katerina2

Back on the couch, Scientiae!

I don't want none of that talk.

You hear?

Tom Ames

I'm sorry, Douglas, but no-one can be said to have scurried away from the biblical equations thread. (Would that we all would!)

Luv,
Unca' Joe

seebs

Ow.

I posted a clarification. Not that it'll change anything, but... Ow.

S2Focus

Something you'd have to pay for, I imagine...

AdamWho

Douglas J. Bender:
Of course this statement is true but it is also irrelavant, math is unitless, period. However, if you want to do physics (or any science) then your units have to work out. If there are units in functions like exp() or ln() then they must all cancel (the arguments must be unitless).

It is not a personal issue it is a fact.

Principia

[ May 26, 2002: Message edited by: Scientiae ]</p>

G-dfree

&lt; Sodomy Alert! &gt;

Deimos

Indeed, take the trigonometric functions as another example. The argument is the radian - a unitless ratio. When used in a physical context the argument is still unitless however the argument contains factors that cancel the units. For example, suppose we want to describe a physical system where some property of it changes in time. Let's say it's described by the function -

x = k*sin(T) + C

if x has units of metres then k*sin(T) must have the units of metres as must C. sin(T) is intrinsically unitless as is its argument, T. The proportionallity constant k assigns units to the sin() function. To give T physical meaning it is written as wt where t is our time coordinate with units of say, seconds, and w is a factor that allows us to relate the dimensionless sin() function to time. w is defined as 2*(PI)*f where f is the angular frequency with units of radians/second.

This is how I understand it anyway.

Ragnarok

Hehe, funny stuff. Dougie's such a kidder. The punchline is that if that we imagine "t" to have units of, say, meters then we are really saying "integrate 1/(some amount of meters) multiplied by dt (which is an infinitesimal quantity of meters) to produce a value which is the limit of a Reimann sum. Does anybody get the joke?

1/(t * meters) * (dt * meters)

The units cancel and the resulting quantity being integrated is - gasp - unitless. And yes, all definitions of a function must agree. This is a basic idea in logic - A is not "not A". The "function" ln (36.5 years) doesn't mean anything and never will. If "x" has units and the limit of the sum doesn't then we are clearly fucked in a cocked hat. Just like Uncle Doug.

<img src="graemlins/boohoo.gif" border="0" alt="[Boo Hoo]" />

[ May 25, 2002: Message edited by: Ragnarok ]</p>

AdamWho

Scientiae, Douglas and others:

Deeper issues that are bothering me about these "math" threads:

1. The false idea that opinion actually counts in mathematical arguments, it doesn't, period.

2. The argument from authority. Both sides have been guilt and they are both wrong when they do it. Math is about proofs and it is irrelevant who gave the proof. Please do not use me as a authority just because I wrote physicist as my job title, my opinion is irrelevant.

3. Any mathematical proof must be clear, concise and 100% accurate, one mistake = 100% wrong. Math / logic are black and white on this issue.

4. Reason is not synonymous with logic. This mistake seems to be hardwired into cranks. Logic is tautologies; no new knowledge can be gained, just manipulated. Reason is the application of logic and empirical data. Just because something is logically consistent doesn't mean that it makes physical sense.

But as stated in bullet two, my opinion doesn’t count so argue on!