Life, the Universe, and Everything

September 6, 2019 9:25 AM

We know the answer is 42 but what is the question? Well, in the sum of three cubes mathland, it's: 42= (-80538738812075974)³ +80435758145817515³ +12602123297335631³ Full story: NEWS: The Mystery of 42 is Solved - Numberphile
posted by zengargoyle (28 comments total)

The question was "what is 6*9"
posted by Dr. Twist at 9:32 AM on September 6, 2019 [9 favorites]

That's NumberWang!
posted by chavenet at 9:37 AM on September 6, 2019 [16 favorites]

Great, now they've changed the answer again.
posted by tobascodagama at 9:52 AM on September 6, 2019

Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space.
posted by lalochezia at 9:59 AM on September 6, 2019 [2 favorites]

And if you have an allergy to peanuts that walk to the chemist seems that much longer.
posted by dances_with_sneetches at 10:32 AM on September 6, 2019 [1 favorite]

This is the official announcement: http://math.mit.edu/~drew/ (the result is from Andrew Booker at Bristol and Andrew Sutherland at MIT).
posted by 3j0hn at 10:40 AM on September 6, 2019 [2 favorites]

The question was "what is 6*9"

It's amazing how many people I've asked don't remember the punchline. I don't mean the specific numbers, but that it =/= 42.
posted by fleacircus at 11:11 AM on September 6, 2019 [2 favorites]

6 * 9 = 42 in base 13, but Douglas Adams specifically disavowed this answer.

The question "Think of a number, any number" appears twice in the books, most conspicuously during Martin's conversation with the talking mattress (and we know Martin knows the question, or at least the corrupted version in Arthur's brain). The mattress guesses "5" and Martin replies "wrong."

I've always suspected that was the actual question to the answer of 42.
posted by Ryvar at 11:25 AM on September 6, 2019 [11 favorites]

Is this something I'd need arbitrary-precision arithmetic to understand?
posted by genpfault at 11:28 AM on September 6, 2019

I was more interested in the explanation for the pairs of numbers labeled "impossible."
posted by fantabulous timewaster at 12:12 PM on September 6, 2019 [1 favorite]

From Reddit:

I saw the front page TIL about Stephan Fry knowing the truth behind 42 in Hitchhiker's Guide to the Galaxy. I am 95% sure it is this, I am not bullshitting you.

ASCII 42

In programming, an asterisk is commonly used as a sort of "whatever you want it to be" symbol, I've heard it called a wildcard.

ASCII language, the original way that computers run, the most basic computer software, in it, 42 is the designation for asterisk. The GIANT COMPUTER was asked what the true meaning was. It answered as a computer would.

Anything you want it to be.
posted by ananci at 12:33 PM on September 6, 2019 [26 favorites]

I was more interested in the explanation for the pairs of numbers labeled "impossible."


Not only did I desperately want to know this after I saw the original video, but I'm pleased to report that the explanation made sense to me!
posted by MCMikeNamara at 12:45 PM on September 6, 2019 [1 favorite]

Could someone explain if there's any practical application to these solutions? I get the "because it's there" aspect, but is there more than that?

And did they at least try Scrabble tiles first?
posted by hypersloth at 1:21 PM on September 6, 2019 [1 favorite]

wait that's my phone number
posted by not_on_display at 4:14 PM on September 6, 2019 [3 favorites]

I had always thought that it was because 9 and 7 look really close when written down (especially when you put the dash in the middle of the seven, which I was taught to do to distinguish it from a 1), that there was a typographical error that messed up the universe. I am going to continue to believe this no matter what you all say.
posted by Quonab at 5:06 PM on September 6, 2019

As far as practical applications go, there is never going to be some useful machine in your kitchen whose functioning depends on this relationship between the numbers 80538738812075974 and 42.

But the thing about puzzles where nobody knows the solution is that you don't know in advance whether the solution will be useful or interesting. Or whether the absence of a solution will be useful or interesting. Take for instance the observation (only hinted at in the title video, but explained in the video linked from my previous comment) that at least two-ninths of the positive integers can never be written as the sum of three cubes. The argument takes about ten minutes to explain, and uses a neat trick where you think about how remainders work when you do division without actually doing more than a little bit of actual division. That neat trick is applicable to lots of puzzles about numbers.

