4 ms·

Maybe I'm wrong, but it doesn't seem hard to argue that 10 is the base in scientific notation purely for the efficiency of reading that humans have with our com

by taeric 3y ago

Maybe I'm wrong, but it doesn't seem hard to argue that 10 is the base in scientific notation purely for the efficiency of reading that humans have with our common numbers. No reason we couldn't have learned hex with 16 as the base exponent, after all? Indeed, for imperial units, this would have made a ton of sense? 1/16th of an inch would directly be .1 (1*16^-1), after all. Would be better if we used 16 symbols for counting, of course, such that we didn't mix decimal in that notation. This, sadly, quickly devolves into debates about metric versus imperial. :(

masklinn 3y ago
> Indeed, for imperial units, this would have made a ton of sense? No. The number of ratios to 16 units is 2 to a few dozens. You have 12in to a foot, 3 ft to a yard, 1760 yd to a mile (because 80 chains or 22 yards). A nautical mile is 10 cables, of 100 fathoms each. 640 acres to a square mile. 20 fl oz to a pint, 2 pt to a quart, 4 qt to a gallon (8 pt to a gal, 160 oz to a gal). There's 16 drachm to an ounce and 16 oz to a pound. Sadly there's then 14 pounds to a stone, 8 st to a hundredweight unless you have abandoned stones and have 100-lb hundredweight because customary units are dumb, which then gives you a different ton of 20 cwt depending on, well, your cwt. > 1/16th of an inch would directly be .1 (1*16^-1), after all. Shame that would be useful for just about nothing else. > This, sadly, quickly devolves into debates about metric versus imperial. :( I wonder why...
- taeric 3y ago
  Marking a measuring stick out to 32nds is relatively easy to do. Marking it down to tenths or hundredths is surprisingly hard. Is why I picked that example, and nothing more. That said, arbitrary numbers are arbitrary was ultimately my point. "base 10" is very inconvenient for the old imperial units, so we moved heavily to metric. And that ultimately makes sense, especially with the path dependence on how we got there. Converting between units is something folks don't like doing, so we moved a long way to turning conversions into radix shifts. Even if the old units each had individual advantages at different scales. (Consider, nautical miles are still the de facto unit in shipping, no?) It is beyond amusing how base 10 does not work for computers that well, such that 2k of data is typically not 2000. :D Edit: I am curious on what the argument for 10 is in scientific notation that isn't path dependent on us using decimal? Or are folks just reading a criticism of metric in my post? (Because I can easily throw in more criticisms of imperial, if that helps. :D )
  - masklinn 3y ago
    > Marking a measuring stick out to 32nds is relatively easy to do. The measuring stick follows the numeral system, not the other way around. And while base 2 has had some historical success, it wasn't much compared to 10, 20, 60, or 12. > Marking it down to tenths or hundredths is surprisingly hard. There's decimal rulers from the indus valley civilisation, it clearly was not sufficiently hard. > Is why I picked that example, and nothing more. From what you're saying you apparently pick that example every time and it goes wrong every time, for completely obvious reasons. Maybe you should consider changing example? > I am curious on what the argument for 10 is in scientific notation that isn't path dependent on us using decimal? Why would there be? We use base 10 numerals, our notation is base 10, therefore a convenient, natural, and uniform system of units would be in base 10. Base 2 is of little help outside of length, and it's hardly critical there either. > Or are folks just reading a criticism of metric in my post? Well yes, 2 out of 3 paragraphs are about imperial and metric and your comment is at best tangential to the one it replies to.
    - taeric 3y ago
      I mean... no? The number system we used is clearly path dependent on the ways that we measured things. Moving measured things to a single number is precisely why metric works so well. And is why many people in the world know their height not as a single number, but as a combination of two units. This seems the case for all measurements. Used to, you wouldn't necessarily combine two units that often. Evidence of the indus valley seems an odd choice? The images I'm finding online about them did exactly as I said, subdivide by half until happy with precision. Indeed, their "lower units of measure" were binary?
  - benj111 3y ago
    >Marking a measuring stick out to 32nds is relatively easy to do Is it? I suppose if that stick is going to be the standard you could get a rope of the same length and fold it in half enough times. Of course you could always make a shorter stick the standard and then find a measuring stick >= 10 times longer and add marks to the longer stick...
nyrikki 3y ago
The Babylonians used a sexagesimal (base 60), and the Egyptians used a duo-decimal (base 12) Because you can trivially count to twelve on one hand. 12 joints times 4 fingers getting you to 69. One The first few colossally abundant numbers: 2, 6, 12, 60, 120, 360 would have been ideal, with 12 most practical in hindsight. But in the golden age of India, decimal math is what they were working on and as they produced some important advancements to mathematics it won out except in areas where abundance matters like degrees, minutes, seconds. IBM 360s supported radix 16, but radix 10, due to decimalized standards was more popular. IEEE 754 has supported decimal floats for decades now, but as it required 4 bits, it wasn't implemented on microcomputers. Deterministic errors with less wafer space fit most needs.
- taeric 3y ago
  Apologies for not responding on this. I felt this was furthering my point on the path dependence of our "scientific notation" being based on a base 10 system. Were you intending this differently? I am curious what the "4 bits" you are referencing? Seems a small number of bits, even for the time. (This is not to be confused with the 4 bit per digit of BCD, which adds up per digit encoded such that you get a lot of waste rather rapidly. Or, do I have that wrong, as well?)

