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Images Created from Prime Numbers

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Re: Images Created from Prime Numbers

#31

Post by Nition »

Causality1 wrote: post #20

Reminds me of a thought I had a while back that given sufficient computational power you could describe any dataset using only two place values in an irrational number and an interpretation rule. For example, the complete data for an h265 copy of Avengers Endgame exists somewhere in the digital expression of the value of Pi. It might be googleplexes of digits deep, but it's there somewhere.

The problem is that the index itself becomes so large, even you use a dataset-optimised number instead of pi, that it's much worse than just storing the original data.

Re: Images Created from Prime Numbers

#34

Post by oefrha »

war1025 wrote: post #28

Semi-related, but reading this article and thinking about it made me wonder if there is any study at all of "gray code" primes, for lack of a better word. Basically, prime numbers that differ by exactly one binary digit in their representation. Probably nothing about that relationship that would be interesting enough to look into beyond just "I ran some calculations and found these numbers that fit the pattern"

This is just a weaker version of the twin prime conjecture. You’re asking for primes that differ by 2^k instead of 2. Last I heard the best result was from Polymath 8a.

http://michaelnielsen.org/polymath1/index.php?title=Bounded_...

Edit: Actually I was wrong, differing by a binary digit is much stronger than a difference of 2^k. But that’s a starting point.

Re: Images Created from Prime Numbers

#36

Post by war1025 »

oefrha wrote: post #34
war1025 wrote: post #28

Semi-related, but reading this article and thinking about it made me wonder if there is any study at all of "gray code" primes, for lack of a better word. Basically, prime numbers that differ by exactly one binary digit in their representation. Probably nothing about that relationship that would be interesting enough to look into beyond just "I ran some calculations and found these numbers that fit the pattern"

This is just a weaker version of the twin prime conjecture. You’re asking for primes that differ by 2^k instead of 2. Last I heard the best result was from Polymath 8a. http://michaelnielsen.org/polymath1/index.php?title=Bounded_... Edit: Actually I was wrong, differing by a binary digit is much stronger than a difference of 2^k. But that’s a starting point.

Neat. Thanks for tying it in to something real. Makes sense now that you phrase it that way. Not something I've ever looked into much.

Re: Images Created from Prime Numbers

#37

Post by oefrha »

war1025 wrote: post #36
oefrha wrote: post #34

Earlier quoted context omitted.

This is just a weaker version of the twin prime conjecture. You’re asking for primes that differ by 2^k instead of 2. Last I heard the best result was from Polymath 8a. http://michaelnielsen.org/polymath1/index.php?title=Bounded_... Edit: Actually I was wrong, differing by a binary digit is much stronger than a difference of 2^k. But that’s a starting point.

Neat. Thanks for tying it in to something real. Makes sense now that you phrase it that way. Not something I've ever looked into much.

Actually I replied without thinking too much, sorry... Your question is (probably a fair bit) stronger than the one I related to. Edited.

Re: Images Created from Prime Numbers

#38

Post by mc3 »

lonelappde wrote: post #23

This is yet another case where "prime" is bolted onto something for no particular reason to make it superficially more interesting. IMO this confused mathematical understanding. Approximately 1/n of all n-bit pieces of data (including bimaps) are prime.

It's like a magic trick. Amazing at first, then you sort of realize how they did it.

Re: Images Created from Prime Numbers

#39

Post by mc3 »

kvakil wrote: post #26
MontyCarloHall wrote: post #25

Earlier quoted context omitted.

Only if that irrational number is also normal ( https://en.wikipedia.org/wiki/Normal_number ), which pi has not been proven to be.

In addition, even if a normal number was used, it's far simpler to describe the data by just using a single number alone. For example, a binary encoding of the data (perhaps using a prefix-free code). Using a normal number and two "positions" is just more complicated.

Nonetheless, it's freaky that our deepest secrets are encoded into pi. If pi is normal.

Re: Images Created from Prime Numbers

#40

Post by yesenadam »

lonelappde wrote: post #24
snowwrestler wrote: post #18

There’s a great scene in the end of the book “Contact” by Carl Sagan where the main character uses super powerful computers to find a raster image of a circle hidden deep in the digits of pi. This is supposed to be a moment of deep spiritual significance. But in fact, it’s basically an expected outcome given what we think we know about pi. At first glance these images were startling to me; that such recognizable imag…

Not quite true. Sagan's version was better than that analysis suggests: http://kasmana.people.cofc.edu/MATHFICT/mf55-spoiler.html > as Sagan puts it in the story itself, the surprise is not that it appears that it appears "so early" in the sequence.

It seems there was a large (unconscious?) religious dimension to SETI. Michael Shermer:

[David Swift in his 1990 book SETI Pioneers] asked each of the SETI pioneers about their parents’ religiosity... most were raised in a religious household but that not one believes in anything like the traditional Judeo-Christian God... Astronomer Frank Drake, ostensively the SETI pioneer if there was one (and creator of the infamous “Drake equation” for computing the probability of ETIs), who was raised “Very strong Baptist. Sunday school every Sunday,” made this observation: “A strong influence on me, and I think on a lot of SETI people, was the extensive exposure to fundamentalist religion. You find when you talk to people who have been active in SETI that there seems to be that thread. They were either exposed or bombarded with fundamentalist religion. So to some extent it is a reaction to firm religious upbringing”. Similarly, John Kraus recalled: “We were very strong churchgoers, members of the Methodist church. I was brought up in a very religious atmosphere…there was never any thought of conflict between science and religion in my thinking or in my upbringing. Science and religion were simply both seeking ultimate truth but using different ways of going at it”. ...

... One might speculate that SETI, as a highbrow, elitist revolution, contains within it quasi-religious and spiritual overtones, in the sense that these scientists, while not believing in God, do believe in ETIs, uniformly portrayed as higher intelligences who, having survived what might be a tendency in species toward self-destruction once advanced technologies are created, must also be morally superior. To the extent that religion involves belief in and hope for transcendence or transcendent beings, SETI is a high-cultural form of religion, and UFOs a low-cultural form of religion.

The Measure Of A Life: Carl Sagan and the Science of Biography http://www.theeway.com/skepticc/newsworthy06.html

P.S. I was very much a child of Sagan and SETI! I was 15 when Cosmos aired, and read every Sagan book I could get my hands on, got a large telescope, became obsessed with astronomy for years... Reading about this religious dimension years later surprised me, it had never occurred to me. (My family was atheist)

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