@starofcctv94 I mean, actually physically write the numbers smaller, like zoom in far so you would use less ink, rather than writing it mesoscopically?
@Alexbrainbox Oh, In that case still no. Grahams number is so massive you couldn't write it out even if you able to write on each individual atom in the observable universe.
When an equation is found and held, literally, to an orbit, we can walk away for 15 years. This, concidered the best effort, worth not continuing by anyone but you. Simplified efforts, held until an agreeable return, is not appropiate.
I see greed and power in holding knowlege here, with a bunch of loud mouth louts, stringing your rule along.
Something that escaped me the first time I seen this, but now that I'm thinking of it:
I'm sure most people who see this assume the problem is "really hard" (and in the sense of solving it, it certainly is). To actually be able to understand what the problem means and to at least begin to understand how one would solve it, however, really is quite trivial once one knows basic algebra/geometry AND what is actually going on in this sort of math. It's simple layers built upon even simpler layers.
Grrr, YouTube won't accept my pseudocode so I'll just write it out in basic logic:
For every prime (example: 2), the total percentage of whole numbers beyond this prime that are also prime is divided by that prime and all previous primes and added to the sum of all primes divided by previous primes (example: after "2", half of the whole numbers beyond it can't be prime because they are divisible by two (ie all even numbers); then for "3", the next prime, 3/2 of future numbers are now also out).
Continued example: Then for "5", the third prime, another 5/3/2 whole numbers greater than it are also out of the running for being a prime as well. Then 7/5/3/2 and so on unto infinity...
So, 100% - 100%/2 - 100%/3/2 - 100%/5/3/2 - ..... to infinity would leave 0% greater whole numbers that are prime past infinity; but yeah again since one can't go past infinity there will always be a small percentage of whole numbers that will be prime.
*pants* I swear that's easier to explain in pure C...
@Truthiness231 Indeed, the density of primes ~ 1/Log[n] as n tends to infinity. Of course, 1/2 + 1/3 + 1/5 + 1/7 + 1/11 + ... still diverges, so they don't drop off *that* quickly :)
@JaxWeb Yeah it drops very very gradually, but then over long enough time (see: infinity)... ^.^
Anyhoo, I think we've well established now that infinity does all sort of crazy nonsense. The sum of the all integers in the series -1, 2, -3, 4... to ∞ isn't an integer is probably my favorite, but there really is no need to pick on one when there are (pardon the pun) nearly countless oddities when working with ∞.
That aside: how sad is it that ∞'s ASCII number is an embarrassingly finite 236? XD
@NCaradoc2008 No, not infinity + 7 XD. Anything finite (as Graham's number is) is an infinite distance away from infinity, so it's as far away from infinity as 1 is.
It's just incredibly, incredibly large. "Large" isn't applicable to things like infinity, despite some people's notion of it.
@Truthiness231 there's different orders of infinity, i can't remember what they're called, but they account for things like the difference between integer infinity and decimal infinity (can't remember their proper names either)
@Neylonx Yeah, like all the numbers between 0 and 1 (decimal) and the last number in the whole number series (integer) are both infinities. I guess the infinity in the integer series could be viewed as "large" given the definition "more than average amount", but I did want to stress that there is that infinity [isn't a size]/[doesn't have an actual size]. It synonymous with "boundless" by another - figurative - definition, and that's exactly what all forms of it are: boundless/arealess/sizeless.
@Truthiness231 In the same sense, if you have people in a square formation, each an infinite amount of distance from each other, standing on an infinitely radial disc. They are all relatively at the center of the disc.
@Ensirum Yeah all sorts of interesting logical things happen near infinity.
I couldn't help notice a function I was working on the other day, checking the percentage of prime numbers given a set of numbers (n); the percentage of prime numbers approaches 0 as n approaches infinity (so "near infinity" the prime numbers will run out; thankfully we can never reach that point; I gotz to have me some primez ^.^).
There's an infinite amount of prime numbers. They aren't running out, they're just spread further out. You were perfectly right with "approaches 0" but then, how many decimal 0's can you fit before a 1? Infinite.
@Ensirum Yeah I concur there is an infinite amount of primes, what I was saying would require "going past ∞" which is both mathematically and philosophically impossible. I've seen the proof (well, glanced at some of the many pages XD) the proves what your statement about the decimals (which is if I remember correctly (I'm almost a decade out of college now... my memory of things I don't use often is fading fast...) related to the proofs for the "ultimate" mathematical proof: 1+1=2)
EDIT: lol some of my sentences cannibalized on some others when I condensed my post to 500 chars... I think you can gather what I was getting at though, you're clearly far brighter than average ^.^
I remembered this from a documentary I watched about the problem of infinity. Sadly, I only remembered when he gave the answer, so that doesn't really count.
