4 ms·

327.55 K

by timack 6y ago

327.55 K

lopmotr 6y ago
Oh no, not this again! https://news.ycombinator.com/item?id=24118715 https://news.ycombinator.com/item?id=24118715 If the diameter of a coin is 19 mm, the circumference is not 59.6902604182 mm
- imtringued 6y ago
  I doubt your coin's diameter is exactly 19mm. By omitting digits after the decimal you are misleading people into believing that your number is more accurate than it really is. If you round 327.55 K to 328K and convert that back to Celsius you end up with 54.85°C instead of the original 54.4°C. Increasing inaccuracy by half a degree for the sake of inaccuracy is bad science.
  - progval 6y ago
    > By omitting digits after the decimal you are misleading people into believing that your number is more accurate than it really is. Digits omitted at the right mean we don't know them, not that they are zero. > and convert that back to Celsius you end up with 54.85°C instead of the original 54.4°C. Yes, inaccuracy accumulates when you convert back and forth. But it's common practice in physics not to increase the number of significant digits to not give the impression a measurement is more precise than it actually is. In this specific case: https://en.wikipedia.org/wiki/Significance_arithmetic#Multiplication_and_division_using_significance_arithmetic https://en.wikipedia.org/wiki/Significance_arithmetic#Multip... And when precision really matters, then one should explicit the range (eg. +/- after the absolute unit)
  - lopmotr 6y ago
    It wasn't 54.4°C though! The original value was only 130 °F which is probably between about 54.2 and 54.7 °C but somebody made it look more accurate during that first conversion which fooled you with the very thing you're saying is OK. You're bound to sometimes lose information doing round trip conversions no matter how many digits you have so don't do that if you care about keeping as much precision as possible. The Guardian reported it as 129.9 °F because they converted twice!
  - phaemon 6y ago
    > 328K and convert that back to Celsius you end up with 54.85°C No, that's wrong. If you convert 328K to Celsius, you get 55C. You can't add arbitrary precision to a number. The correct calculation for a whole degree is: 54C => (54 + 273)K => 327K If you want a single decimal place of precision: 54.4C => (54.4 + 273.2)K => 327.6K You can then subtract 273.2 to convert back, and you get the 54.4C you started with.
- hansvm 6y ago
  I find it a bit amusing that we treat as gospel the use of in-band signaling to try to cram a half-assed error propagation into the value we're trying to convey. It's not a terrible system, but there's nothing inherently better about throwing away a modest amount of information about both a value and its error than throwing away a negligible amount of information about a value and a majority of what we know about its error.
  - lopmotr 6y ago
    Yea it's not nature's way, just a convention. But it's an intuitive convention because it's easy to assume that digits which are shown are correct and digits which aren't shown are unknown. The alternative - throwing away the majority of information about the error would make lots of numbers pretty useless. Is 130 F really 100 F with too many digits?

327.55 K

by timack 6y ago

327.55 K

Oh no, not this again! https://news.ycombinator.com/item?id=24118715 https://news.ycombinator.com/item?id=24118715 If the diameter of a coin is 19 mm, the circumference is not 59.6902604182 mm

imtringued 6y ago
I doubt your coin's diameter is exactly 19mm. By omitting digits after the decimal you are misleading people into believing that your number is more accurate than it really is. If you round 327.55 K to 328K and convert that back to Celsius you end up with 54.85°C instead of the original 54.4°C. Increasing inaccuracy by half a degree for the sake of inaccuracy is bad science.
- progval 6y ago
  > By omitting digits after the decimal you are misleading people into believing that your number is more accurate than it really is. Digits omitted at the right mean we don't know them, not that they are zero. > and convert that back to Celsius you end up with 54.85°C instead of the original 54.4°C. Yes, inaccuracy accumulates when you convert back and forth. But it's common practice in physics not to increase the number of significant digits to not give the impression a measurement is more precise than it actually is. In this specific case: https://en.wikipedia.org/wiki/Significance_arithmetic#Multiplication_and_division_using_significance_arithmetic https://en.wikipedia.org/wiki/Significance_arithmetic#Multip... And when precision really matters, then one should explicit the range (eg. +/- after the absolute unit)
- lopmotr 6y ago
  It wasn't 54.4°C though! The original value was only 130 °F which is probably between about 54.2 and 54.7 °C but somebody made it look more accurate during that first conversion which fooled you with the very thing you're saying is OK. You're bound to sometimes lose information doing round trip conversions no matter how many digits you have so don't do that if you care about keeping as much precision as possible. The Guardian reported it as 129.9 °F because they converted twice!
- phaemon 6y ago
  > 328K and convert that back to Celsius you end up with 54.85°C No, that's wrong. If you convert 328K to Celsius, you get 55C. You can't add arbitrary precision to a number. The correct calculation for a whole degree is: 54C => (54 + 273)K => 327K If you want a single decimal place of precision: 54.4C => (54.4 + 273.2)K => 327.6K You can then subtract 273.2 to convert back, and you get the 54.4C you started with.
hansvm 6y ago
I find it a bit amusing that we treat as gospel the use of in-band signaling to try to cram a half-assed error propagation into the value we're trying to convey. It's not a terrible system, but there's nothing inherently better about throwing away a modest amount of information about both a value and its error than throwing away a negligible amount of information about a value and a majority of what we know about its error.
- lopmotr 6y ago
  Yea it's not nature's way, just a convention. But it's an intuitive convention because it's easy to assume that digits which are shown are correct and digits which aren't shown are unknown. The alternative - throwing away the majority of information about the error would make lots of numbers pretty useless. Is 130 F really 100 F with too many digits?