Originally posted by: alexruiz
2) Cyclo, your example is wrong. You are just picking a pair of linear equations where one is displaced in the X axis, hence making the result match the first equation. It obviously will have the same values. To make a VALID comparison, you need to take the SAME equation and pick different points in time. Again, as you would say "use math properly" The model usage you are trying to use doesn;t apply to this situation.
The explanation is perfectly valid. It was just very simple so the knuckle draggers in this thread would be able to understand. Both of them are solutions to the same differential equation (dy/dt=5). The only difference is the initial condition and relative time. The exact same principle applies to the field equations relevant to relativity, mass/heat/momentum transfer, viscoelasticity, or any other time-dependent phenomenon. The only reason I didn't use such an example is that it's needlessly complicated and would at best serve to demonstrate the same point I just made using such a simple example.
Now cyclo, you are the mathematician, or so you say. You are right that having only only measure cannot reveal the initial state of the equation. You are wrong that it cannot be shown at all.
Here is your proof of the universe age, or at least that YOU really can measure the age of some things from the past:
http://en.wikipedia.org/wiki/Exponential_decay
Unlike your example, where you have a
pair of equations, hence making it invalid, you need to use only one equation. Geologists measure the amount of some isotope, measure it some point in time later, and then, because we already know the half life of such isotope, calculate the initial amount in the same equation N(t) = N0 * e^(-tau/t) Or, if you wanna do it properly, use the differential equation and solve it
dN/dt = -tau/N Your assessment about carbon 14 not being useful is wrong, and you know it. Oh, I forgot, we don't want to know No, we want to know the value of "t" at N0.... simple, just rearrange the equation. Use the values of the 2 measures in time as the integration limits, and you are set.
No, I never said I was a mathematician. I'm an engineer. And your "proof" is meaningless in attempting to say anything about the two "theories" being discussed for reasons I've already gone in to in this very thread. Since you obviously missed the boat in the first example, I'll rework it in terms of your example. Since you brought it up, I'll assume you understand the derivation of exponential decay. However, I'll go into it for the sake of tradition.
To begin, we have a differential equation governing the number N of a given isotope. The rate of disappearance (appearance is achieved by simply switching the sign) of this isotope, dN/dt, is proportional to the size of the current population with proportionality constant tau. This is expressed mathematically as a differential equation,
dN/dt=-tau*N.
This is a very simple differential equation which may be solved by separating and integrating, yielding
ln(N)=t/tau, or N=e^t/tau,
evaluated with the initial condition N(t=0)=N0. This gives
ln(N)-ln(N0)=e^(-(t-t0)/tau), or N=N0*e^(-(t-t0)/tau).
Well, who cares? you might ask. I'll tell you. If you assume that all carbon started out as C14 at t0=0, you get a certain solution for t>0. If instead, you assume that carbon started out in an isotope ratio given by the previous case at time t0 then you will get an identical curve for all times t>t0.
Thus, both theories predict the exact same result. I have even solved one example of this for you in Excel for your convenience, because no one here believes me or they just can't figure it out on their own. Here it is - the middle column is the "Big Bang" theory and the other is the "more recent appearance of everything at the initial state predicted by the BB theory." Enjoy.
tau 6
t0 0 3
N0 1 0.60653066
t Nbb N10k
0 1.000000
1 0.846481725
2 0.716531311
3 0.60653066 0.60653066
4 0.513417119 0.513417119
5 0.434598209 0.434598209
6 0.367879441 0.367879441
7 0.311403224 0.311403224
8 0.263597138 0.263597138
9 0.22313016 0.22313016
edit: forgot to define tau. Not that it matters.