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0 degrees celsius + 0 degrees celsius -

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Re: 0 degrees celsius + 0 degrees celsius -

#51

Post by jcdreads »

mhansen wrote: post #9

It's meaningless to add temperatures when the zero level is at +273. It's like adding years relative to 2010 years ago - it would be meaningless to add this year - 2010 - with (say) 1666 - the year of the Great Fire of London. It's meaningful to take differences (the Great Fire happened 344 years ago), but not to add. (Unless we converted to some kind of absolute time units e.g. years since the big bang) I'd say what…

It's meaningless to add temperatures in any circumstance. You can average temperatures, and you can add amounts of heat energy, but it is semantic garbage to try to add temperatures.

I'd say what it's doing--converting to an absolute scale then adding--is an interesting bug.

Re: 0 degrees celsius + 0 degrees celsius -

#52

Post by viraptor »

serichsen wrote: post #42
antileet wrote: post #27

Earlier quoted context omitted.

Seems it is easy enough to confuse even Wolfram Alpha http://www.wolframalpha.com/input/?i=0+degrees+kelvin+%2B+0+... Funnily enough the original query is handled well[1] by W|A: http://www.wolframalpha.com/input/?i=0+degrees+celsius+%2B+0... And the query that fails in Wolfram Alpha, works fine in Google's Calculator: http://www.google.com/search?sourceid=chrome&ie=UTF-8&#3... :) 1: By "well", we probably mean accor…

Actually, Wolfram Alpha is doing a sensible thing in each case: it is not adding the temperatures, it is comparing them, resp. calculating the difference, when you give different scales. You can see that in the output, where it says "difference". The confusion is all on your side.

I'm not sure about the confusion... the question to W|A is not well-defined, but lets say someone asks you "2 + 4?" and you answer "the difference is 2". Does it make any sense? Not to me.

Re: 0 degrees celsius + 0 degrees celsius -

#53

Post by omaranto »

_delirium wrote: post #7

It looks like it must be using kelvin as its canonical units: 0C + 0C = 273.15 K + 273.15 K = 546.3 K = 273.15 C The weirdness is that conversions like that don't work for units that have different zero points. Perhaps addition of temperatures isn't really well defined? If 273.15 K + 273.15 K does not equal 0 C + 0 C, despite 273.15 K = 0 C, it's not clear what addition "means" in this context. One restricted form of…

You're absolutely right that two different things are measured in degrees: temperatures and temperature differences. And they work as you said: you can add temperatures differences, you can add a temperature difference to a temperature, but you can't add two temperatures. (This is like pointers and ints in C.) Mathematically temperature differences form a group under addition and temperatures (idealized to have no minimum temperature) form a torsor for the group. A good introduction to torsors is John Baez's Torsors made easy: http://math.ucr.edu/home/baez/torsors.html

Re: 0 degrees celsius + 0 degrees celsius -

#54

Post by Retric »

nkassis wrote: post #33
antileet wrote: post #27

Earlier quoted context omitted.

Seems it is easy enough to confuse even Wolfram Alpha http://www.wolframalpha.com/input/?i=0+degrees+kelvin+%2B+0+... Funnily enough the original query is handled well[1] by W|A: http://www.wolframalpha.com/input/?i=0+degrees+celsius+%2B+0... And the query that fails in Wolfram Alpha, works fine in Google's Calculator: http://www.google.com/search?sourceid=chrome&ie=UTF-8&#3... :) 1: By "well", we probably mean accor…

That last one is odd. Should it not convert them first on the same base first? But then which on should it convert to? If you go for 0 celsius to 273.15 K then you'd get 0 K + 0 C = 273.15K if you do the other way you get -273.15 C. Whoa now I have a new tool to explain that A B is not always = B A to friend ;)

No, swapping them gives the same value.

http://www.google.com/search?hl=en&q=0+degrees+celsius+%...

Google always convert temperatures to Kelvin for this stuff.

http://www.google.com/search?hl=en&q=0+degrees+celsius++...

The assumption is if your doing math with temperature you are using it in a physics context.

Re: 0 degrees celsius + 0 degrees celsius -

#55

Post by dhimes »

viraptor wrote: post #52
serichsen wrote: post #42

Earlier quoted context omitted.

Actually, Wolfram Alpha is doing a sensible thing in each case: it is not adding the temperatures, it is comparing them, resp. calculating the difference, when you give different scales. You can see that in the output, where it says "difference". The confusion is all on your side.

I'm not sure about the confusion... the question to W|A is not well-defined, but lets say someone asks you "2 + 4?" and you answer "the difference is 2". Does it make any sense? Not to me.

The + operator is overloaded. You interpret it automatically as addition; the SE read it as "search (or: tell me about) 2 and 4."

Re: 0 degrees celsius + 0 degrees celsius -

#56

Post by cabalamat »

_delirium wrote: post #7

It looks like it must be using kelvin as its canonical units: 0C + 0C = 273.15 K + 273.15 K = 546.3 K = 273.15 C The weirdness is that conversions like that don't work for units that have different zero points. Perhaps addition of temperatures isn't really well defined? If 273.15 K + 273.15 K does not equal 0 C + 0 C, despite 273.15 K = 0 C, it's not clear what addition "means" in this context. One restricted form of…

> The problem is that "degrees C" is overloaded here, to mean both a position on a scale, and the size of a unit on that scale

I understood that Celsius always referred to the position on the scale, and the unit was always Kelvin. At least, that's how I use the terms.

Re: 0 degrees celsius + 0 degrees celsius -

#57

Post by serichsen »

viraptor wrote: post #52
serichsen wrote: post #42

Earlier quoted context omitted.

Actually, Wolfram Alpha is doing a sensible thing in each case: it is not adding the temperatures, it is comparing them, resp. calculating the difference, when you give different scales. You can see that in the output, where it says "difference". The confusion is all on your side.

I'm not sure about the confusion... the question to W|A is not well-defined, but lets say someone asks you "2 + 4?" and you answer "the difference is 2". Does it make any sense? Not to me.

What if someone writes you the question "what is 12, Park Avenue + 34, Park Avenue?" Wouldn't you assume that this cannot be about addition, and instead tell him who lives in those two places and perhaps the walking distance?

Re: 0 degrees celsius + 0 degrees celsius -

#58

Post by alextgordon »

jcdreads wrote: post #51
mhansen wrote: post #9

It's meaningless to add temperatures when the zero level is at +273. It's like adding years relative to 2010 years ago - it would be meaningless to add this year - 2010 - with (say) 1666 - the year of the Great Fire of London. It's meaningful to take differences (the Great Fire happened 344 years ago), but not to add. (Unless we converted to some kind of absolute time units e.g. years since the big bang) I'd say what…

It's meaningless to add temperatures in any circumstance. You can average temperatures, and you can add amounts of heat energy, but it is semantic garbage to try to add temperatures. I'd say what it's doing--converting to an absolute scale then adding--is an interesting bug.

Yes, temperature addition is garbage, but the addition of an interval to a temperature is not. Consider:

    "It was 20 °C yesterday and someone told me it's 10 °C
     hotter today. What temperature is it?"
The difficulty comes when you try to write that out using addition. This is OK

    "10°C + 20°C"
because all of the units share the same null point so there is an implicit null point at 273.15 K.

This is not OK:

    "293.15 K + 10 °C"
because the null point could be either 0 K or 273.15 K.

If I were google I'd just show two answers in this case:

    "10 °C hotter than 293.15 K = 303.15 K
    "293.15 K hotter than 10 °C = 303.15 °C"
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