ONE OF THE EARLY pieces I posted on line used a little elementary algebra to make a point about the kind of calculation that liberal politicians had to go through to decide if an issue a group of their constituents or others was interested in was worth the cost it would inevitably be to them if they championed that issue.
I called it " They Can Hold Their Breath Long As They Want That Won’t Turn The Country Blue Single Issue Politics,"
and thought it was brilliant and elegant in its obvious simplicity. Readers were unimpressed. I remember someone at the time telling me even that much math was too much because peoples' eyes glazed over as soon as numbers and an equals sign were introduced.
They wanted no more than a number maybe with a percent or dollar sign attached to it, that was the extent to their desire to have numbers attached to things. I think that accounts for why Jim Jordan kept haranguing Dr. Fauci for a number last week when Dr. Fauci, not willing to lie with numbers wouldn't give him that kind of lie even at the cost of knowing Jordan and the worst of the Republican-fascist caucus in the Congress would use his refusal to lie against him and the American People.
As recently as yesterday I was going to leave out the mere descriptions of the more complex math that A. S. Eddington gives MERELY AS EXAMPLES of the kind of mathematical structuring that is the very heart of modern science, though I think he really meant by that modern physics and cosmology more than the sciences that deal with things on the atomic, molecular level, chemistry, and the legitimately called life sciences. I think that kind of thing gets turned on its head not infrequently in the pseudo-social sciences such as psychology and numbers are used to lie in a way that Jim Jordan was insisting on, not to mention even more dishonestly and ideologically in economics and sociology.
I'm thinking that my original intention of going through A. S. Eddington's well developed logical arguments in The Concept of Structure from The Philosophy of Physical Science is not going to work the way I had hoped it would due to eye-glazing. My original inspiration was to present it to counter some of the perennial objections to my anti-materialism that come in whenever I get close to violating that enforced requirement of respectability. Eddington's arguments are always strong though when he chooses to make them through the modern physics of the early 20th century, they quickly stop being effective as a means of persuading most people.
I am tempted to go to his conclusions, the ones he comes to along the way and his later ones that incorporate those. Those are the things important to my point about the absurdity that thinking even the grooviest of current physics is going to come up with anything like a complete explanation of everything. But I'm going to use Eddington's complete argument for as long as its useful. I'm not even sure exactly how current some of it is but it would have been at the time he was making his points and I don't think those have aged at all. So here goes.
A terminable set of operations, or as it is technically called a group, has a structure which can be described mathematically. The fact that the operation which changes P into Q is always another member R of the group furnishes a set of triangular connections as the groundwork of the structure. These triangular connections that interlace in a great variety of patterns; and it is the pattern of the interlacing which constitutes the abstract structure. The mathematical description of the group specifies only the pattern of interlacing, and pays no attention to the physical nature of the operations with the same group structure, and therefore equivalent so far as mathematical description is concerned.
Which is not that shocking, though it might lead you to consider not the validity of what they are doing but in the more outlandish claims made that, in effect, the mathematical description of things does, in fact, determine the physical nature and, really everything, about the things they use mathematics to study. I think a lot of the rasher claims for what they can figure out using this level of mathematics is an act of faith in the potency of this mathematical treatment to envelop everything about anything when, as Eddington said, it is unable to go beyond that point.
The usefulness of what Descartes started, the power of it has made us forget the limits of what is claimed for it. The absurdity rises entirely when they want to make it do things it can't do and which only sometimes can be tested with the methods of science. They should admit when that is not possible and so there is no possibility of verification of their thinking, and it's not only a problem on the subatomic level and farther down but when phenomena of life are too complex, too hidden from observation, too diffuse to capture or, in some cases, to even know if there is a phenomenon there or if it's the product of the not infrequently self-interested scientist or social-scientist wanting to make claims about it.
Going on, you'll see the problem with using the complete lecture to make my point.
One of the important groups in physics is the group of rotations in six dimensions. There are fifteen independent planes of rotation in six-dimensional space (corresponding to the three independent planes of rotation in three-dimensional space); and since we have always to add the operation of "leaving things as they are", which is an ex officio member of every group, we have sixteen elements with which to form a group-structure. A definite interlocking patter is constituted by the association of these elements (other than the ex officio element) in six sets of five (pentads), each element being a member of two pentads. Interlacing with it is an association of the elements in triads, the triads themselves being associated in conjugate pairs. Each of the fifteen elements plays an equivalent part in the pattern.
Rotation in six dimensions is only one of many sets of operations which yield this particular group-pattern. For example, if we place four different coins on the table, the operations of interchanging them in pairs, with or without turning one pair the other way up, form a group with this structure. The same pattern of relations turns up in the geometry of Kummer's Qadratic Surface, in the theory of Theta Functions, and - most important of all for our purposes - the specification of an elementary particle (proton or electron) in an elementary state, including the specification of its charge and spin.
