1. Shanghai
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    15 Feb '12 02:02
    How about making the thermometer with a circular tube, in fact maybe we can standardise all measurements by making the equipment we measure with circular. The radian can then rule supreme.
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    15 Feb '12 11:20
    Originally posted by sonhouse
    Can you imagine the circuitry needed to make a temperature exactly PI C?
    You mean exactly pi, and not just some rational value near enough pi centigrades?

    No, I cannot.
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    15 Feb '12 12:02
    You have a temperature circuit controlled by two sliders. The temperature the circuit is set to is a/b + K where a and b are the slider settings.

    Bend one slider into a circle and set the other slider to be a diameter of the circle.

    Now slide the circular slider to the end, and the diameter slider so it touches the circumference of the circle.

    The temperature the circuit is now set to achieve is Pi + K
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    15 Feb '12 12:14
    Originally posted by iamatiger
    You have a temperature circuit controlled by two sliders. The temperature the circuit is set to is a/b + K where a and b are the slider settings.

    Bend one slider into a circle and set the other slider to be a diameter of the circle.

    Now slide the circular slider to the end, and the diameter slider so it touches the circumference of the circle.

    The temperature the circuit is now set to achieve is Pi + K
    Exactly? Or just near enough?
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    15 Feb '12 14:12
    Originally posted by sonhouse
    Can you imagine the circuitry needed to make a temperature exactly PI C?
    It's meaningless to even talk about something having a temperature of exactly pi degrees, for long enough for it to be measured at all. Sure, if you go from 3 to 4 you must, for some indivisible moment, have passed through pi; but in the time it takes to measure that temperature, you will also have passed through 22/7, 3.1415, 3.1416, 355/113, and Indiana.
    There simply is no such thing as a stable temperature. Temperatures may be stable enough for almost all purposes, but if you want to determine that it is exactly, not more or less, but exactly, pi, you need it to be stable enough to distinguish it from its rational neighbours, not in the third, not in the hundredth, not in the googolplexth, but in every single one of its infinite number of decimals. Brownian motion alone puts paid to that idea.

    Richard
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    15 Feb '12 15:131 edit
    If you can't get exactly pi degrees, then you can't get exactly 1 degree either, or any other temperature you choose. However since temperature is a measure of the kinetic energy of the particles in the system I would have thought you could get things pretty exact with a small number of particles and/or a well insulated experiment.

    By the way, internal Brownian motion does not change the temperature of a system.
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    15 Feb '12 18:24
    Originally posted by iamatiger
    If you can't get exactly pi degrees, then you can't get exactly 1 degree either, or any other temperature you choose.
    That's right. I agree. You can never measure a temperature to its last decimal. You can only get a 'good enough' value of a temperature at hand.

    Same things with lengths. How tall are you? To the last decimal? You don't know? Samo samo.
  8. R
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    15 Feb '12 20:54
    Originally posted by FabianFnas
    That's right. I agree. You can never measure a temperature to its last decimal. You can only get a 'good enough' value of a temperature at hand.

    Same things with lengths. How tall are you? To the last decimal? You don't know? Samo samo.
    Which is why I say in the physical situation the ratio of C/F can never be exactly Sqrt(3)...Because to measure a true irrational would have to have infinite precision. Right or Wrong?
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    15 Feb '12 21:10
    Define a temperature scale where 0 is absolute zero and the boiling point of water is Pi units. 🙂
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    15 Feb '12 21:16
    Originally posted by joe shmo
    Which is why I say in the physical situation the ratio of C/F can never be exactly Sqrt(3)...Because to measure a true irrational would have to have infinite precision. Right or Wrong?
    I think it is wrong. If temperature varies continuously it must have had that that value at some point if is observed to be one side of it and then the other. Temperature cannot be precisely measured, but nevertheless at any instant in time the system is at some precise temperature.
  11. R
    Standard memberRemoved
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    16 Feb '12 02:341 edit
    Originally posted by iamatiger
    I think it is wrong. If temperature varies continuously it must have had that that value at some point if is observed to be one side of it and then the other. Temperature cannot be precisely measured, but nevertheless at any instant in time the system is at some precise temperature.
    but we measure temperatures essentially using integers, and no irrational can be expressed as a ratio of two integers, a and b, by definition...so how can the ratio of C/F = sqrt(3) ???
  12. Standard memberforkedknight
    Defend the Universe
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    16 Feb '12 05:07
    Originally posted by joe shmo
    but we measure temperatures essentially using integers, and no irrational can be expressed as a ratio of two integers, a and b, by definition...so how can the ratio of C/F = sqrt(3) ???
    We measure distance in integers also, but you can have an irrational distance.

    How is temperature different?

    Look at continuous probability scales.

    For any continuously variable probability function, the probability that a value is exactly t is precisely 0, and yet, it must have some value. Is this a paradox? You might says yes, I say no.
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    16 Feb '12 08:02
    Originally posted by joe shmo
    Which is why I say in the physical situation the ratio of C/F can never be exactly Sqrt(3)...Because to measure a true irrational would have to have infinite precision. Right or Wrong?
    Wrong, I would say.

    You cannot measure an irrational temperature, but temperature are irrational by its very nature, even if they can have any temperature on the real line.

    A temperature can have any value, even sqr(3), pi, or 1 or whatever. But we cannot measure a temperature with infinitly many decimals. We cannot know for sure that a temp is pi degress, only when it is near enough.

    If you heat a specimen from 3 to 4 degrees, it must be pi degrees at some specific time, but we cannot know when.

    We can define the temp scale from e = the freezing point of water, to pi = the boiling point of water, that's easy. The less easy is that the temperature when water boils and freezes is dependant of preasure, and only a well defined preasure gives the exact result. This exact preasure has the same difficulty as the temp itself - you can't measure it to its exact value, to the last decimal, only to a value quite ner, but not near enough. So this doesn't help you.

    So I would say that your statement is wrong. It's impossible to measure the exact value of sqr(3) degrees centigrade.
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    16 Feb '12 08:05
    Originally posted by forkedknight
    We measure distance in integers also, but you can have an irrational distance.

    How is temperature different?
    It isn't.

    Temperatures, lengths, times, masses, to take some examples, cannot be measured with irrational values. But they usually have irrational values. But the values are not exactly measurable.
  15. Shanghai
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    16 Feb '12 10:58
    Originally posted by forkedknight
    We measure distance in integers also, but you can have an irrational distance.

    How is temperature different?

    Look at continuous probability scales.

    For any continuously variable probability function, the probability that a value is exactly t is precisely 0, and yet, it must have some value. Is this a paradox? You might says yes, I say no.
    A good example of why something with a probability of 0 is not necessarily impossible!
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