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> nothing can be measured to billionth decimal place surely that depends on the unit of measurement :-)

by hnarn 8y ago

lmilcin 8y ago
No, actually it does not. Universe that we have does not have anything that would vary by more than couple dozen of orders of magnitude. Only about 10^247 of instructions could have been performed by a computer since beginning of our universe (if the entire universe was converted into a computer and it would do calculations in theoretically optimal way). The observable universe volume to planck volume ratio is only of the order of 10^185. 247, 185, that's still long way to 1000000000 orders of magnitude, whatever way to look at it. Even if you decide your unit of measurement of volume is the volume of entire observable universe then the planck volume, which is orders of magnitude less than any particle volume, is still just 10^-185. That is just 185 decimal places, far from billion decimal places. Or, in other words, if you like something more tangible: 0.00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 0000000000000000000000000000000001 This is 1 at 185th decimal place. If I did this for 1 billion decimal places the entire document would be gigabyte in size and you would spend a bit of time downloading and scrolling it, assuming HN would first allow me to upload it.
- repsilat 8y ago
  > Even if you decide your unit of measurement of volume is the volume of entire observable universe then the planck volume Sure, but if your unit of measurement is (for whatever reason) 10^billion times the observable universe that statement holds. I don't think any amount of pedantry will let us distinguish a billionth significant figure though.
- perl4ever 8y ago
  Suppose that you are considering a particular one of the possible permutations of planck volumes in the universe, of which there are about (10^185)!. According to Stirling's approximation, (10^185)! is more than 10^10^187, which makes a billion decimal places look very small indeed.
  - lmilcin 8y ago
    Well, you are just throwing random numbers. The topic is an article saying "Precision studies of antihydrogen atoms, for example, have shown that their characteristics are identical to hydrogen atoms to beyond the billionth decimal place." This suggest the "characteristic" is some kind of physical property that can be measured and compared.
    - perl4ever 8y ago
      Well, we all know that "the billionth decimal place" is an error. Nevertheless, my point was that far larger numbers can be related to physical things.

> nothing can be measured to billionth decimal place surely that depends on the unit of measurement :-)

by hnarn 8y ago

> nothing can be measured to billionth decimal place surely that depends on the unit of measurement :-)

No, actually it does not. Universe that we have does not have anything that would vary by more than couple dozen of orders of magnitude. Only about 10^247 of instructions could have been performed by a computer since beginning of our universe (if the entire universe was converted into a computer and it would do calculations in theoretically optimal way). The observable universe volume to planck volume ratio is only of the order of 10^185. 247, 185, that's still long way to 1000000000 orders of magnitude, whatever way to look at it. Even if you decide your unit of measurement of volume is the volume of entire observable universe then the planck volume, which is orders of magnitude less than any particle volume, is still just 10^-185. That is just 185 decimal places, far from billion decimal places. Or, in other words, if you like something more tangible: 0.00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 0000000000000000000000000000000001 This is 1 at 185th decimal place. If I did this for 1 billion decimal places the entire document would be gigabyte in size and you would spend a bit of time downloading and scrolling it, assuming HN would first allow me to upload it.

repsilat 8y ago
> Even if you decide your unit of measurement of volume is the volume of entire observable universe then the planck volume Sure, but if your unit of measurement is (for whatever reason) 10^billion times the observable universe that statement holds. I don't think any amount of pedantry will let us distinguish a billionth significant figure though.
perl4ever 8y ago
Suppose that you are considering a particular one of the possible permutations of planck volumes in the universe, of which there are about (10^185)!. According to Stirling's approximation, (10^185)! is more than 10^10^187, which makes a billion decimal places look very small indeed.
- lmilcin 8y ago
  Well, you are just throwing random numbers. The topic is an article saying "Precision studies of antihydrogen atoms, for example, have shown that their characteristics are identical to hydrogen atoms to beyond the billionth decimal place." This suggest the "characteristic" is some kind of physical property that can be measured and compared.
  - perl4ever 8y ago
    Well, we all know that "the billionth decimal place" is an error. Nevertheless, my point was that far larger numbers can be related to physical things.