I just wanted to thank this channel for existing. A little over a year ago I started watching numberphile videos which helped me discover my interest in math. I am now back in school because of it and just completed calculus 1 with an A+ and am currently taking Calculus 2! Update: got an A in calc 2, now onto calc 3! Thanks so much Numberphile!
@husa1n4 жыл бұрын
All the best bud
@rebelli654 жыл бұрын
how is it?
@goose3001834 жыл бұрын
That's great! Best of luck for your second course.
@OLApplin4 жыл бұрын
Computerphile (and Numberphile) are part of the reason I went back to school in computer science! (Where I did kind of an equivalent to calc-3, advanced linear algebra and probability and statistics classes). Best decision I made in my life! Kudos to you
@benjaminricci54584 жыл бұрын
I'm sure the people running this channel live to see comments like yours. Thanks for sharing!
@hedger0w4 жыл бұрын
What I want to know is, if the sentence: "We don't know if it's true but we know one thing." is the most common sentence in Numberphile videos.
@TheAncientOneOfDays4 жыл бұрын
I know! The same reason he has a wenoos which is unused
@nadionmediagroup4 жыл бұрын
Should be the most common sentence in SCIENCE, actually. This is how these guys talk. They actually try to admit what they don’t know. Imagine that.
@gilessmedley6194 жыл бұрын
However, you need it after ‘however’
@arpitdas42634 жыл бұрын
Most common sentence in all of mathematics
@leif10754 жыл бұрын
Why does he think 40 occurs a lot? It could just as easily not.
@IWubYooz4 жыл бұрын
1 is the 1st digit of pi 3: :( We could count 1 as the 0th digit of pi 3: :C
@NonDelusional746114 жыл бұрын
I laughed too long at this
@gwahli96204 жыл бұрын
I thought so too. At least we'd get a 3rd way of counting with 3 as 1st digit, making 1 the 2nd.
@BigCheese774 жыл бұрын
This. All of this. When he said "there's another way to count" I'm expecting to number 3 as the 1st position, but no, poor 3 always gets left out
@sirmoonslosthismind4 жыл бұрын
in context, he means the first fractional digit of pi. 3 of course is the whole number portion of pi.
@kookeekwisp4 жыл бұрын
Those that make you 0 are scum. But... those that make your friends 0 are worse than scum.
@anamika35424 жыл бұрын
You think the strings are common. *THEY'RE NOT*
@anthonyross75874 жыл бұрын
Anamika Sinha they are common. There’s an infinite number of self locating strings
@shmonn.4 жыл бұрын
Anthony Ross Doesn't mean they're common, if one in a million is a string, it isn't common but there are a lot of them
@anthonyross75874 жыл бұрын
s dude I guess it’s just a debate of what common means things that are common in some areas might not be common in other parts
@pasymows4 жыл бұрын
3:14
@nelynx_4 жыл бұрын
@@anthonyross7587 that's where density comes in
@samuele97354 жыл бұрын
Numberphile: there are loops and self-locating numbers in the decimals of π! Engineers: what decimals??
@alexdixon2654 жыл бұрын
Samuele Nobody: Engineers: sin(0.1) = 0.1
@hetsmiecht10294 жыл бұрын
π = sin(π) = 0
@whatisthis28093 жыл бұрын
isnt pi like 4
@samuele97353 жыл бұрын
@@whatisthis2809 yes
@topilinkala15942 жыл бұрын
@@whatisthis2809 If you're buying lace to attach into the rim of a circular table cloth, pi is 3,4, just to be safe. 4 costs too much.
@GoranNewsum4 жыл бұрын
3:24 Or in other words "left as an exercise for the reader"
@kaezon4 жыл бұрын
@Goran Newsum I have read it somewhere 🙃
@Souls_p_4 жыл бұрын
*3:14
@Triantalex9 ай бұрын
false.
@Lovuschka4 жыл бұрын
13598 "It's not far away from the 16000" Car salesman detected!
@SupriyoChowdhury52014 жыл бұрын
Hey the navier stokes guy.
@demerion4 жыл бұрын
Supriyo Chowdhury Had the same thought :D
@m1m1snake4 жыл бұрын
Aka the Pokeballs guy
@Terrantular4 жыл бұрын
Cute boy with big brain
@TheMultiRaphael4 жыл бұрын
the navier stonks guy*
@OLApplin4 жыл бұрын
from Navier-Stokes fluid dynamics to number theory, this guy is quite versatile I'd say!!!
