If the digits of pi really are random (or at least patternless, see The digits of pi are not random.) then every finite sequence of digits must be in there somewhere (Or to put it a little more precisely, the probability that any given sequence isn't in the first N digits tends to 0 as N tends to infinity), so all you have to do is code up the above phrase into a string of digits by whatever means you like, then hunt through pi until you find it.

It's mildly entertaining to estimate how far you have to look: say we use a nice simple coding where we assign 2 digits to each character, so A=01, B=02, etc, and SPACE=27 (plus whatever other punctuation you like). Then for a phrase of n characters, we need a 2n string of digits. The chance that any digit in pi matches the one you want is 1/10, so the chance that your string occurs at a given point is 1/(10^2n). So you probably need to look at 10^2n digits of pi before you find your phrase.

So to find 'God is mathematics' you probably need to look at the first 10^36 digits of pi.

For 'To be or not to be', it's also 10^36. To find the complete works of Shakespeare it's unimaginably huge, but they will be in there somewhere (though the infinite number of monkeys might get there before pi does).

For 'Pi', it's just 10000 digits, so a place where it occurs has probably already been calculated.

Does any of this have any meaning? .1415

Okay if you care about mathematical accuracy please ignore the comments about probability in this node and read ariels nodes instead. I'm leaving them in because they show what I mean and this isn't meant to be a factual node anyway.

At http://www.angelfire.com/mt/ofolives/pisearch.html you can search the first 1,500,000 decimal digits of Pi, converted into base 27 and assigned to the letters A through Z (no space, though). The string 'GODISMATHEMATICS' does not appear in the first million digits of Pi-base-27, but 'GOD' appears 46 times, the first time at position 29639.

You can also find numeric strings of digits in the first 50 million decimal places of Pi at http://www.angio.net/pi/piquery

Mike Keith found God in the decimals of pi. If you print the base-26 digits of pi in rows of 14061 characters, and you will see God, the Alpha and the Omega around position 148655:

u r r n d a c i v r g c w n p e u b
w f p r z c v k m m p u d p w g l y
v y u q s v b m u y s n v m r k l i
z a k x u g v s e d h m p l l x l d
g n j d u v m x w e s y i e g q i z
f q o p q t k u s j s r z o k v v d
k e n z k a y j n d c f t s r n b r
s m i z d h p s i r d u f u w f o i
p u f r e c n l f f z f o q l h b j
c h n y e a h O M E G A r d r x k p
w a e a i p l d f l o a H p i u s q
o n i q e n z b r i n d t P v k z h
e q g p l s c r v a s g j s L j l v
p i e x s z t t z y v j k p u A l s
y g n q q e j l e l v k v w o o h m
D r q f n g x k b r p i v e x m f f
O y e q h z a x v b q r t p k r s c
G a k z d h s j j o q x f m b h e i

Or maybe it's not a dog and not a god.

From Mike Keith, http://users.aol.com/s6sj7gt/picode.htm.
Again, what people here are asking is "is pi normal?". That's the only way that makes sense.

hamandpineapple says:

Or to put it a little more precisely, the probability that any given sequence isn't in the first N digits tends to as N tends to infinity
[my links], which is not the question at all. After all, the digits of π are a fixed string. Suppose I ask "do 20 consecutive 7's appear in the first 1019 digits of the decimal expansion of π?" I don't know the answer to this question. But since there is no randomness involved, the probability of 20 consecutive 7's appearing in the first 1019 digits of the decimal expansion of π is either 1 (if the answer to the question is "yes") or 0 (if it's "no").

It's best to make the question precise. Either ask if pi is a normal number or ask if every finite sequence of digits appears in the expansion of pi. And the answer to both questions (an affirmative answer to the first would imply an affirmative answer to the second) is unknown.

If it were possible to prove that π is normal, 'God is Mathematics' would certainly appear somewhere in the digits of pi in both base 27 (any case plus space) and base 53 (case sensitive plus space).

This is also true for the phrases 'Mathematics is just plain stupid', 'Mathematics my arse', 'God is in my arse' and 'Jesus that feels good'.

In fact we would without doubt be able to find in π a sequence of digits in any base, convert them to a binary string and, when sent via gzip to a web browser, they would present users with web site full of annoying flashing pop-ups showing actual photographs of God in my arse, complete with lense flare and bodily fluids.

I must remember to check that out sometime...

2005 update: - modern pop-up blockers and firefox or safari may prvent the pop-ups, but the rest of the gzip argument holds true......
...to those who are offended on religious grounds, have you ever thought that text isn't true? Maybe the written 'Jesus' and the thought can be separated....... to the betterment of us all huh???

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