"Let's call it phi. We don't know what phi is" **stares in suspicion**
@kamoroso944 жыл бұрын
As soon as I saw 1.1 in the last video, I thought it would've had something to do with Pascal's triangle.
@Nah_Bohdi4 жыл бұрын
"fee"? Yeah...Ive heard enough, read him his rights.
@leonardozhou78444 жыл бұрын
@@Nah_Bohdi i dont want any bills
@yin-yang92313 жыл бұрын
Phi = Greek letter
@yin-yang92313 жыл бұрын
@@leonardozhou7844 buybjhbjjnnkm
@ChrisConnett4 жыл бұрын
Never have I clicked to the Numberphile2 video so quickly.
@oltman4 жыл бұрын
Cliff hanger.
@aatheeswarank70254 жыл бұрын
@@oltman IFKR
@dkamm654 жыл бұрын
I just gotta say I NEED to see a fractal of these numbers between 1 and 10 with a different color representing each of the 5 possibilities.
@jowl52034 жыл бұрын
Bruh same
@thomasrad52024 жыл бұрын
same
@Maharani19914 жыл бұрын
Yes
@NLGeebee4 жыл бұрын
But.... Since the number and the base (to infinity) are the same, don't you just get a line on the x-axes with microscopical coloured dots?
@pwhqngl0evzeg7z374 жыл бұрын
Sounds cool, but how would it work? It seems the function you propose to graph like a fractal is f : N -> {1,2,3,4,5} where f(x) = the color assigned to the behavior of x_x_x_x_..., but as far as I know to graph something like a fractal you need a three dimensional function (although it may not obviously be three dimensional, e.g. z : C -> R). Two spatial axes and color as the final dimension, I think, although there may be more (HSV). (See Q's comment below for an addendum to my naïveté.) That is an interesting concept in itself: a number system with a complex base, i.e. d_(p-1) … d_1 d_0 . d_-1 d_-2 … d_-r in base a+bi is \sum_{k = -r}^{p-1} (d_k)(a+bi)^k. So with complex bases you could have a graph (which might be fractal, I don't see any reason for it however) of the sort you describe.
@recklessroges4 жыл бұрын
The Sloane Ranger rides again. Showing us a tiny part of the horizon of math.
@Maharani19914 жыл бұрын
Bwahaha :D
@danielsahlberg45764 жыл бұрын
Neil: “This is a number. What is that number, would you like to guess?” Also Neil: “LeT’s JuSt CaLl It PhI.”
@rosiefay72834 жыл бұрын
Or, rather, call it "fee".
@pbj41844 жыл бұрын
@@rosiefay7283 But then the joke 'Phi is one H lot more cooler than pi' won't work :)
@MarkWaner4 жыл бұрын
master of disguise
@N3rys2 жыл бұрын
@@rosiefay7283 Here's a paragraph from Gary Meisner's article about Φ: My Greek phriend Tassos Spiliotopoulos offers the following: The letters of the Greek alphabet are written as words and not as single letters, for example the first letter A is written AΛΦA and sounds like Alpha. When it comes to letters like Π, Χ, Φ (written ΠI, ΧI and ΦI respectively), the misunderstanding comes from the pronunciation of the letter ‘I’ which in English rhymes with fly but in Greek is pronounced EE. The letter Φ is always pronounced PHEE in Greek, and it does not differ if followed by a vowel or a consonant.
@CastorQuinn4 жыл бұрын
I would *very much* like some more videos on symbolic dynamics. This is absolutely fascinating.
@BryanWLepore4 жыл бұрын
Neil Sloane : “... symbolic dynamics.” Me : ... AAAND?!? Go on?!?!
@Bronco5413 жыл бұрын
this man is wearing a Jimi Hendrix shirt and the walls in his room are decorated like a circus. I like it.
@OlliWilkman4 жыл бұрын
I wrote a quick code to do this and experimented with some numbers. Seems to me that if you start with any number of the form x+0.1, where x is a single-digit number, you converge to a constant whose powers, rounded to the nearest integer, generate a series of integers where a(n) = x*a(n-1) + a(n-2).
@OlliWilkman4 жыл бұрын
Analytically speaking, starting with x+0.1, that leads to an equation like x + 1/r = r, which has the positive solution r = (x + sqrt(x^2 + 4))/2. With x=1, that's leads to the golden ratio. For x=2, the constant is 1 + sqrt(2), and so on.
