manim “math animation” community version: www.manim.community
Grant of 3blue1brown fame: / 3blue1brown
This video was made possible by my Patreon supporters who this time only had to buy me some wooden blocks Lego. They also helped stress-test the ABC site before the video was released. You can also help support and shape the videos I make! / standupmaths
CORRECTIONS
- Yes, the Big Techday was actually two weeks ago. We had unavoidable website issues so this video just had to wait patiently.
- Let me know if you spot any other mistakes!
Editing, filming and Lego gluing by Alex Genn-Bash
Manim by Sebastian Stamminger
Site coding by Daniel Pape
Stop-motion by Matt Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/collections/b... - บันเทิง
There's no way I could confuse this video with 3Blue1Brown. You're wearing a red t-shirt - this is clearly a Tom Scott video.
Underrated comment
Yes, red t-shirt is car away from a blue Pi.
I cackled. Great joke.
I wanted to make a 3b1b joke, but you nailed it, managing to bring Tom in too. Well done.
I laughed embarassingly loud at this comment, thank you
Matt: I can't use an O as a zero.
Also Matt: Lobster is a plus and Peas are equals.
That's not a lobster. It's a plustacean.
Ahem, "peaquals"
@@Eagris . . .
@thomas vargas but fractions are division. You’re going to divide to get zero?
Mathematical standards have no rules about what the lobsters and peas represent.
I’m worried that Matt has somehow got himself into a duel at dawn, and is trying to get all his maths out in one night.
I wonder which clone issued the challenge? I hope it's not Beard Matt.
Is this a Galois reference?
This should be top comment!
I get that reference!
If you want to make primes with LEGO bricks, you don't glue bricks together. You use technic bricks which come with versions with 2, 3, 5, 7, 11 and 13 holes.
LEGO Technic, the official LEGO theme of mathematicians who work with prime numbers.
This is how physicists do maths. It's true but with a finite number of exceptions
bricks?
@@beaconblaster33lego bricks
Obviously the Parker = Not Parker conjecture is the hottest thing in the math research world recently, as in 2019
He's a Parker Parker!
Parker = Not Parker confirmed because we can tell he's working very hard.
"Will you accept a lobster as plus?"
I have to say, I've never heard that one before
In my experience, the presence of a lobster has invariably been a negative 🦞
Hail Lobster
@@archivist17 How dare you!
in case you are wondering, the tshirt says "Geek".
Yeah... I did the work though.
@@cpt_nordbart Me too :-)
I also did it, but thought it said Leek 😛🤷♂️
@@timangus I thought it said Guuk. I guess I gave it a Parker go, and misplaced a bit. Geek makes way more sense.
Can you explain how? I get that it’s binary, but how does that become the letters?
Geez Matt is going crazy here with the upload schedule!
He's spoiling us. And a numberphile video too!
He's going crazy to hit 1M subscriber ASAP
A sprint for 1 million? Or does he know something we don't and is manipulating the youtube views market in a dark and mysterious ways?
@@QuantumHistorian probably the latter
He filmed these ages ago and then edited them all and uploaded them in a very short span of time.
"I'm gonna use this to measure the earth!"
The security staff at the Shard: I'm about to end this man's whole career
Soooo True.
Whole video*
I mean, they still got a pretty reasonable estimate for R
Oi! You got a loisence for that protractor?
@@harry.tallbelt6707 They were within an order of magnitude or something. In the overarching scope of the universe, they were basically 100% accurate.
Wow, that looks like a really dangerous weapon at the end there
**Quality or Quantity?**
Matt: That's where you're wrong kid. I choose both!
3 vids in a week (+1 on Numberphile)
👏👏
Quality is based on the English word “Quality”
radical
I spent the whole episode waiting for a 3B1B cameo and the minute I look away I hear Grant's voice. Then I look back and it's coming out of Matt's mouth 😅
Exact same thing happened to me hahaha
I love the way Matt pulled that one. I'm sure quite a few of us were hoping this would lead up to a cameo, but nobody expected it to happen like that.
19:52 I see your unspoken flex of one-upping a log-log axis with a loglog-loglog axis. I've never seen it done and I am so impressed.
End of the video comment:
Matt could have given away two Matt sized Cubits, but Hannah Fry seemed to have "misplaced" them. ;)
Thank you Matt for the opportunity to highlight this topic, we are really overwhelmed by the contributions ❤
"... in general. It turns out there are infinitely many exceptions." Mathematicians lol :P
That’s not as crazy as it sounds. Positive integers in general are not prime, but there’s infinitely many exceptions.
@@jessehammer123 I know it's not, and that is indeed a good example of why! It's just funny to put those words together in that order and have it mean something real, and maths is kind of the only domain where that happens.
