Hi Jeanie,
Like yourself, I struggle with the type of math that CTD and RAZD discuss on here and in all serious, it's over my head. However, because of this, I cannot in all honesty state who in this area is correct and who isn't.....
Yes, the math may be beyond some readers. But one only needs to take my original claim to someone who knows a little math.
You & Linear's claim is just like claiming interest compounded annually = interest compounded weekly merely because you can take the annual rate and backtrack it to any given week and produce a result. The results will not be the same, and anyone who really cares can find out for themselves. This isn't hard at all.
Now RAZD disputed this, and in his own insulting manner, turned right around and verified it several times above in an unprecedented display of arrogance.
Now to see how compounding works, without Greek letters and such, you can just take $1000 and a rate of, say 20%. Compounding it annually, you just take $1000 x .20 = $200. Added to the original $1000, you get 1200.
Compounding Quarterly, you take the same $1000, and the same 20%, but you don't have to wait a whole year to start earning interest. The first payment comes at 3 months. Since 20% is the annual rate, the quarterly rate is 1/4 x .20 = .05. $1000 x.05 = $50. The balance after one quarter is $50.
Now as soon as the next quarter rolls around, you don't just make money on the $1000, because your balance is $1050. That's what compounding means. The interest rates don't change. 5% x $1050 = $52.50. $1050 + $52.50 = $1102.50. That extra $2.50 is the result of quarterly compounding! It isn't much, but it's more than what you'd get if the quarterly compounding had not taken place.
Compounding is simply earning interest on your interest. The more frequently this interest goes into the account, the more little payments you get, and all these little payments themselves earn interest too.
It doesn't sound like much at all, but it's very sneaky because it grows exponentially. Ever hear the story about putting a grain of rice on the first square of a chessboard, and doubling it for each of the following squares?
There's a well known Einstein quote where he calls compound interest the most powerful force in the universe or some such. I'm confident someone will "show me up" by providing it.
Anyhow, given enough time, exponential curves make huge differences. Believe it or not, compounding a 20% interest rate can cause the money to double easily in under 4 years, compared to 5 years for simple interest. Think of how much difference that makes in only 20 years. Compounded interest will result in
more than double the balance one would have with simple interest in just 20 years!
Another way to investigate: go to the interest calculator I linked to. Type in some numbers you like, and see the result with annual compounding. As soon as you switch it to monthly compounding, the result will increase. That's exactly what I said it would do, and RAZD said wouldn't happen.
He has now taken to arguing that since it happens, it doesn't count - that we should call the net result the interest rate. But which net result? The one obtained by annual compounding, or the one obtained by monthly compounding? Which one of these two obviously different numbers which he claimed must be equal?
In our analogy, annual compounding = calculating decay by means of half-lives. Compounding every 1/2 year = calculating by means of quarter-lives. It's easy to see why half-lives are preferred: it takes longer for things to decay. The little amounts that don't look like much add up over time to huge differences.
Likewise, compounding monthly will result in higher interest than compounding quarterly. The more frequently the compounding takes place, the more little bits come into play, and the faster & harder they play.
As long as I'm posting, I might as well point out a couple more things.
So you openly condemn CTD's frequent ad hominem comments to anyone that disagrees with him.
As usual, putting words in someone else's mouth. Anyone surprised? Anyone at all?
... anybody that maybe "fooled" by believing something or "someone" that maybe wrong...
We are, however, talking about math, the "perfect science" according to some, and which has nothing to do with belief. It is relatively easy to show that you are either right or not when doing math.
Sure is!
As pointed out, CTD made a mistake when he calculated his "quarter-life" as half of a "half-life" and then compounded his error when he claimed that the value of the curve at his half of a half-life was a linear interpolation between the value at time "o" to the value at time "t" ... a claim that is obviously false because the curve is ... curved, not a straight line.
A claim I never made. Anyone surprised? Anyone at all?
Now, instead of simply admitting that he was wrong, CTD tries to hide the fact by first substituting a different formula for the decay curve. As we have seen this new formula is for interest calculations based on a nominal (read approximate) initial rate:
Not so. I never suggested substituting one for the other. Anyone surprised? Anyone at all?
Yet he wastes your time pretending I have done so. I skipped over that part myself. I hope not too many fell victim to this ruse.
(a) When you ask your banker what the real rate of interest is, he will tell you (if he is an honest banker) that it is the APR rate, not the nominal rate. This means that any calculation for interest to compare with decay you would have to use the same APR rate (and as noted previously, that when you do that you get the same results, ones that are still not CTD's results.
Changing arguments. Anyone surprised? Anyone at all?
(b) The formula used for compound calculations is a relatively easy to use approximation of a constant growth curve.
{bogus content omitted}
One does not even need to graph this to show that it is not a curve function but a step function.
Notice that he first calls it a curve, then says it isn't a curve?
All exponential growth results in a curve when plotted on a graph. He now portrays a curve as a linear function - just exactly what he & Linear falsely accused me of doing. Educated visitors will see this for what it is right off the bat.
The decay formula is actually easier to use (fewer inputs, fewer calculation steps),
The half-life paradigm means they've already factored in the compounding period of their choice (a slow one), so they don't allow for any other variables. Of course it's simpler!
"Life is just simpler if you assume evolutionists are right" might convince some, but it's hardly meaningful to me.
Which, curiously, is the square root of 1/2 as a percent value. This is the true amount for any decay curve at half of a half-life. So once again CTD cannot be right when he claims the value is 75%. Wrong is wrong.
Again, not a claim I made. Anyone surprised? Anyone at all?
The entertainment value is mixed. But it's not hard for those who can do a little math to see you've totally given up hope. I look forward to seeing more follow suit. Shoot, even those who bother to read what you yourself have written, without doing any math at all can see how you've pathetically attempted to reverse your argument. You hide this behind many unsavoury words, but it's there plain as day.
Those who care to can scroll up to his Post #42008 for this false accusation against Russ
Hey Russ. Trying another distraction from the topic?
It was RAZD's own post #41902 that started the "distraction"
Note that there are NO university definitions that state this is the definition of evolution, nor any museums of Natural History, nor does Darwin state this. It is in fact a falsehood, and a misrepresentation of how evolution is used in biological science.
One thing you have to grant RAZD: he is comprehensive. He doesn't produce quality inaccuracies, but he does spread a lot of them around in a lot of directions.
And had nobody responded, rest assured there'd be complaints about that too... It is still possible to enjoy some aspects of participating here.
Maybe my posts are off-topic here as well? I'm not slinging false accusations at myself, after all.
