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Fossil Trove Sheds Light On a Stage of Evolution
September 10, 2011
11:54 pm
at1with0
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http://online.wsj.com/article/SB1000142 ... 36242.html

They dated the finds at 1.977 million years old, based on a laboratory estimate of the rate of decay of uranium traces in the cave sediments.

I'm highly skeptical that the decay rate of uranium is constant throughout 2 million years. Right now, I'm working on an alternative model that would mimic the decay rate as observed in a lab yet not be constant for all time. I don't know how they figured out the decay rate but I assume it was by observations that lasted over the course of less than a decade (maybe even a lot shorter, like a matter of days).

In the mathematical model used to calculate the age, it is assumed that the decay rate of uranium (or carbon, for carbon dating) is constant. I'm working on a different model that would appear to roughly be constant over a decade but would actually be a lot different 2 million years ago.

I will then use that model to recalculate the age ranges of the sample and compare to 1.977 million.

"it is easy to grow crazy"

September 11, 2011
2:46 am
at1with0
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I worked out an example casting doubt on the whole idea of carbon dating.
I worked with an isotope of Carbon whose half-life is allegedly 5700 years.

Suppose a sample of decayed C14 was found to be .5% of what was originally there.

Then the usual carbon dating model would suggest that item is about 43,000 years old.

In other words, 100% of the original C14 decays into only .5% of original mass in that much time.

The mathematical model for this is based on a differential equation. The working assumption is that the relative rate of decay is proportional to however much is currently present. Meaning that if there's a lot there, the rate of decay is faster. Conversely, when there isn't much left, the rate of decay is slower.

That model's accuracy is a fundamental assumption here.

So I came up with a different model based on that one but with a twist. The twist is that the relative rate of decay is NOT proportional to the amount currently present.
In the usual model, the differential equation looks like this:

dy/dt = k y

The left hand side says "the rate of decay" and the right hand side says "is proportional to the amount present, y." What k is depends on the compound. For C14, k turns out to be - ln(2)/5700 (that's the natural logarithm base e of two all divided by 5700).

I changed the model into something more general, asking the question: is the rate of decay truly proportional to the amount present or is it only NEARLY proportional to the amount present.

dy/dt = (k + ct)y.

In the case that c = 0, my model becomes the standard model. But interesting things happened when I let c be a small percentage of k.

When c is one trillionth of k, I still get about 43,000 years old. That's because the ct term is virtually nonexistent when c is so small.

When c is one billionth of k, I still get 43,000 years old.

When c is one millionth of k, I get around 42,000.

When c is one hundred thousandth of k, I get 33,000.

When c is one thousandth of k, I get 6,000.

The question is whether the age of the sample is 6,000 or 43,000 years. There's a huge difference, obviously, and I wonder if measuring the decay constant down to one thousandth of k is even possible in a lab.

"it is easy to grow crazy"

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