That part made me laugh
18:18 "No one is gonna confuse this with a 3 Blue 1 Brown video".
yes. it's a 3 Red 1 Beard video lol
It's Brown. the Beard is Brown.
Matt: "Measure angles?"
Beard Matt: "Measure the Earth"
Matt: (Mumbles behind his own bearded self) "Measure badly"
To be fair, it was the mr-i-don't-understand-humour security guy's fault for taking away his protractor.
Now I'm curious if this is just a short burst of extra creativity or if Matt has upped the ante, gunning for the 1mil subs.
Let's hope it's the latter, but also for him not being satisfied with only 1mil. He might still try to surpass Steve Mould.
I feel like we're kind of getting spoiled here.
he's still isn't there yet :(
"Would you accept a lobster as 'plus?'"
That phrase is so quintessentially Matt, I love it
Cracked me up when it went into Grant's voice!
You broke the 7! How? It has no factors!
He broke maths too
2:50 "It pains me to use an O for a 0..."
Casually uses lobster for a plus.
Good-sized fresh lobster is always a plus
8:48 Nice catch, you have Matt-like reflexes
At this pace, matt will have finished maths in about a month (except the magic square of squares ofc)
"Snappy, specifically the peas." I don't know Matt, I think the lobster is pretty snappy too...
Gotta love maths, where there's a perfect rule with infinite exceptions.😂
i was promised something and got "We found 0 triples for 269 ≦ rad(a) < 270, 417 ≦ rad(b) < 418." Thank you.
i think it's normal - i'd have to watch this again to say i definitely understand the math 100% but it seems reasonable that the site is only searching a certain "region" of the graph at a time and some regions just won't have any hits. alternatively it might be double checking previous work (if there is some reason that some processors would make a mistake, idk) and reporting zero *new* hits. as you keep trying, you'll see the numbers changing and you'll get results sometimes.
It took me several tries to get a non-zero result. Le sigh
"12.38, uh, and some stuff" spoken like a true mathematician.
To be honest even after watching this whole video I still don't understand the ABC conjecture. And I first heard about this conjecture like 10 years ago.
Exquisite syncing on Grant's voiceover :D
You went from a log-log plot to a log-log-log-log plot at about 20:00. I'm not sure I believe the graph actually goes 10^0, 10^10, 10^100, 10^1000.
yes, the steps change from multiples to order of magnitudes
now i need A 🦞 B (Pea pod) C t-shirt 😭
Matt I love how you've clearly taken steve's advice to heart! Love that recent videos!
Where did you get your shirt? "Geek" in binary feels exactly like the sort of shirt I'd wear but I've never seen one before that doesn't also have horrible logos or some insulting comment at the bottom claiming the wearer is smarter than the reader.
“GEEK” in ASCII?
“Geek” to be precise
@@zXrabidrabbitXz I wondered about the case but not enough to check myself. Thanks, Jason!
@@MrConverse You can see by the 6th bit (3rd from the left): 0 = upper case, 1 = lower case.
@@Wouter10123 Yep!
I wondered what Matt's take on the IUTT controversy was. I'm glad to see he's an adherent of the Redundant Copies School.
Oh yeah, gosh. Have there been any news on that since Mochizuki's own journal went ahead and published his proof, without clearing up Scholze and Stix's concerns at all? I couldn't really find anything more recent.
You're an amazing content creator Matt! Keep doing great maths!
he tried so hard to avoid being 3blue1brown that he turned into science asylum.
i for one am loving the mattiverse
Great video as always. This is the first explanation I've seen that clarifies the ABC conjecture enough for me to feel like I understand the problem (if not the solution). Thanks!
It seems that Mochizuki's alleged proof still contains some hand-wavey parts. If you don't accept its validity, you just "haven't understood it properly", which they can always repeat, no matter what their opponents say.
So many Matt videos ! love them all, and i love your geek t shirt
Never had I thought that two Matts could overlap! Wild stuff happens when you rush the upload schedule.
I love your videos! So great for learning math and having fun with it
Loving the frequent uploads!
Poor bearded Matt has no idea what is in store for him and Hannah
18:00 That's some top tier editing
8:59 Ah yes, the famous "Parker vs. Non-Parker" conjecture.
18:23 More like a 3Red1Matt video lmao
hands up everyone who went looking for a binary-to-ascii converter to read his shirt. Well done, sir.
No need - I have ASCII memorized from much time spent poring over TRS-80 Color Computer ROM disassembly listings in the 80s. 🤓
my most favorite 3blue1brown so far! Nice work Grant.
Awesome Sir Matt loving the video schedule!!!!also the content is awesome ✨😎😎
That's a T Shirt only a Geek would wear. I approve.
