Very large numbers
March 9, 2010 10:16 AM Subscribe
The Shannon number? Skewes' number? Graham's number? Please. When you're ready to get serious, here are some truly large numbers. (previously, but with dead links)
I made the mistake of jumping to Inaccessible Infinities first.
It's going to take forever* to clean up all the exploded bits of my brain.
* I was going to say "an infinitely long time" but that might have been going too far.
posted by tommasz at 10:21 AM on March 9, 2010 [1 favorite]
It's going to take forever
posted by tommasz at 10:21 AM on March 9, 2010 [1 favorite]
I just added one to the largest number ever. Put me in the Guinness Book!
posted by Babblesort at 10:24 AM on March 9, 2010
posted by Babblesort at 10:24 AM on March 9, 2010
My son loves talking about huge numbers (his favorite number is a quadrillion); he's even made up one of his own - a quadrillion quadrillions is a wondred!
Anyway he also loves the idea that, if someone asks what number is bigger than x you can just say x + 1. Smart boy, don't know where he gets his math aptitude from though...
posted by Mister_A at 10:26 AM on March 9, 2010 [1 favorite]
Anyway he also loves the idea that, if someone asks what number is bigger than x you can just say x + 1. Smart boy, don't know where he gets his math aptitude from though...
posted by Mister_A at 10:26 AM on March 9, 2010 [1 favorite]
Is today secretly Math Geek Day or something? Cause it's awesome, but I'm sad nobody told me.
posted by kmz at 10:26 AM on March 9, 2010
posted by kmz at 10:26 AM on March 9, 2010
My son loves talking about huge numbers (his favorite number is a quadrillion)...
A couple of mine like the same thing. The youngest's favorite huge number is "one thousand and ninety-nine nine ninety-nine".
posted by DU at 10:30 AM on March 9, 2010 [1 favorite]
A couple of mine like the same thing. The youngest's favorite huge number is "one thousand and ninety-nine nine ninety-nine".
posted by DU at 10:30 AM on March 9, 2010 [1 favorite]
The youngest's favorite huge number is "one thousand and ninety-nine nine ninety-nine".
He's sixteen.
posted by shakespeherian at 10:31 AM on March 9, 2010 [1 favorite]
He's sixteen.
posted by shakespeherian at 10:31 AM on March 9, 2010 [1 favorite]
Also previously, a slightly more accessible description of the BB numbers.
posted by mr_roboto at 10:32 AM on March 9, 2010 [1 favorite]
posted by mr_roboto at 10:32 AM on March 9, 2010 [1 favorite]
Are these numbers Hella big?
posted by yeloson at 10:34 AM on March 9, 2010 [4 favorites]
posted by yeloson at 10:34 AM on March 9, 2010 [4 favorites]
Man I used to be pretty good at math. AP Calculus as a highschool junior, I read DFW's book in infinity, etc. And now every link in this FPP seems to be some variation on 'The Skewes number is a derivation of the squeedle of ultra-π raised to the 32nd trimester algorithmically, as can be expressed laterally, or as an inverse goost (see the nano-Zanzibar proposition).'
posted by shakespeherian at 10:40 AM on March 9, 2010 [3 favorites]
posted by shakespeherian at 10:40 AM on March 9, 2010 [3 favorites]
I know Shannon, and that's not her number.
posted by w0mbat at 10:40 AM on March 9, 2010 [5 favorites]
posted by w0mbat at 10:40 AM on March 9, 2010 [5 favorites]
+1
posted by joelf at 10:40 AM on March 9, 2010 [2 favorites]
posted by joelf at 10:40 AM on March 9, 2010 [2 favorites]
A bit back, reading about Graham's Number and I worked my way through the Knuth's up-arrow notation to try and get some sort of sense of how big it was... you can think about the towers of exponents and reiterating and such like but it's still mind-blowing trying to relate it to anything. 'Infinity' is much easier.
posted by fearfulsymmetry at 10:40 AM on March 9, 2010 [1 favorite]
posted by fearfulsymmetry at 10:40 AM on March 9, 2010 [1 favorite]
I remember being very happy to find out about "centillion" as a kid reading an encyclopedic dictionary my parents had.
Behold the concentrated nerdosity in that sentence. In my defense, I also looked up "naughty" words in that dictionary.
posted by kmz at 10:41 AM on March 9, 2010 [1 favorite]
Behold the concentrated nerdosity in that sentence. In my defense, I also looked up "naughty" words in that dictionary.
posted by kmz at 10:41 AM on March 9, 2010 [1 favorite]
There was a good recent BBC Horizon on big numbers/infinity, the website of which links to a couple of related radio programs, which you can download as podcasts
posted by fearfulsymmetry at 10:44 AM on March 9, 2010 [1 favorite]
posted by fearfulsymmetry at 10:44 AM on March 9, 2010 [1 favorite]
auch god my brain. It rare to encounter sentences that awaken parts of my frontal lobe so viscerally.
