I AM LEAVING OUT some of the mathematical example in section III of Eddington's lecture, The Concept of Structure because it is, in a way, a recapitulation of what he has already said using mathematical examples. Hey, if science can leave things out, so can I. I hope this has encouraged you to read his book which contains a lot of information and ideas worth thinking about, hard. Especially when encouraged to buy, wholesale, the ideological claims of well positioned, well thought of sci guys, especially as they almost always make those claims about things well outside of what made them famous. Though, as I've continually pointed out, BY COMMON AGREEMENT AMONG SCIENTISTS huge areas of human experience are excluded from their study and, also, something I've never seen admitted anywhere in science, the experience of other presumably sapient creatures not human, such scientists continually want to use the science that cannot touch those things or even has a means of including them in their specialized and limited calculations and measurements and connecting numbers on graphs even as they claim they can do so and, guess what, what they find generally supports what they wanted to find. At least that's what gets reported. Though, to some extent, that is also a product of the selective choices of journal editors and referees, department heads and the not exactly ideologically disinterested general culture of science and academia. The farther away from the idealistic definition of science you get, the more obvious that becomes. Though there are honest people who work in all of the physical sciences, that, too, diminishes rather fast the more attenuated the claims of using scientific method becomes.
. . . In order to formulate this point explicitly we shall distinguish between a structural concept and more general kinds of concepts. A structural concept is obtained from the corresponding general concept by eliminating from our conception everything which is not essential to the part it plays in a group-structure. It is an element in a specified pattern without any properties except in connection with the pattern. Its properties are those of a mathematical symbol, which consist solely of its associations (or, more strictly the associations of its associations) with other symbols. The corresponding general concept, if any, is our conception of what the symbol represents in our ordinary non-mathematical form of thought. A general concept lacks the precision of a mathematical concept, and is often difficult to pin down to anything definite. Except as applied to sensations, emotions, etc. of which we can be directly aware, it is doubtful if the general concept is more than a self-deception which persuades us that we have an apprehension of something which we cannot apprehend. Nevertheless, such concepts must be reckoned with is part of our ingrained form of thought.
I object to this claim by Eddington as the ability to do math about something is no guarantee that what is claimed is not a self-deception, an "apprehension of something which we cannot apprehend." The history of even physics and mathematics contains such things, the aether which he admitted about half of physicists of his time still believed was there and had explanatory power, I can't recall which eminent British physicist of the late 19th or early 20th century claimed he knew it was there because he could measure it (one wonders if he meant the same way that today's cosmologists "know" that dark matter and, or dark energy is there because it makes their equations balance). One looks at the unspoken of boneyard of discontinued science and looks at the papers that supported the existence of such science and find it is chock full of numbers, equations, tables of data, etc. And I've mentioned here, recently "ego-depletion" in what gets called science by scientists but which, when looked at using basic formulations of scientific method - checking to see if they could replicate the original studies - it disappeared. I would not call the many years that the concept inserted itself not only into the formal science of psychology but also into public policy and educational babbling and practice a success of the scientific method or of the mathematization of what is supposedly a study of the mind.
The ideal that Eddington is presenting here is as capable of being used to create elaborate, sciency stuff out of the faith in its potency, ignoring the requirement of observation but also even when things are observed and interpreted by scientists and, especially, because they want to see what they only believe they see.
I don't always disagree so strongly with what Eddington says, perhaps by "eliminating from our conception everything which is not essential to the part it plays in a group-structure" all of that inconveniently discontinued science, but his description as a general definition of scientific method is obviously not covered by what people mean when they say "science". It is kind of surprising to me that someone as sharp in his insight into science as a human and social activity could ignore the actual history of the subject.
. . . The concept referred to in Chapter VIII were general conceptions occurring in our ordinary form of thought. It is now possible to add that in employing them to furnish the frame of thought in which our scientific knowledge is contained, we have gradually eliminated their general aspects, until now we recognize only the corresponding structural concepts. Correspondingly the resulting frame of thought has become a mathematical frame, and the knowledge contained in it is mathematical knowledge - a knowledge of group structure. By introducing the mathematical theory of structure modern physics is able to carry out in a precise manner the general principles described in the last chapter. For example, we there insisted that the significance of a part cannot be dissociated from the system of analysis to which it belongs. As a structural concept the part is a symbol having no properties except as a constituent of the group structure of a set of parts.
To show how these ideas are applied, let us consider the concept of space. Taking first the general concept, we usually regard infinite Euclidean space as the simplest kind of space to conceive. One would have thought that the infinitude would be rather a serious obstacle to conception; but most people manage to persuade themselves that they have overcome the difficulty, and even profess themselves utterly unable to conceive a space without infinitude [or more likely, they don't think about it that hard or just pretend to]. But, whatever the truth about the general concept, the structural concept of Euclidean space is exceptionally difficult. Since I want to give here a comparatively easy illustration, I shall consider uniform spherical space which has a much simpler structural concept.
