Big numbers
July 16, 2023 8:46 AM Subscribe
The human body has around 30 trillion cells. The vigintillion is a cardinal number represented in the US by 1 followed by 63 zeros, and in the UK by 1 followed by 120 zeros. Before this post, there were 325 (5x5x13) posts which contained 'potato' and 2522 (2x13x97) wich contained 'cat'. A bajillion is a huge number. Rayo's number was claimed to be the largest named number. If you could stack $44 billion in $100 bills, it'd be 30 miles high. Some populations are huge, but others less so. The Eddington number, the number of protons in the observable universe, is currently estimated to be 10 to the power of 80. Even 200,000 is a big number.
A myriad is technically 10,000. The word comes from ancient Greek.
posted by heatherlogan at 9:32 AM on July 16, 2023 [2 favorites]
posted by heatherlogan at 9:32 AM on July 16, 2023 [2 favorites]
Is Graham Number still the biggest used in an actual proof? Or has it been surpassed?
posted by indianbadger1 at 9:35 AM on July 16, 2023 [4 favorites]
posted by indianbadger1 at 9:35 AM on July 16, 2023 [4 favorites]
nonillion keeps turning up in the NYT's "Spelling Bee" puzzle.
posted by chavenet at 9:41 AM on July 16, 2023 [2 favorites]
posted by chavenet at 9:41 AM on July 16, 2023 [2 favorites]
The 200,000: that is very nicely done. You have made my day.
posted by spindle at 9:47 AM on July 16, 2023 [27 favorites]
posted by spindle at 9:47 AM on July 16, 2023 [27 favorites]
A shite out for our microbiome! There are [orders of magnitude here, folks: nobody is going to count them] an equal number of cells in and about our person which don't have 46 chromosomes comprising about 2x 3.3 billion ATCGs. These smaller cogs in the great machine weigh ~200g = 7oz and would comfortably sit in a Starbucks short.
posted by BobTheScientist at 9:47 AM on July 16, 2023 [6 favorites]
posted by BobTheScientist at 9:47 AM on July 16, 2023 [6 favorites]
Wow, the 24th anniversary post was 27 short of 200,000. I had not noticed that.
posted by bitslayer at 9:47 AM on July 16, 2023 [2 favorites]
posted by bitslayer at 9:47 AM on July 16, 2023 [2 favorites]
Okay, lets just get these two (2) out of the way:
42
69
posted by Clever User Name at 9:48 AM on July 16, 2023 [2 favorites]
42
69
posted by Clever User Name at 9:48 AM on July 16, 2023 [2 favorites]
42
69
No 49?
Anyway, there are as many cells in the human body as there are stars in the universe, and as we discover more stars, we seem to notice more cells. Or so I heard someone say some years ago. And then I couldn't help but follow with, "I don't know why but every time I hear the universe is even more vast and incomprehensible than we imagined, I'm strangely reassured."
posted by philip-random at 9:57 AM on July 16, 2023 [2 favorites]
69
No 49?
Anyway, there are as many cells in the human body as there are stars in the universe, and as we discover more stars, we seem to notice more cells. Or so I heard someone say some years ago. And then I couldn't help but follow with, "I don't know why but every time I hear the universe is even more vast and incomprehensible than we imagined, I'm strangely reassured."
posted by philip-random at 9:57 AM on July 16, 2023 [2 favorites]
total tangent but as a trans woman i prefer to describe my height with larger than conventional numbers: i'm somewhere between 4' 20" and 69" tall
posted by polyhedron at 10:06 AM on July 16, 2023 [11 favorites]
posted by polyhedron at 10:06 AM on July 16, 2023 [11 favorites]
Is Graham Number still the biggest used in an actual proof? Or has it been surpassed?