"Since the infinities all have an integer subscript, the "number of infinities" (or number of classes, if you are working within an ordinal system) is ℵ0, and the "limit" of the process of defining higher infinities..." and that's when my brain goes "okay buddy you stop right there that's about enough."
posted by Baby_Balrog at 10:45 AM on March 9, 2010 [2 favorites]
"Since the infinities all have an integer subscript, the "number of infinities" (or number of classes, if you are working within an ordinal system) is ℵ0, and the "limit" of the process of defining higher infinities..." and that's when my brain goes "okay buddy you stop right there that's about enough."
posted by Baby_Balrog at 10:45 AM on March 9, 2010 [2 favorites]
I was thrilled when I first discovered there was a number named after me.
posted by brundlefly at 10:47 AM on March 9, 2010
posted by brundlefly at 10:47 AM on March 9, 2010
The Law of Large Numbers: You must be this tall to ride in the numerator position.
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posted by blue_beetle at 10:51 AM on March 9, 2010 [7 favorites]
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posted by blue_beetle at 10:51 AM on March 9, 2010 [7 favorites]
The limit for class-1 numbers is around a million, 1,000,000 or 106. You can just barely put 1,000,000 dots on a large piece of paper and stand at a distance such that you can perceive each individual dot as a distinct dot, and at the same time be within viewing distance of the other 999,999 dots. (I have actually done this, just for fun!)
This guy has way too much free time.
posted by metaxa at 11:43 AM on March 9, 2010
This guy has way too much free time.
posted by metaxa at 11:43 AM on March 9, 2010
This is just weird. I was at this very moment preparing an FPP about famous conjectures for which the first counterexample is some extremely large number, including Polya's conjecture and the Skewes' numbers. Now I needn't bother, I guess. It really must be math geek day or something.
posted by albrecht at 11:50 AM on March 9, 2010
posted by albrecht at 11:50 AM on March 9, 2010
A bit back, reading about Graham's Number and I worked my way through the Knuth's up-arrow notation to try and get some sort of sense of how big it was... you can think about the towers of exponents and reiterating and such like but it's still mind-blowing trying to relate it to anything. 'Infinity' is much easier.
The biggest thing I found when reading about and trying to understand Graham's Number is that it gives me a totally new perspective on just how big infinity really is. Because Graham's Number is far, far bigger than any impression I get when I try to comprehend the idea of infinity.
Realizing that a number is so big that if every atom in the universe contained it's own universe of the same size as ours, and every atom in those universes were able to represent a digit, that you still couldn't represent just the number of digits in Graham's Number... then you get just that inkling of how big it truly is.
posted by evilangela at 12:08 PM on March 9, 2010 [2 favorites]
The biggest thing I found when reading about and trying to understand Graham's Number is that it gives me a totally new perspective on just how big infinity really is. Because Graham's Number is far, far bigger than any impression I get when I try to comprehend the idea of infinity.
Realizing that a number is so big that if every atom in the universe contained it's own universe of the same size as ours, and every atom in those universes were able to represent a digit, that you still couldn't represent just the number of digits in Graham's Number... then you get just that inkling of how big it truly is.
posted by evilangela at 12:08 PM on March 9, 2010 [2 favorites]
For certain values of 5.
posted by cortex at 12:13 PM on March 9, 2010 [2 favorites]
posted by cortex at 12:13 PM on March 9, 2010 [2 favorites]
My Erdős number is bigger than all of them.
posted by The_Auditor at 12:28 PM on March 9, 2010 [2 favorites]
posted by The_Auditor at 12:28 PM on March 9, 2010 [2 favorites]
Shut up! Quit your counting! You're a buncha cajoles. I'm trying to read the damn racing form. 24's the highest number, and that's it! Let it go.
posted by Earthtopus at 1:04 PM on March 9, 2010 [2 favorites]
posted by Earthtopus at 1:04 PM on March 9, 2010 [2 favorites]
The largest number is about 45 billion -- although mathematicians suspect there may be even larger numbers.
Take the quiz here.
posted by not_on_display at 1:46 PM on March 9, 2010 [1 favorite]
Take the quiz here.
posted by not_on_display at 1:46 PM on March 9, 2010 [1 favorite]
Realizing that a number is so big that if every atom in the universe contained it's own universe of the same size as ours, and every atom in those universes were able to represent a digit, that you still couldn't represent just the number of digits in Graham's Number... then you get just that inkling of how big it truly is.
