| Where Recherche duTemps Perdu
---- meets Kirchliche Dogmatik
Happy Fourth of July to all relatives, friends, acquaintances, fans, colleagues and work associates of the past, present, and future. Whether you’re celebrating or not, the day is on your calendar, and I hope it is a good one for you. The question here in Smalltown USA and environs is whether the weather will clear up for fireworks tonight. Just like yesterday, it’s cold (for July), dark, cloudy, and drizzly outside. The hour-by-hour forecast has it clearing up by around 9 pm tonight, which would be the time that it started to get dark enough for our incendiary displays. We’ll see.
Late addition: The weatherman hit the proverbial nail on the head. June and I just got back from a wonderful evening with Nick & Meghan and Seth & Amber at the former’s house in the country. N&M had everything ready for hoboes for supper and strawberry shortcake for dessert, and we had some awesome fireworks. Obviously, Sunako was there, since she lives there, and S&A brought Misha, the aging whippet, and Evey, the baby Great Dane.
I have added all of the previous posts relating to this series to the Phi website. Let’s get ourselves caught up on where we are in this long and drawn-out series, beset by many a tangent. I’ve stated that a Christian, scientist or not, should see God’s hand in the beauty and order in the world that God has created, and that such beauty should extend to the world of numbers with a beauty all its own. I expressed my disappointment with those Christians who are too eager to maintain standing in the so-called community of scientists to acknowledge that even the question of whether there is scientific evidence of intelligent design in the cosmos is a legitimate one. The subtopic at this point is those scientific luminaries who appear to go in the opposite direction and seem to be finding God in the mathematical structure of the universe itself.
Michio Kaku (1947– ) is known as a successful physicist who invented string theory and some of its subsequent developments, such as super string theory. He is also an adept populariser of physics and mathematics, and, consequently, has become well known; he quite obviously enjoys talking to the world’s population at large about science and himself, not reluctant to express opinions outside of his area of expertise. As promised in the last entry, here is his YouTube video, entitled “Is God a Mathematician?”
I’m going to follow Professor Kaku fairly closely in this round. Don’t worry; I’m not going to challenge him on the validity of string theory. There are three major figures mentioned in this short talk: Newton, Einstein and Kaku. In the actual video he does not address the question whether God is a mathematician, but of what good math actually is.
Note: I have tried several ways of formatting this discussion, and I found it to work best for me if I include my responses and critiques right along with the summaries.
(1) Isaac Newton. Kaku uses Isaac Newton as an example of a time when innovations in mathematics and physics came up together.
(a) Kaku applauds Newton for asking the question: “If an apple falls, does the moon also fall?” He classifies this question as among the greatest that any member of homo sapiens has ever asked in the 6 million years since we departed from the apes.
Response: Along with all other members of our species, Kaku is entitled to his opinion, as long as we are clear that it is nothing more than his opinion. Personally, I have a problem with his evolutionary assumption, and even if I didn’t, I’m pretty sure that I would not include Newton’s concern among the top questions ever asked by humankind. But that’s a matter of perspective.
(b) Kaku’s narrative goes on: Newton’s answer to his own question was that, yes, the moon also does fall (viz. the moon is attracted to the earth by the pull of gravity). However, Newton lacked the mathematical tools to explain this idea. So, he invented calculus in order to make it possible.
Response: Is that how it happened? I don’t think so. Newton described gravity with a famous equation, oftentimes referred to as the Inverse Square Law (ISL), where G is called the gravitational constant.
The force of gravity between two objects is obtained by multiplying the mass of the two objects, dividing that number by the square of the distance between them, and multiplying the result by the gravitational constant.
I do not see any calculus here. This formula was included in Newton’s Principia Mathematica, which came out in 1687, and which did not contain any calculus. His first publication on calculus did not appear until 1693.
(c) Kaku then summarizes Newton’s conclusion: “The moon falls because of the Inverse Square Law. So does the apple.”
Response: I replayed that segment of the video several times in order to make sure I heard correctly, and the closed captions also bore me out.
“The moon falls because of the ISL.”
Scientists don’t usually say such things. The laws of science are descriptions. Often they are statistical generalizations, and frequently they appear so ironclad that there appears to be no way around them. But there is one thing that they never are, namely causal agents. The ISL describes the earth/apple and earth/moon attractions mathematically. It tells us how to calculate the gravitational force, but it does not explain the presence of a gravitational force. Both the moon and apple would still be falling, regardless of whether we had the ISL or not.
Is this just verbal nit-picking? Should I just dismiss Kaku’s phrasing as a momentary and careless slip of the tongue, something that happens to all of us from time to time? Usually I would say so, but in light of the status that Kaku eventually gives to the laws of nature a little later on, I can’t rule out that he looks at the ISL—among others laws of nature—as more than just a description. Also, as I said above, scientists are usually far too careful to use such careless phrasing, especially, I would think, in a video published to the entire world (at least the part covered by YouTube), so I can’t help but see some intentionality in Kaku’s remark.
(2) Albert Einstein. Albert Einstein is Kaku’s example of a case where a physicist was able to draw on a mathematical method that was already available prior to making an innovation in physics.