@अण्वायुवरीवर्त4 жыл бұрын
Yeah he stripped equation but KZbin doesn't allow further explanation of Navier-stokes equation And also waiting for female version
@mpaxra4 жыл бұрын
@@अण्वायुवरीवर्त wdym KZbin doesn't allow further explanation?
@TomRocksMaths4 жыл бұрын
it seems the comments have entered an infinite loop in the far reaches of the decimal expansion of pi, never to be seen again...
@leif10754 жыл бұрын
40 wont necessarily show up more than once though..its not guaranteed right unless you can prove that it is...can you please correct this or clarify what you meant.
@hui-yuanchen84544 жыл бұрын
Hi, Tom, thanks for the very interesting video! I was wondering what would happen if you skip the self-locating string and choose the next/secondary matching string to avoid local looping when searching for the global loop? For example, 211-93-14-1-3-9-5-4-2-6-7-13-110-174-155-314-2120-5360-24671-...
@TomRocksMaths4 жыл бұрын
@@hui-yuanchen8454 Nice idea - i imagine you would create an infinite string disappearing further and further into pi...
@hui-yuanchen84544 жыл бұрын
@@TomRocksMaths Yes..., it looks like that. So I kept tracking after 24671-119546- 193002-240820-274454-153700-..., then 153700 doesn't exist in the first million digits of pi. How come the numbers in "169's circle" are so special that they can form a loop!?
@cityuser3 жыл бұрын
@@leif1075 40 shows up 6 times in the first 1000 digits of pi. Now it's proven!
@GrammeStudio4 жыл бұрын
I didn't know Machine Gun Kelly does math as a side hustle. It's great to see there is at least an intellectual in the music industry.
@अण्वायुवरीवर्त4 жыл бұрын
Well he kinda did a small brain move with Eminem
@patrickwumbo82714 жыл бұрын
My exact same thought haha
@jadude3784 жыл бұрын
I think Kurt Hugo Schneider went to yale university and studied physics or something
@dominickmancine60334 жыл бұрын
Brian May
@melodyivers4 жыл бұрын
HAHAHA love it
@jaredislversteindrums4 жыл бұрын
The fact that 169 looped back to itself is the wildest shiz to me. I guess I'm easily impressed.
@ralfoide4 жыл бұрын
Years ago I'd have said "recreational math" was an oxymoron. Not anymore. One thing great about Numberphile / Computerphile is that they have great speakers who are passionate and know how to express their passion. That's also due to their hosts & editing skills. As viewer we don't see just the cool maths, we also choose to absorb all that passion, and that makes a whole difference compared to the boredom of a grade school math class where students have no idea _why_ they are learning that stuff to begin with.
@superscatboy4 жыл бұрын
Maths guy: My brain: spike in his ear spike in his ear spike in his ear spike in his ear spike in his ear spike in his ear spike in his ear spike in his ear
@stephlrideout4 жыл бұрын
They might be spacers but I have spike earrings that are just an ~illuuuusioonnnn~
@kindlin4 жыл бұрын
I was checking out his pokeball.
@SunriseFireberry4 жыл бұрын
Next: Strings and Loops within e?
@ashtonsmith17304 жыл бұрын
Its 2.718281828459045235360 to 21 d.p
@floydmaseda4 жыл бұрын
The 338th-340th digits of e are 338. The next self-locating string is at 2543, then 91668.
@stevethecatcouch65324 жыл бұрын
@@floydmaseda If you start counting at the 2, the first self-locating string is at position 8.
@MichaelWBauer4 жыл бұрын
Strings and loops within arbitrary irrational numbers?
@erikkonstas4 жыл бұрын
@@MichaelWBauer Nonono, _transcendental_ numbers!
@ProfOmarMath4 жыл бұрын
Curious what this all looks like when pi and the positions are written in base 2.
@1R0QU0124 жыл бұрын
Have you seen binary decimals? They're a trip.
@LucaBl4 жыл бұрын
No they are not. The only time you got a better chance with binary is from 1-8. For 7 you have a chance of 1/10 in decimal, 1/8 in binary. For 8 you have a chance of 1/10 in decimal, 1/16th in binary. For 512 you have a chance of 1/100 in decimal, and a chance of 1/1024 in binary. For 8192 you have a chance of 1/1000 in decimal and a chance of 1/16384 in binary.
@ahmedouerfelli47094 жыл бұрын
@@1R0QU012 they are not decimals, because "decimal" refers to the digits of the base ten expansion.
@1R0QU0124 жыл бұрын
@@ahmedouerfelli4709 lol you've obviously don't work with computers.
