I’ve been reading a lot lately on the nature of time and space from the perspective of physics, and I cannot help thinking of the drunk looking for his car keys under a streetlamp. Asked by a passerby where he last saw them, he replies, “In that dark alley.”
“Really?” asks the bystander. “Then why are you looking here?”
“Because the light’s better!”
To a physicist, mathematics is the light. It is the hammer for which all problems resemble a nail. It is the hail and farewell of a journey not taken.
Don’t get me wrong, I am fully aware and appreciative of the power of mathematics. Without it, I couldn’t be “writing” this post — tapping on plastic bumps, confident that not only will the resultant deviations of light on an entirely separate slab in front of me configure themselves to reflect my thoughts, but also send mysterious invisible waves into the night so that you can see those same squiggles on your slab. But the formulas that describe these processes are not identical to the processes themselves, as phenomena in the real world. They are models, or
… task-driven, purposeful simplification[s] and abstraction[s] of a perception of reality … [emphasis mine]
In other words, take out all the messy, inconvenient bits and see if you can’t come up with something useful. There have been powerful models of reality throughout history that have enabled marvelous results, and that we have since decided are inaccurate. I need only mention shamanism and acupuncture. And even physicists, despite all their rhapsodizing about mathematics, still can’t make all their theories play well with each other without imaginative gymnastics.
Mathematical models are by far the most universal and fruitful of these, but are they real, in the sense that the universe works that way a priori? Not according to Raymond Tallis:
The mathematics of light does not get anywhere near the experience of yellow, nor does the mathematical description of patterns of nerve impulses reach pain itself. This is sometimes seen as evidence that neither the colour nor the pain are really real – although it might be difficult to sell this claim to the man looking at a daffodil or a woman with toothache.
I have no quibble with the idea that models, mathematical or otherwise, are indispensable for our understanding of the real world, but physicists have been insisting that they are the real world. They cite Occam’s Razor, the axiom that the simplest explanation is always not only the most likely to be true, but is actually true.
Ironically, William of Occam, the late medieval monk for whom this principle is named, did not believe in the existence of universal laws of nature. Humans, he thought, had made them all up for convenience.