In particular, thinking about how remainders work without doing division is important in deciding whether a number is prime or not. And deciding whether a given large number is prime was a "because it's there" problem from antiquity until the 1970s, when the fact that it's hard was exploited by the inventors of public-key cryptography. Which invention has dramatically transformed how humans communicate over the past forty years. Imagine if I had told you in 1970 that, because remainders are annoying when you're doing division, that in fifty years most people would store all of their financial information, music collections, personal correspondence, and photographs on computers whose locations they would not know. I hardly believe it today.

There are several different ways that this story could have resolved:

• A solution to the problem could be found using existing methods, just by searching bigger numbers. (This is actually what happened, as I understand it.)
• A solution to the problem could be found using a new computational method. (This is what happened in the sum-of-three-cubes problem ten years ago, if I'm understanding the history correctly.)
• It could have turned out that, for 42 and for numbers that are somehow "shaped like" 42, there's no solution at all. That teaches us something interesting --- which may or may not turn out to be useful --- about what numbers do.
• It could have turned out that, for 42, there isn't any solution --- but for a reason that applies only to the magic number 42 and no others. That would be a big surprise whose usefulness would depend on the details of the proof.

The thing that actually happened here --- that we already had the tools to solve the problem, we just needed the computational power and the patience --- is probably the least interesting of these possible outcomes. And as the interviewee says in the video, he's not currently planning to continue the search for solutions for the remaining three-digit integers whose three-cube decompositions aren't yet known. But this because-it's-there problem is certainly adjacent to problems which do have practical uses.
posted by fantabulous timewaster at 5:32 PM on September 6, 2019 [13 favorites]

"The answer to this is very simple," Adams said. "It was a joke. It had to be a number, an ordinary, smallish number, and I chose that one. Binary representations, base 13, Tibetan monks are all complete nonsense. I sat on my desk, stared in to the garden and thought 42 will do. I typed it out. End of story."
posted by Ursula Hitler at 6:34 PM on September 6, 2019 [11 favorites]

I was more interested in the explanation for the pairs of numbers labeled "impossible."

For those who don't want to watch the video: Those are numbers which are 4 away from a multiple of 9. All cubes are either a multiple of 9, or one less or one more than a multiple of 9. I don't know a nice conceptual explanation for that but it's a bit of algebra, once you realize that every integer is either a multiple of 3, one more than a multiple of 3, or one less than a multiple of 3:

(3n)^3 = 27n^3 = 9(3n^3).
(3n+1)^3 = 27n^3 + 27n^2 + 9n + 1 = 9(3n^3 + 3n^2 + n) + 1.
(3n-1)^3 = 27n^3 - 27n^2 + 9n - 1 = 9(3n^3 - 3n^2 + n) - 1.

So if you're only adding up three cubes you can't get more than 3 away from a multiple of 9.
posted by madcaptenor at 6:42 PM on September 6, 2019 [5 favorites]

One interesting thing about this is that the original 2015 Numberphile video on the sum of three cubes had a lot to do with finding solutions to 74, 33, and 42 since then. Sander Huisman specifically cited the video as inspiration in his paper on the 74 solution in 2016. Andrew Booker says in his video on finding a solution to 33 that he was inspired by the video on the 74 solution (he hadn't seen it until this year) to make a new search algorithm that's more efficient at trying to solve particular numbers. He says in this post's video he got lots of offers to help search for a 42 solution after publishing that.