@ahmedouerfelli47094 жыл бұрын
@@1R0QU012 I do programming, but my main field is mathematics. I don't understand your response though, do you mean that computer scientists call binary digits "decimals" even though they are not decimal digits? Or do you mean something else?
@fusion674 жыл бұрын
If I saw this man on the street my last expectation would be that he is a recreational mathematician.
@recklessroges4 жыл бұрын
Not just a recreational; he's a professional mathematician.
@HabeKeinMitleid4 жыл бұрын
Mas628 he’s a professor at Cambridge
@AG-zo5es4 жыл бұрын
@@HabeKeinMitleid he's a professor at oxford actually😡
@TomRocksMaths4 жыл бұрын
@@AG-zo5es correct!!
@fusion674 жыл бұрын
@@recklessroges i rest my case
@robertcarroll98554 жыл бұрын
The digits tattooed on his right arm are part of the decimal expansion of e.
@bakkerem19674 жыл бұрын
Never could have thought you could fill up 14 minutes, talking about pi ;-) Now that's some contagious enthousiasm Tom ! Nice topic !
@heyandy8894 жыл бұрын
I am a software developer by trade. It never ceases to amaze me how mathematicians come up with these problems that seem simple but are actually far beyond the bounds of mere computation; you could never have a "brute-force" solution to a problem like this.
@keyofallworlds75494 жыл бұрын
Ahhhh Tom so dashing and smart! Tom, i think you're the first alt/rocker looking person I've seen be into math.
@d34d10ck4 жыл бұрын
"You don't really need more than 7 decimal places" - Continues to write down the first 100 digits of pi.
@nicks2106844 жыл бұрын
On brown paper as well. Should have gone with a subtle off-white colouring.
@tedbo18194 жыл бұрын
You survived the 80s?
@Rekko824 жыл бұрын
We don't need more. We can write though.
@d34d10ck4 жыл бұрын
@@zeldaandTwink Let's use a simple encryption algorithm: EncryptedMessage = character(x) XOR decimal(x)ofPi To decrypt 1 MB of Data you would need to know pi up to 1 million of decimal places. Not just 31.
@BrianBlock4 жыл бұрын
@@d34d10ck That is using Pi as a seed, which is not using it as the mathematical constant. When using it it as the ratio of a circle's circumference to diameter, the largest physical circle we know of would be the circumference of the universe. Pi to 31 places is the correct ratio within the width of a hydrogen atom, so you never need to go to more digits for PHYSICAL purposes. Any smaller circle, pi to 31 digits is even more accurate as the ratio, very quickly getting below the planck length in terms of error (i.e., pointless for modern physics). That is what was meant by practical applications, not using it as a random large seed, which always benefits from having more digits.
@racsosov4 жыл бұрын
I literally learned the first 100 digits of Pi by making it my password for a couple of weeks, and now I can't get them out of my system anymore, btw great channel. Keep it up!!!
@cubicinfinity24 жыл бұрын
I loved his explanation for why one would bother with this problem. It gives me hope with my own research.
@matrixstuff35124 жыл бұрын
I love how classic numberphile this is!
@feliciabarker92104 жыл бұрын
As well as self-locating strings, there's another way to show that some numbers don't sit within the loop they settle into, which accommodates loops larger than 1 - If we take the 169 example, the next digit is a 3. If 169 first appears at the 40th place in pi, then 1693 ALSO first appears at the 40th place in pi. So 1693 has to settle into a loop that doesn't pass through 1693 again.
@marcoottina654 Жыл бұрын
does this mean that it's very likeable that there exist some numbers whose loop actually did not end? Would that numbers be called "primes" by some means?
@DrKaii4 жыл бұрын
Tom Crawford: "You don't really need more than 7 decimal places". Emma Haruka Iwao: "What have I done with my life" Rajan Mahadevan: "I know right" Matt Parker: "Amatuer!"
@noisefarm4 жыл бұрын
Considering that NASA uses pi to 16 decimal places in software that stabilizes spacecraft trajectories, the national institute for standards and technology uses pi to 32 decimal places when calculating the fundamental constants of the universe, and pi to 100 decimal places, if memory serves, would be sufficient to calculate the circumference of the observable universe to a precision of less than the width of a hydrogen atom (if the geometry of the universe allows that such a calculation would make sense and we had enough precision in our measurement of the diameter to make such a calculation meaningful, of course), I think it’s safe to say that most of us unwashed lumpenproletarians are in no danger from using a value of pi with seven decimal places in our day-to-day lives!
@gurrrn11024 жыл бұрын
PI IS EXACTLY THREE
@VenomOnPC4 жыл бұрын
gurrrn Nah, by rounding down as 3 is less than 5, Pi is therefore 0.