1
Grant, my man, outstanding video as always
I love extra Matts just pointing and nodding ❤️
“I have discovered a truly remarkable proof which this margin is too small to contain.” (hint: it uses the proof of Fermat's Last Theorem to work the other way)
log estimation tip: The log of a number is roughly the count of the digits in the number, when the log base is the same as the base of its argument.
log(238140) ~ 6 and log(210) ~ 3, so log(238140)/log(210) ~ 6/3 = 2. So we know the answer will be greater than 1 and less than 3. But since the beginning digits of the numerator 238... is larger than 210, The answer is greater than 2 and less than 3.
This is sometimes useful for me. Like in your video, I had the estimate in my head right away: 6/3 = 2
Not a complex tip, but has been useful for me.
Love all you videos and your book (hope there comes another one), have you thought about making a book about the randomness of mine sweeper?
We got a Parker Square update video, a Hannah and Matt video, and 4 days in a row with Matt videos being released. Christmas came early this year! I wish Parker Christmas lasted forever!
Wait, I think this is the first time I saw a graduate scholarship sponsored an educational youtube video. I'm crying...
You usually don't see longer odd-numbered LEGO pieces because you can build up anything from the smaller prime pieces of 2 and 3.
I like how the whole time Matt's talking about and looking towards these graphics that someone else made for the video, there's just no graphic on screen and it's an ad pitch for the wall decorations.
I really though epsilon was pronounced epsi-lon not e-psi-lon
epsilon comes from 'e psilon' i.e. 'simple e'. So pronouncing it with an emphasis on the psi rather than the e is closer to the Greek original, though not generally pronounced that way by most Classicists, at least in the US, who use the 'conventional' pronunciation.
That graph... I got lost, but the conclusion i got from "if you zoom out far enough they're essentially the same" is that low margins of error = no margin of error... That sounds like a parker mentality to me all right! 🤣
very geeky tee :) love it
Grants animation software is revolutionizing the world of math.
Ngl, the vague phrases of "the radical of all these together" and "the quality of the triple" (probably the technical phrasing, but I digress) had me lost for a bit. I'm really glad you showed the comparison of the quality against the epsilon term, that really told me what that meant lol.
As soon as Matt got the 2x5 and 2x7 lego pieces, my brain flipped. "They don't exist do they?" Later on... "ah..."
Matt’s videos are like London buses… you wait ages for one and then three come at once 🤣
Great video! Much fun!
Sometimes I worry i’m not going to enjoy your videos, but you are honestly, genuinely, really funny.
Why are there like 5 new videos wirh Matt in the last 2 days?! I LOVE IT
I've long since forgotten the meanings of most of the words you use, but I'm happy to be here all the same.
When you first pulled out the blocks I thought you were going to present the following problem. What is the minimum number of blocks required to spell all words of N length?
I found your strategy: Make as many videos, using different easter-eggs in order to gain more viewers and subscribers. You used Steve Mould, CGP Grey, Numberphile and 3blue 1 brown.
The 1 milion subscribers reward is comming soon.
Thank you so much for this 3Bald1Bearded Video 😎
Matt is talking about a conjecture, which if proved would give an alternate proof for likely the second most famous theorem in maths, and only starts mentioning that fact 20 minutes into the video.
Classic Parker move
So... a move which _almost_ works?
As someone who plays Four 4s on a regular basis, 210 is very familiar to me, since it's easy to get with one 4 (σ(4)#, aka sigma 4, and then the primorial of that).
Oh wow, 3 videos in a row ! Lucky week !
Corollary: squaring a number doubles the quality
Great shirt, Matt!
2x5 and 2x7 Lego bricks are a horrifying sight to any Lego fan… what unholy beast have you unleashed‽
I love that JPL poster!
I knew I recognised that font but couldn’t for the life of me figure out where from! I love that style of animation
1:34 wait, did I travel back to the 50s or smth?
It would have been even funnier if at 18:00 there were 3 Matt with a Blue shirt and q Matt with a Brown shirt. Then no one would ever confuse it with a 3Blue1Brown video for sure.
Who else was wondering "Where's he going to get five- and seven-stud Lego blocks?"
Then to hear GLUE! Matt, I thought more of you than that!
8:18 follow up. Matt, I spotted a mistake: the quality is not the average height. In your example:
n = 238140 = 2^2 * 3^5 * 5^1 * 7^2
radical = 2*3*5*7 = 210
quality = log(n) / log(radical) = ~2.315
Lego construction
base = 2+3+5+7 = 17
area = 2*2 + 3*5 + 5*1 + 7*2 = 38
avg height = 38 / 17 = ~2.235
The quality and avg height are definitely related in some way, but they're not equal.
See my other comment as well.
Average is a more general term than just the arithmetic mean. See for example geometric mean and harmonic mean, which are also averages.
