I do not take any pleasure in this, but the point has been reached where CTD needs to deal with the reality that he was wrong. Continued denial and avoidance will not make this issue go away.

In Post 39563 on the "How old was that again?" thread CTD made a mistake:

This is a falsehood, and he was corrected by LinearAQ as well as myself. The half life is variously defined as the time it takes for 1/2 of the original to decay, or as the time where only 1/2 of the original material is left, however that calculation is based on the rate of decay.

One could calculate the time for any fractional amount to remain from the same decay rate, and when graphed you would have the same curve.

CTD compounds his error by insisting that he is correct in Post 39635 on the same thread

The problem with this approach is that the time period is not a scalar value, and a "quarterlives" is not half of a "halflife" ...

LinearAQ in Post 39667 on the same thread shreds this argument:

Now one could calculate from the decay formula how much would be left after 2 x 0.415 x t(half) ... and one can predict that the amount will be 9/16 ...

But CTD is still in denial that his math is wrong. On Post 40010 on the same thread he offers this response:

As you can see he still doesn't own up to being mathematically proven to be wrong, instead going off on some paranoid rant and hiding behind smilies. It's not "spam" CTD, it's reality.

When challenged again on it, he was still in denial (Post 41757 on the "Evolution: The Big Joke" thread

This too is a false statement, but more to the point, it demonstrates that either:

(a) CTD does not understand the math (does not understand that he is wrong), or

(b) CTD is incapable of admitting that he is wrong.

Let's use CTD's example of interest rates and see if this helps. When you calculate the ratio of interest to principal for one week (and anyone can take this problem to their local bank to have them verify it) you don't calculate it at 1/52 x the annual rate (what CTD did on the decay curve) but at the annual rate ^(1/52). Curiously when you do this you will also get the same curve as using an annual rate to graph interest versus time.

For simplicity let's calculate the interest due at 21% annual interest compounded annually and compounded semiannually on $100:

(1) compounded annually:

At the beginning of one year you have $100.00

At the end of the first year you have 1.21 x $100.00 = $121.00

(2) compounded semi-annually:

Calculating the interest rate to compound at 1/2 year (Nt/No)^1/2 = (121/100)^1/2 = 1.10

At the beginning of one year you have $100.00

At the end of 1/2 year you have 1.10 x $100.00 = $110.00

At the end of one year (two half years) you have 1.10 x $110.00 = $121.00

You can do the same for 1/3 years, 1/4 years, or 1/277 years, however no matter what interval you pick the annual interest rate will be the same, and the results will be the same curves.

Certainly this fact of interest calculations should be a part of high-school education that everyone should learn, as it directly affects your everyday life, so there is no rational excuse for not knowing this.

Using CTD's bank example we can look back at the original decay formula and calculate the %decay that has occurred in half of a halflife and then "compound" that %decay over two half halflives:

(a) N(t) = N(0)e^-?t and N(t)/N(0) = e^-?t

for t = h (= 1 halflife)

(b) N(h)/N(0) = 1/2 = e^-?h = e^-?h = 1/e^?h

for t = h/2 (= 1/2 halflife)

(c) N(h/2)/N(0) = e^-?(h/2) = 1/e^{(?h)(1/2)} = {1/e^?h}^1/2

From equation (b), substituting N(h)/N(0) for 1/e^?h

(c) N(h/2)/N(0) = {N(h)/N(0))}^1/2 = (1/2)^1/2 = 0.70710678118654752440084436210485...

Seeing as this is the square root of 1/2, it is obvious that compounding two such periods will always - no matter how you try to hide the pea - be the same as the amount of decay that occurs in one halflife.

As noted on another thread, anyone that does not understand the truth can be classified as either ignorant, stupid, deluded, insane, or wicked (feel free to add any other possibilities that you can think of).

We can eliminate ignorant and delusions due to being mislead by noting that sufficient information has been provided to properly calculate the amounts of decay at any time, calculations that can be made with a scientific calculator.

We are left with these possibilities:

(a) CTD admits that he was wrong about the math.

(b) CTD does not understand that he is wrong about the math (stupid, insane, or wicked).

(c) CTD is incapable of admitting that he is wrong about the math.

Time for CTD to belly up. Continued denial and avoidance of the issue make it difficult to give his posts any credence at all.

Being wrong is no big deal, being unable to recognize when you are wrong and admitting it IS a problem.