Any point in spherical space can be changed into any other point by a rotation of the sphere. [by which I assume he means it can be made to serve the same function in the structure, taken as a mathematical object] Thus to the points or elements of spherical space, A, B, C, . . ., there correspond operations P, Q, R, . .. which are the rotations of the sphere; and the group of the operations is simply the group of rotations in the proper number of dimensions (in this case four dimensions). Regarding "space" as a structural concept, all that we know about spherical space is that it has the group-structure of this group of rotations. When we introduce spherical space in physics we refer to something - we know not what - which has this structure. Equally, if we refer to Euclidean space we refer to something - we know not what - with a specifiable group-structure, though it requires rather more advanced mathematical conceptions to formulate the specification. Similarly the space of irregular curvature which appears in Einstein's theory is something with a group-structure requiring rather more elaborate specification.
The general concept, which attempts to describe space as it appears in familiar apprehension - what it looks like, what it feels like, it's negativeness as compared with matter, its "thereness" - is an embellishment of the bare structural description. So far as physical knowledge is concerned, this embellishment is an unauthorized addition. Philosophically it is all to the good that we find a difficulty in conceiving in non-mathematical form of thought the kinds of space which modern physics has introduced; for we are thereby discouraged from making such embellishments.
I think whatever good there is in that is all fine and good as long as physicists don't mistake what they've abstracted out of the reality which we find ourselves in as "everything." Though to be fair to Eddington, I don't think he or Einstein or others of his generation were as totalizing in their attempts to find a "Fundamental Theory" or a "Grand Unified Theory" as the even more overtly ideological of the next generations up to and including so many of those who are chasing that same end and far more arrogant in their claims for what they are doing, and far more openly ideological in their motivations.
Again, I think Eddington was being overly naive in the general conception of things that even pure physicists hold. I don't think there is any way for most people to conceive of even imagined objects without "embellishment" though they might be hard pressed to put those into numbers. And, as I pointed out, not only have they in the past but they still do create imaginary objects, claim those have external existence independent of their (or scientists sharing their) imagined mathematically or theoretically created objects. As I pointed out Stephen Hawking demanded that such mathematically created universes be admitted into science apparently for, among other things, him being able to claim he's eliminated the possibility of there being a God - it not being in the imagination of Hawking that the God who created one universe could create as many or an an infinitude of universes, in which case no probabilistic argument against such a fecundly creating God would have any logical validity. I know of at least two precedents in the Scriptures of two world religions for that idea.
And scientists of his time were already doing that. If history is told by the winners, the lore of science is told in terms of its currently held retained ideas, seldom in the ideas that fall by the wayside and in the null results which have such a hard time getting published, even when the tester of an idea comes up with disconfirming evidence and writes it up honestly.
We value science for the things that scientists were right about, we aren't' supposed to admit that even some of the brightest have not always gotten it right, we aren't supposed to notice the ideas that were current for a time, sometimes a very long time but which are then discarded as I hope natural selection will be before it generates even more depravity. We are not supposed to be even as modest in the claims made for what is discovered by even the most honest of scientists such as Eddington in making claims for the completeness of its knowledge on the day we are making or taking such a claim for granted. That is, unless, you don't like something that science gets right for entirely ideological reasons, such as the Darwinian economists and the unqualified doctor that fed their ideology as science into the ear of Trump and through FOX and News Max or as sold by the extraction industries through an icy blonde during the Sunday Morning Lie Hours on American network TV.
It is the tragedy of science in our time that it is not done on a consistent basis as honestly or as carefully as it is supposed to be, as divorced from ideology, as uninfluenced by the desire of people with PhDs after their name and, even, faculty appointments at prestigious universities or associated with some ideological outfit attached to one. It is the tragedy of science how much of it is a malignant source of poisons and environmental destruction which is far better funded and far more influential than the enormously important science of environmental preservation and protection. It is a tragedy that so many eminent theoreticians in real science, such as physics and the pseudo-sciences, such as psychology and the mix of the two in evolutionary science are the opposite of modest in pursuing their ideological agendas through their claimed and granted expertise.
I use the word "tragedy" merely as a convention, ignoring the involuntary implications of that word, I do it because to say "immorality" or, more ideologically consistent with their own materialist-atheist-scientism, "amorality" would be to introduce something not considered polite or done in the intellectual milieu of modernism.
When you take a critical though not entirely hostile look at science, that thing which is at any given time what scientists say it is or allow to go under that label, it looks as varied, as good and as bad, as idealistic and as grubby as religion does. I am not interested in the naively idealistic and optimistic view of anything, religion, science, certainly not of music or the arts or history or anything. I'm all in favor of looking at it realistically or, rather practically, looking at what's wrong with it to make it better. Like a good janitor does.
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