@DrKaii4 жыл бұрын
@@VenomOnPC In base pi, pi = 1, and 1 is a transcendental number. Don't mess.
@emperortbw4024 жыл бұрын
@@DrKaii Where did you get your doctorate? In base π 1 is merely 1, and no funny business happens until you reach 10 which, of course, is π.
@nosuchthing84 жыл бұрын
What an amazing world where we have people thinking these deep thoughts. Million thumps up.
@kylecobb99824 жыл бұрын
Best newcomer at the numberphile awards 2020: Tom Crawford
@TomRocksMaths4 жыл бұрын
Kyle
@SteppingStonevlogs4 жыл бұрын
I am not a maths person....but you explained this so well that I watched it all
@TomRocksMaths4 жыл бұрын
Thanks Lauren, that's awesome.
@amgn0074 жыл бұрын
Commenting to check what's going on with missing comments. Great video btw
@kashgarinn4 жыл бұрын
Self-location can’t be infinite as the increasing enumeration order means it becomes an order of magnitude less likely that one appears. You can use statistics to prove this. An argument can be said about the loops, i.e. That there are no infinite loops, because you can always find the next index, and you always select the lowest valid index, meaning there will for any multiple number be a lower index to be selected, which cuts out the possibility of infinites.
@joeyw.71314 жыл бұрын
But wouldn’t there still be countably infinite self-locating numbers? Just because they become less common doesn’t mean they stop completely. Would love to see an explanation for that
@hidgik4 жыл бұрын
This is looking more and more like numerology.
@swiadomy14 жыл бұрын
71 with Blue for table number 21
@danielbird19074 жыл бұрын
car reference to the Pi movie?
@denelson834 жыл бұрын
So, something oogy-boogy.
@codycast4 жыл бұрын
car it looks more like a meaningless attempt at being interesting. This has zero math implication
@kazedcat4 жыл бұрын
@@codycast Actually I can see a possibility of this technique being use to prove if pi or e is normal.
@Poppacap794 жыл бұрын
The detail of that pokeball tattoo is amazing.
@TomRocksMaths4 жыл бұрын
Thanks!!
@cleonanderson17224 жыл бұрын
Reminds me of letting youtube autoplay videos. I've noticed loops and onramps to major loops.
@AMR-5554 жыл бұрын
The leading 3 is so neglected. It would be interesting knowing what happens if indexing starts there.
@ekaingarmendia4 жыл бұрын
This is suspiciously equivalent to the collatz conjecture
@NatetheAceOfficial4 жыл бұрын
Can't wait for the next Vsauce video to be about self-locating strings.
@Wyattporter4 жыл бұрын
Coming out tomorrow
@erik-ic3tp4 жыл бұрын
@@Wyattporter, sadly, it didn't happen. :(
@netstatgrep4 жыл бұрын
Coming out tomorrow
@erik-ic3tp4 жыл бұрын
@@netstatgrep, how do you know that?
@---si3nu3 жыл бұрын
Coming out tomorrow
@jakoblenke30124 жыл бұрын
I wonder what the function will look like if you graph Looplength(x), y being the number of iterations before terminating or getting stuck
@Phondrason4 жыл бұрын
Pretty random I'd guess
@erikbrendel32174 жыл бұрын
was actually thinking the same :D Maybe I should do a script to plot that for me...
@extremeswissgerman25364 жыл бұрын
@@erikbrendel3217 Notify us when done :)
@jakoblenke30124 жыл бұрын
Erik Brendel oh yes that‘d be cool
@alonamaloh4 жыл бұрын
The statement at 10:36 doesn't seem right: Self-locating strings may or may not map to themselves, because the string could appear earlier.
@kirkanos7714 жыл бұрын
You answered to your own mistake in that sentence.
@alonamaloh4 жыл бұрын
@@kirkanos771 Sorry, I don't understand. Care to explain what my mistake is?
@alonamaloh4 жыл бұрын
Actually, I just checked, and when he said "...or you get to 16,470 and then loop around", he's incorrect: 16,470 maps to 1,602 and you keep going.
@nicfink53104 жыл бұрын
@@alonamaloh Because you always go to the earliest appearance of the number. Which means that if you happen to end up at a self-locating string, it will have to be the first appearance of that string.
@nicfink53104 жыл бұрын
But you're correct in that not every self-locating string will act as a deadend to those sequences.
@PLMYT4 жыл бұрын
Curious as to how these strings function under different number systems, such as those of base 8 or 12
@SierraDN4 жыл бұрын
Prime bases better...
