“Are Numbers Real?”

I’ve been reading a book by Brian Clegg titled Are Numbers Real? The Uncanny Relationship of Mathematics and the Physical World (New York: St. Martin’s Press, 2016).  It deals with a really interesting topic that, in my view, may point suggest the falsehood of materialist/reductionist views of the universe.

I’ll share just a few passages from it:

“Would numbers exist without people to think about them, or are they just valuable human inventions, the imaginary inhabitants of a useful fantasy world?”  (1-2)

“Similarly, when mathematicians played around with an idea like the square root of a negative number, called an imaginary number, they were initially simply enjoying a new direction to take their mathematical game.  But, as it happened, because of the rules they decided to apply to this magical class of numbers, it became a hugely useful tool for physics and engineering.

“No scientist or engineer ever said prior to the introduction of imaginary numbers, ‘What we want is the square root of a negative number.  They would really help us with this problem we’ve got.’  Similarly, no one in mathematics thought, ‘How can we solve this particular problem that the physicists have?’ before dreaming up imaginary numbers.  The mathematicians just played with the implications of their new concept and the set of rules attached to it.  The applications emerged later.”  (7-8)

“Some scientists, such as physicist Max Tegmark, go so far as to suggest that the universe is mathematical.  That numbers aren’t just real, but are what make everything happen.”  (10)

The Pythagoreans, whose motto, carved on the lintel of the door to their principal school, was “All is number”:  “They were of the opinion that everything in the universe was structured on numbers — that numbers were not merely a human creation, but provided the underlying architecture of reality.”  (30)

“You could . . . say that mathematics is an agreed fiction, a shared mental world that mathematicians agree to collectively inhabit.  But their world isn’t allowed the looseness of literary fiction, because here all the rules have to be pinned down and agreed.  As long as a piece of mathematics is consistent with those rules it is acceptable, whether or not it has any parallel with the physical universe.  Yet we keep coming back to the fact that a sizable subset of mathematics not only has parallels, but has an uncanny ability to mirror what the real world can offer.  It could just be because so much of the essential structure that mathematics is built on — like the nature of whole number arithmetic — started as a reflection of the real world.”  (52)

Brian Clegg is looking at the same general issue as that raised by the Nobel-laureate physicist Eugene Wigner in his famous 1960 paper “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”

The English physicist, astronomer, and mathematician Sir James Jeans (d. 1949) had perhaps been thinking along similar lines when he remarked, in his 1944 book The Mysterious Universe, that “The stream of knowledge is heading towards a non-mechanical reality; the Universe begins to look more like a great thought than like a great machine. Mind no longer appears to be an accidental intruder into the realm of matter. . . .  we ought rather hail it as the creator and governor of the realm of matter.”