I knew it would be the Chinese Remainder Theorem, maybe the most fundamental theorem with the worst name.
@Rougarou993 сағат бұрын
Physics: π ≈ e ≈ 3, therefore π+e=6. QED
@CaedmonOS7 сағат бұрын
You know, probably would have been nice to know about this before it happened.
@the_eternal_student11 сағат бұрын
I have been wanting to see an example of sq rt 5.
@darkpulcinella969014 сағат бұрын
never closed numberphile so fast
@pingnick14 сағат бұрын
I wonder if any of them is on 11 year cycle!? Anyway, wild that areas of Eastern Illinois in particular got hit this year in particular by BOTH!?🤯
@willo773416 сағат бұрын
Awesome video. I had heard something about why this is a huge cicada year but you explained it perfectly in a way that’s a lot easier to understand.
@iugoeswest16 сағат бұрын
I wonder how Leap Years affect these bugs over millions of years
@TastySalamanders14 сағат бұрын
Leap years wouldn't effect them, since they are invention of humans to reconcile the fact the actual year doesn't have an integer amount of days and yet we kind of want an integer amount of days to have a workable calendar. i.e. Each year is actually 365.25 days. But a regular calendar year is 365 days, so every 4 years our calendar starts to diverge from Earth's actual rotation so we add an extra day every 4 years to resync it.
@ComboClass7 сағат бұрын
Like the other reply mentioned, leap years probably wouldn't effect it, since the bugs are on year-based cycles and not 365-day-based cycles.
@iugoeswest16 сағат бұрын
Like an awesome version of Beakmans world
@phyarth808216 сағат бұрын
Feigenbaum bifurcation constant and "predatory and prey" chaos dynamic. I think people will bifurcate to 300 billion population Feigenbaum German baum is tree and bifurcation means branching that a coincidence :) Humans have no diseases or natural predator's. Cordyceps: attack of the killer fungi - Planet Earth Attenborough BBC wildlife - kzfaq.info/get/bejne/jtt7naV6p6ilfGw.html. None of species even with zero predator's cannot have upper hand. The only threat to humans is natural disasters where people uncappable geoengineer climate, maybe climate change is ironic "God's Finger".
@donwald343617 сағат бұрын
I mean if he really did have a proof he could slip an extra piece of paper between the pages? lol
@jkid113418 сағат бұрын
I have listened to the cicadas a several times this year, it's nice to know that there's actually like a cicada happening
@TymexComputing19 сағат бұрын
Cicada emerge'ncy!
@TymexComputing19 сағат бұрын
I thought Cicada 17-29 years is long enough :)
@monoman408320 сағат бұрын
hocus pocus where's my locust ???
@timetravl3r20 сағат бұрын
As always, love your work ❤️
@EricDMMiller20 сағат бұрын
The bioshphere won't support their re-emergence 221 years from now. This will be the last time ever. Hope everyone enjoyed it.
@ennayanne21 сағат бұрын
I love your channel, please don't set yourself on fire that would suck
@jessehammer12322 сағат бұрын
The cheerful insanity of these videos never fails to delight me.
@stickmcskunky434523 сағат бұрын
Sweeeeeeeet
@tomkerruish298223 сағат бұрын
I keep worrying that someone is going to narc on you about your fires to the Envirostapo, I mean, the BAAQMD.
@Sam_on_YouTube23 сағат бұрын
I took a look at a map of the overlaps of the various broods. There's a double brood emergence somewhere in the country roughly once every 20 years if I remember correctly. Each of these double emergences happens once every 221 years, but there's about 10 places with double emergences happen (again, from memory, I'd have to look at the map again to be sure).
@ComboClass23 сағат бұрын
Yeah it would be cool to visit one of those places at the right time. As I mention in the episode, these particular broods have notable traits about their size, which is why the 221 year cycle is extra notable.
@Sam_on_YouTube23 сағат бұрын
@@ComboClass There may not be much to see, at least not much more than a normal emergence (which is already plenty). The overlaps are generally pretty small, so even when they are forecasted, they don't always happen in the same place and they also don't necessarily happen at the same time. Each brood is synchronized based on temperature, but not necessarily 2 different broods that are in different cycles, so the emergence may happen twice in a small area rather than having a double emergence in one spot. This one I think was in a small corner of Eastern Illinois and the next one is in North Carolina if I remember correctly.
@stickmcskunky434523 сағат бұрын
Double emergences can also happen occasionally unexpectedly when a brood doesn't emerge when predicted for whatever reason.
@TheGrassman451Күн бұрын
this is the math i want
@yasin_karaaslanКүн бұрын
I don't know why but your videos feel like therapy, my chronic headache stops for a moment and I regain my joy of life. Thank you
@jellybeanfactory21Күн бұрын
Gotta love the sirens in the background as he introduced fire into the video 🤣
@taskfailedsuccesfully738Күн бұрын
Cicada
@brain_snakesКүн бұрын
Man spends 25 minutes blaming analog clock for his inability to read them.