@toshirokardevaand27724 жыл бұрын
@@SierraDN No? You want many divisors to reduce the amount of infinitely repeating expansions, like 0.333333... etc.
@glenmatthes88394 жыл бұрын
I was thinking base 16 since there's a method to determine the nth digit of pi in base 16 without having to calculate all the digits before it. Google BBP Formula to see the method.
@christopherellis26634 жыл бұрын
Pi base sixty is finite
@DavidB55014 жыл бұрын
@@christopherellis2663 Huh? Is that a math joke (like Grothendieck's Prime), or am I missing something?
@jeremybuchanan47594 жыл бұрын
This reminds me of Melancoil numbers ... great to see Numberphile getting back to its 'roots'!
@Booskop.4 жыл бұрын
This reminded me of the Collatz Conjecture.
@jakobskwarski44354 жыл бұрын
First thing that came to mind once they started talking about loops and that they can get "stuck"
@matiastripaldi4064 жыл бұрын
Wow this went deeper than I thought
@charliejulietdavies87154 жыл бұрын
i love their energy
@BunchaWords4 жыл бұрын
I'm reminded of a much earlier video they did on the recreational "happy numbers" and "melancoil", which also had loops and various self-locating numbers, specifically at 1.
@rovingfortune3954 жыл бұрын
The most attractive male mathematician in the world. Calling it right now.
@realcolby2 ай бұрын
If the digits of pi were completely random you would expect there to be infinitely many self locating strings, but each one should be bigger than its predecesor by about 12.915 (10^(10/9)) times. This aligns roughly with whats shown. Ignoring the massive gap at the start, the average ratio of succesive terms is about 12.184.
@ShakeMilkyWay14 жыл бұрын
Poor 3, often left out. What if you count 3 as the first position?
@lostpockets22274 жыл бұрын
that's mental!
@rileyhughes85304 жыл бұрын
I had the same idea, it’s prob been tested though and there’s probably a reason it’s only decimals they use
@hyperhippyhippohopper4 жыл бұрын
I did the numbers. The self locating strings with 3 as the first digit are as follows: 5 , 242424 , 271070 , 9292071 , 29133316, 70421305
@glowstonelovepad92943 жыл бұрын
@@hyperhippyhippohopper 242424.
@arcioko21423 жыл бұрын
@@hyperhippyhippohopper 242424 is actually very nice, i hate the fact that they not only skipped 3, but they even had the audacity to say "What if we consider 1 to be the 0th digit of pi?"
@greencoder15944 жыл бұрын
[12:37] «It's not the peak that's amazing, it's the awesome landscape and the methods and techniques you're going to learn and use to climb a mountain when you try.»
@SamYaZdian4 жыл бұрын
i would give this guy 10/10 on fashion and looks
@nickhiggins98914 жыл бұрын
thanks for the video, all of them really, i do quite enjoy them all, but i would also like to see more of Tom on here too, i especially enjoyed the Navier-Stokes and Reynolds number episodes, glad to see him back with this.
@JNCressey4 жыл бұрын
1:25 I think it would be more natural and general for the 1 to be in the 11th position and the 2 to be in the twelth. Since 12 trillionths would have the 1 and 2 in those positions. (and 10^-12 is a trillionth) That's _kind of_ like having a 12 in that position. Except we don't have a digit for 12 and the 10 carries over to 1 in the position to the left.
@FredSmith1104 жыл бұрын
Very interesting and thought-provoking.
@bobderbobs15214 жыл бұрын
There is a shorter circuit: 19, 37, 46 and again 19
@kindlin4 жыл бұрын
EDIT: I failed, see post 3 lol. I made a quick excel to try this, and found it is incorrect. Using the first 32759 digits of pi (the most excel can hold in 1 cell, seems an odd number, 2^15-9, anyways...) the following order/list is produced: 19, 39, 45, 62, 22, 137, 861, 269, 1395, 6482, 228, 2529, 18335; and then it doesn't find '18335' in the first ~32k digits.