.....it is so large that the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume, possibly the smallest measurable space. But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe. Nor even can the number of digits of that number—and so forth, for a number of times far exceeding the total number of Planck volumes.
posted by lalochezia at 10:17 AM on July 16, 2023 [3 favorites]
.....it is so large that the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume, possibly the smallest measurable space. But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe. Nor even can the number of digits of that number—and so forth, for a number of times far exceeding the total number of Planck volumes.
posted by lalochezia at 10:17 AM on July 16, 2023 [3 favorites]
I think it's interesting trying to make these very large numbers intuitively understandable. I just finished Exponential Idle, a fairly deep math-oriented idle game. Like all these kinds of games they deal in very very large numbers, so large that regular exponential notation isn't sufficient. Instead you mostly see "ee numbers": 3ee500 is 3 * 10^1e500 or 3 * 10^(10^500). Pretty soon your eyes glaze over and you just see that number as "500", that's the scale the game operates at.
A lot of idle games deal with ridiculously large numbers. break_infinity is the Javascript library folks use for dealing with them, or the embiggened break eternity. The Python equivalent expol has a bunch of options for printing the numbers out.
A lot of idle games deal with ridiculously large numbers. break_infinity is the Javascript library folks use for dealing with them, or the embiggened break eternity. The Python equivalent expol has a bunch of options for printing the numbers out.
e - Engineering 1.23e45680 el - Engineering Log-looped 1.23ee4.660 k - Engineering K 123.000k15226 kl - Engineering K Log-looped 123.000kk1.394 s - Scientific 1.23×10^45680 sl - Scientific Log-looped 1.23×10^10^4.660 sk - Scientific K 123.000×1000^15226 skl - Scientific K Log-looped 123.000×1000^1000^1.394 i - Illions 123.000 QuinVigintDucent-QuinDecMillillion is - Illions Shorthand 123.000 QiVgDt-QiDcMl r - Roman Numerals CXXIIIˣᵛ⚂^ᶦposted by Nelson at 10:21 AM on July 16, 2023 [7 favorites]
polyhedron, I've seen people express their weight in carats.
posted by Nancy Lebovitz at 10:31 AM on July 16, 2023 [2 favorites]
posted by Nancy Lebovitz at 10:31 AM on July 16, 2023 [2 favorites]
My favorite specific big number is 不可説不可説転 ("fukasetsufukasetsuten" in Japanese; loosely, "the ineffable, ineffable revolution") which is exactly 107*2122, a number with 1029 digits.
It arose from a conversation between Bodhisattva and the Buddha (see translation) where the Buddha starts with a lakṣa (lakh, 105) and koṭi (crore, 107), squares the koṭi, then squares the result many, many times.
posted by kurumi at 10:35 AM on July 16, 2023 [6 favorites]
It arose from a conversation between Bodhisattva and the Buddha (see translation) where the Buddha starts with a lakṣa (lakh, 105) and koṭi (crore, 107), squares the koṭi, then squares the result many, many times.
posted by kurumi at 10:35 AM on July 16, 2023 [6 favorites]
Let me introduce you to The Ackermann Function, a totally computable function which takes in two non-negative integers (m, n) and outputs a single integer such that:
If m=0, then A(0, n) = n+1, else
If n=0, then A(m, 0) = A(m-1, 1), else
A(m, n) = A(m-1, A(m, n-1))
Because every step of the function will definitely decrease either m or n, it's guaranteed that this function will always terminate and output an answer. Unfortunately, because of that recursively calling for the function, the time it takes to compute, and the magnitude of the answer quickly become stooooopid huge.
It's all fun and games until you get to a value of m or n > 4. For example:
A(4, 0) = 13
A(4, 1) = 65533 and will hang your computer for about 2 minutes while it computes
A(4, 2) = (2^65536) − 3, an integer that is 19,729 digits long
A(4, 3) is for all purposes totally incomputable, because it's answer is 2 raised to the power of A(4, 2), minus 3
Just as with Graham's Number, up-arrow notation gets used very quickly. But! -- and this is very important -- they are always finite answers.
posted by The Pluto Gangsta at 10:38 AM on July 16, 2023 [5 favorites]
If m=0, then A(0, n) = n+1, else
If n=0, then A(m, 0) = A(m-1, 1), else
A(m, n) = A(m-1, A(m, n-1))
Because every step of the function will definitely decrease either m or n, it's guaranteed that this function will always terminate and output an answer. Unfortunately, because of that recursively calling for the function, the time it takes to compute, and the magnitude of the answer quickly become stooooopid huge.
