7 ms·

> Or the machine language expression of the most advanced expert systems, though by then the notch might be small enough that Planck’s constant got in the way.

by magnat 8y ago

> Or the machine language expression of the most advanced expert systems, though by then the notch might be small enough that Planck’s constant got in the way. With Planck's length being roughly 10^-35m, I'd say you'd hit the limit trying to store more than 15 bytes.

hamilyon2 8y ago
This is insightful. 15 bytes is not a lot. I wonder what are other narural limits on information density? For example, magnetic field. Is there a least measurable difference?
- AmericanChopper 8y ago
  The limit on information density is called the Bekenstein Bound, the point after which adding more information to the volume would create a black hole. https://en.m.wikipedia.org/wiki/Bekenstein_bound https://en.m.wikipedia.org/wiki/Bekenstein_bound
Tepix 8y ago
Also depends on the length of the metal rod, doesn't it?
- OscarCunningham 8y ago
  The observable universe is 2^205.5 Planck lengths across, so you can store at most 205 bits, or 25 bytes.
  - soVeryTired 8y ago
    And at that length your latency gets reeeeeeal bad.
jtrip 8y ago
How are you calculating a value of simply 15 bytes? The proposal is that the mathematical value of the ratio of the lengths of rod and the notch will deliver a value on the number line, which in effect can be of any desired length. You actually could find a number that can represent the complete contemporary knowledge of Humanity. The limitations mentioned in the above comment relate to the fact that to know you'd arrived at the number designed into the Notch and the Rod, you'd have to have agreed to beforehand the tolerance limits on measurement of this 'device' so that the uncertainty in measurement can be ignored and the ratio derived. To maybe get the right number you would have to expand your possible number of ratios (at a certain measurement sensitivity you would have a certain number of lengths you could use, and thus certain number of ratios would be available to you) and to get just the right number to describe your whole "machine language expression of the most advanced expert systems" you would have to delve into tolerances of the Plank length. Or adjust the size of your rod length and notch, make them bigger, to get that sweet number with a 'poorer' level of sensitivity. .. Or find a number with enough usable number sequences to serve the purpose and program in the numbers surrounding gibberish as markers/jump points to the next sequence of usable numbers. I suppose you could find enough usable sequences in the full expression of pi (as it's rational expression is without end) to write a program that can decode the full linux kernel out of it.
- rcxdude 8y ago
  Assuming the length of the rod is 1m, and you have a resolution of one plank length, there are 10e35 possible ratios you can express (because that's the number of possible locations of the notch). that's about 2^113, which is a number which fits in 15 bytes of information. As discussed below, if you also allow for the bar to be the size of the observable universe, this doesn't increase by much. A notch or ratio is linear, information and combinatorics grows a lot lot faster than that.
  - jtrip 8y ago
    How would you say a rod to notch ratio of 22/7 compares? How much information would you say that has?
    - rcxdude 8y ago
      Meaningless on its own. What matters is how many distinct ratios are possible.
      - stevenhuang 8y ago
        > Meaningless on its own. That's the crux. What we're saying is that, of these set of ratios, there exists one whose infinite decimal representation contains our intended data. Yes we'd be limited to Planck length resolution, but the idea is that we would determine such a ratio and construct the notch and bar in such a way that it yields the decimal sequence desired; the # of particular ratios is not relevant. I wouldn't be surprised if it can be proven this can't be done, but then that would be proper question to ask.
- utopcell 8y ago
  you can loosely think of it as writing down a number in unary where each "digit" takes 1.6 x 10^-35 m space to draw.
  - jtrip 8y ago

by magnat 8y ago

hamilyon2 8y ago

This is insightful. 15 bytes is not a lot. I wonder what are other narural limits on information density? For example, magnetic field. Is there a least measurable difference?

AmericanChopper 8y ago
The limit on information density is called the Bekenstein Bound, the point after which adding more information to the volume would create a black hole. https://en.m.wikipedia.org/wiki/Bekenstein_bound https://en.m.wikipedia.org/wiki/Bekenstein_bound

Tepix 8y ago

Also depends on the length of the metal rod, doesn't it?

OscarCunningham 8y ago
The observable universe is 2^205.5 Planck lengths across, so you can store at most 205 bits, or 25 bytes.
- soVeryTired 8y ago
  And at that length your latency gets reeeeeeal bad.

jtrip 8y ago

How are you calculating a value of simply 15 bytes? The proposal is that the mathematical value of the ratio of the lengths of rod and the notch will deliver a value on the number line, which in effect can be of any desired length. You actually could find a number that can represent the complete contemporary knowledge of Humanity. The limitations mentioned in the above comment relate to the fact that to know you'd arrived at the number designed into the Notch and the Rod, you'd have to have agreed to beforehand the tolerance limits on measurement of this 'device' so that the uncertainty in measurement can be ignored and the ratio derived. To maybe get the right number you would have to expand your possible number of ratios (at a certain measurement sensitivity you would have a certain number of lengths you could use, and thus certain number of ratios would be available to you) and to get just the right number to describe your whole "machine language expression of the most advanced expert systems" you would have to delve into tolerances of the Plank length. Or adjust the size of your rod length and notch, make them bigger, to get that sweet number with a 'poorer' level of sensitivity. .. Or find a number with enough usable number sequences to serve the purpose and program in the numbers surrounding gibberish as markers/jump points to the next sequence of usable numbers. I suppose you could find enough usable sequences in the full expression of pi (as it's rational expression is without end) to write a program that can decode the full linux kernel out of it.

rcxdude 8y ago
Assuming the length of the rod is 1m, and you have a resolution of one plank length, there are 10e35 possible ratios you can express (because that's the number of possible locations of the notch). that's about 2^113, which is a number which fits in 15 bytes of information. As discussed below, if you also allow for the bar to be the size of the observable universe, this doesn't increase by much. A notch or ratio is linear, information and combinatorics grows a lot lot faster than that.
- jtrip 8y ago
  How would you say a rod to notch ratio of 22/7 compares? How much information would you say that has?
  - rcxdude 8y ago
    Meaningless on its own. What matters is how many distinct ratios are possible.
    - stevenhuang 8y ago
      > Meaningless on its own. That's the crux. What we're saying is that, of these set of ratios, there exists one whose infinite decimal representation contains our intended data. Yes we'd be limited to Planck length resolution, but the idea is that we would determine such a ratio and construct the notch and bar in such a way that it yields the decimal sequence desired; the # of particular ratios is not relevant. I wouldn't be surprised if it can be proven this can't be done, but then that would be proper question to ask.
utopcell 8y ago
you can loosely think of it as writing down a number in unary where each "digit" takes 1.6 x 10^-35 m space to draw.
- jtrip 8y ago