4 ms·

I guess to one billionth, because nothing can be measured to billionth decimal place.

by lmilcin 8y ago

saagarjha 8y ago
Yeah, I’m sure that’s what they meant, but I still feel like it could have been worded better…
- deleted 8y ago
  [deleted]
- dhimes 8y ago
  Agree. Also, "billion" is ambiguous across countries. So, 10^{-9} would have been great (or is it 10^{-12}?).
  - Navarr 8y ago
    In which countries is 10^12 still billion? My immediate research only renders that it used to be this in British English
    - lagadu 8y ago
      Every non-English speaking one, in my very anecdotal and limited experience. I've never seen it used like that outside the US and sometimes UK. No offense meant but it's usually shown as an example of the "Americans can't count" stereotype: 1,000,000,000 is a thousand millions.
      - jerf 8y ago
        Both systems are broken. The British system is a bit more nominally consistent, but the names are poor; million and milliard are stupidly phonetically similar for what they are (generally we prefix those differences, probably because it's the ends of words that tend to get slurred, hence we have milli-meters and not meter-millis), and staggering the names out two chunks of 3 at a time doesn't really make much sense. It isn't very user-focused. The American naming system uses roots more clearly and doesn't have the weird pointless bundling together of two groups of 3, but it has a bizarre off-by-one issue... and not the usual 0->1 or 1->0 issue, but a 1->2 issue. For consistency, the order ought to be "ones, millions, billions, trillions, quadrillions", so that the prefix on the digit counter indicates the number of factors of 1000 in question, from zero, one, bi=two, tri=three, etc. However, "thousands" get stuck in there wrecking the whole thing up, so where the names say you have 1 group of 1000, you in fact have two, and so on. It's not an imperial vs. metric sort of thing, it's more an arguing which is the "real" temperature, Fahrenheit or Celsius, when in fact the answer is basically neither because the "real" temperature scale ought to have its 0 at absolute zero, like Kelvin [1] or the lesser-known Rankine [2], which is basically "Kelvin, except the degree is 1 degree Fahrenheit". These are both more "real" because now you can add and subtract temperatures meaningfully, which you can't do with either of Fahrenheit or Celsius. And likewise, neither number system is abstractly all that great. But then, that's part of why we have scientific notation. [1]: Which I just learned is about to be redefined, as of May 20th, 2019: https://en.wikipedia.org/wiki/Kelvin#2019_redefinition https://en.wikipedia.org/wiki/Kelvin#2019_redefinition [2]: https://en.wikipedia.org/wiki/Rankine_scale https://en.wikipedia.org/wiki/Rankine_scale
        afwaller 8y ago
        This "off by one" issue, combined with the problem of words related to latin "mille" for thousand in many languages, is why in money people often use K for units of "1,000", MM for units of "1,000,000", and B or sometimes BB for units of "1,000,000" (BB has no meaning as far as I'm aware, people just copy the style of MM). Unfortunately it is likely too late to really adopt the metric system for financial transactions. But the K has crept in for thousands.
        ajuc 8y ago
        What's wrong with the long scale? It's pretty consistent. Each name is the last times 1000, each new prefix is 1 000 000 times the previous one, and each -iliard is 1000 times -ilion with same prefix. milion = 10^6, miliard = 10^9 bilion = 10^12, biliard = 10^15 trylion = 10^18, tryliard = 10^21 kwadrylion = 10^24, kwadryliard = 10^27, ... Compared to that American way is just insane (as always). But I agree that writing 1.23 * 10^6 is preferable.
        jerf 8y ago
        To put what I said another way, it emphasizes the wrong things. Nobody cares how many collections of 6 digits something has. 3 digits are what people care about. (Except where they care about 4, or actually vary the number of digit groupings they care about depending on where they appear, but then, this debate has no meaning to them anyhow.) It's consistent, but it's consistent with something that doesn't match people's usage. Both systems are roughly equally broken, so either side mocking the other for their number system is a display of parochialism above and beyond the usual levels one would see.
        toast0 8y ago
        > Nobody cares how many collections of 6 digits something has. 3 digits are what people care about. I respectfully offer the Lakh [1] (1,00,000) and the Crore [2] (1,00,00,000) for other things people care about. :) [1] https://en.wikipedia.org/wiki/Lakh https://en.wikipedia.org/wiki/Lakh [2] https://en.wikipedia.org/wiki/Crore https://en.wikipedia.org/wiki/Crore
    - vbarrielle 8y ago
      In french "un billion" is 10^12.
    - kgwgk 8y ago
      In all the blue contries in this map: https://en.m.wikipedia.org/wiki/Long_and_short_scales#Current_usage https://en.m.wikipedia.org/wiki/Long_and_short_scales#Curren... “The traditional long scale is used by most Continental European countries and by most other countries whose languages derive from Continental Europe (with the notable exceptions of Albania, Greece, Romania, and Brazil).”
    - AegirLeet 8y ago
      German: Million (10⁶) Milliarde (10⁹) Billion (10¹²) Billiarde (10¹⁵) etc.
    - gnulinux 8y ago
      Most non-English languages borrow French word "Milliard" to say English "Billion". Some non-English languages use "Trillion" for English "Trillion" and some use "Billion" for English "Trillion".
    - csunbird 8y ago
      Very interestingly, In Turkey(Turkish) we use: 10^6 : Million 10^9 : Milliarde (instead of billion) 10^12 : Trillion 10^15 : Quadrillion
hnarn 8y ago
> nothing can be measured to billionth decimal place surely that depends on the unit of measurement :-)
- 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.

