Still trying CTD,
So any story which manages not to invalidate itself must be considered validated?
That would fit with the definition of valid as used in science. The logical conclusion drawn from the physical properties of radioactive elements is actually found in the evidence of actual radioactive decay. Thus the concept has been tested, and the results validate the conclusion.
The Theory of Skunk Funk looks to be unstoppable!
Just as unstoppable as the "theory" of invisible little pink unicorns, because they are not testable. Anyone can make up stuff, the difference between fantasy and science is testing and testing and testing the concepts for validity.
Ever notice that self-validation = circular reasoning, RAZD? If you have ever noticed this, please remind yourself.
Except we are not talking about self validation, we are talking about validating an intellectual concept with real physical objective evidence (the part where your "skunk funk" fails). It is evidence that validates (or invalidates) theoretical concepts.
I haven't ruled out the possibility entirely, but past claims of such materials have failed more than once. I don't think there is any such thing. Should I?
And should I omit (as some do) to make this clear to others, who might mistake the term to be literal rather than relative? What purpose would that serve?
The difference is that one can recognize that we are talking orders of magnitude of difference in solubility, measured as the maximum density of the solute in the solution. 1 atom in a gallon is not what I would call soluble. When Wiens says "but essentially no thorium (because of its much lower concentrations in the water)" that would be because it is very insoluble. Meanwhile you may have floating particles with some thorium, caused by the same process, but those would not be consider dissolved in the water, while they would be available for marine organisms to ingest. You should be happy to see that scientists don't assume there is
no thorium based on it being insoluble, but consider that there could be initial levels present.
This still does not address the issue that uranium is many times more soluble in water than thorium is, and that when uranium decays into thorium many of those atoms will then come out of solution and be deposited.
This is pretty simple math. After the first 1/4 life, 3/4 remain. After the next 1/4 life, 9/16 remain. 9/16 ain't 1/2.
1/4 x 1 = 1/4 First ql
1/4 x 3/4 = 3/16 Second ql
1/4 + 3/16 = 7/16 Total
-7/16 + 1 = 9/16 Result
So 2 quarterlives do not give the same result as one halflife. Other fractions will do this too. Care to see four 1/8 lives?
LinearAQ has already provided some information about why you are wrong here, and yes, it has to do with your using a linear interpolation rather than one based on the mathematical curve involved.
You can also compare this by simply to using two half lives as the original time frame: after the double half life you have 0.5x0.5 = 0.25% remaining.
Using your approach we now calculate the amount at half that time as (1+0.25)/2 = 0.625 = 62.5% ... but we
know that at a single half life we have 50%, so you obviously have an error in your assumption, in this case of a linear correlation as opposed to an exponential one.
You can actually calculate your 1/4, 1/3 1/whatever lives (properly - see LinearAQ's post) and then plot the results and you will end up with exactly the same curve as you get with half-life.
Enjoy.
