The Maths Thread

[PhoenixFire]

Originally Posted by cover drive man

Couldn't you say that all constants are irrational?

No. The two things are quite unrelated. Some constants like e and pi are irrational, but not all of them by any means.

Actually that said, I can't actually think of any mathematical constants that are rational, but I'm sure there are some. I know of some physical ones however...

Edit again, i is rational. That said, there is no absolute definition of what is and what isn't a constant, it's more a general term used to describe some numbers and not others. I'm sure an argument could be made that googol/googolplex are constants of sorts and they are both rational.

[Neil Pickup]

Originally Posted by cover drive man

Couldn't you say that all constants are irrational?

1 is a constant (the result derived when you divide something by itself)

[Uppercut]

Originally Posted by PhoenixFire

Edit again, i is rational.

No you're not.

[Spark]

Remember though, that physical constants - aren't. They depend completely on your choice of units which is completely arbitrary. (w/ the exception of alpha and its friends)

[Quaggas]

Originally Posted by PhoenixFire

No. The two things are quite unrelated. Some constants like e and pi are irrational, but not all of them by any means.

Actually that said, I can't actually think of any mathematical constants that are rational, but I'm sure there are some. I know of some physical ones however...

Edit again, i is rational. That said, there is no absolute definition of what is and what isn't a constant, it's more a general term used to describe some numbers and not others. I'm sure an argument could be made that googol/googolplex are constants of sorts and they are both rational.

Am I missing something? i \neq n/m, for any n,m integer, assuming you mean i \equiv \sqrt(-1).

[Spark]

i ain't rational, as the rationals are a subset of the reals.

[Redbacks]

Originally Posted by Neil Pickup

I appreciated that, even if nobody else did.

You have made a young man happy

[Redbacks]

Originally Posted by cover drive man

Question:

What's the difference between an irrational number and a constant?

Not really an apples v apples comparison.

[Quaggas]

Originally Posted by Spark

Remember though, that physical constants - aren't. They depend completely on your choice of units which is completely arbitrary. (w/ the exception of alpha and its friends)

The units go along with the physical constant - so changing units doesn't change the constant.

[Spark]

Originally Posted by Quaggas

The units go along with the physical constant - so changing units doesn't change the constant.

it changes the value of the constant... and the value is the only thing that matters, isn't it?

Again, with the exception of alpha and its friends (i forget what they all are) which are dimensionless, so are completely independent of your units. alpha is always 1/137-point-something regardless if you're in SI, Gaussian, Planck, whatever.

[silentstriker]

Well, no. It's the underlying physical phenomena that matters. The speed of light is the speed of light, regardless of whether you use km or miles...

The inherent quantity doesn't change, just the number you use to express it.

[Quaggas]

Originally Posted by Spark

it changes the value of the constant... and the value is the only thing that matters, isn't it?

Again, with the exception of alpha and its friends (i forget what they all are) which are dimensionless, so are completely independent of your units. alpha is always 1/137-point-something regardless if you're in SI, Gaussian, Planck, whatever.

e.g., mass of proton is 938.2...MeV/c^2 = 0.9382...GeV/c^2 = 1.67...E-27kg. The "numbers" change, the constant doesn't (those equals signs have the usual meaning).

Of course, there is some evidence that physical "constants" change/have changed through time (I'm not advocating that the world is 4000 years old because the decay constant of C14 has changed)

Edit Beaten to it

[Spark]

Originally Posted by silentstriker

Well, no. It's the underlying physical phenomena that matters. The speed of light is the speed of light, regardless of whether you use km or miles...

The inherent quantity doesn't change, just the number you use to express it.

yeah but we're talking about the constants themselves here, not what they mean. so to talk about the physical constants as if they have some intractable fixed value is wrong. i mean, for any of those constants c, e, h, G, whatever, i could pick a units system such that it's 1 and dimensionless, which kind of "eliminates" the constant.

it's just a thing we chuck in our equations to make sure they work. but they all have to be consistent with the dimensionless constants, that's the central rule.

[silentstriker]

Originally Posted by Spark

yeah but we're talking about the constants themselves here, not what they mean. so to talk about the physical constants as if they have some intractable fixed value is wrong. i mean, for any of those constants c, e, h, G, whatever, i could pick a units system such that it's 1 and dimensionless, which kind of "eliminates" the constant.

it's just a thing we chuck in our equations to make sure they work. but they all have to be consistent with the dimensionless constants, that's the central rule.

I think we're arguing semantics here. When CDM asked and I said physical constant, I was referring to the 'meaning', rather than a specific number. Obviously (many) constants are things that we just need to fudge our equations with to make them work, and then assign probably 'meanings' to them later on, but in other cases, it is still a fundamental quantity that means something. G might be 'chucked in', but c has a much more concrete meaning.

BTW, natural units FTL.

[silentstriker]

Originally Posted by Quaggas

Of course, there is some evidence that physical "constants" change/have changed through time (I'm not advocating that the world is 4000 years old because the decay constant of C14 has changed)

Sure you aren't. Get away from me.

It was hilariously epic when the news came out that c may not have always been c. Millions of creationists became faux-physicists for a day and waxed poetically for weeks.