@WakingLife55 I don't think they are too clear here, but what they means is as follows: There is some problem they are trying to solve, related to how many dimensions you need a cube to be so that every colouring of it has some property. Now, Graham (and Rothschild) proved an upperbound for this value - called Grayham's number now. So whatever the answer is, it is less than Grayham's number.
The actual number is between 12 and this. It is Grayham's number which ends in a 7, now the answer.
@WakingLife55 the Graham number ends with a 7. The answer to the question about the amount of dimensions does not have to end with a 7. The possible answers just range between 12 and that number that definetely ends with a 7
@WakingLife55 They aren't saying the number to make it possible ends in a 7. They are saying that it lies between 12 and graham's number, which ends in a 7. xxxxxxxxxxxxxxxxxxxxxxxxxxxx
@WakingLife55 The question asks to find a number n (satisfying some property). It might so happen that there is no number that satisfies the required property, in which case searching for it would be a waste of time. So Graham constructed his larger than astronomical number in such a way that he could prove there definitely was some number (less than or equal to Graham's number) that would indeed satisfy the property for n. So Graham's number is just an upper bound to the solution.
@Varoonmg Hey Varoonmg. I just had a list through to the source, and it doesn't appear to be in this one. There is a little bit about IQ though, and David Mitchell mentions about exams a little.
If this is still of interest, I can post it though.
@Varoonmg They're not. The exams today are just better, because we learn what is worthy of testing and what is not. There are many things in old text books that are utter twaddle. One such example is grading based on grammar. A basic understanding is required at certain levels, and a deeper understanding is required for certain professions, but there certainly isn't any value in forgoing more important topics to encourage 18 year olds to place apostrophes in correct places.
Ramsey Theory: "Put a bit of f**king passion into it!"
Kitlun79 3 weeks ago 2
Uh... Surely you could just write Graham's number smaller?
Alexbrainbox 3 weeks ago
@Alexbrainbox Graham's number is the maximum value for this problem to work. It's the largest number ever used in an equation.
starofcctv94 3 weeks ago
@starofcctv94 I mean, actually physically write the numbers smaller, like zoom in far so you would use less ink, rather than writing it mesoscopically?
Alexbrainbox 3 weeks ago
@Alexbrainbox Oh, In that case still no. Grahams number is so massive you couldn't write it out even if you able to write on each individual atom in the observable universe.
starofcctv94 3 weeks ago
@starofcctv94 I wrote it out once, for an exam. I was the only one though, there wasn't enough room for my classmates to also write it out.
Raznor83 1 week ago
@starofcctv94 They should use pencil then.
TheMikeyReilly 1 week ago
When an equation is found and held, literally, to an orbit, we can walk away for 15 years. This, concidered the best effort, worth not continuing by anyone but you. Simplified efforts, held until an agreeable return, is not appropiate.
I see greed and power in holding knowlege here, with a bunch of loud mouth louts, stringing your rule along.
o2UglyKJ 4 weeks ago
Something that escaped me the first time I seen this, but now that I'm thinking of it:
I'm sure most people who see this assume the problem is "really hard" (and in the sense of solving it, it certainly is). To actually be able to understand what the problem means and to at least begin to understand how one would solve it, however, really is quite trivial once one knows basic algebra/geometry AND what is actually going on in this sort of math. It's simple layers built upon even simpler layers.
Truthiness231 1 month ago
Grrr, YouTube won't accept my pseudocode so I'll just write it out in basic logic:
For every prime (example: 2), the total percentage of whole numbers beyond this prime that are also prime is divided by that prime and all previous primes and added to the sum of all primes divided by previous primes (example: after "2", half of the whole numbers beyond it can't be prime because they are divisible by two (ie all even numbers); then for "3", the next prime, 3/2 of future numbers are now also out).
Truthiness231 1 month ago
Continued example: Then for "5", the third prime, another 5/3/2 whole numbers greater than it are also out of the running for being a prime as well. Then 7/5/3/2 and so on unto infinity...
So, 100% - 100%/2 - 100%/3/2 - 100%/5/3/2 - ..... to infinity would leave 0% greater whole numbers that are prime past infinity; but yeah again since one can't go past infinity there will always be a small percentage of whole numbers that will be prime.
*pants* I swear that's easier to explain in pure C...