@Maharani19914 жыл бұрын
+
@RealLifeKyurem4 жыл бұрын
Olli Wilkman Ah, so the metallic means.
@sergey15194 жыл бұрын
@@OlliWilkman How does your code work? Is it symbolic math? Cuz i think my code might be a bit broken. I imagine that i take some number z, then it maps roughly to number z_2, but since it's not exactly z_2, i won't get z_3 even roughly since the iteration is very discontinuous. I am suspecting this since 1.1 for me doesn't approach golden ratio and instead falls into a cycle. So that shows that i do something wrong
@OlliWilkman4 жыл бұрын
@@sergey1519 If you're using Python, I recommend computing the contribution of each digit into a list, then adding them together with math.fsum, which computes floating point sums with better precision than the regular sum function or just adding together terms one by one.
@MisterAppleEsq4 жыл бұрын
It's gonna be the Golden Ratio, because it's another way of stating the 1+1/(1+1(.... continued fraction.
@MisterAppleEsq4 жыл бұрын
Aaaand, he called it phi, definitely the golden ratio.
@GrandRezero4 жыл бұрын
My exact thought as soon as I saw 1.1 repeating like that..
@SWebster104 жыл бұрын
And it was teased in the opening to the first episode
@wesleydeng714 жыл бұрын
also: sqrt(1+sqrt(1+sqrt(1+sqrt(1+...))))
@hotdogskid4 жыл бұрын
My thoughts exactly, although i might have been primed by the whole phi thing :)
@GelidGanef4 жыл бұрын
Maybe the real golden ratio was the different bases we made along the way
@ceruchi20844 жыл бұрын
Computer programming is the only way I got to second base.
@bgnelson68214 жыл бұрын
He has some interestingly labeled folders on that shelf above his desk.
@RobKlooster4 жыл бұрын
Fun fact: the infinite tower of 1.12 also converges to 2. It is the solution to x = 1 + 1/x + 2/x^2.
@MrRyanroberson14 жыл бұрын
any tower of the form ceiling(10^n/0.9)/10^n does this, starting from n=0: ceiling(1/0.9)/1 = 2, ceiling(10/0.9)/10 = 1.2, 1.12, 1.112...; all such polynomials have a solution at x=2, since this produces 1+1/2+1/4...+1/2^n +2/2^(n+1), which collapses back up to 2, no matter how many terms
@Ragnarok5404 жыл бұрын
This part was the most interesting, it should be on the main channel.
@nymalous34284 жыл бұрын
Great. Now, suddenly, I'm slightly obsessed with symbolic dynamics... even though all that I know about it comes from this pair of videos!
@Starguy2564 жыл бұрын
When he said 2 sub 2 = 2, isn't 2 sub 2 just nonsense? The sub 2 means it's in binary, and the symbol 2 doesn't exist in binary. Isn't that like asking for the value of Q in decimal?
@Selicre4 жыл бұрын
You can assume that you _can_ go out of range, which means that there's more than one representation of a number, for example, 3₂ == 11₂, and B₁₀ == 11₁₀.
@Zejgar4 жыл бұрын
Yes, but in this case at 0:25 he gave the definition of what "a sub b" means for any "a" and "b". Within that definition, "2 sub 2" works.
@brunojambeiro67764 жыл бұрын
I think is like asking the value of A(hexadecimal) in decimal, A doesn’t exit in decimal, but it has the value of 10.
@spagetychannel50704 жыл бұрын
It’s not nonsense. It’s just a nonstandard representation, like writing 131 as twelfty-eleven.
@pbj41844 жыл бұрын
He assumes you're not restricted to the digits of the base, instead he just represents the value in a different, intermediate base
@NNOTM4 жыл бұрын
Hm I wonder if you can have complex bases, and if so, what would happen if you graphed the behavior for each base in an Argand diagram. First guess would be it might produce some sort of fractal
@m1lkweed4 жыл бұрын
Nnotm according to Wikipedia, yes. You can have complex, negative, fractional, transcendental, and even mixed bases.
@pbj41844 жыл бұрын
Wow! Leave it to the mathematicians to generalize stuff and figure out its properties :)
@masheroz4 жыл бұрын
Yep. Donald Knuth did a bunch of work on complex bases, if I recall correctly.