@kindlin4 жыл бұрын
EDIT: I failed, see post lol. I disliked the 32b limitation of excel cells, so I did a bit more exceling and made some formulas to read multiple cells and find the correct text. Long story short, I didn't find anything interesting, even tho at first I thought I found a cool 188 step loop (I had had a bug in one of my formulas). Using a total of 1 million digits of pi, the sequence terminates as follows (without finding the next step, it presumably will find one with enough digits, per this video): 19, 39, 45, 62, 22, 137, 861, 269, 1395, 6482, 228, 2529, 18335, 68539, 22166, 169545, 96010, 67419, 272547, 414384, 148332 (can't find this in the first 1 million digits)
@kindlin4 жыл бұрын
OK, final thoughts, cuz this is pointless unless I wanna python this. I tried numbers 0 to 100 with the first 1 million digits and found just 2 loops, your loop and one that starts at 40 with a cycle length of 20: 40, 70, 96, 180, 3664, 24717, 15492, 84198, 65489, 3725, 16974, 41702, 3788, 5757, 1958, 14609, 62892, 44745, 9385, 169, 40 This 20 length loop also can have a relatively long lead-up phase starting with 61, which has a 7-step lead-up phase: 61, 219, 716, 39, 43, 23, 16, 40 I also found a number of values that terminate at repeating 1's: 1, 14, 21, 45, 73, 93 The longest path to 1 starts at 45 and is 10 steps to 1, and has the following steps: 45, 60, 127, 297, 737, 299, 2643, 21, 93, 14, 1 In that path, you can see that the other digits 14, 21 and 93 pop up (and 45 obviously), but not 73, which has the following path: 73, 299, 2643, 21, 93, 14, 1 This is at least a little interesting that both 73 and 737 both go to 299, which then leads to 1's. The next couple digits starting at position 299 are 737(2458), so we know a couple more large numbers that go to 1.
@AbhishekSomaniTheGreat4 жыл бұрын
In love with numbers. Thanks Numberphile!
@davidgerick98714 жыл бұрын
10:35 This statement is not correct: self-locating strings could already appear earlier. For example, 44899 could also appear at a smaller position, meaning you would not loop at position 44899
@sudheerthunga21554 жыл бұрын
Yes ikr! I commented the same few seconds back
@Tedmusic164 жыл бұрын
@#Miqdaad Indori It can only stop when 44899 is found at position 44899, and there is no 44899 in an earlier position. (This is not the case as 44899 also appears at position 13714)
@KiraIsGod4 жыл бұрын
Indeed, 44899 occurs at position 13714 first.
@qubatistic47884 жыл бұрын
@David Gerick Yes, but you would still get 44899, which will take you yet again yo 44899 and so on... You would only het 44899, so in a sense you don't loop between numbers
@KiraIsGod4 жыл бұрын
@@qubatistic4788 The sequence for 44899 is: 44899 -> 13714 -> 120330 -> 2293915 -> 43742 -> 126470 -> ...
@giant39094 жыл бұрын
I was also wondering why we weren't using base 0 index and was pleased to watch the following
@Tfin4 жыл бұрын
Hmm... Pi to the 0th place... well, it wouldn't have a decimal.
@arkaig14 жыл бұрын
Love it. I like how you said "decimal", occasionally, too. Thanks. "P.s." Gee I wish I could... (recollect pi easily today now ...)
@sudheerthunga21554 жыл бұрын
At 10:47, guys I got a doubt..what say the self locating string was met ...but that's doesnt mean that it is the first occurence of that self locating no. ... please clarify
@alimanski79414 жыл бұрын
Are there any co-locating pairs known? i.e, numbers that point to each others location (or, a loop of length 2)
@msbhv_jin4 жыл бұрын
la that wouldn’t be possible as the numbers would contradict with each other if you think about it.
@alimanski79414 жыл бұрын
@@msbhv_jin Why contradict? Consider the number 132, and start looping by looking up string "2". It's in the 3rd place. Search for string "3". it's in the 2nd place.
@stevethecatcouch65324 жыл бұрын
In another comment someone asked if there were loops of length n for any integer n. I suspect the answers to both questions is "yes".
@alimanski79414 жыл бұрын
@@stevethecatcouch6532 i agree, i was wondering about known pairs. Ill give it a try over the weekend, right now eyes are set on exams in Algorithms :)
@simi55mega Жыл бұрын
This is so cool I wonder if the relationship between those numbers in loops can be generalized
@gardenhead924 жыл бұрын
Are we assuming Pi is incompressible in this video?
@bencushwa89024 жыл бұрын
Why exclude the 3? What happens when you put the first position on the leading 3, so second position is 1, third position is 4, fourth position is 1, etc.? A quick check of the first sixty digits of pi yielded no self-locating strings.
@zstanojevic95744 жыл бұрын
Now, as a completely new rule, start counting from the infinite side towards 0th position. :]
@GabeKorgood4 жыл бұрын
There's another possibility for a chain: ending at a smaller loop. For example, if you found one of the strings that were part of a known loop in a position not in that loop, tracing the path back up the chain would be infinitely long, but would end with a loop of known (finite) length.