Truthiness231 1 month ago
@Truthiness231 Indeed, the density of primes ~ 1/Log[n] as n tends to infinity. Of course, 1/2 + 1/3 + 1/5 + 1/7 + 1/11 + ... still diverges, so they don't drop off *that* quickly :)
JaxWeb 1 month ago
@JaxWeb Yeah it drops very very gradually, but then over long enough time (see: infinity)... ^.^
Anyhoo, I think we've well established now that infinity does all sort of crazy nonsense. The sum of the all integers in the series -1, 2, -3, 4... to ∞ isn't an integer is probably my favorite, but there really is no need to pick on one when there are (pardon the pun) nearly countless oddities when working with ∞.
That aside: how sad is it that ∞'s ASCII number is an embarrassingly finite 236? XD
Truthiness231 1 month ago
well, after all, 7 is a good number!!!
moon666watcher 1 month ago
when i first the question, all i had in mind was "what?". i didnt even catch up to what stephen was saying.
FlippyMyDog 1 month ago
Watch up to 0:33 and you've got the single most intelligent gameshow ever
Then tell Americans that's what QI is
TheTomReid 1 month ago
exams are getting harder tho...
MissLittleear 1 month ago
Between 12 and that incredibly huge number, and ends in a seven. So then 17 was probably a valid answer.
ShawnRavenfire 1 month ago
Quite. Sarcasm anyone?
NCaradoc2008 1 month ago
So....infinity plus 7?
Shessh. 7.
NCaradoc2008 1 month ago
@NCaradoc2008 No, not infinity + 7 XD. Anything finite (as Graham's number is) is an infinite distance away from infinity, so it's as far away from infinity as 1 is.
It's just incredibly, incredibly large. "Large" isn't applicable to things like infinity, despite some people's notion of it.
Truthiness231 1 month ago 3
@Truthiness231 there's different orders of infinity, i can't remember what they're called, but they account for things like the difference between integer infinity and decimal infinity (can't remember their proper names either)
Neylonx 1 month ago
@Neylonx Yeah, like all the numbers between 0 and 1 (decimal) and the last number in the whole number series (integer) are both infinities. I guess the infinity in the integer series could be viewed as "large" given the definition "more than average amount", but I did want to stress that there is that infinity [isn't a size]/[doesn't have an actual size]. It synonymous with "boundless" by another - figurative - definition, and that's exactly what all forms of it are: boundless/arealess/sizeless.
Truthiness231 1 month ago
@Truthiness231 In the same sense, if you have people in a square formation, each an infinite amount of distance from each other, standing on an infinitely radial disc. They are all relatively at the center of the disc.
Ensirum 1 month ago
@Ensirum Yeah all sorts of interesting logical things happen near infinity.
I couldn't help notice a function I was working on the other day, checking the percentage of prime numbers given a set of numbers (n); the percentage of prime numbers approaches 0 as n approaches infinity (so "near infinity" the prime numbers will run out; thankfully we can never reach that point; I gotz to have me some primez ^.^).
Truthiness231 1 month ago
@Truthiness231 Actually you're wrong there :P
There's an infinite amount of prime numbers. They aren't running out, they're just spread further out. You were perfectly right with "approaches 0" but then, how many decimal 0's can you fit before a 1? Infinite.
Ensirum 1 month ago
@Ensirum Yeah I concur there is an infinite amount of primes, what I was saying would require "going past ∞" which is both mathematically and philosophically impossible. I've seen the proof (well, glanced at some of the many pages XD) the proves what your statement about the decimals (which is if I remember correctly (I'm almost a decade out of college now... my memory of things I don't use often is fading fast...) related to the proofs for the "ultimate" mathematical proof: 1+1=2)
Truthiness231 4 weeks ago
EDIT: lol some of my sentences cannibalized on some others when I condensed my post to 500 chars... I think you can gather what I was getting at though, you're clearly far brighter than average ^.^
Truthiness231 4 weeks ago
I remembered this from a documentary I watched about the problem of infinity. Sadly, I only remembered when he gave the answer, so that doesn't really count.
hungryman211 2 months ago
Lol, I just guessed while he was explaining and said 6. XD
Rackou87 2 months ago
When the clip first started I thought Alan was having a nosebleed.
LihAniaih 3 months ago
my brain just fell out through my nose....
0deer7 3 months ago
If they know the number ends in 7 then why are they saying it can be anywhere from 12 to that number?