@DavidBeaumont4 жыл бұрын
That was my first thought. Colour according to eventual behaviour and see what it looks like.
@dankmeme53364 жыл бұрын
You can in fact have complex bases In fact, base i only requires 4 digits
@Krekkertje4 жыл бұрын
I love it when a very simple game and corresponding sequence leads to a complete new area of mathematics.
@caleblatreille82244 жыл бұрын
this was better than part 1! ! that explanation for 213.56 is a treasure
@Henkecool154 жыл бұрын
Ah man, the most interesting bits are always in the extra video! Great seeing Neil again, always great!
@RandomBurfness4 жыл бұрын
3:42 How is 2 base 2 even defined? In base 2, you don't have the digit "2", you only have the digits "0" and "1".
@noahniederklein80814 жыл бұрын
Exactly what I was thinking
@poesiatododia89104 жыл бұрын
2 base 2 is 10. 2 base b is 2 for any b greater than 2
@livedandletdie4 жыл бұрын
well how is 10 base 10 defined. Same question, it was just him explaining things, it didn't have to be rigorous. And seeing as 10 base 10 isn't really defined at all. I mean who am I to decide that sub b must always be in base 10(ten) notation? I mean 10 sub 10 can be almost everything.
@dizont4 жыл бұрын
@@livedandletdie 10 base 10 is 1 * 10 + 0. in base 10 there is no digit "10". like in hex, there is no 16. so in base 2 there shouldnt be 2
@Maharani19914 жыл бұрын
+
@caelanfreemantle58314 жыл бұрын
Was watching this to procrastinate. Then it simply explains what a limit cycle is. Exactly what I needed to help with my revision. Thanks numberphile.
@TheGreatAtario4 жыл бұрын
Wait a minute. How can you have 2 sub 2? Base 2 only has 0s and 1s!
@aliifliss1144 жыл бұрын
Thank you !
@AlfredJacobMohan4 жыл бұрын
It is bracketed from the bottom up. So, let us skip forward to the "Last" term in 2_2_2_2_2_2_2_... which is as you said 2_2 = 10. So, what would the next term be? 2_10=2 and I think It will keep fluctuating between 10 and 2 and finally yields 2. At least, that is what I think. Maybe he chose the answer 2 instead of 10, to prove his point that the answer was boring. This is some SERIOUS Grandi Series Action going on here. So it might be under the diverging category. I don't know.
@frechjo4 жыл бұрын
Hh, yes. Maybe he's taking 2 as an equivalent to 10 b2. And if you think about it, that's the only thing that would make sense for a 2 in base 2. There are number systems that have a normal form, but equivalent intermediate forms are also used in operations. It would be like having A3 b10 mean 103, for instance.
@pbj41844 жыл бұрын
Yes you can't but when you're number doesn't contain digits equal or greater than it, you can. Is there any way to figure out which towers are possible and which towers are ruled because of this?
@PhilBoswell4 жыл бұрын
I think what it means is that "2 sub 2" is 10b (or 10₂ or %10 or 0b10 or even 2b10, whichever takes your fancy ;-) which equals the number "2". Bear in mind that he's writing all the eventual results in base 10.
@Qermaq4 жыл бұрын
If you pronounce φ as"fee" then you gotta pronounce π as "pee".
@Jocedu064 жыл бұрын
Correct in base french
@superze264 жыл бұрын
@@Jocedu06 and Greek
@thajobe46234 жыл бұрын
and German
@xnopyt6474 жыл бұрын
and Dothraki
@angelmendez-rivera3514 жыл бұрын
Φ is pronounced /fi/ in every single major language. English speakers are literally the only people in the planet who refuse to pronounce it correctly.
@yashrawat94094 жыл бұрын
*Waiting for this sequel felt longer than entire year*
@KatzRool4 жыл бұрын
Every time one of these sequence videos comes out, it blows my mind. Neil Sloane officially endorsed by the Funky Dungeon Dwellers.
@StormwaterIsOneWord4 жыл бұрын
Neil might be the best guest. What a gift he is to humanity!
@oz_jones3 жыл бұрын
Sloane RIder is one of my favourites on this channel (and the main one, obviously).
@larryd95774 жыл бұрын
How could you not out this in the main video. This is the whole point of the prologue...
@ceegers4 жыл бұрын
I like this mystery better than the main video!
