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42

johncarlosbaez.wordpress.com

528 pointsrobinhouston58 comments

Obviously the article is written for fun, but for those interested Douglas Adams' answer to why 42 was:

"The answer to this is very simple. It was a joke. It had to be a number, an ordinary, smallish number, and I chose that one. Binary representations, base thirteen, Tibetan monks are all complete nonsense. I sat at my desk, stared into the garden and thought '42 will do'. I typed it out. End of story."

It's a bit silly he had to say this-- this is made very explicit in the books. I feel like a lot of people missed the point of the whole exercise.

Probably subconscious effects affecting D.A. after pan-dimensional rodents played with us for eons

While I do agree that the amount of speculation over such a simple joke is a little ridiculous, Douglas Adams' actual thought process doesn't invalidate the alternatives as valid interpretations of the text. While Adams may have had no particular question in mind when he wrote the joke, it is nonetheless a key point of the story that there is such a question, and as such it is to be expected that some people's interpretations of the story will include one.

Now personally, I would argue that the actual question is unknowable, and that this is central to the point of the story, but this is just my opinion.

I always thought that this was interesting...

I am sure that many of you are familiar with Dr. Feynman's 7-part lecture series entitled The Character of Physical Law, which were part of the "Messenger Lectures" [1], given at Cornell University in 1964.

In the first lecture, Law of Gravitation - An Example of Physical Law, Feynman states the following:

"Question: what is the ratio of the gravitational force to the electrical force? That is illustrated on the next slide.

The ratio of the gravitational attraction to the electrical repulsion is given by a number with 42 digits, and goes off here: all this is written very carefully out, so that's 42 digits.

Now, therein lies a very deep mystery: where could such a tremendous number come from? That means if you ever had a theory from which both of these things are to come, how could they come in such disproportion? From what equation has a solution which has for one, two kinds of forces, an attraction and a repulsion with that fantastic ratio? People have looked for such a large ratio in other places.

They're looking for a large number.

They hope, for example, that there's another large number.

And if you want a large number why not take the diameter of the universe to the diameter of a proton.

Amazingly enough, it also is a number with 42 digits." [2]

[1] https://en.wikipedia.org/wiki/Messenger_Lectures

[2] https://www.youtube.com/watch?v=j3mhkYbznBk#t=48m11s

42 digits in base 10 though, and base 10 is just an arbitrary convention. It can be more or less in other equally valid bases.

Yes, but within that base it's significant. Just as within other bases the corresponding number would be significant.

This is important because if you operate a system universally with the same base, the significant number begins to take on an objective importance intra-system.

Stated another way, it's mathematical semantics, the same as arguing an idea is not significant because you can express it in a multitude of different languages, each having an arbitrary words.

Developing via Django (Python) or Rails (Ruby) is similarly predisposed to making one think it's all relative, but when you look closely, the framework doesn't matter at all - there are universal abstractions inherent in web development.

The representation is arbitrary and insignificant, what is significant is what the number or word represents, and what you can do by unraveling it.

I didn't really consider it like that, interesting

"Just as within other bases the corresponding number would be significant."

Numbers are independent from any base. You may mean the numeral in another base, which would have a different number of digits.

But what is more important, note that not necessarily the two ratios from the quote will have the same number of digits in another base.

Yes, the numeral representation of the number is exactly what I mean, you clarified my comment perfectly. Numbers are independent from any base.

Yes, but the other number will have a similar number of digits in whatever base you choose. More precisely, the number of digits will be multiplied by ln(10)/ln(base) for both numbers.

I see what you mean, sounds right

Irrelevant. Two numbers with the same number of digits when expressed in base 10 will necessarily be within a factor of 10 of each other. This is just a different way of saying these numbers are close.

All bases are base 10 within that base. So actually, base 10 is about as non-arbitrary as it gets. </nyuknyuk>

http://math.stackexchange.com/questions/166869/is-10-a-magic...

Isn't the universe still growing? Which means that at some point in the very far off future, the ratio of of the diameter of the universe to the diameter of a proton will be 43 digits? Passing thought -- since 42 _is_ the the answer to the Great Question of Life, etc., perhaps only a universe with this ratio of certain length can support life, e.g. when the universe becomes too large, there will be too much entropy in the universe for life?

let's wait and see if proton grows too to keep the equation!

Of course it grows. Accelerated growth even. How else would you explain that when walking out a window the earth grows to meet you?

Hurwitz's automorphisms theorem always astounds me. 84 is such a weird number to see in it. Fun fact: a group for which the maximum of 84(g-1) is reached is called a Hurwitz group. The Monster Group a Hurwitz group. So there is a Reimann surface of genus 9619255057077534236743570297163223297687552000000001 whose group of automorphisms (via orientation-preserving conformal mappings) is the Monster group. I don't even want to start trying to imagine that surface.

For more unlikely Monster Group fun, there's also http://en.wikipedia.org/wiki/Monstrous_moonshine.

http://en.wikipedia.org/wiki/Monster_group http://en.wikipedia.org/wiki/Hurwitz%27s_automorphisms_theor...

The Monster made me a Platonist. Group classification is damn alien stuff. It's like discovering Moby Dick except a million times larger and scarier, buried in the dark depths between science and philosophy.

> But why is this stuff the answer to the ultimate question of life, the universe, and everything? I’m not sure, but I have a crazy theory. Maybe all matter and forces are made of tiny little strings!

Come now, be serious!

Handy reminder: All natural numbers are interesting.

http://en.wikipedia.org/wiki/Interesting_number_paradox

This is where I point out that the answer was wrong.

