Little temperature puzzle:

Originally posted by FabianFnas
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 d ...[text shortened]... statement is wrong. It's impossible to measure the exact value of sqr(3) degrees centigrade.

"So I would say that your statement is wrong. It's impossible to measure the exact value of sqr(3) degrees centigrade.[/b]"

I thought that is exactly what I was saying, its impossible to measure it.

What was confusing about my statement?

Originally posted by joe shmo
"So I would say that your statement is wrong. It's impossible to measure the exact value of sqr(3) degrees centigrade."

I thought that is exactly what I was saying, its impossible to measure it.

What was confusing about my statement?[/b]

You wrote: "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 answer "Wrong", meaning as your said "its impossible to measure it".

It's not confusing, what confuses me is why I became confused. Of yourse you're right when you said "wrong".

Originally posted by iamatiger
By the way, internal Brownian motion does not change the temperature of a system.

Yeah, but if there's a readable thermometer attached, the system isn't completely closed, and the Brownian motion cannot be totally internal...

After all, even if you enclose the entire system in a vacuum with a glass window to read the thermometer, photons will enter and escape, changing the energy level ever so slightly, perhaps hitting an atom just right to excite it, and cause its motion to change.

Richard

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.

True, but the task at hand is not to create a system to make a temperature pass through any exact infinite number of decimal digits. The task is to put the system at that temperature. The former is achievable, for any T between 273 and 373 centigrade, by nothing more complicated than boiling water. The latter is impossible (although "sufficiently" closely approachable, of course).

Richard

Originally posted by Shallow Blue
True, but the task at hand is not to create a system to make a temperature pass through any exact infinite number of decimal digits. The task is to put the system at that temperature. The former is achievable, for any T between 273 and 373 centigrade, by nothing more complicated than boiling water. The latter is impossible (although "sufficiently" closely approachable, of course).

Richard

One thing we do to calibrate thermocouples to zero C is to just put it in a cup of ice water, the mix of ice and water will be at zero, so that is a good starting point for calibration. Then at 100 C you can put it in boiling water and factor in the altitude and you have the proper boiling point calibrated. It won't of course be 100 C at say, 5,000 meters.

In our cryopumps are TC's which measure very close to zero K, cryopumps operate at about 10-11 degrees Kelvin. It is a bit harder to calibrate that close to absolute zero but they manage to do it. I think our TC's in the cryopumps are less than one degree K off.

Originally posted by sonhouse
One thing we do to calibrate thermocouples to zero C is to just put it in a cup of ice water, the mix of ice and water will be at zero, so that is a good starting point for calibration. Then at 100 C you can put it in boiling water and factor in the altitude and you have the proper boiling point calibrated. It won't of course be 100 C at say, 5,000 meters. ...[text shortened]... o but they manage to do it. I think our TC's in the cryopumps are less than one degree K off.

Your wealth of random knowledge is deep!

Originally posted by sonhouse
One thing we do to calibrate thermocouples to zero C is to just put it in a cup of ice water, the mix of ice and water will be at zero, so that is a good starting point for calibration.

Nope. Exact same problem there. The mix will be at very close to zero C, but how can you guarantee that it will be there exactly, to the non-existent final digit? By controlling the atmospheric pressure around the mix to exactly one atmosphere? How are you going to measure that?
We can't measure these things to the millionth, thousandth or even hundredth digit - in many cases not even to the tenth - so we certainly can't do it to the end of the infinite, transcendental string of digits required to get exactly pi. We can get close enough that you won't see a meniscus of mercury tremble, but we simply can not get close enough to tell the difference between 3.1415926535897900000 and pi.

Richard

Originally posted by Shallow Blue
Nope. Exact same problem there. The mix will be at very close to zero C, but how can you guarantee that it will be there exactly, to the non-existent final digit? By controlling the atmospheric pressure around the mix to exactly one atmosphere? How are you going to measure that?
We can't measure these things to the millionth, thousandth or even not get close enough to tell the difference between 3.1415926535897900000 and pi.