@@SmileyMPV I'll Grant you that, but average height sort of implies arithmetic mean. Anyways if he didn't mean arithmetic mean, which mean did he mean, know what I mean?
@@joseville It's the weighted arithmetic mean of the stack heights, weighed by the natural logarithm of the prime base.
Indeed, for n=p1^a1...pk^ak we have q(n) = log(n)/log(rad(n)) = (a1*log(p1)+...+ak*log(pk)) / (log(p1)+...+log(pk)).
A 🦞 is always a plus.
I've been seeing a lot of Matt lately on TH-cam. in October. and it's barely just begun.
5:53 this is an interesting equivalence relation on the set of natural numbers, there is literally an equivalence class that is 2^x for all natural numbers x
If you use a tiny drop of acetone on the surface of a LEGO, you can more permanently fuse bricks together.
Great video, Grant!
Get Matt to a Million 2021 !!!!!
Love the shirt Matt - you certainly are!
I'm so confused and excited at the same time like what?!? 3 vids back to back?
For anyone wondering, the shirt is the binary representation of the ASCII codes for
G
e
e
k
Sorry to be this person but G e e k. Only the G is an uppercase in the ascii conversion.
@@christopherdwyer9496 Good point. That 32 bit makes all the difference.
Matt's t-shirt says, "Geek."
8:18
Matt, I think I spotted a mistake and somebody please correct me if I am wrong or confirm if I'm right, but the quality is not really the average height.
Given a number whose prime factorization is
a^x * b^y * c^z
The average height of the corresponding Lego construction is
(a*x + b*y + c*z) / (a + b + c)
Meanwhile the quality of said number is
log(a^x * b^y * c^z) / log(a*b*c)
Which is equal to
(xlog(a) + ylog(b) + zlog(c)) / (log(a) + log(b) + log(c))
Which is not at all equal to the average height!
Average height looks like A/B meanwhile the quality likes like log(A)/log(B).
There is definitely a relation between quality and average height, but that relation is not an equality relation. I'm curious if given the quality, how do you manipulate it to get the average height or vice versa.
Parker's mean
I believe it is a mistake. When he said that it just sounded off for some reason, so I calculated the actual area of all the blocks (2*2 + 3*5 + 5*1 + 7*2 = 38 if we say the height of one block is 1) and the length of all the blocks (2 + 3 + 5 + 7 = 17) and with quik mafs, 38/17 = 2 + 4/17 < 2.25. Sure enough, a calculator confirmed that the average height is 38/17 ~ 2.2353. Once I realized this I started scrolling through the comments to see if anyone else thought this or if it was just me, so I’m glad to see I’m not the only one lol. You also went a step above me and found the general relation, so props to you!
@@MathIsFun137 Same here! It sounded off to me as well. I made a related comment as well. In the comment thread for the other comment, it was concluded that the quality is actually a weighted arithmetic mean, but even if that's what Matt meant he didn't communicate it very well.
Well, I'm glad I saw James Grime's video on this topic first - and the Mathologer one about partitons. So many things need defining to understand the terms like radicals, partitions, etc.
I'm wondering if putting numbers in different bases will help. If one of the numbers a and b is the base, e.g. b, in its own base it is '10' and any power of it is 100, 1000, 10000, etc. If a and b have no common factors then adding them together in the base b (or a) means the result (c) has the same last digit(s) as a (or b). If the bigger number b is the base, then 'a' is a single digit number 'a' and a+b would be written '1a'. OK if these numbers get large we don't have enough symbols to have single digits up to b-1! I suppose up to base 34 we can use letters other than I or O which look too much like 1 and 0!
A neat thing I noticed was that in any base >5 the square of b+1 is 121 and the square of b+2 is 144, and b+3 squared is 169 [base 10+ of course - no '9' before that], etc, and the cube of b+1 is 1331. Makes sense when expanding (b+n)(b+n) =b^2 + 2nb + n^2 - until the digits become bigger than b and have to shunt values along. Trying to find squares of a smaller number 'a' that are '100 in base b' less than these squares... so (for Pythagoras integer triangles) we want values of a that square to 21, 44, 69 or 96, etc in base 'b'. Oh good I found one early on... in base 4 '21' means '2x4+1' = 9 = 3^2 and 121=(4+1)^2.
Or perhaps the best base to use if 'b' is not prime is the product of its prime factors then 'b' would still end in 0 because it is a multiple of the base?! Like if b=24 use base 6 and b=4 sixes = 40.
PS I was also a little frustrated with Lego not doing 'normal' bricks or plates 5 or 7 units long!
PPS about the end bit:
A protractor with a plumbline? I made one with Mum's help to try to measure my latitude by trying hard to line it up with the pole star and see what its altitude angle was. Not particularly accurate setting up the line of sight with one end of it leaning against the car.
that matt->grant vocal transition was wild!