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HungryGuy's avatar

What are the chances that somewhere in the infinite string of digits of Pi there's a recognizable embedded graphic image?

Asked by HungryGuy (16008points) October 20th, 2011

Like, convert Pi from decimal to hex and treat it as if it was a BMP image. What if someone did that and it contained a recognizable image?

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14 Answers

Qingu's avatar


(I’m serious.)

Imadethisupwithnoforethought's avatar

I believe that there is a 100% chance that in an infinite string of numbers all of our avatars will appear at least once.

Now that I think about it, an infinite amount of times.

HungryGuy's avatar

Mmmmm, yes. I think you’re both correct.

Male's avatar

Wow…that’s crazy to think about. Thought never crossed my mind.

Qingu's avatar

Infinity is really weird.

It’s not for nothing that Georg Cantor spent the last years of his life in an insane asylum.

gasman's avatar

Agree w/ all of above. I recently touched on this issue answering another question.

Any specified finite pattern of digits (including those that encode images) will occur in the decimal expansion of every irrational number.

Mariah's avatar

I’ve heard this idea before! It’s fun to think about.

I’m pretty sure that irrational numbers all contain, at some point in their sequence, every possible combination of digits, so not only does it contain an image, it contains every image.

HungryGuy's avatar

And since it contains every image, it also contains every film ever produced. If the digits were converted to a MP3 audio track, you’ll also get every soundtrack for all those films. And if the digits are converted to ASCII text, you’ll get every story ever written.

Perhaps there’s plans for an interstellar starship in there…

Male's avatar

So what we’re seeing here is a sequence of infinite random digits (or at least until pi repeats- if ever), that ecompasses every single digital audio and visual that exists in the world today, is that right?

So we’re literally saying that every digital image, song, movie, visual, or any type of digital medium out there has its own code represented somewhere in pi’s numerical sequence?

For example, if I took a song and extracted the code for it, that exact code would be found somewhere in pi? Down to the very exact digit?

Has this actually been tested or is this all theory?

Sorry for the repetitive questions…my mind is blown at this very moment…

Imadethisupwithnoforethought's avatar

@Male they appear more than once, essentially infinite times

gasman's avatar

@Male We can prove mathematically that pi’s digits will never repeat, i.e., simply start over again with the preceding sequence. That would make it rational, and we know pi is irrational.

Yes, it’s mind-blowing to realize that every possible finite sequence will arise repeatedly, even ones that contain the total information content of the universe. Infinity is a long way…

Qingu's avatar

The implications of that for physics are interesting.

Because if we operate from the assumption that the universe is “infinite,” then it is not just possible but inevitable that there is some configuration of the universe’s matter that is just a brain floating in spaceā€”a brain that is at that moment hallucinating the entire reality that you, personally, believe you are experiencing.

At this given moment it is inevitable, in a hypothetical infinite universe, at some point, that there is a disembodied brain floating in empty space that thinks it’s you.

See Boltzmann brain.

gasman's avatar

Speaking of images in the digits of pi, the sci-fi novel Contact by Carl Sagan (his only work of fiction, on which the Jodie Foster movie was based) has a sort of last-page epilogue where a supercomputer, grinding away at pi, discovers a “message” hidden in the digits:

“The anomaly showed up most starkly in Base 11 arithmetic, where it could be written out entirely as zeros and ones…The program reassembled the digits into a square raster, an equal number across and down. The first line was an uninterrupted file of zeros, left to right. The second line showed a single numeral one, exactly in the middle, with zeros at the borders, left and right. After a few more lines, an unmistakable arc had formed, composed of ones. The simple geometrical figure had been quickly constructed, line by line, self-reflexive, rich with promise. The last line of the figure emerged, all zeros except for a single centered one. The subsequent line would be zeros only, part of the frame.

“Hiding in the alternating patterns of digits, deep inside the transcendental number, was a perfect circle, its form traced out by unities in a field of noughts.

“The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover a miracle—another circle, drawn kilometers downstream of the decimal point. There would be richer messages farther in…”

(c) 1985 by Carl Sagan, Simon & Schuster, New York*

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