Irrational numbers are an infinite source of information.
Irrational numbers are an infinite source of information.
They're probably the only things that "create" information in the sense that you can always grab another slice. Thank you delicious pi!
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Is it actually information? I can give you the number two, but it's not useful information until I also tell you which digit is significant and what the number means. Communicating information is still limited by the speed of light.
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From one of my favorite college professors: apparently in the Chevy Chase days of Saturday Night Live he would do the Weekend Update and had a recurring bit that went like this.
And now it's time for the basketball scores. 98-82; 102-99; 95-76.
That's data. Without context there's no useful information.
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Very nice! The Permittivity of Free Space is doing a handstand and would like a word with you.
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I don't see why not, it's just numbers, which is all we store most data as.
You could use it as a source of pseudorandom numbers to encrypt an infinite data steam, e.g. we'll encrypt using e, starting at position 40468.
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Randomness is the opposite of information.
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It is not. If I in July in Europe will say "there is no snow outside", I give you very little information. If in same conditions I will say "there is snow outside", I will give a lot of information.
Amount of information is proportional to (logarithm of) improbability of outcome.
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It's irrational, which just appears random (which is why I said pseudorandom).
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Situationally, yes. "I want the next digit of pi" is information in that sense of the word. It's not a particularly useful piece of information unless you're building something that requires a circle with a circumferential precision larger than the width of our entire universe.
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How many digits of Pi would you have to read for you to be able to reconstruct all of the information in the Universe up to this moment?
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None, because the digits of π have absolutely nothing to do with the universe.
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Is it actually information?
Yes. For every bit of number pi you get one bit of information.
I can give you the number two
You gave me log2(10) bits of information. Thanks.
but it's not useful information until I also tell you which digit is significant and what the number means.
You are misunderstanding what informatiob is.
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I can give you √2 which is 16-bits of information as characters. It's also an irrational number. How you express something doesn't change the amount of information is contained in the message.
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How you express something doesn't change the amount of information is contained in the message.
Welcome to the world of entropy coding.
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How you express something absolutely does change the amount of information in the message. That’s the foundation of compression.
Bitmap image files tend to be larger than png files, even when they both represent the same image.
1.41421… can be thought of as an expanded form of sqrt(2). In this case, the expansion is to an infinite number of digits.
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