Substituting mathematics for experiments
A friend of mine from Dallas sent me this quote earlier this evening:
Today’s scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.
Nikola Tesla, Modern Mechanics and Inventions, July, 1934
Tesla was certainly on to something, and if he thought things were bad in 1934, he would be aghast at science, today. Mathematics (as all knowledge) is never any better than its underlying assumptions, and without experimentation and empirical observation, it’s hard to know whether or not your assumptions have any basis in reality. Mathematical conclusions are not true, in and of themselves – they are only true if (A) their underlying assumptions are true and (B) the laws of mathematical grammar and syntax that have been used to derive them are valid. I’ve often felt (though not always felt and not consistently felt) that it is best to view mathematics as a language – as Galileo said, the language with which God has written the universe. (Actually, he didn’t mention God… here’s the full quote: “Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth.”)
We can’t understand the workings of the universe without mathematics, yet mathematics alone is certainly not enough. The standard procedure should be (A) observe reality, (B) build a mathematical model that seems to fit it, (C) use the mathematical model to extend knowledge about the model, and (D) check to see if the new knowledge about the model corresponds to previously unknown facts about reality. But a lot of assumptions often go into step (B), and step (D) is sorely lacking in some avenues of research (string theory, evolution, cosmology, etc.).
[FYI: I base this simple "standard procedure" on something I read in Jerry P. King's The Art of Mathematics, a book I HIGHLY recommend to anyone who is or is not a mathematician and who wants to understand what mathematics is "all about" and how it can be described as "beautiful," "elegant," and "poetic." Really, it's a marvelous book.]
What I love most about mathematics is what I see in it about the mind of God, in the spirit of Romans 1:20. But that is a post for another day…
A lot of the reason why step D has been foregone is because our understanding of mathematics has advanced to the point that many of the conclusions that we reach are “untestable”…at least at our current level of technology. That’s one of the beautiful aspects of mathematics. Mere observation and experimentation don’t allow for steps C and D with the same relative ease that mathematics allows.
Here’s an interesting read for you:
http://physicsweb.org/articles/world/18/9/3
It talks about the possible topological structure of the universe, and suggests some fascinating possibilities that CAN be tested…eventually.
Where’s a good quantum computer when you need one, eh?
Did someone say String Theory?? Although there are fun thought experiments out there on it:
http://www.tenthdimension.com/flash2.php
Howdy, Ben & Mike –
Mike: That is a pretty nifty animation out there! I have found one of the most helpful discussions of visualizing multiple dimensions (for me, at least) to be Rudy Rucker’s book, “Geometry, Relativity and the Fourth Dimension.” He also wrote a great book (again, for me, at least) called “Infinity and the Mind,” which is what really got me into the concepts of different sizes of infinity, transfinite cardinals, and the like. I’d recommend either of them (though it’s been a long time since I have read them).
Ben: I agree with you! The fact that the structure of law and principle with which God has imbued the universe can be described so cleanly by mathematics makes it so very easy, especially today, to extend our ideas far beyond today’s “testable” boundaries! Perhaps, I suppose, in a similar fashion to the way that our use and mastery of other more common languages — English and the like — have extended various philosophical models of practical morality to the point that their “testing” could not happen until many years down the road, when the “fruit” is finally ripe. (Fortunately, God will cut short that harvest, a la Matthew 24:22! :^) )
Unfortunately, mathematics is so dependent on initial assumptions and accurate initial modeling that a grain of salt must always be included while digesting the results of step C before step D is possible. And I would hate it if highly popular mathematical models (such as the billion-or-so variations of string theory, of which I am fond) suck all the air out of the room, so to speak, and do not leave any oxygen behind for the creation of alternate models. For example, it seems to me (in my uneducated opinion) too soon to accept the dark matter/energy “standard model” of cosmology when there are other interesting possibilities out there, such as the F=ma to F=m(a^2)/a0 modification.
Actually, that one doesn’t really bother me as much as evolutionists pointing to the results of mathematical models and claiming “proof,” when the models are *incredibly* dependent on the chosen assumptions. The relative ease with which one can elegantly and beautifully mathematically model a universe is a bit too seductive, and I think that too often an “alternate” universe is modeled unknowingly.
I suppose that is why I am fond of experimenters, although I personally hate doing experiments. That’s why I went against my college counselor’s recommendation and pursued pure mathematics instead of applied — I’d rather prove why the theorems work than figure out which one of them uses asumptions that actually fit the data. (Odd that I eventually became an actuary and had to do just that sort of stuff…) That’s also why I did not take the related lab when I took the nuclear physics and relativity class at Texas A&M: I didn’t need the credit and I wanted the equations without the hassle! :^) Yet, when it comes to believing that the model matches the reality, I tend to be more hesitant than I used to be. Maybe it’s the ghost of Godel, I don’t know…
Thanks for the article, by the way! It’s a neat one. I have only had the time to start it, but I plan to read the rest later. Have you read much on the David Bohm holograph universe model thingy? Ever since reading an article about the discovery (a step A, B, & C “discovery,” I think!) that a black hole’s entropy was determined by its surface area and not by its volume and the implications of this on “maximum information,” I have found the idea of “universe as hologram of a deeper something” to be fascinating, but I have never had the time to read up on it any further. (Apparently I had no time because I was busy writing long-winded comments…)
Thanks, guys, for writing. Hope to see one or both of you at the Midwest Regional Family Weekend!