It's all fun and games until you get to a value of m or n > 4. For example:
A(4, 0) = 13
A(4, 1) = 65533 and will hang your computer for about 2 minutes while it computes
A(4, 2) = (2^65536) − 3, an integer that is 19,729 digits long
A(4, 3) is for all purposes totally incomputable, because it's answer is 2 raised to the power of A(4, 2), minus 3
Just as with Graham's Number, up-arrow notation gets used very quickly. But! -- and this is very important -- they are always finite answers.
posted by The Pluto Gangsta at 10:38 AM on July 16, 2023 [5 favorites]
An old twitter thread on big computable numbers (nitter). Push the idea too far though and you run the risk of your mathematics being inconsistent and the "numbers" not actually being numbers at all.
posted by mscibing at 10:41 AM on July 16, 2023 [1 favorite]
posted by mscibing at 10:41 AM on July 16, 2023 [1 favorite]
As a kid I was fascinated with big numbers and tried to memorize million billion trillion... undecillion was as far as I can remember now .
But then googol. When I learned of centillion in 6th grade I had to write 103 zeroes after 1 just to see what it looked like.
Big numbers are cool
posted by symbioid at 10:42 AM on July 16, 2023 [2 favorites]
But then googol. When I learned of centillion in 6th grade I had to write 103 zeroes after 1 just to see what it looked like.
Big numbers are cool
posted by symbioid at 10:42 AM on July 16, 2023 [2 favorites]
An additional thing that always boggles my mind is that for all it's bigness, Graham Number is still basically zero when compared to infinity as a mathematical concept!
posted by indianbadger1 at 10:43 AM on July 16, 2023 [1 favorite]
posted by indianbadger1 at 10:43 AM on July 16, 2023 [1 favorite]
Faint memory of Chaitin (?) math-- while there are simply described big numbers like a googleplex, there are untidy numbers in between the describable numbers and you can do math of sorts with them.
posted by Nancy Lebovitz at 10:52 AM on July 16, 2023 [1 favorite]
posted by Nancy Lebovitz at 10:52 AM on July 16, 2023 [1 favorite]
This is an excellent post which thoroughly delighted me. I'm all smiley now.
Thank you, Wordshore, for this marvelous celebration of 200,000, and its even larger kin!
posted by kristi at 11:10 AM on July 16, 2023 [1 favorite]
Thank you, Wordshore, for this marvelous celebration of 200,000, and its even larger kin!
posted by kristi at 11:10 AM on July 16, 2023 [1 favorite]
pretty sure "Illinois Shorthand" is also a slang term for a made-up sexual act
posted by glonous keming at 11:45 AM on July 16, 2023 [1 favorite]
posted by glonous keming at 11:45 AM on July 16, 2023 [1 favorite]
Before this post, there were 325 (5x5x13) posts which contained 'potato'
I really miss potato week.
posted by inflatablekiwi at 12:11 PM on July 16, 2023 [2 favorites]
I really miss potato week.
posted by inflatablekiwi at 12:11 PM on July 16, 2023 [2 favorites]
Graham's number is 1 (in base Graham's number)
posted by DeepSeaHaggis at 12:30 PM on July 16, 2023 [3 favorites]
posted by DeepSeaHaggis at 12:30 PM on July 16, 2023 [3 favorites]
No, it would be 10.
posted by vacapinta at 12:42 PM on July 16, 2023 [7 favorites]
posted by vacapinta at 12:42 PM on July 16, 2023 [7 favorites]
Rayo's number was claimed to be the largest named number.