Well exactly, I did the universe of universes thing... to me it's a lot more 'my brain can't cope with this' than butterflies/birds flying to a sun made of iron every 1000 years stuff.
posted by fearfulsymmetry at 1:51 PM on March 9, 2010
Well exactly, I did the universe of universes thing... to me it's a lot more 'my brain can't cope with this' than butterflies/birds flying to a sun made of iron every 1000 years stuff.
posted by fearfulsymmetry at 1:51 PM on March 9, 2010
Does tetration have any use besides maybe seeking grant money from a hypothetical fascist dictator with a mathematical bent?
posted by BrotherCaine at 2:31 PM on March 9, 2010
posted by BrotherCaine at 2:31 PM on March 9, 2010
I hate math with almost every fiber of my being*, but I've always** been fascinated by the concept of infinity and very large numbers. Great post, thanks!
* because I suck at it, not because there's anything wrong with math
** "always" in this case can be read to mean "since the first time I kept squaring numbers on my calculator until I got an error message"
posted by The Card Cheat at 2:39 PM on March 9, 2010
* because I suck at it, not because there's anything wrong with math
** "always" in this case can be read to mean "since the first time I kept squaring numbers on my calculator until I got an error message"
posted by The Card Cheat at 2:39 PM on March 9, 2010
I'm told math geek day is actually 5 days from today. For certain values of 5 geek.
posted by Someday Bum at 3:23 PM on March 9, 2010
posted by Someday Bum at 3:23 PM on March 9, 2010
640K ought to be enough for anybody.
posted by erniepan at 4:01 PM on March 9, 2010 [2 favorites]
posted by erniepan at 4:01 PM on March 9, 2010 [2 favorites]
I invented the Jenny number : 8,675,309
posted by newfers at 4:11 PM on March 9, 2010 [1 favorite]
posted by newfers at 4:11 PM on March 9, 2010 [1 favorite]
Are these numbers Hella big?
I swear to God, if you bastards from the internet succeed in making 'hella' an SI prefix, I'm leaving science forever and taking up curling.
posted by anifinder at 4:21 PM on March 9, 2010
I swear to God, if you bastards from the internet succeed in making 'hella' an SI prefix, I'm leaving science forever and taking up curling.
posted by anifinder at 4:21 PM on March 9, 2010
Better practice your sweeping, anilfinder, 'cuz that shit is coming!
posted by ph00dz at 5:06 PM on March 9, 2010
posted by ph00dz at 5:06 PM on March 9, 2010
I've got your f***ing number.
posted by Jumpin Jack Flash at 5:22 PM on March 9, 2010
posted by Jumpin Jack Flash at 5:22 PM on March 9, 2010
...I'm leaving science forever and taking up curling.
Oh come on, hella is not much worse than declaring Pluto a non-planet, or defining homosexuality as a mental illness or classifying ethnic groups into Xanthrochroi and Melanochroi... Science has always had wackiness, at least go in knowing why you should be laughing.
posted by yeloson at 5:48 PM on March 9, 2010 [1 favorite]
Oh come on, hella is not much worse than declaring Pluto a non-planet, or defining homosexuality as a mental illness or classifying ethnic groups into Xanthrochroi and Melanochroi... Science has always had wackiness, at least go in knowing why you should be laughing.
posted by yeloson at 5:48 PM on March 9, 2010 [1 favorite]
Man, I love stuff like this. My theory is that there is a mathematician inside me who is frustrated by my artsy proclivities and gets revenge by obsessing over odd time signatures.
posted by danb at 6:58 PM on March 9, 2010 [1 favorite]
posted by danb at 6:58 PM on March 9, 2010 [1 favorite]
I went to a talk by Ron Graham once at MIT (yep my IQ was 2/3's the average). The topic was "problems that can never be handled by computers". It was a wild roller-coaster ride with loops but always at a steeper than imaginable arc up into the stratosphere of really beeg numbers. That goggol number was just a constant tossed off in the first sentence. And he got a gasp or two out of that audience!
posted by sammyo at 8:07 PM on March 9, 2010
posted by sammyo at 8:07 PM on March 9, 2010
The Penguin Book of Curious and Interesting Numbers is good.
posted by neuron at 9:49 PM on March 9, 2010
posted by neuron at 9:49 PM on March 9, 2010
The alefs I'm not so keen on as I am on the beth numbers.
posted by oonh at 11:08 PM on March 9, 2010
posted by oonh at 11:08 PM on March 9, 2010
The largest number is about 45 billion, although mathematicians suspect there may be even larger numbers.
posted by Electric Dragon at 7:58 AM on March 10, 2010
posted by Electric Dragon at 7:58 AM on March 10, 2010
Dammit now I see not_on_display got there first. (Sets calculator to stun).
posted by Electric Dragon at 8:00 AM on March 10, 2010
posted by Electric Dragon at 8:00 AM on March 10, 2010
This is a very nicely developed discussion, but somehow these things always remind me of this comic.
posted by PMdixon at 9:52 AM on March 10, 2010
posted by PMdixon at 9:52 AM on March 10, 2010
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lolnonmathematicians
posted by DU at 10:20 AM on March 9, 2010