@WiseSquash4 жыл бұрын
@4:40 Matlab user: *suffers*
@azhar074644 жыл бұрын
Haha yes
@minimalisticbits12324 жыл бұрын
I've memorized 51 digits of PI. Honestly if I were to replace PI everywhere in my renderers with the number 3.0, then you would barely notice the difference.
@zacharyhandy96064 жыл бұрын
Impressive, somehow I have memorized Tau better than Pi
@minimalisticbits12324 жыл бұрын
@@zacharyhandy9606 Quite nice actually, perhaps some day we're going to switch to Tau.
@CSmyth-4 жыл бұрын
That moment when you actually see your phone number in pi...
@kyleboffa7934 жыл бұрын
there are search pages that can find any 7 digit string
@walkingwriter43254 жыл бұрын
Really enjoyed this video--AND understood it to the end! All of his previous ones were way over my head, so I couldn't finish them. This one was fun. π rocks!
@EmperorZelos4 жыл бұрын
The task of writing down all digits of pi is left as an exercise to the viewer.
@menpee4 жыл бұрын
Tom Crawford: "You don't really need more than 7 decimal places". Somewhere on the Earth SImon Pampena shed a single tear.
@SoleaGalilei4 жыл бұрын
Jeez, so many comments about the topic not being serious enough or people clutching their pearls about the bloke having a few piercings. Lighten up, guys!
@GXTRON4 жыл бұрын
I like this new format of LinusTechTips
@Saareem4 жыл бұрын
I thought that too. He has the same contagious energy too! 😂
@bhanujchowdhary37414 жыл бұрын
When machine gun Kelly decided to drop his career after getting dissed by Eminem twice
@micky2be4 жыл бұрын
What if the number position is represented by the last digit instead?
@amariebeaubien4 жыл бұрын
the loops remind me of an orbit in chaos/dynamical systems...
@varunsrivastava64214 жыл бұрын
Alisa Beaubien congrats on your comment
@smoorej4 жыл бұрын
This reminds me of the Collatz conjecture, which on its own does not have any real significance but the techniques and strategies used to attack it will probably be important tools in solving other problems.
@JNCressey4 жыл бұрын
0:30 "2rd"
@fantasticphil38634 жыл бұрын
Top notch camera skills.
@adityakumbhar77774 жыл бұрын
Remember first 8 digits of pi...... "May I have a large cup of coffee." Thanks me later 🙏
@soumilshah10074 жыл бұрын
"cup" can't be right. Pi is 3.14159265 not 3.1415326
@oops32664 жыл бұрын
@@soumilshah1007 May I have a large container of coffee
@juanramonvazquez32124 жыл бұрын
There is another behaviour that can happen, you could start the path and then getting inside a loop without the number you actually started with, i found the example of the number 71, it can easily be checked if you look at the sheet of paper with the 100 first digits of the pi decimal expansión in the video, it goes, if i'm not mistaken, ...71-43-23-16-(40-(...)-169-40), this is due to the fact that every position in the decimal expansión has infinitely many numbers that have their first appearance in it, for example 169(part of a loop) and 16, 1693, 16939... , or 23, 238, 2384, 23846(non of wich part of a loop).
@Jesse__H4 жыл бұрын
ngl this fella is my man-crush.
@alexolas12464 жыл бұрын
why do the multi-digit numbers extend to the right? it’d be more consistent, imo, if the “center” digit was always the 1’s digit, and the additional digits were to the left.
@nianyiwang4 жыл бұрын
the path could be in a ρ shape imo
@Moowell24 жыл бұрын
Step 1: Choose a self-locating string. Step 2: Concatenate the self-locating string with the digit immediately subsequent to the string Step 3: Travel to the location of the new string Step 4: Concatenate numbers starting from the first digit of the new location until a string is reached which has not previously appeared in the irrational number Step 5: Record the string Step 6: Repeat steps 3-5 Example: 1->14->93->21->264->603->etc... Every number listed on the new series is a number eliminated as a candidate for infinite loops. You can also freely concatenate additional digits in steps 2 and 4 to obtain new branches and add to the list because the first portion of those numbers only appeared in that step. For example, the 211 used in the video isn't actually the lowest number which leads to location 93. That honor belongs to 21, and 211 is concatenated from there.
@johnsherfey36754 жыл бұрын
Dude looks and sounds like he's about to yell at me for my math being half baked and still raw.
@greatscott92314 жыл бұрын
@@awindwaker4130, I thought he was a golfer. He stores his tees in his ear lobes.