It was, until dephlogisticated's number was created, which is defined as Rayo's number + 1.
posted by dephlogisticated at 1:08 PM on July 16, 2023 [3 favorites]
It was, until dephlogisticated's number was created, which is defined as Rayo's number + 1.
posted by dephlogisticated at 1:08 PM on July 16, 2023 [3 favorites]
I had to run the numbers on this to determine it was correct, but if we placed the population of viruses end to end, they would extend to Alpha Centauri.
posted by dances_with_sneetches at 1:22 PM on July 16, 2023 [2 favorites]
posted by dances_with_sneetches at 1:22 PM on July 16, 2023 [2 favorites]
I'm pretty sure that 24 is the highest number.
posted by The Great Big Mulp at 1:24 PM on July 16, 2023 [7 favorites]
posted by The Great Big Mulp at 1:24 PM on July 16, 2023 [7 favorites]
posted by Wordshore
Eponysterical?
posted by ChurchHatesTucker at 1:55 PM on July 16, 2023 [1 favorite]
Eponysterical?
posted by ChurchHatesTucker at 1:55 PM on July 16, 2023 [1 favorite]
Who else saw the headline and thought of the wrong Big Numbers?
posted by kimota at 1:57 PM on July 16, 2023 [1 favorite]
posted by kimota at 1:57 PM on July 16, 2023 [1 favorite]
Can't track it down right now but ask some mathematicians for an example of a really big significant number and they might say 3. A lot goes on from 0 to 1, then 3 and all those others then infinity. The difference between 0 and 3 or 0 and Googolplex or 0 and Grahams number almost trivial compared the biggest named number to infinity.
Also 3 is the first odd prime. ;-)
posted by sammyo at 2:05 PM on July 16, 2023 [1 favorite]
Also 3 is the first odd prime. ;-)
posted by sammyo at 2:05 PM on July 16, 2023 [1 favorite]
A shite out for our microbiome!
Indeed!
posted by obfuscation at 2:22 PM on July 16, 2023 [2 favorites]
Indeed!
posted by obfuscation at 2:22 PM on July 16, 2023 [2 favorites]
The largest number is about forty-five billion, although mathematicians suspect that there may be even larger numbers.
posted by polytope subirb enby-of-piano-dice at 2:30 PM on July 16, 2023 [5 favorites]
posted by polytope subirb enby-of-piano-dice at 2:30 PM on July 16, 2023 [5 favorites]
I just want to know how long Wordshore has had this post ready and waiting.
posted by Night_owl at 2:34 PM on July 16, 2023 [2 favorites]
posted by Night_owl at 2:34 PM on July 16, 2023 [2 favorites]
Philip J Davis’ The Lore of Large Numbers was a favorite book about this kind of stuff when I was a teen. It’s still in print.
posted by wittgenstein at 2:39 PM on July 16, 2023 [1 favorite]
posted by wittgenstein at 2:39 PM on July 16, 2023 [1 favorite]
Is Graham Number still the biggest used in an actual proof? Or has it been surpassed?
Long since surpassed by TREE(3), I believe.
Happy milestone, Metafilter!
posted by qntm at 3:21 PM on July 16, 2023 [2 favorites]
Long since surpassed by TREE(3), I believe.
Happy milestone, Metafilter!
posted by qntm at 3:21 PM on July 16, 2023 [2 favorites]
There is an answer to the +1 strategy: inaccessible cardinals which are, roughly, numbers that can’t be reached by any ordinary arithmetic operation on lesser numbers indexed with those numbers — and which may or may not exist.
If ℵ0 is allowed into consideration, there is at least one, but I’ve always read that if there are any others, then it’s possible to prove the consistency of ZF set theory, which contradicts one of Gödel's theorems, therefore none exist.
The Wikipedia article I’ve linked seems to be saying something different, but I can’t tell how different or what, exactly, it is saying instead.
Which to me means that the simple act of trying to count something immediately calls into existence an overworld of enormous, overwhelming, and even somewhat frightening complexity that is beyond my grasp.