As for Douglas Adams and 42, it's pretty clear he just chose it because it sounds funny. Hitchhikers Guide started as a radio program, and an incredulous "42" was a punchline.
posted by netowl at 6:50 PM on September 6, 2019 [3 favorites]

42 is also how many months it's been since I've cleaned my towel. It's soaked in nutrients.
posted by not_on_display at 10:11 PM on September 6, 2019 [4 favorites]

All this is pointless, because we all know the highest number is 24.
posted by Rykey at 5:24 AM on September 7, 2019 [2 favorites]

> In programming, an asterisk is commonly used as a sort of "whatever you want it to be" symbol, I've heard it called a wildcard.

on the one hand in regular expressions * can be used to represent zero or more copies of the preceding character, on the other hand it's used to represent multiplication. but when i see someone refer to * in a programming context or whatever, i most often think they're talking about how in languages derived from c the * operator is used to declare and dereference pointers, which are variables that don't directly store values but instead store the address in memory of values. pointers are often indispensable, if frustrating to work with — especially when you have to deal with multiple layers of indirection and so must carefully keep track of whether you're dealing with a value or the address of a value or the address of the address of a value or etc. but also: if pointers of all things are the answer to life, the universe, and everything, then there truly is nothing worth living for and therefore we might as well go get handguns and use them to dereference our own null pointers right now.

really, it is indeed nothing more than a smallish number used in a joke in a sci-fi comedy. it's just that a bunch of people in the gen x/xennial/millennial age range cathected onto this sci-fi comedy when they were in middle school or whatever and ended up assigning great meaning to every single detail, in the way that children tend to assign great meaning to nonsense, and especially to nonsense jokes that come down to them from the adult world. adams wasn't joyce or whatever. hell, joyce wasn't joyce.

as the author of several acclaimed but also famously difficult novels, i can say with mid-range confidence that we're all pretty much just free-associating and then making up justifications for it later.
posted by Reclusive Novelist Thomas Pynchon at 7:01 AM on September 7, 2019 [4 favorites]

Thank you, fantabulous timewaster!
posted by hypersloth at 8:59 AM on September 7, 2019 [1 favorite]

42 is also how many months it's been since I've cleaned my towel. It's soaked in nutrients.

Ugh. Which end is soaked in antidepressants?
posted by loquacious at 9:04 AM on September 7, 2019 [1 favorite]

The propensity and ability for humans to construct a variety of coherent, interesting narratives providing meaning to something that does not have any intrinsic meaning seems like a pretty good Solution to the Question.
posted by biogeo at 9:49 AM on September 7, 2019 [1 favorite]

I thought Douglas Adams' 42 was homage to Lewis Carroll - it appears in the Alice books and Hunting of the Snark. Examples cited here.
posted by JonJacky at 8:13 PM on September 7, 2019

I am so pleased that the comments have crossed back and forth and all over the place.

"In programming, an asterisk is commonly used as a sort of "whatever you want it to be" symbol, I've heard it called a wildcard."

I give you Perl6's "whatever" '*': class Whatever.

It's pronounced "whatever" and is mostly an auto-currying term that creates anonymous code blocks. In ranges it creates infinite lists.

$ perl6 -e 'my @fib = 1, 1, * + * ... *;say @fib[1..10];'
(1 2 3 5 8 13 21 34 55 89)

# same - anonymous subroutine
$ perl6 -e 'my @fib = 1, 1, sub ($x,$y) { $x + $y } ... *;say @fib[1..10];'
(1 2 3 5 8 13 21 34 55 89)

# same - pointy block
$ perl6 -e 'my @fib = 1, 1, -> $x,$y { $x + $y } ... *;say @fib[1..10];'
(1 2 3 5 8 13 21 34 55 89)

# same - auto implicit lexically ordered arguments
$ perl6 -e 'my @fib = 1, 1, { $^a + $^b } ... *;say @fib[1..10];'
(1 2 3 5 8 13 21 34 55 89)
$ perl6 -e 'my @fib = 1, 1, { $^x + $^y } ... *;say @fib[1..10];'
(1 2 3 5 8 13 21 34 55 89)

It's a wonderful thing.
posted by zengargoyle at 11:12 PM on September 7, 2019 [1 favorite]

And just because...

$ perl6 -e 'say -80538738812075974³ + 80435758145817515³ + 12602123297335631³'
42

posted by zengargoyle at 8:08 AM on September 9, 2019