Richard

In the semiconductor industry, if we get within ONE degree C at say, 1300 degrees C, we are happy as a pig in shyte! Some of the processes we use need to be within 5 degrees at those higher temps, but that's about as close as we need to get. Certainly calibrating our TC's with ice water is good enough for our purposes. Anyway, even if you could get to the last digit, the uncertainty principle would stop you eventually.

Originally posted by Shallow Blue
Nope. Exact same problem there. The mix will be at very close to zero C, but how can you guarantee that it will be there exactly, to the non-existent final digit? By controlling the atmospheric pressure around the mix to exactly one atmosphere? How are you going to measure that?
We can't measure these things to the millionth, thousandth or even not get close enough to tell the difference between 3.1415926535897900000 and pi.

Richard

So the ratio may exist, but it can never be measured...does measurement constitute proof of its existance, or does it exist irrespective of the ability to measure it?

Fot that matter, can time be measured accurately and continuously, can we have 2 seconds? 3 metres? A gravitational acceleration of e m/s/s? I gave an electronic apparatus that would tend to pi degrees, which people didn't like, but can we actually have any exact quantity of anything continuous?

I think people can generally agree that real numbers exist.

I would hope that people would agree that measurements like temperature, distance, time, etc all fall on the real number line.

All measuring tools are accurate to a certain level of precision, and increments smaller than that level of precision are difficult or impossible to measure.

On the real number line, increments exist that are smaller than the precision level of all measuring tools (this is by definition, as there are infinitely small increments on the real number line).

The ability to measure a precise value is not a requirement for that value's existence.

Given all these facts (I think these are all facts, you are welcome to counter-argue any of them)
Why are people arguing that an irrational ratio of two real numbers cannot exist because we cannot measure it precisely?

Originally posted by forkedknight
I think people can generally agree that real numbers exist.

I would hope that people would agree that measurements like temperature, distance, time, etc all fall on the real number line.

All measuring tools are accurate to a certain level of precision, and increments smaller than that level of precision are difficult or impossible to measure.
...[text shortened]... at an irrational ratio of two real numbers cannot exist because we cannot measure it precisely?

Actually, I don't agree that real numbers exist, as handy as they are, they are figments of our imagination in reality. I suppose the whole of mathematics falls into the same category.

Originally posted by joe shmo
Actually, I don't agree that real numbers [b]exist, as handy as they are, they are figments of our imagination in reality. I suppose the whole of mathematics falls into the same category.[/b]

So now we need a physical object for something to exist?

Do thoughts and ideas not exist? I think we're getting a bit too philosophical for this argument to continue in any meaningful way.

Originally posted by forkedknight
So now we need a physical object for something to exist?

Do thoughts and ideas not exist? I think we're getting a bit too philosophical for this argument to continue in any meaningful way.

You don't belive that physical objects and thoughts/ideas are fundamentally different phenomena? Perhaps if I think I can hold an elephant above my head using nothing but thought, I can...

And I didn't bring philosophy into it, you did.

I still hold that number, quantity, defined space of any kind, ect... only exist in our thoughts/ideas which is different from them existing in the real world.

Originally posted by joe shmo
So the ratio may exist, but it can never be measured...does measurement constitute proof of its existance, or does it exist irrespective of the ability to measure it?

No, don't be silly. Of course the ratio does exist. There's no "may" about it. Yes, there is such a thing as a temperature of pi degrees, and yes, it is not only possible but necessary to pass through it* if you raise the temperature from frozen to room temperature. Nobody denies that, AFAICT - certainly I do not.

What I do deny is that it is possible to, intentionally, put a body (of water, iron, or oxygen, take your pick of state) exactly at that temperature. That requires much more than the mere existence of pi degrees centigrade.

Richard

* Although, given that the temperature of a piece of liquid is never quite even, and the temperature of sufficiently small parts of that liquid (certainly of single molecules) are essentially undefinable, even that is nigglable.