In HHGTG, a massive computer was built to answer the Question. The computer spent millions of years calculating, and arrived at the answer "42". The problem, it said, was that the Question had never been formulated. The computer then designed another computer to calculate the Question. After millions of years of calculation, this computer was inadvertently destroyed. The last remnants of the computer were only able to provide the question "What is six times nine?"

Also, knowing the answer without knowing the question is Jeopardy!

The number on HN lately seems to be 300,000.

Fascinating read. He did say what the question was though: "What is six times nine?"

http://www.urbandictionary.com/define.php?term=6%20times%209...

But note that that isn't the "real" question, just the incorrect result of the Earth experiment.

Wow all these numbers put me into an endorphine rush, I love these kind of posts!! Keep them coming, it's no as theoretical as you may expect, it's applications are endless.

    42, (Endo-)Fullerenes, the Omega Particle.

Do you remember the Star-Trek series that was about the Omega Particle? Isn't it crazy that they were right?!

They actually exist. https://en.wikipedia.org/wiki/Fullerene https://www.youtube.com/watch?v=454uu96gFzU

Good stuff.

Also,

    The picture of Klein’s quartic curve was made by Greg Egan, and you should also check out his page on Klein’s quartic curve.

For anyone curious, Greg Egan writes interesting hard scifi. A particularly interesting and hardcore piece of scifi which rests on a significant pile of graph theory et al. is his novel "Schild's Ladder." [1] (one of these days, one of these days I am bound to attempt to finish it..)

[1] http://en.wikipedia.org/wiki/Schild%27s_Ladder

I read his novel Incandescence recently which was also really interesting. It's about a seemingly primitive civilization of non-humanoids who have to work out relativity quickly to avert disaster. I can't claim to follow it entirely but I enjoy his work nonetheless.

wow, that schild's latter book sounds very interesting. Is there any more similar kind of books like it (that deals with hardcore scifi themes)?

I'd ditto the question ;)

Semi-recent thread with some interesting-looking suggestions, not sure of 'hard' scifi label though: http://www.reddit.com/r/printSF/comments/1eyt3b/is_there_any...

I'd recommend other books by Greg Egan, though. Permutation City (http://en.wikipedia.org/wiki/Permutation_City) is particularly interesting and makes some very interesting conjectures dealing with computation, cognition, 'quantum ontology', etc. Character development is somewhat poor, but eh! (there's also a FAQ on the author's website: http://gregegan.customer.netspace.net.au/PERMUTATION/FAQ/FAQ...)

I'm not a math guy, but I was thinking about a number series the other day, and 42 popped up. Do the numbers 1,806; 3,263,442; and/or 10,650,056,950,806 happen to have any significance as well?

That sequence is called "Sylvester's sequence":

http://oeis.org/A000058

The Online Encyclopedia of Integer Sequences is one of the coolest things on the net.

Thanks! Interesting that mine's off by one...

The explanation that I liked the most was:

For-tea-two

Tea for two

I was never quite sure whether the number (42) or the decimal representation thereof (4*10 + 2) was relevant. Your interpretation would tend to the latter…

I believe I read this in The Salmon of Doubt, where Douglas Adams explained he pretty much chose it arbitrarily. "42 will do", were his words, IIRC.

I second that: I definitely remember reading something in which Douglas Adams explained that he chose 42 arbitrarily. And I think he was surprised at and amused with everyone’s theories of the significance of the number.

What if it turns out that 42 really is the answer? :)

Then "The Simpsons" would be right about the one true religion being a mix of an amazon tribe belief and Mormons... and we are all going to hell...

Is this guy a, genius?

Yes.

See http://en.wikipedia.org/wiki/John_C._Baez for some basic background. See http://math.ucr.edu/home/baez/ for more articles from him if you enjoyed this one.

One of my favorites is http://johncarlosbaez.wordpress.com/2012/12/27/our-galactic-... which describes our galactic neighborhood. Everyone knows that Alpha Centauri is our nearest star. But I bet you don't know a lot more about it. It is a much more complex place than I had realized.

Every number has special properties :)

Edit: In fact, I'd be astounded to encounter a number that did not exhibit any special properties. Until, of course, one makes "having no special properties" a special property. In that case, I would no longer be astounded.

We proceed by induction. Clearly n=1 is special, as it divides every integer. Assume k is special. If k+1 is not special, then it is special, as it is the first non-special number to come after a special number. This is a contradiction; then k+1 is special. ■

We may also proceed by ordinary semantics: every number is special, as it specifies itself.

Can you categorize the next non-special number in the same way? Now k+1 is no longer non-special, but the reason why it is special still exists, so you can't use it a second time.

I think it was meant to be in jest.

That was extremely enjoyable to read.

I can't find it on the net, but in Umberto Eco's 'Foucault's Pendulum' the final monologue by the wife illustrates that really well.

He's my favorite math popularizer these days. This article's a good sample of why.

He's a somewhat successful mathematician. Does that make him a genius?

No. But its fun to play with numbers. One of the reasons I like 12, its so dividable.

If you like 12, should definitely check out 60! It has so many factors, especially prime factors.

Probably my second favorite number after 12. And not surprisingly nearly the ideal "small" company size, as it tends to provide excellent team partitioning.

This article is making me hungry for mathematically perfect hyper donuts.

See the Strong Law of Small Numbers, of which 42 is one.

it's also the Jackie Robinson number

42 is the age after which women can not be expected (without the help of 21st century technology) to produce children.

And thus is exposed the meaning of the life the universe, and everything: "eat, stay alive, and produce more units that do the same". It is not your responsibility to decide what the meaning of life is, it is the universe's and physics responsibility to decide which loops are best at creating more eaters/stay-alivers/reproducers.

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