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I once had an idea for a file transfer system based on digits of pi that sounds the same as this idea. You'd give everybody DVDs of digits of pi (or they could

I once had an idea for a file transfer system based on digits of pi that sounds the same as this idea. You'd give everybody DVDs of digits of pi (or they could calculate them themselves) , and then transfer files faster by just sending them the offset into pi. At the time I thought it could work with a big enough bank of digits of PI on both sides. If transfer was expensive, and calculating digits was cheap then you could give everyone an infinite supply of digits of pi and have a nearly infinite compression system. I discovered that often the offset into pi is much larger than the data you are sending. Turns out it's an expensive way to sent things. Also, it turns out that this area was already well understood. There are no free lunches with entropy. But it was a fun idea to kick around.

troupe 3y ago
Glad to hear I'm not the only person who tried this. :)
alfanick 3y ago
It "exists" at https://github.com/philipl/pifs https://github.com/philipl/pifs
tzs 3y ago
Another potential problem with that approach is that it is possible that not all finite files appear in the digits of pi. It is believed that all appear but it hans't been proven.
deleted 3y ago
[deleted]
eternityforest 3y ago
Neural network encoding seems like the closest thing to that idea that's actually practical.
- thomasmg1985 3y ago
  Yes 100% true.
6510 3y ago
could just count in stead of pi, the offset would be the same number as the value at the offset.
amelius 3y ago
You first have to prove that pi contains all possible finite substrings, which I believe is still an open problem.
- scj 3y ago
  Neat. Although a flat memory space / full file approach would be nice, I wonder if a paging scheme would be possible? Where you would only need all possible finite strings of length N, where N would ideally be the max page size of RAM, but could be less if the substring could not be found within a reasonable offset... Ignoring compression speed, I suspect it'd have a practical limitation where using a maximum offset would mean that some strings wouldn't be as big as the cell needed to describe them. That's usually the gotcha in schemes like this... In order to entertain this, I think all possible 12 byte strings (64bit offset + 32bit size) would need to be found within whatever a reasonable amount of storage is. I suppose the computational challenge is "How big an offset is required to have all possible strings of length N?"

troupe 3y ago

Glad to hear I'm not the only person who tried this. :)

alfanick 3y ago

It "exists" at https://github.com/philipl/pifs https://github.com/philipl/pifs

tzs 3y ago

Another potential problem with that approach is that it is possible that not all finite files appear in the digits of pi. It is believed that all appear but it hans't been proven.

deleted 3y ago

[deleted]

eternityforest 3y ago

Neural network encoding seems like the closest thing to that idea that's actually practical.

thomasmg1985 3y ago
Yes 100% true.

6510 3y ago

could just count in stead of pi, the offset would be the same number as the value at the offset.

amelius 3y ago

You first have to prove that pi contains all possible finite substrings, which I believe is still an open problem.

scj 3y ago
Neat. Although a flat memory space / full file approach would be nice, I wonder if a paging scheme would be possible? Where you would only need all possible finite strings of length N, where N would ideally be the max page size of RAM, but could be less if the substring could not be found within a reasonable offset... Ignoring compression speed, I suspect it'd have a practical limitation where using a maximum offset would mean that some strings wouldn't be as big as the cell needed to describe them. That's usually the gotcha in schemes like this... In order to entertain this, I think all possible 12 byte strings (64bit offset + 32bit size) would need to be found within whatever a reasonable amount of storage is. I suppose the computational challenge is "How big an offset is required to have all possible strings of length N?"