(a) Kaku tells us that Einstein came up with a new way of looking at gravity. The key to Einstein’s general theory of relativity was that he envisioned space as curved, and gravity is due to that curvature, not a force of attraction. The fact that he remains in a chair, Kaku assures us, is not because gravity pulls him, but because curved space pushes him down.
Response: I will just say that I have never heard it put that way. More commonly the explanation is that mass and energy create curvatures in space, so that my sitting in a chair causes a little protuberance in space into which I have sunk myself. Kaku seems to substitute one mysterious force for another, i.e. pushing instead of pulling, and I’m just a little confused on why he would put it that way. Still, I’m not going to argue with Kaku over matters that are purely physics. Maybe someone else can comment (nicely) on that description.
(b) According to Kaku, Einstein was also in need of a mathematical means to describe his innovation in physics. But he did not have to come up with anything new; he could simply avail himself of “differential calculus,” which already was in place. After all, he reminds us, studying calculus usually begins with the motion of falling objects, i.e. gravity.
Response: The last part of that little summary is true. Among other things, differential calculus analyzes the rate of change in the velocity of an object in motion at a particular time, e.g., the acceleration of a moving object, or even the acceleration of the acceleration. This is one part of calculus that Isaac Newton and Leibniz had already invented, and if Einstein would first have had to learn differential calculus at that point in time, he would not have been much of a physicist. (The other part of calculus is called integral calculus.)
Einstein did not need differential calculus to make his theory of space rigorous. Professor Kaku's statement implies that we begin the study of calculus with differentiation (aka “finding derivatives”), and that would most likely be true for pretty much everyone, I would think. But Einstein’s math goes far, far beyond “differential calculus.” Yes, there is calculus involved, but so are addition, subtraction, multiplication, and division. Surely all of these mathematical procedures become trivial characterizations in connection with Einstein’s work. If we were to try to cover Einstein’s math with short expressions, we might want to say that it was “tensor calculus” for the special theory of relativity and “Riemann field geometry” for the general theory. I don’t understand why Kaku trivialized Einstein’s work with the expression he used.
Could this just be a sloppy choice of words, and am I maybe nit-picking again? Once again, I doubt it. Who, given just a small amount of understanding of what is involved, would say that Einstein resorted to “differential calculus” for his general theory? This is not just careless, but misleading. One of the world’s foremost scientists must know better than to make such a mistake. My hunches: Kaku is trying to put us at ease by using a term that is not going to frighten us away. After all, we’ve all studied calculus, right? Could there be a further reasons to minimize Einstein and, thereby, establish a contrast to himself?
To get a flavor of relativity math—or maybe even to learn it—may I suggest Peter Collier, A Most Incomprehensible Thing: Notes toward a (very) gentle introduction to the mathematics of relativity (Incomprehensible Books, 2012). I must say, though, that Collier and I might just disagree on the meaning of “very gentle.” I suspect that there actually is no gentle way of learning this material.
(3) Michio Kaku. As you can see in the video, Professor Kaku is not exactly humble about his accomplishments, and I, for one, want to congratulate him on his life’s work. Even if string theory, super-string theory, M-theory, etc. are not going to hold up in the long run (and I am definitely in no position to judge that), his ideas have been significant in keeping the search for ultimate physical reality moving ahead.
(a) The holy grail, so to speak, of theoretical physics is a unified field theory, an explanation for everything. Einstein spent the majority of his life in a futile quest for it. Kaku believes that he has found it with his super-string theory. Such a theory should be able to be captured in a short equation, not more than an inch or so long. He has accomplished it, and here it is:
Response: I have no idea what this equation says, and am in no way qualified to evaluate it. It represents the vibrations of really tiny strings in the 10th and 11th dimensions, and I understand that the high degree of difficulty in understanding it is not just limited to us amateurs who like to read books about math.
(b) The math for Kaku’s string theory is analogous to that of topology, much of which was first formulated towards the end of the nineteenth century. It is an extension of algebraic geometry, reaching into higher and higher dimensions. As Kaku tells it, those who contributed to the development of topology took great delight in the fact that this was math at its best, namely, math that would never have any practical applications since it includes multiple dimensions beyond our usual three (or four if you count time).
Response: The more dimensions you give yourself to work with, the more problems you can solve. If you only had two spatial dimensions, you could have a flat depiction of the eye of a needle and some thread, but you could never thread the needle. To do that, it takes three dimensions. Topology uses that principle and develops some truly bizarre models of algebraic objects in greater spatial dimensions. I’ll leave it to Professor Kaku to judge to what extent the mathematicians delighted in the so-called lack of applicability.
(c) Along came Michio Kaku, who used 10 and 11 dimensions in order to come up with his super-string theory. Mathematicians were surprised, if not shocked and appalled.
Response: As well they should be. You’ve got to be in awe of Kaku’s work.
(d) The vibration of these strings constitute the “music of the spheres,” and the very voice of God. He, Michio Kaku, has had a glimpse of the core of the universe, where he finds God communicating to him through the equation that he, Professor Kaku, has constructed.
Response: It would appear that Michio Kaku has endowed himself with the offices of prophet and priest in the religion of super-string physics. He has departed from physics and is trying to do theology, and the result is dubious.
We need to leave the more specific content of this religion for next time.