Sometimes I read some math popularization books and think, “What has that guy been smoking?”
The article by Wigener about “The unreasonable effectiveness of math” about why math seems so unreasonably effective in describing and in fact, predicting how the physical universe acts is one such case.
What has he been smoking?
OF COURSE MATH IS EFFECTIVE AT DESCRIBING THE PHYSICAL UNIVERSE.
The words we use in math, and the processes and algorithms math uses have been directly derived and mimic and reflect ONLY objects and actions that hold true in a strictly defined generalized physical universe.
Start with numbers. ONLY in a fairly restricted definition of physical universe can a discrete (defined as “apart or separate”) object be considered. One rock is only a separate object if you don’t look too closely at it, but we then generalize the ideal concept to indicate a discrete physical object.
One rock plus one rock equals two rocks only in a generalized macro physical world. Hate and fear plus three people usually equals a murder. Cheese and spaghetti equals a flavor different than both of them separately. Two ounces of vodka and a cup of Orange Juice equals a screwdriver. One cup of water and two cups of sugar equals one and a half cups of syrup. You can add love and fear and get another emotion entirely, with no clear way to separate them. Love that is shared is multiplied, love that is restricted is diminished. One electron and one positron equals a sheet of energy.
The arithmetic operations of addition, subtraction, multiplication and division only make sense if they are symbolic representations of physical processes. All our mathematical understandings of proof, and refutation depend on reflections of our understanding of physical processes. Existence of a contradiction or impossibility of the result of a logical argument are inherently based on our understanding of basic physical existence or non-existence. Emotions, flavors, sound, ideas and inspirations do not follow physical processes. You can hold two contradictory concepts or emotions or ideas at the same time, they do not add together as two discrete rocks do.
So, it is no more surprising that math reflects and predicts actions in the physical universe, than if I were to tell you the Sun will rise tomorrow. The words I use, the name of the Sun, and the action I describe are specifically used to name the object, and describe the action and reflect the physical universe.
What was he smoking that he did not see this? And why have math popularizers not recognized the unreasonableness of his argument before now?