@peterisbb4 жыл бұрын
God, I love the golden ratio. I was suspicious as soon as he started calling it Phi but I still wasn't prepared.
@helleye3114 жыл бұрын
Ah, golden ratio. Pops up in random places just like pi does.
@aasyjepale52104 жыл бұрын
One unwanted quest was enough...
@lonestarr14903 жыл бұрын
It's not so random in this case, for what he did was simply a rephrasing of the continued fraction expansion of the golden ratio.
@cheshire12 жыл бұрын
@@lonestarr1490 Actually I've never seen an example where it was truly random. It only ever seemed random until you explored the math behind it.
@_MimiTsuki_4 жыл бұрын
I’m so glad it was the golden ratio because I was really starting to get confused
@jetzeschaafsma12114 жыл бұрын
This video has about 30% of the views of the preceding one. That's just due to inconvenience, not disinterest.
@astphy2 ай бұрын
I was hoping for a different ratio.
@gballou864 жыл бұрын
This may be the first time I've watched a Numberphile and the presenter seemed to be sad by the fact that we don't know something. It made me want to see if I can help!
@Martin-qb2mw4 жыл бұрын
This vid is much much much better than the vid on Numberphile 1.
@LiamE694 жыл бұрын
ϕ ϕ fo fum.
@brettonjohansen16193 жыл бұрын
beautiful comment
@mirrimiau3 жыл бұрын
I smell the blood of an Englishman who has lived very long in the States and therefore pronounces some words the American way and also the Greek alphabet the Greek way
@diceblue68174 жыл бұрын
This is one of the best numberphiles I've seen...... and suddenly phi........ wtahhhh.... so we need another video on this!!
@yassinenacif4184 жыл бұрын
Wow! This is truly beautiful!
@mattj658164 жыл бұрын
This guy is to Numberphile as Professor Brailsford is to Computerphile: pure bliss.
@alexandrepetrassicardoso75394 жыл бұрын
The best parts are always on numberphile2
@TheBlueArcher4 жыл бұрын
Numberphile 2 is usually just kinda extra optional stuff but I feel like this video should have been the conclusion to the first. the "numbers growing" bit and "not growing as large as the exponents" was very unsatisfying. Like, a non-result. This one demonstrating that some numbers converge to the golden ratio makes it interesting.
@collectionneurdaphorismesf62104 жыл бұрын
Those notations give another way to express polynomial equations ... don't know whether it can be useful or just a notation view
@vikaskalsariya94254 жыл бұрын
It can be used to sexually harras barack obama
@vladimir5204 жыл бұрын
What's interesting to me is that each number x between 1 and 10 gives creates the iteration f(f(f(...f(x)...))) with f being a polynomial equation like you said, and that you cannot predict the outcome of the iteration (one of the 5 states).
@prasanttwo2814 жыл бұрын
I can't seem to think of a way to express polynomials with specific negative coefficients with this method; would be quite nice if that was possible
@spagetychannel50704 жыл бұрын
@@prasanttwo281 Just use negative digits.
@collectionneurdaphorismesf62104 жыл бұрын
@@prasanttwo281 Think further.... you put egality between two numbers... smt like 902820_(lambda)=070002_(lambda)
@JBOboe7204 жыл бұрын
The nature of humanity is just that every so often someone invents continued fractions again.
@fluffly36063 жыл бұрын
or circles
@jamirimaj68804 жыл бұрын
Numberphile in 2020s: Brady be like "The viewers are ready. Advanced Math it is."
@Rattiar4 жыл бұрын
The main video was interesting...this was way more engaging and fascinating. Thanks!
@Rattiar4 жыл бұрын
I love hearing "we don't know, but it does this cool thing..." in both math and science.
@danielg92754 жыл бұрын
that's pretty cool
@RefluxCitadelRevelations3 жыл бұрын
Funnily enough, I like it when phi pops up with absolutely no relation to "nature". It's literally everywhere for some reason, and it's usually in where we're doing arithmetic and modular stuff, but it'll just pop out of no where.