If, by the end of that your eyes were glazing over, well, I would imagine that may have been the case of many of Eddington's audience for the lecture. Eddington was one of the most accomplished mathematical minds in England and the world, at the time. Even very accomplished mathematicians will have entire realms of mathematical thought to which they are not even novices, it being such a huge and hugely varied field. We mere mortals have to take what the ones who are masters of the currently accepted applications of their mathematics as knowing what they're talking about, we, like even very accomplished mathematicians and scientists in unrelated fields, are reliant on their honesty and integrity which is, of course, based in nothing to do with this but with their sense of morality. Eddington was an extremely moral person who I wish would have written more about the relationship of his moral reliability to his Quakerism which doesn't seem to have been at all diminished by his learning in science and mathematics. I can tell you that from what I've read of his life and his reputation, I would trust him a lot more than some of his colleagues who rejected the foundations of morality on the basis of their knowledge of mathematics and physics and biology.
Properly to realize the conception of group-structure, we must think of the pattern of interweaving as abstracted altogether from the particular entities and relations that furnish the pattern. In particular, we can give an exact mathematical description of the pattern, although mathematics may be quite inappropriate to describe what we know of the nature of the entities and operations concerned in it. In this way mathematics gets a footing in knowledge which intrinsically is not of a kind suggesting mathematical conceptions. Its function is to elucidate the group-structure of the elements of that knowledge. It dismisses the individual elements by assigning to them symbols, leaving it to non-mathematical thought to express the knowledge, if any that we may have of what the symbols stand for.
If you can't see the problem with that practice WHEN IT IS APPLIED TO NOT ONLY THINGS WHICH CAN'T HONESTLY BE TREATED THAT WAY BUT, ALSO WHEN MATHEMATICS IS USED TO CREATE AN ILLUSION OF A SUBSTRATE OF A STRUCTURE BEING REAL YOU SHOULD LOOK AT WHAT MUCH OF THEORETICAL PHYSICS HAVE BEEN DOING FOR THE PAST FOUR DECADES* and what the social sciences have done on a continuing basis whenever a lot of mathematics is used to support the existence of things which not infrequently have been deemed later to have been illusory. It may well be that one of the most frequently pursued and sited "phenomena" of psychology in recent years, ego depletion, is such an illusion. And on such illusions rests a great deal of current racist, class-discriminatory public policy which blights the lives of hundreds of millions if not billions, of which the racist "Bell Curve" of Herrenstein and Murray and championed by the likes of Andrew Sullivan is based. The entire history of the use of "IQ" at least in the Anglo-American manner is based on a far more primitive use of mathematics divorced from the actual things it was alleged to do.
It does get even more interesting, among other reasons, for showing just how limited an "everything" the allegedly almost in hand "theory (theories, really) of everything," ideologically proclaimed and used by even physicists who should know better but, especially, ideologically motivated cosmologists, how not "everything" their theories and the applications of their proposed rock bottom "TOE" or unified-theory will be. Yet they make the most outlandish claims about what they are on the cusp of producing.
That started long, long ago, with the dawn of modern science when the current best knowledge supported that claim ever so much less and the habit was established. And all along the way, certainly as early as Mandeville in the early 18th century and even earlier and to even more lasting evil effect, Thomas Hobbes, extending then current science on a faith that, having an attachment to numbers extrapolated from their usefulness in measuring observations, using such imaginary structure to apply them where they never had any business going. I think my modest use of them, which I admitted was a thought experiment was on far firmer ground and to far better effect. But, then, my motives were to extend equality and the common good. Which didn't come from any math I knew or science.
It is supremely ironic and something visible in the "evangelical" and "prosperity gospel" Trump vote that the Hobbesian and Mandevillian thinking that starts in the ideological uses of 17th century science, or at least found its excuse through its misuse, seems to have thoroughly rotted out that most "Anglo-Saxon" branch of popular religion that mistakes itself for Christian in such a big way. I'll add as a provocative observation on my part, passing up the opportunity to include Nietzsche, who I think is more of a shadow on the neo-con side of things.
* I will again mention what the world's favorite recent theoretical physicist and cosmologist, Stephen Hawking demanded, that his branch of universe creation through numbers be accepted as a valid part of physical science even though there is no possibility of finding evidence that such mathematical structures are anything more than imaginary. I mention it so often because I thought it was offensively dishonest and because I thought it exposes the ideological nature of that kind of thing within science at its highest levels of accomplishment and repute. As I argued, beginning with Hobbes and Mandeville, that kind of ideological use of science has the most devastating of consequences for morality and the production of a decent life, not in a small way by rotting out the culture of the educated class.
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