Recently, British physicist David Tyler wrote about the interesting research done with a very small South American tribe whose 200 members shun arithmetic, as well as other abstractions.  Many of us are tempted to join them - until

we suspect that we have been accidentally overcharged at the checkout counter ... Then we want math justice immediately!

In that case, we must talk about very specific numbers. About $24.99, for example, vs. $49.98 ... a double ring on the same item? But for only one item, and we know we didn’t buy two?

Many scientists have pondered the evolution of mathematical ability. In The Design of Life, in the General Notes (on the CD), three key ideas about how mathematical ability comes to exist are discussed:

The adaptationist hypothesis - math skills got Fred Flintstone through his day!

An “adaptationist” hypothesis means that mathematical ability helped our ancestors survive and produce fertile children.

Yes, perhaps, ... but only up to a point.

It will certainly help you in a dispute with the checkout counter supervisor over $24.99 vs. $49.98, when you only bought one $24.99 item and have the whole bag with you, unopened.

These dramas surely played out in markets worldwide for many tens of thousands of years, whether they involved a pair of jeans, a toga, or a parka.

But what use would Einstein’s Field Equations be in such a case, assuming we understand them?

Actually, most key mathematics advances have NOT been driven by a need to get on in life. As C.S. Lewis wrote,

Egyptian and Babylonian Mathematics were practical and social, pursued in the service of Agriculture and Magic. But the Free Greek Mathematics, pursued by Friends as a leisure occupation have mattered to us more.

Lewis did not, of course, mean to disparage the practical uses of mathematics, which enabled the pyramids and the ziggurats, as well as the impressive Egyptian system for managing the water flows of the Nile.

What Lewis meant - and this is the difficulty all such for adaptationist theories of mathematics - is that the major theoretical advances do not typically arrive in response to an urgent practical problem. Urgent practical problems can be solved by fairly limited advances.

Major advances (which lead to insights that solve problems which were not anticipated) more commonly depend on a need to understand how the universe really works and to express that understanding in the most elegant way.

So if mathematics is really an adaptation, it is an adaptation that suggests design rather than chance as the origin of our universe. That is, mathematics is a means of discovering meanings that we suspect and then discover once we get there - even though we do not clearly understand how the discovery will benefit us.

The byproduct hypothesis - Math didn’t kill Fred Flintstone!

According to this hypothesis, math didn’t help your cave ancestors but it didn’t hurt them either, and that’s why you can do math now. (Or, okay, maybe you can’t - but let’s not go there just now.) The basic idea is that the ability to figure out higher math just sort of happened because people don’t die just because they can solve the math problems you can’t solve. So they happen to live anyway.

About this, the The Design of Life authors say,

Some free lunches are just too good to be true. And precisely when they are too good to be true, they require explanation. That’s especially true of mathematics: Here we have a human capacity that not only emerges, according to the byproduct hypothesis, from other capacities, but also provides fundamental insights into the structure of the physical universe (mathematics, is, after all, the language of physics). How could a capacity like that arise as the byproduct of a blind, evolutionary process, unguided by any intelligence? It is not a sufficient explanation here simply to say that it could have happened that way. Science does not trad in sheer possibilities. If our mathematical ability is the byproduct of other evolved traits, then the connection with those traits needs to be made explicit. To date, it has not been. (P. 6, General Notes)

In short, the main question is not "How does the ability to do math survive?", but "How does it arrive?" - and then turn out to be just what we need to understand the universe?

Woo hoo!! Wilma Flintstone fell in love with Fred because he understands higher math!

Some theorists, seeking an explanation for advanced human mathematical ability, turn to the “sexual selection hypothesis.” The ability to do math, even useless math, attracts mates. So that guy who spends all his time trying to find the next biggest prime number is a hot date. And the only girl in the class who understands non-Euclidean geometry is the belle of the ball.

Is that the popularity index at your school? Naw, it wasn’t at my school either, forty years ago, and no one expects things to change much in this area.

The skinny: Math puts us in touch with the universe and that is its job

As Bill Dembski and Jonathan Wells write,

In short, the main difficulty with all three hypotheses is that they attempt to account for an existing state of affairs without hard evidence of the factors that brought it about - only speculation. In the case of mathematics in particular, that is an especially severe deficit because higher mathematics is not obviously useful when it first emerges. The fact that uses are sometimes found later is, on conventional evolutionary grounds, irrelevant to its emergence. It becomes relevant only if one is justified in thinking that here is purpose in nature. (GN7)

They add,

... from an intelligent design perspective, mathematics is readily viewed as an inherent feature of intelligence and rationality. Moreover, the fact that the mathematical theorems we prove mirror the deep structure of physical reality suggests that intelligence is fundamental to nature and not merely an accidental or historical byproduct of blind material forces. (GN7)

Well, maybe we live in a designed universe after all. You couldn’t prove otherwise from mathematics.

Further Reading

Eugene Wigner - The Unreasonable Effectiveness of Mathematics

George Gilder on how we know that the universe is top down, not bottom up