11:54 pm

April 9, 2009

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"

2:46 am

April 9, 2009

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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