@pratik31064 жыл бұрын
he does look like ramsy lol
@Saareem4 жыл бұрын
He looks like a mash-up of Gordon Ramsay and Linus from Linus TechTips. 😄
@mef5264 жыл бұрын
Very curious look into PI. What happens when the radix is changed? What if the radix is e or sqrt(2) or some other irrational number? Would that give even more insight to the nature of PI?
@rileyhughes85304 жыл бұрын
Why couldn’t you put the first number 3 and label it 1 and carry on from there
@natan90654 жыл бұрын
You could but it's probably no less interesting
@pierreabbat61574 жыл бұрын
The 3 is in position 0, because it's 3×10^0+1×10^-1+4×10^-2+....
@stevethecatcouch65324 жыл бұрын
@@pierreabbat6157 By that reasoning, the 1 is in position -1. That would put the 4 is position 0 because we always increase the index by 1. The digit in position 1 is a 1.
@rileyhughes85304 жыл бұрын
Steve the Cat Couch he wasn’t referring to 1 being -1 as an index but instead in the literal sense of 0.1 = 1x10^-1 and 0.04 being 4x10^-2 and so the index is the power with a flipped sign
@dennismuller11414 жыл бұрын
for each position n, log n consecutive digits have to match. The probability for a match is 10^-(log n), which is ~ n^-1. Since the sum of all reciprocals of natural numbers is infinite, there should be infinitely many of strings which match their position, at least if pi is a normal number in base 10. Please correct me if I'm wrong.
@bencushwa89024 жыл бұрын
So...Tom could rattle off all of these decimal expansions of Pi but couldn't remember more than the first seven digits of Pi? Mathematicians are weird.... (Says a physicist....)
@hypercoder-gaming3 жыл бұрын
Ik the first 20 something digits. 3.1415926535897932384626338. Not saying it's neccessary, just memorize digit after digit every so often.
@TalathRhunen4 жыл бұрын
I wrote a program to try this out myself and apart from the 1-cycle on the 1 and the 20-cycle with 169->40->..., there is also a 3-cycle with 19->37->46, but apart from that my program has not found any cyles up to 100,000,000 (though I am not certain yet that my program does not contain any mistakes). Not all self-locating strings necessarily form 1-cycles, since they may also appear earlier, in fact only 1 does. Starting the numbering at zero, I also found two more self-locating strings (which also happen to form 1-cycles): 71,683,711 and 78,714,901
@gladhobo4 жыл бұрын
Since we are considering the number pi (not the number pi-minus-three), we have the initial three at position zero. So there is a 4-cycle with 0->32->15->3. There is also another 1-cycle at 711939213.
@mason41404 жыл бұрын
Everyone ignores the 3... They should instead say pi - 3
@ChrisWalshZX4 жыл бұрын
And why not make the 3 the 1st position? All self-locators and loops will be completely different.
@Tferdz4 жыл бұрын
Just put 3 at the 0th location.
@crustysocks57424 жыл бұрын
/ivide by 10
@bobbycraig25834 жыл бұрын
@@ChrisWalshZX i found by hand that 5 is a self locating string but everything else i think is massive
@BenAkenobi4 жыл бұрын
pi is 3 if the circle is drawn on a sphere and so diameter of said circle is a slightly elevated arc. how would one approach finding such sphere's diameter?
@neruneri3 жыл бұрын
"You don't really need more than seven decimal places" Matt Parker will remember that.
@Henrix19984 жыл бұрын
How about doing this in binary
@JoeMama-dc5jw4 жыл бұрын
if your number is something like 1 and you go to the first position instead of stick in a loop you could go to the second digit 1 so it would be in position 3 and so on. Maybe this is also an interesting “idea“ ( sorry for my bad english I am an Austrian student😅)
@BukanGamingOfficial4 жыл бұрын
13:38 when english auto-translate got drunk
@goose3001834 жыл бұрын
Really a strange error that one!
@BigCheese774 жыл бұрын
So, unless I'm missing something, another way to terminate a string without it being a loop is to hit a closed loop. For example, if you ever hit the 1693th position, you'll hit the 169 to 169 loop and be stuck there. I feel that should give a way to prove that there's no infinite setting that doesn't loop possible...
@egesorguc34574 жыл бұрын
Yes, exactly. I think, we can consider hitting a self locating string as hitting a closed loop for completeness.
@ddiq474 жыл бұрын
Frankie’s Theorem: There is a trivial sequence for finding these numbers. Proof. Exercise 1 QED
@tamirerez2547 Жыл бұрын
I have a suggestion for a follow-up video: Ask the computer to generate a 100 million digit random number. Check if it also works with this random number. The conclusion would be that the value pi behaves like a random number, which means that there is no regularity or order in pi.