Large numbers and Creationism

Let’s start with half-lifes. My foray into ridiculously long ass periods of time started with this article. That article reminded me of conversations I’ve had with a friend of mine who is a creationist who questioned all of the science, and how we know how old something is. I am not a creationist, as most people know the term; I think the Universe, and obviously the Earth, was created by God through the laws of physics as He knows them, although He might have cheated with the probabilities along the way. Therefor I believe that the science as we know it is relatively stable, but we would be foolish to think that what we know is all that there is to know. The occasional shake up is good for science, keeps the cobwebs and dogmatism away.

I digress; on the face of it, he did bring up some very good questions, and thinking on those questions, I asked myself, “How can we tell something has a half-life of 4.5 billion years?” Obviously, the “bright boys” were on to something, because the whole concept of radioactivity transformed our lives at the end of World War Two. So I did some digging through Wikipedia, trying to get a handle on the problem. Unfortunately, the half-life and radioactivity articles didn’t quite help me. I’m not stupid (I’ve taken college level physics, calculus, and chemistry courses) but I haven’t exactly kept up on my nuclear physics equations, and the math was dense on both of those articles (most of my science information comes from and; no, not high end information, but it works for me.) So with nothing better to do, I dug further until I hit the article on U238.

The mean lifetime of uranium-238 is 1.41 × 10^17 seconds divided by 0.693 (or multiplied by 1.443), i.e. ca. 2 × 10^17 seconds, so 1 mole of uranium-238 emits 3 × 10^6 alpha particles per second, producing the same number of thorium-234 (Th-234) atoms. In a closed system an equilibrium would be reached, with all amounts except lead-206 and uranium-238 in fixed ratios, in slowly decreasing amounts. The amount of Pb-206 will increase accordingly while U-238 decreases; all steps in the decay chain have this same rate of 3 × 10^6 decayed particles per second per mole uranium-238.

OK, that I understand, because it references what little I remember from chemistry class. But for those of you that never took chemistry, I give you the mole. And for some background on how large a number Avagadro’s constant is:

Several popular science texts contain “examples” of the mole which ignore this part of the definition, for example:

* 1 mole of marshmallows would be enough marshmallows to make a 12 mile thick layer of marshmallows covering the entire face of the Earth.[9]
* A mole of popcorn kernels could be spread uniformly over the USA if the thickness of the layer was about 9 miles.[9]
* A mole of donut holes would cover the earth and be 5 miles (8 km) deep.[10]
* A mole of blood cells would be more than the total number of blood cells found in every human on earth.[10]

These (and similar) are examples of the fact that atoms and molecules are very small compared to everyday objects. Marshmallows, popcorn kernels, donut holes and blood cells are not “elementary entities”, nor are they “substances” whose amount is measured in moles.

In the end, when you are talking about numbers that are very, very large. As an aside, I take issue the condescending tone in that the editor of the article; popular science texts are about demonstrating science in a way that people can understand, especially when it comes to very large numbers, like 6.022 141 79(30)×10^23. Nit picking how exact the term is used doesn’t exactly endear “common people” with scientists. Nowadays, scientists only get work done because of the common people’s taxes, so don’t aggravate the problem of lack of understanding by being a prick about it, ‘mkay?

In the end, I finally got around to nailing down an explanation of half-life that I understand. If scientists could only present that information in a way that doesn’t threaten someone’s religion, it would go a long ways to easing tension.

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