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.
Originally posted by iamatigerExactly? Or just near enough?
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
Originally posted by sonhouseIt'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.
Can you imagine the circuitry needed to make a temperature exactly PI C?
Originally posted by iamatigerThat'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.
If you can't get exactly pi degrees, then you can't get exactly 1 degree either, or any other temperature you choose.
Originally posted by FabianFnasWhich 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?
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.
Originally posted by joe shmoI 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.
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?
Originally posted by iamatigerbut 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) ???
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.
Originally posted by joe shmoWe measure distance in integers also, but you can have an irrational distance.
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) ???
Originally posted by joe shmoWrong, I would say.
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?
Originally posted by forkedknightIt isn't.
We measure distance in integers also, but you can have an irrational distance.
How is temperature different?
Originally posted by forkedknightA good example of why something with a probability of 0 is not necessarily impossible!
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.