Which kind of brings things full circle for me, since I can remember an extended period in grade school where everybody else was counting like crazy, and I had no idea what was going on.
posted by jamjam at 3:23 PM on July 16, 2023 [1 favorite]
If ℵ0 is allowed into consideration, there is at least one, but I’ve always read that if there are any others, then it’s possible to prove the consistency of ZF set theory, which contradicts one of Gödel's theorems, therefore none exist.
The Wikipedia article I’ve linked seems to be saying something different, but I can’t tell how different or what, exactly, it is saying instead.
Which to me means that the simple act of trying to count something immediately calls into existence an overworld of enormous, overwhelming, and even somewhat frightening complexity that is beyond my grasp.
Which kind of brings things full circle for me, since I can remember an extended period in grade school where everybody else was counting like crazy, and I had no idea what was going on.
posted by jamjam at 3:23 PM on July 16, 2023 [1 favorite]
i saw Inaccessible Cardinals open for Kataklysm and Graveworm in 2006 and iirc it was... challenging. it wasn't abundantly clear who, if anyone, was playing which instrument.
posted by glonous keming at 5:13 PM on July 16, 2023 [4 favorites]
posted by glonous keming at 5:13 PM on July 16, 2023 [4 favorites]
24 is the highest number
Merlin Mann said this on one of his podcasts last week and I didn't get the reference. I've never seen Mr Show but it's high on my list.
-
The Penguin Dictionary of Curious and Interesting Numbers is very good.
posted by neuron at 6:30 PM on July 16, 2023 [2 favorites]
Merlin Mann said this on one of his podcasts last week and I didn't get the reference. I've never seen Mr Show but it's high on my list.
-
The Penguin Dictionary of Curious and Interesting Numbers is very good.
posted by neuron at 6:30 PM on July 16, 2023 [2 favorites]
A myriad is technically 10,000. The word comes from ancient Greek.
Thank you; it means a lot.
posted by TedW at 7:29 PM on July 16, 2023 [8 favorites]
Thank you; it means a lot.
posted by TedW at 7:29 PM on July 16, 2023 [8 favorites]
24 is the highest! That's it, alright?
posted by ChurchHatesTucker at 7:41 PM on July 16, 2023 [2 favorites]
posted by ChurchHatesTucker at 7:41 PM on July 16, 2023 [2 favorites]
According to Michael and Marcus, the correct order of numbers is:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 44, 68, 27, 35, 42, 58, 47, 63, 85, 74, 67, 66, 51, 79, 42, 24, 45, sixty-ten, 6, 7, 56, 65, 44, 53, 44, 17, 13, 23.
...with the largest number being the cardinal orange.
posted by Wordshore at 9:32 PM on July 16, 2023 [2 favorites]
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 44, 68, 27, 35, 42, 58, 47, 63, 85, 74, 67, 66, 51, 79, 42, 24, 45, sixty-ten, 6, 7, 56, 65, 44, 53, 44, 17, 13, 23.
...with the largest number being the cardinal orange.
posted by Wordshore at 9:32 PM on July 16, 2023 [2 favorites]
I've seen people express their weight in carats.
How about speed in atto-parsec per micro-fortnight?
(roughly an inch per second in units more familiar to most)
posted by DreamerFi at 1:59 AM on July 17, 2023 [1 favorite]
How about speed in atto-parsec per micro-fortnight?
(roughly an inch per second in units more familiar to most)
posted by DreamerFi at 1:59 AM on July 17, 2023 [1 favorite]
I've seen a suggestion for furlongs per fortnight, which I think is also about an inch per second.
posted by Nancy Lebovitz at 4:43 AM on July 17, 2023 [1 favorite]
posted by Nancy Lebovitz at 4:43 AM on July 17, 2023 [1 favorite]
Speaking of 200,000 - a recent FPP also featuring that specific number was based on a crime report which has just reached its conclusion. Mr Joby Pool has been sentenced to 18 months in jail (though only has to serve another three).
posted by Wordshore at 11:47 AM on July 20, 2023
posted by Wordshore at 11:47 AM on July 20, 2023
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posted by Nancy Lebovitz at 8:58 AM on July 16, 2023 [3 favorites]