# Creationist Physicist Doesn’t Understand Mathematics, Either

If there’s one consistent aspect of creationism, it’s that people lacking understanding and training are put forth as experts. Here we have yet another example, from the creationist blog Uncommon Descent. There  physicist Rob Sheldon is quoted as saying

THere [sic] can even be uncertainty in mathematics. For example, mathematicians in the 1700’s kept finding paradoxes in mathematics, which you would have thought was well-defined. For example, what is the answer to this infinite sum: 1+ (-1) + 1 + (-1) …? If we group them in pairs, then the first pair =>0, so the sum is: 0+0+0… = 0. But if we skip the first term and group it in pairs, we get 1 + 0+0+0… = 1. So which is it?

Mathematicians call these “ill-posed” problems and argue that ambiguity in posing the question causes the ambiguity in the result. If we replace the numbers with variables, do some algebra on the sum, we find the answer. It’s not 0 and it’s not 1, it’s 1/2. By the 1800’s a whole field of convergence criteria for infinite sums was well-developed, and the field of “number theory” extended these results for non-integers etc. The point is that a topic we thought we had mastered in first grade–the number line–turned out to be full of subtleties and complications.

Nearly every statement of Sheldon here is wrong. And not just wrong — wildly wrong, as in “I have absolutely no idea of what I’m talking about” wrong.

1. Uncertainty in mathematics has nothing to do with the kinds of “infinite sums” Sheldon cites. “Uncertainty” can refer to, for example, the theory of fuzzy sets, or the theory of undecidability. Neither involves infinite sums like 1 + (-1) + 1 + (-1) … .

2. Ill-posed problems have nothing to do with the kind of infinite series Sheldon cites. An ill-posed problem is one where the solution depends strongly on initial conditions. The problem with the infinite series is solely one of giving a rigorous interpretation of the symbol “…”, which was achieved using the theory of limits.

3.  The claim about replacing the numbers with “variables” and doing “algebra” is incorrect. For example if you replace 1 by “x” then the expression x + (-x) + x + (-x) + … suffers from exactly the same sort of imprecision as the original. To get the 1/2 that Sheldon cites, one needs to replace the original sum with 1/x – 1/x^2 + 1/x^3 – …, then sum the series (using the definition of limit from analysis, not algebra) to get x/(1+x) in a certain range of convergence that does not include x=1, and then make the substitution x = 1.

4.  Number theory has virtually nothing to do with infinite sums of the kind Sheldon cites — it is the study of properties of integers — and has nothing to do with extending results on infinite series to “non-integers etc.”

It takes real talent to be this clueless.

1. robert79 says

It’s “ill posed” in the sense that it’s unclear what is being asked in “1 – 1 + 1 – 1 + …”

From wikipedia:
“The mathematical term well-posed problem stems from a definition given by Jacques Hadamard. He believed that mathematical models of physical phenomena should have the properties that:

1.) a solution exists,
2.) the solution is unique,
3.) the solution’s behavior changes continuously with the initial conditions.”

The given problem fails on the first two points, not the third.

After that I agree it’s just gobbledygook. His problem is so ill posed that we cannot even talk about a solution, so it’s nonsense to claim that the solution is 0, 1, or 1/2 until you define exactly what you mean.

“The point is that a topic we thought we had mastered in first grade–the number line–turned out to be full of subtleties and complications.”
This is actually a point I agree with. I’ve heard university professors discuss whether they should teach the definition of a real number to first year maths students. We may think we have a reasonable idea what real numbers are, but in fact we mostly just understand rational numbers. There ARE a lot of subtleties and complications.

• shallit says

You may think you understand what an “ill-posed problem” means for mathematicians by quoting Wikipedia, but you don’t.

No actual mathematician would agree that 1 + (-1) + 1 + (-1) + … is “ill-posed” in the sense understood by mathematicians.

Here, check this out.

• shallit says

We may think we have a reasonable idea what real numbers are, but in fact we mostly just understand rational numbers.

• Lee Rudolph says

We may think we have a reasonable idea what real numbers are, but in fact we mostly just understand rational numbers.