by taeric 3y ago

masklinn 3y ago

> Indeed, for imperial units, this would have made a ton of sense? No. The number of ratios to 16 units is 2 to a few dozens. You have 12in to a foot, 3 ft to a yard, 1760 yd to a mile (because 80 chains or 22 yards). A nautical mile is 10 cables, of 100 fathoms each. 640 acres to a square mile. 20 fl oz to a pint, 2 pt to a quart, 4 qt to a gallon (8 pt to a gal, 160 oz to a gal). There's 16 drachm to an ounce and 16 oz to a pound. Sadly there's then 14 pounds to a stone, 8 st to a hundredweight unless you have abandoned stones and have 100-lb hundredweight because customary units are dumb, which then gives you a different ton of 20 cwt depending on, well, your cwt. > 1/16th of an inch would directly be .1 (1*16^-1), after all. Shame that would be useful for just about nothing else. > This, sadly, quickly devolves into debates about metric versus imperial. :( I wonder why...

taeric 3y ago
Marking a measuring stick out to 32nds is relatively easy to do. Marking it down to tenths or hundredths is surprisingly hard. Is why I picked that example, and nothing more. That said, arbitrary numbers are arbitrary was ultimately my point. "base 10" is very inconvenient for the old imperial units, so we moved heavily to metric. And that ultimately makes sense, especially with the path dependence on how we got there. Converting between units is something folks don't like doing, so we moved a long way to turning conversions into radix shifts. Even if the old units each had individual advantages at different scales. (Consider, nautical miles are still the de facto unit in shipping, no?) It is beyond amusing how base 10 does not work for computers that well, such that 2k of data is typically not 2000. :D Edit: I am curious on what the argument for 10 is in scientific notation that isn't path dependent on us using decimal? Or are folks just reading a criticism of metric in my post? (Because I can easily throw in more criticisms of imperial, if that helps. :D )
- masklinn 3y ago
  > Marking a measuring stick out to 32nds is relatively easy to do. The measuring stick follows the numeral system, not the other way around. And while base 2 has had some historical success, it wasn't much compared to 10, 20, 60, or 12. > Marking it down to tenths or hundredths is surprisingly hard. There's decimal rulers from the indus valley civilisation, it clearly was not sufficiently hard. > Is why I picked that example, and nothing more. From what you're saying you apparently pick that example every time and it goes wrong every time, for completely obvious reasons. Maybe you should consider changing example? > I am curious on what the argument for 10 is in scientific notation that isn't path dependent on us using decimal? Why would there be? We use base 10 numerals, our notation is base 10, therefore a convenient, natural, and uniform system of units would be in base 10. Base 2 is of little help outside of length, and it's hardly critical there either. > Or are folks just reading a criticism of metric in my post? Well yes, 2 out of 3 paragraphs are about imperial and metric and your comment is at best tangential to the one it replies to.
  - taeric 3y ago
    I mean... no? The number system we used is clearly path dependent on the ways that we measured things. Moving measured things to a single number is precisely why metric works so well. And is why many people in the world know their height not as a single number, but as a combination of two units. This seems the case for all measurements. Used to, you wouldn't necessarily combine two units that often. Evidence of the indus valley seems an odd choice? The images I'm finding online about them did exactly as I said, subdivide by half until happy with precision. Indeed, their "lower units of measure" were binary?
- benj111 3y ago
  >Marking a measuring stick out to 32nds is relatively easy to do Is it? I suppose if that stick is going to be the standard you could get a rope of the same length and fold it in half enough times. Of course you could always make a shorter stick the standard and then find a measuring stick >= 10 times longer and add marks to the longer stick...

nyrikki 3y ago

The Babylonians used a sexagesimal (base 60), and the Egyptians used a duo-decimal (base 12) Because you can trivially count to twelve on one hand. 12 joints times 4 fingers getting you to 69. One The first few colossally abundant numbers: 2, 6, 12, 60, 120, 360 would have been ideal, with 12 most practical in hindsight. But in the golden age of India, decimal math is what they were working on and as they produced some important advancements to mathematics it won out except in areas where abundance matters like degrees, minutes, seconds. IBM 360s supported radix 16, but radix 10, due to decimalized standards was more popular. IEEE 754 has supported decimal floats for decades now, but as it required 4 bits, it wasn't implemented on microcomputers. Deterministic errors with less wafer space fit most needs.

taeric 3y ago
Apologies for not responding on this. I felt this was furthering my point on the path dependence of our "scientific notation" being based on a base 10 system. Were you intending this differently? I am curious what the "4 bits" you are referencing? Seems a small number of bits, even for the time. (This is not to be confused with the 4 bit per digit of BCD, which adds up per digit encoded such that you get a lot of waste rather rapidly. Or, do I have that wrong, as well?)