I guess to one billionth, because nothing can be measured to billionth decimal place.

saagarjha 8y ago

Yeah, I’m sure that’s what they meant, but I still feel like it could have been worded better…

deleted 8y ago
[deleted]
dhimes 8y ago
Agree. Also, "billion" is ambiguous across countries. So, 10^{-9} would have been great (or is it 10^{-12}?).
- Navarr 8y ago
  In which countries is 10^12 still billion? My immediate research only renders that it used to be this in British English
  - lagadu 8y ago
    Every non-English speaking one, in my very anecdotal and limited experience. I've never seen it used like that outside the US and sometimes UK. No offense meant but it's usually shown as an example of the "Americans can't count" stereotype: 1,000,000,000 is a thousand millions.
    - jerf 8y ago
      Both systems are broken. The British system is a bit more nominally consistent, but the names are poor; million and milliard are stupidly phonetically similar for what they are (generally we prefix those differences, probably because it's the ends of words that tend to get slurred, hence we have milli-meters and not meter-millis), and staggering the names out two chunks of 3 at a time doesn't really make much sense. It isn't very user-focused. The American naming system uses roots more clearly and doesn't have the weird pointless bundling together of two groups of 3, but it has a bizarre off-by-one issue... and not the usual 0->1 or 1->0 issue, but a 1->2 issue. For consistency, the order ought to be "ones, millions, billions, trillions, quadrillions", so that the prefix on the digit counter indicates the number of factors of 1000 in question, from zero, one, bi=two, tri=three, etc. However, "thousands" get stuck in there wrecking the whole thing up, so where the names say you have 1 group of 1000, you in fact have two, and so on. It's not an imperial vs. metric sort of thing, it's more an arguing which is the "real" temperature, Fahrenheit or Celsius, when in fact the answer is basically neither because the "real" temperature scale ought to have its 0 at absolute zero, like Kelvin [1] or the lesser-known Rankine [2], which is basically "Kelvin, except the degree is 1 degree Fahrenheit". These are both more "real" because now you can add and subtract temperatures meaningfully, which you can't do with either of Fahrenheit or Celsius. And likewise, neither number system is abstractly all that great. But then, that's part of why we have scientific notation. [1]: Which I just learned is about to be redefined, as of May 20th, 2019: https://en.wikipedia.org/wiki/Kelvin#2019_redefinition https://en.wikipedia.org/wiki/Kelvin#2019_redefinition [2]: https://en.wikipedia.org/wiki/Rankine_scale https://en.wikipedia.org/wiki/Rankine_scale
      - afwaller 8y ago
        This "off by one" issue, combined with the problem of words related to latin "mille" for thousand in many languages, is why in money people often use K for units of "1,000", MM for units of "1,000,000", and B or sometimes BB for units of "1,000,000" (BB has no meaning as far as I'm aware, people just copy the style of MM). Unfortunately it is likely too late to really adopt the metric system for financial transactions. But the K has crept in for thousands.
      - ajuc 8y ago
        What's wrong with the long scale? It's pretty consistent. Each name is the last times 1000, each new prefix is 1 000 000 times the previous one, and each -iliard is 1000 times -ilion with same prefix. milion = 10^6, miliard = 10^9 bilion = 10^12, biliard = 10^15 trylion = 10^18, tryliard = 10^21 kwadrylion = 10^24, kwadryliard = 10^27, ... Compared to that American way is just insane (as always). But I agree that writing 1.23 * 10^6 is preferable.
        jerf 8y ago
        To put what I said another way, it emphasizes the wrong things. Nobody cares how many collections of 6 digits something has. 3 digits are what people care about. (Except where they care about 4, or actually vary the number of digit groupings they care about depending on where they appear, but then, this debate has no meaning to them anyhow.) It's consistent, but it's consistent with something that doesn't match people's usage. Both systems are roughly equally broken, so either side mocking the other for their number system is a display of parochialism above and beyond the usual levels one would see.
        toast0 8y ago
        > Nobody cares how many collections of 6 digits something has. 3 digits are what people care about. I respectfully offer the Lakh [1] (1,00,000) and the Crore [2] (1,00,00,000) for other things people care about. :) [1] https://en.wikipedia.org/wiki/Lakh https://en.wikipedia.org/wiki/Lakh [2] https://en.wikipedia.org/wiki/Crore https://en.wikipedia.org/wiki/Crore
  - vbarrielle 8y ago
    In french "un billion" is 10^12.
  - kgwgk 8y ago
    In all the blue contries in this map: https://en.m.wikipedia.org/wiki/Long_and_short_scales#Current_usage https://en.m.wikipedia.org/wiki/Long_and_short_scales#Curren... “The traditional long scale is used by most Continental European countries and by most other countries whose languages derive from Continental Europe (with the notable exceptions of Albania, Greece, Romania, and Brazil).”
  - AegirLeet 8y ago
    German: Million (10⁶) Milliarde (10⁹) Billion (10¹²) Billiarde (10¹⁵) etc.
  - gnulinux 8y ago
    Most non-English languages borrow French word "Milliard" to say English "Billion". Some non-English languages use "Trillion" for English "Trillion" and some use "Billion" for English "Trillion".
  - csunbird 8y ago
    Very interestingly, In Turkey(Turkish) we use: 10^6 : Million 10^9 : Milliarde (instead of billion) 10^12 : Trillion 10^15 : Quadrillion

hnarn 8y ago

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

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.