WakingLife55 3 months ago 2
@WakingLife55 I don't think they are too clear here, but what they means is as follows: There is some problem they are trying to solve, related to how many dimensions you need a cube to be so that every colouring of it has some property. Now, Graham (and Rothschild) proved an upperbound for this value - called Grayham's number now. So whatever the answer is, it is less than Grayham's number.
The actual number is between 12 and this. It is Grayham's number which ends in a 7, now the answer.
JaxWeb 3 months ago
@WakingLife55 the Graham number ends with a 7. The answer to the question about the amount of dimensions does not have to end with a 7. The possible answers just range between 12 and that number that definetely ends with a 7
myvidutube 3 months ago 2
@WakingLife55 They aren't saying the number to make it possible ends in a 7. They are saying that it lies between 12 and graham's number, which ends in a 7. xxxxxxxxxxxxxxxxxxxxxxxxxxxx
macting1 2 months ago
@WakingLife55 The number itself may not end with 7, but the upper limit of what it could be happens to end with 7.
dickie4thepeople 2 months ago
@WakingLife55 grahams number ends in a 7.....but the range of possible numbers of the theory goes from 12 to grahams number !
BowlingForHenry 2 months ago
@WakingLife55 The question asks to find a number n (satisfying some property). It might so happen that there is no number that satisfies the required property, in which case searching for it would be a waste of time. So Graham constructed his larger than astronomical number in such a way that he could prove there definitely was some number (less than or equal to Graham's number) that would indeed satisfy the property for n. So Graham's number is just an upper bound to the solution.
mediteight 2 months ago
he ends by saying "they do know it ends in a 7", poor show Stephen.
patrickgpking 3 months ago
@patrickgpking Indeed, you can work out the right hand digits of it. It ends, "...4195387", in fact =]
JaxWeb 3 months ago
@JaxWeb Graham's number is just the upper limit, not the solution, so we do not know that it ends in 7.
patrickgpking 3 months ago
@patrickgpking No, you misunderstand. We know Grayham's number ends with a 7. It is unknown what the last digit of the actual solution is.
JaxWeb 3 months ago
@JaxWeb Then we are in agreement, super.
patrickgpking 3 months ago
@patrickgpking Yes, in fact it appeared that I misunderstood your comment :) [In particular, what 'it' referred to]
JaxWeb 3 months ago
@JaxWeb @patrickgpking
'what a hilarious misunderstanding'
watch?v=mA64dPVO3RU
MikeGasm 3 months ago 6
Well, we know that pi starts with 3.14, and Graham's number ends with 7.
So that's a start.
Lulzman69 4 months ago
@Lulzman69 there's a man who has memorised Pi to 60.000 decimals...
RectumPilum 4 months ago
@RectumPilum You didn't get the joke, apparently.
Lulzman69 4 months ago
@Lulzman69 I got the joke, it was just that it had a flaw =P
RectumPilum 4 months ago
@RectumPilum If you think that was a flaw, then you kinda missed the point, eh? :P
Lulzman69 4 months ago
what episode is this from ?
BurnSpangler 5 months ago
@BurnSpangler Series G, Ep 6: "Genius".
JaxWeb 5 months ago
@JaxWeb thank you :)
BurnSpangler 5 months ago
@JaxWeb
The next question was "Why are exams easier nowadays?".....I would really like to know the answer please....
Varoonmg 6 months ago 10
@Varoonmg Hey Varoonmg. I just had a list through to the source, and it doesn't appear to be in this one. There is a little bit about IQ though, and David Mitchell mentions about exams a little.
If this is still of interest, I can post it though.
JaxWeb 6 months ago
@JaxWeb Oh I'm truly sorry about the late answer, my apologies...
It was the Holidays and the start of University
Well, yes I'm truly interested to know, if of course it's not to late to post the vid...
Thanks for your answer and sorry again for the late reply
Varoonmg 2 months ago
@Varoonmg Sure. But which video was it you wanted me to post? I've forgotten now, sorry!
JaxWeb 2 months ago
@JaxWeb Lol...It was on "Why are exams easier nowadays?"
Thanks in advance...:))
Varoonmg 2 months ago
@Varoonmg People are smarter - that's why.
IoEstasCedonta 2 months ago
@Varoonmg I believe the answer was "they aren't."
PT8475 1 month ago
@Varoonmg They're not. The exams today are just better, because we learn what is worthy of testing and what is not. There are many things in old text books that are utter twaddle. One such example is grading based on grammar. A basic understanding is required at certain levels, and a deeper understanding is required for certain professions, but there certainly isn't any value in forgoing more important topics to encourage 18 year olds to place apostrophes in correct places.
sdarvell 1 month ago