@MrRyanroberson14 жыл бұрын
in general for a number between 1 and 10 that is A + B/10, then the equation should be A+B/x = x, and then x^2 = Ax+B, and then we get from the quadratic formula sqrt(A^2/4-B) - A/2, which should work so long as A^2 > 4B. So some stable numbers to investigate are... 1.1, 2.1, 2.2, 3.1, 3.2, 4.1, 4.2, 4.3, 4.4, 5.1 ... 9.9; for example 9.9 stabilizes around 9.9083 no matter how far you go, and holds the property 9+9/x = x
@danhoenn4 жыл бұрын
Again Neil proves himself the best numberphile guest for ASMR
@ryonenmoon64804 жыл бұрын
I loved the video. I note there is an exception to the assertion that 2 (sub b) always equals "2". In base 1, 2 = "11", or "||" perhaps, depending on how you prefer your unary notation.
@E942-h2d4 жыл бұрын
In the sense it is taken here, the claim is true. It just says to evaluate the digits you have in base b with the corresponding position and then get back to base 10 again. So it is 2.
@FurpNate4 жыл бұрын
Numberphile is a drug to me man I can't get enough of this stuff lol
@Bovineprogrammer4 жыл бұрын
A big part of this is that we interpret the base as a decimal number (so with something written with the subscript 12, we always interpret that as being double 6, and not say 12 base 3). What if that wasn't the case? 1.111... and 10 would be in a cycle whichever base we use (but the actual values of the two numbers would change), converging in the case of 2 being static in base 2. There's a lot more to explore here, simply by removing the requirement of reading the base as a base 10 number.
@fluffly36063 жыл бұрын
"Let's call it phi..." *narrows eyes*
@jburtson4 жыл бұрын
This reminds me a lot of the Mandelbrot set. I wonder if you similarly tried to create a visual for this function from 1->10 what it might look like. And of course, whether complex numbers would work in this function and if that has similar properties.
@eliyasne96954 жыл бұрын
That's brilliant! And you can go farther by replacing 1.1 by 1.2 or 1.3 and so on... to get the nine first metallic ratios!
@E942-h2d4 жыл бұрын
Sorry, I think this is not correct. 1.2 leads to 2 and 1.3 to something around 2.3 which is also no metallic ratio.
@ButzPunk4 жыл бұрын
What happens if you use negative or complex bases? Is it still unpredictable or does it become regular again?
@RadeticDaniel4 жыл бұрын
-1 in base -1 is 1, which in base -1 is -1. So you know at least one case gives a flip-floping signal o/ If you take the polynomial approach, by which you can have more than one way of writing the same numbers and no constraints on the digits used, then every x in base x written with a single digit in a negative base also switches between x and -x infinitelly
@teneleven51324 жыл бұрын
isnt -1 in base -1 still just -1? like, in base -1, the unit columns would flip between being worth 1 and -1, depending on position. 100 would be (-1)^2 = 1, so -100 would be -1. 10 would be (-1)^1 = -1, so -10 would be 1. 1 would be (-1)^0 = 1, so -1 would be -1.
@RadeticDaniel4 жыл бұрын
@@teneleven5132 you are absolutely right! My mistake
@DrDirtyHarry4 жыл бұрын
@@teneleven5132 Could you explain further? Wouldn't -1 base -1 be 1/[(-1)^0]?
@teneleven51324 жыл бұрын
@@DrDirtyHarry that's what 1 in base -1 would be. -1 in base -1 is -1 * (-1)^0 = -1 * 1 = -1.
@MetaaR7 ай бұрын
I was messing around with my python code that was calculating it for any a, and I've found out that if a is 2.1 the result after 100 iterations was silver ratio, I tested it more and I've found this formula: a(n+0.1)=(n+sqrt(n+4)/2, where a(x) is the function mentioned in this video always* works. *Edit: It only works for n
@blackholesun4942Ай бұрын
Interesting! 👍
@BryanLeeWilliams4 жыл бұрын
It would be neat to see another video more in depth on this.
@bobvance9519 Жыл бұрын
I don't understand why it "wouldn't change" if we add another 1.1.
@nayutaito94214 жыл бұрын
I wrote a program and noticed that the "converging point function" is not continuous on any finite decimals. For example, the chain of 1.999... converges to 4, but the chain of 2 is obviously 2.
@PeterVC4 жыл бұрын
lol, my totally random guess was: oh, how about the golden ratio, it always appears in random places... and it actually is...