@ComboClassКүн бұрын
This is a short episode about the mathematical explanation behind a rare natural event that happened this year…. In a week or two, I’ll have a longer number theory episode out, and then after that will be the Combo Class Grade -2 finale (and then the beginning of Grade -3).
@tristantheoofer2Күн бұрын
oh shit grade -2 is finally ending??? damn i remember grade -1 ending a year ago. i cant believe we are nearly at the end of the next one, and damn its taken so long to get here
@ComboClassКүн бұрын
@@tristantheoofer2 This grade is taking a little longer than a year since I wanted to do 36 main episodes like last time, but a lot of these episodes were longer (among other factors). Also, I decided I wouldn't cut my hair/beard at all during Grade -2 as a personal experiment, so soon I'll finally get to shave haha.
@JerehmiaBoaz15 сағат бұрын
@@ComboClass I think the Catweazle look contributes to the atmosphere of strange and unlikely events happening while you explain the world to us peasants. The gods must be angry with you for casually revealing their secret knowledge.
@tristantheoofer213 сағат бұрын
@@ComboClass yeah ive noticed the hair hasnt been cut at all (and being real i kinda envy it lmao). and i was also thinkin that there would be 36 episodes like last time so that makes sense :P
@osgubbenКүн бұрын
In some countries 1000 millions are called a milliard. And a billion is 1000 milliards etc, Here in Scandinavia.for instance.
@recklessrogesКүн бұрын
Balanced_ternary mentioned. Just need that implemented with Fredkin gates and we will be living in the future.
@dontask76572 күн бұрын
Artificial intelligence could totally be used to find the most ideal way to pack squares
@willo77343 күн бұрын
Wow man, the fact that you compose your own music for the videos is super impressive. It’s really good and fits these videos perfectlv.
@AnoNymous-dh2sv3 күн бұрын
The real Beast channel.
@BELLAROSE212124 күн бұрын
🐥👈he says these numbers are not repeating and must be rational, see the zero at the end ..Let’s say A= 2.8502930912661030 B=3.4328922159134830 Then this must be true A plus 1/xB=3.14159265358793 This could be simply checked in “polynomial-time” 2.8502930912661030 + 0.291299562323690= 3.141592653589793 “Not-pie” as irrational number, however if you divide “Not” pie by 3.141592653589793…… your gonna get 1(approximately or with my counting machine exactly 1) 3.4328922159134830 times 0.291299562323690 equal 1… Therefore B minus 1/xB= 3.141592653589793 This is transcendental equation of one kind or another …. Very useful for quantum mechanics…. This is one of various functions that could be done.. Should we apply this same to Bminus sinB= 3.141592653589793 And A plus sinB= 3.141592653589793???
@blaz28924 күн бұрын
I haven't done any real analysis or research for this, but I'd guess that the recursive domain increases mentioned at the end of the video would work as long as it stays finite - you can probably continue that to ω, but not to ∞. Continuing it to infinity would probably make it possible to create powers like log₂(3), which fully breaks the unique prime factorization rule. If there is some finite combination of powers of rational powers of integers that can produce logₚ(q) where p and q are distinct primes, that would disprove my conjecture, and I think proving that impossible would prove my conjecture. I might give it a shot.
@AT-271824 күн бұрын
Beautiful lesson. Thank you.
@luisg.ontoriaalvarez23345 күн бұрын
Thank you for sharing your passion!
@RSLT5 күн бұрын
If there are different sizes of infinity, how can it be that 0.999... equals 1? For instance, if we can say there are infinitely many numbers between 0.999... and 1, such as 1/ℵ₁ or 1/ℵ₂, doesn’t this contradict the equality?
@ComboClass4 күн бұрын
1/(an aleph number) is not a defined quantity on the real number line. You can't take the reciprocal of an aleph number in the same way as we are used to doing with a real number. We typically assume that every number non-zero (n) has a version (1/n) in its system, but aleph numbers aren't the same. Some branches of math allow that sort of thing, but those systems are different and lose many typical properties of arithmetic we take for granted. When proving things about .999 repeating we are typically discussing real numbers, not systems that allow infinitesimals of that form.
@RSLT3 күн бұрын
@@ComboClass Here is proof that ℵ0 ∈ N. The cardinality of the set {1} is 1, the cardinality of the set {1, 2} is 2, and the cardinality of the set {1, 2, 3, ..., N} is N. and the cardinality of the set of natural numbers is ℵ0 (aleph-null). Thus, ℵ0 is a natural number. we know that all natural number are real number . Because ℵ0 is a number in the real number system, 1/ℵ0 is a real number as well ( not zero) . Since ℵ0 < ℵ1, it follows that 1/ℵ0 > 1/ℵ1, which implies that the claim of no gap in the real numbers is false. Therefore, there must be a gap between 0.99... and 1; thus, they cannot be equal in the real number system. So, if this video is correct, which is my opinion, it is 100% accurate and the best one I have seen in years. It proves that 0.99... cannot be equal to 1 in the real number system, although that may not be your intention but it did.