@BAbdulBaki4 жыл бұрын
Let n = a.b, with a the integer and b the decimal part. Assume, n_(n_(n_...)) [where _ is the dungeon function]is equal to m=c.d where c is an integer and d is the decimal part. Assume a.b_c.d = c.d. Thus, a + b/c.d = c.d or axc.d +b = c.dxc.d = (c.d)^2. Hence we get (c.d)^2-axc.d-b=0 = m^2-axm-b. Since this is a quadratic equation, it has either 0, 1, or 2 positive solutions. If it's 0, it should diverge. If it's 1, it should converge. If it's 2, it should oscillate between two numbers. Examples: Let n=1.1. Then a=1 and b=1. This gives us the quadratic equation m^2-m-1=0 and m=the golden ratio. Let n=1.2. Then a=1 and b=2. This gives us the quadratic equation m^2-m-2=0 and m=2 (unique positive solution). Let n=2.3. Then a=2 and b=3. This gives us the quadratic equation m^2-2m-3=0 and m=3 (unique positive solution). Let n=3.4. Then a=3 and b=4. This gives us the quadratic equation m^2-3m-4=0 and m=4 (unique positive solution). Let n=a.(a+1). Then a=a and b=a+1. This gives us the quadratic equation m^2-am-a-1=0 and m=a+1 (unique positive solution). I honestly haven't seen examples of the other two since I haven't programmed this.
@nerkulec2 жыл бұрын
symbolic dynamics sounds badass
@leitecumcarne4 жыл бұрын
Help, where that 5 come from at 2:56 ?
@CamAlert24 жыл бұрын
Le magic pentagon number strikes again
@Macieks3004 жыл бұрын
What happens outside of the range (1,10)? If we don't know what's going on inside then does that mean that numbers outside of the range behave in some obvious way?
@petros_adamopoulos4 жыл бұрын
Outside of this range it can only diverge and is boring. For integers between 1 and 10 it's also boring because it's constant.
@duskyrc13734 жыл бұрын
I suspect it depends on the base you read the 'bottom' number in. Here with the 1.1 example at the bottom of the dungeon it was read in base '9+1' (I don't want to use the term '10' since by definition any number is '10' in base itself). There shouldn't be anything special about '9+1' in and of itself. So it's probably that the number needs to be a non-integer between 1 and '10' where '10' is read in whatever base you read the 'bottom' of the dungeon in. For example something like A.6 in hexadecimal or M.B1 in base '27+1' (don't actually know what that would do). That's my thought on it, at least. I'll leave it to someone else to work out if I'm right.
@TheBasketboss3 жыл бұрын
the "extra video" is phi^phi^phi^phi... better than the original video
@leonardozhou78444 жыл бұрын
that smile is just big
@QlueDuPlessis4 жыл бұрын
So this is what mathematicians do when they're bored. Great cliffhanger, I just had to click the card...
@quarkraven3 жыл бұрын
okay but he's also wearing a Jimi Hendrix shirt, he's in the top Φ mathematicians in my book
@johnloony684 жыл бұрын
I started with (1.1 in base 1.1) which is 1 + (1/1.1) which is 1.9090909... and then (1.1 in base 1.9090909...) which is 1.90909... + (1/1.90909...) which is 2.4329 and then (1.1 in base 2.4329...) which is 2.4329... + (1/2.4329...) which is 2.8439... It eventually goes up to infinity, but it takes approximately n iterations to get up from approximately n to approximately n+1, so it increases at an ever decreasing rate.
@datarioplays4 жыл бұрын
No one is talking about that this video is UNLISTED.
@daddymuggle4 жыл бұрын
a_a immediately raises the question of how to interpret it. I'm rather tickled by the blithe way Neil leaps right past the question.
@NathanZamprogno4 жыл бұрын
Neil Sloane is my favourite Numberphile personality. Well, and Cliff Stoll. Both treasures. Here's my question: this behaviour of numbers in symbolic dynamics sounds like they could be visualised. If you graphed all the numbers from 1 to 10, based on themselves to infinity, and the behaviour could settle or diverge -- that sounds an awful lot like fractals like the Mandelbrot Set in which every point on the complex Argand plain might be bounded or unbounded when an operator is applied to itself recursively, and which defines the shape of the fractal. Has anyone tried to see if there's a visual pattern to whether a particular number a base a becomes bounded or unbounded?
@bourgeoiscaesar4 жыл бұрын
I wonder what would happen if you did phi sub phi, or if you can even have irrational bases.