@JohnJones-tx6rt5 күн бұрын
You made a mistake, I thought a big one. You weren't talking about the "number" one, or 1, you were talking about the numeral 1, which is a nameless object. Why do I say that? Because anything could stand for standalone "one's" or "1's", such as a chicken, pi, e, sq.rt 2.etc. Numbers only arise in an application, and there is no transfer of numbers between applications. Outside its application, a number is simply a numeral, any object or objects.
@ComboClass4 күн бұрын
Not sure what you mean with that, since 1 is certainly being used as a number here, not just a symbol. When we say things like (1+1)(1+1+1) = 6 here, it is not true that (e+e)(e+e+e) = 6, and if you mean that in general (a+a)(a+a+a)=6a, that's true but is really just describing that (a)(1+1)(1+1+1) = (a)(6) which is just a multiple of the equation using 1's. You can multiply most equations by a random variable, but that doesn't mean that their simpler form using 1's isn't using numbers.
@JohnJones-tx6rt4 күн бұрын
@@ComboClass (Your series is one of the best btw, but I am always a dark critic.) Yes, quite right, you used 1 as a number, I reminded myself of that after I posted, but I let it ride because when you first asked "how many one's ...?" (if I remember right) I saw a fly in the ointment, and wondered if that fly had infected the whole jar. "One" standing alone, is a monad (see Liebniz?) , and not countable as there is nothing to distinguish it as separate. (How do we include THAT in the number series which is, after all, a spectator perspective?) So we cannot then speak of "many one's". If we insist that "one" is countable, then there are consequences, including the one where you said that by replacing 1 with e we would get a different addition result. But on that point (there are others) I'm in stormy seas, the timbers creak. There is another reality (ontology) underpinning mathematics, one that mathematicians rarely look at, but sometimes go there. But as Wittgenstein said, the philosophy of mathematics is not mathematical, and not everyone's cup of tea of course. Still, it can be very interesting. almost mystical. Thanks for responding.
@mathtonight10845 күн бұрын
Suppose that it is rational, and then find a contradiction
@ComboClass4 күн бұрын
I used proofs by contradiction, yes. The tricky part for a given type of number isn't to know that you want to use that technique, but to find the contradiction.
@DarucaudEdspecial5 күн бұрын
Yes❤️🩹❤️🩹❤️🩹
@Hi7here6 күн бұрын
3:14 I'm telling my kids this was Dr. Seuss 😂
@aidenwallin35236 күн бұрын
0:17 Were you just putting your face in a brugmansia? Also, nice fig tree at 1:13!
@ComboClass6 күн бұрын
At 0:17 I'm next to an apple tree
@aidenwallin35236 күн бұрын
That really fooled me! The leaves on your apple tree are 3-4 times larger than the leaves on mine, and look just like my orange brugmansia's leaves.
@samb4436 күн бұрын
16:45 this is the issue with cantors diagonal argument "I wrote random digits", is not how you construct real numbers. None of what you had written down was actually a number, they were just finite sequences of digits followed by "..." they literally have no more meaning than that. If you wrote down every "real number defined by a finite string", and diagonalize on those, then you would get an infinite word, which is not a valid wff. There are not "more" real numbers than there are natural numbers. Though it is still the case that a bijection doesnt exist in ZFC, but interpreting "no bijections" as "different sizes" for infinite sets is incorrect.
@thomaskember34126 күн бұрын
I think a step has been left out in the proof for the square root of 2. If a perfect square is even, it may seem obvious that its square root is also even. But this proposition still has to be proved.
@ComboClass4 күн бұрын
We have to choose which things we take for granted when writing a proof, because you don't want to have to re-prove every basic thing (like that 1+1=2, or a+b = b+a) within every proof. It's true that in this episode I somewhat took the "if a square is even so is the square root" as a pre-existing assumption, although I did briefly explain the logic that if any (x) was odd then (x^2) would also have been odd. If you wanted to prove that part within the proof instead of using it as an assumption, you could use the definitions of even and odd number as 2k or 2k+1 for different integers k and do some arithmetic. But any proof will still have "missing steps" unless it includes dozens of other proofs that people consider already proven/obvious.
@Wielorybkek6 күн бұрын
you made me curious about Magic so I did some quick research and found out that someone proved that this game is Turning-complete. wow. xD
@DrZip6 күн бұрын
The most unsettling part of this video is how you write your 'a' to somehow look like a '9'. :P @2:40
@hendrikd21136 күн бұрын
We should have clocks going from 1 to -i to -1 to i. a (half) day could have 4 or 8 or 16 hours. Also, why is everything in Math and the world always counter clockwise, except for clocks?!