@E942-h2d4 жыл бұрын
I tried it just now a little. In the first iteration you end up with something like 8.14... After about 30 iterations I saw the value you get is somewhere between 3.23 and 3.2. So it converges to something (looks a bit like 2 times phi...mmmmh) But this is also subject to little precision.
@torlumnitor82304 жыл бұрын
That wallpaper makes me want whataburger.
@Djake3tooth Жыл бұрын
Fun fact: 3/2 creates a cycle of length 3 instead of 2
@shaunaherrera59814 жыл бұрын
Thanks for letting me know my phone still getting hacked
@BAbdulBaki4 жыл бұрын
D'oh! I realized my limitation.
@triplebog4 жыл бұрын
I would love to see some sort of mandelbrot esque graph to see which numbers resolve to what to see if there is some sort of fractal pattern
@_vicary4 жыл бұрын
3.35 sounds like the Mandelbrot set, isn’t it?
@friedchickenUSA2 жыл бұрын
from what it seems, the numbers that dont diverge in this algorithm seem to be an overly complicated reinvention of finding the zeroes of a polynomial. the power of a polynomial being the same as the number of digits given. because 1,1 has 2 digits, it gave a quadratic equasion, for example.
@Skwertydogs4 жыл бұрын
How can anyone work with those orange stripes on the walls. That would drive me crazy.
@nuberiffic3 жыл бұрын
I've never been so lost so quickly in a video. Still can't see how you can have a base that is not a positive integer
@lauritoivonen21624 жыл бұрын
Call it how it is... Neil Sloane
@SteinGauslaaStrindhaug4 жыл бұрын
This is a pretty pure example of mathematics being making up some rules and see what happens.
@robfenwitch74034 жыл бұрын
Why am I here? Cos someone (I'm looking at you, Brady) decided to split the video!
@nopianocovers66284 жыл бұрын
What would happen if you worked with base in the dungeon number context? What about in a broader context? Would there be any pragmatic value to it or would it just make everything unnecessarily complicated and confusing without any helpful application?
@FrostFire16494 жыл бұрын
Does anyone have the OEIS code for the infinite subbing sequence?
@sebwiers1 Жыл бұрын
What if the result of one of these cycles within a fixed range, but never settles into a loop? IE, Chaotic behavior? I did not see that possibility mentioned as one of the 5 outcomes (which I take to be zero, infinite, unchanged from input, converging, or cyclic). Am I missing something, or is it somehow known to not be possible? To me it seems not only possible, but almost unavoidable at the boundary of the other 5 outcomes.
@madcapprof4 жыл бұрын
Technically, if A is a single digit integer A_A does not make sense.
@m1lkweed4 жыл бұрын
Why did I get another notification for this?
@Garbaz4 жыл бұрын
Very interesting topic. The difficulty with this operation seems to be that "interpreting the decimal expansion of X in base b" is pretty clunky to express in general terms. Getting the nth digit of the decimal expansion (or any base of course) of a number is not a nice clean mathematical operation. It's something like `a[n] = floor(a*10^n)%10` with % standing for the modulo operation. So `a_b = sum(a[n] * b^n) = sum(floor(a*10^n)%10 * b^n)` which is no fun to work with. There probably is a nicer expression for a[n] than that, but in the end it just isn't very natural.
@LuigiElettrico4 жыл бұрын
Imagine a rogue-like game with numbers instead of letters interpreted as monsters... and the final boss is Golden Ratio :D
@brianmiller10774 жыл бұрын
It's an infinite headed hydra, Chop off a head there's still an infinite number left.
@otakuribo4 жыл бұрын
"phi equals root one plus phi equals root one plus phi equals root one plus phi equals root one plus - "*the proportion is divine~*" ♪ *YOU'LL FIND YOUR WAY TO PHI TO PHI TO PHI*
@frankharr94664 жыл бұрын
How interesting.
@rogerkearns80944 жыл бұрын
Can you extend to the complex non-reals?
@Luper1billion4 жыл бұрын
Can you do imaginary base numbers? 🤔 if so maybe you can plot on a 2d graph which numbers converge and which numbers diverge, like the mandelbrot set
@prometheus73874 жыл бұрын
The beauty.
@OG_CK20184 жыл бұрын
Now thats golden
@puncherinokripperino2500 Жыл бұрын
But how can you read 2 in base 2 if all base 2 numbers are supposed to be written with digits 0 and 1?