James Edward Oliver (1829-1895), having trained in almost every branch of science, became professor of mathematics (and eventually chairman of the mathematics department) at Cornell University, serving there for almost a quarter century. His interests were extremely varied. He was an early advocate of (possibly Bayesian, although this is not quite clear) statistical methodology for economics. He studied the "imperfect whiteness" of snow, the soaring of birds, the rotation of the sun ... He also could have been one of the first great American research mathematicians. Unfortunately, as the apostle of non-Euclidean geometry George Bruce Halsted wrote of him in his obituary [Science 1, 544 (1895)], "he seemed to have no ambition to leave an adequate record of his mental life in print. In personal character he resembled Lobachévsky, whom he intensely admired." In an 1896 Biographical Memoir of Oliver for the National Academy of Sciences, G. W. Hill lamented: "All the efforts of his friends to tie him down to a sustained labor in one direction until rounded completion was reached were unavailing."
The following rare specimen of his thought can be read in at least three ways: as an artifact of its age, as an early prefiguring of the debates at the Solvay Conferences forty years after his death, and as a hint of possible future directions in the physics of complexity.
For Oliver, mental events take place in a completely physical world that happens to be "quasi-perpendicular" (i.e. at least formally, and perhaps "actually", orthogonal to the three dimensions of ordinary space). He implies that, rather than a single "fourth dimension", there might be several higher dimensions, and (more importantly) that they are imaginary rather than real, so that the ordinary and quasi-perpendicular worlds together make up what would today be called a Minkowski spacetime manifold (but without time as such).
This idea was not so far from the Nineteenth Century mainstream as one might think: the 1890s were the extended pre-dawn hour of special relativity, when the speculations of Clifford, Zöllner, and others about the fourth dimension were widely discussed but thought to have no contact with experiment. Spiritualism, Theosophy, and Hermeticism were also very much in the air, and attracted several leading figures in mathematical physics. Oliver does not seem to have been an occultist, and his proposal was not necessarily an endorsement of Victorian occultism's vision of unseen worlds, but it is certainly compatible with it.
The founders of Twentieth Century quantum mechanics and their heirs in the second generation despised the old-fashioned table-rapping mysticism of the Kelvin-Tait era æther-theorists, preferring their own austerely modern brand of weirdness. However they, more than their predecessors, had to face the issue of consciousness as they grappled with the paradox of Wigner's Friend and the collapse of the wave-function in the moment of observation. For some (notably the Kaluza-Flint-Fisher school of the 1920s and '30s) the answer to this problem lay in a "hyperdimensional" interpretation of the Dirac equation, an approach quite similar to Oliver's. Some of the "hippies who saved physics" (or at least kept the pre-War philosophical tradition on life support) during the 1970s speculated along much the same lines.
Today, "multiverse" is a scientifically respectable word, neurology has more prestige than physics, and the "hard problem" of consciousness remains unsolved. The philosopher Galen Strawson recently commented [Times Literary Supplement, 2015 February 25] "At the root of the muddle lies an inability to overcome the Very Large Mistake so clearly identified by Eddington and others in the 1920s ... The mistake is to think we know enough about the nature of physical reality to have any good reason to think that consciousness can't be physical. It seems to be stamped so deeply in us, by our everyday experience of matter as lumpen stuff, that not even appreciation of the extraordinary facts of current physics can weaken its hold. To see through it is a truly revolutionary experience." Strawson probably has in mind a certain ineffable, irreducible, apophatic quality of matter that cannot be described by mathematics -- certainly that is what Eddington meant in the 1928 passage to which he is referring. However, it is worth noting that in later life Eddington modified his views, even coming perilously close to identifying the Inner Light of his Quaker religion with photons; although the famously unreadable Fundamental Theory does not (so far as I can tell) locate consciousness in the quasi-perpendicular, Eddington would probably not have dismissed the idea out of hand.
Oliver (also a Quaker, though a lapsed one) was as unembarrassed as Eddington about using the word "spiritual" in his scientific writings; the spiritual, for him, was as much a part of the world, and therefore of the proper subject-matter of science, as the material. Right or wrong, Oliver's proposal seems to me one of the few ways classical mind-body dualism could be reintroduced into biology.
A MATHEMATICAL VIEW OF THE FREE WILL QUESTION
by J. E. Oliver
[ The Philosophical Review 1, 292 (1892)].
Oliver's words are in bold
BEFORE discussing objections to the doctrine of Freedom, let me try to state what, in my own thought, that doctrine really is.
My notion of the matter is more or less analogous to the ordinary theory of Attention. As the current of suggestions, whether determined mechanically or otherwise, passes before the ego, the ego puts forth a free selective power whose result is physically directive. Here [Dugald] Stewart's account of attention may or may not come in : either the ego may merely arrest the current long enough for the mechanism to do the rest, like the "type-wheel" in the telegraph, which prints whenever it stops, or else, possibly, the ego may deflect the current without arresting it.
Does the ego here act apart from motives, feeling no pressure from them, or as one among motives, and often against some of the others? i.e. if by "Volition" we understand, not the observable resultant of the ego's free and original act as combined with other causes, but only that act, pure and simple, then are all volitions alike as to strength, intensity, degree of effort, -- or do they differ in this respect according to the strength of the opposing motives ? Either alternative appears to be tenable ; but, in so far as they really differ, I incline to the second one.
This raises the question of relative strength of will-power and determined motives, and I incline to believe that the will-power, in its possibilities, and perhaps even as commonly exerted, is by no means infinitesimal in comparison.
Thus motives and volitions would belong to a system of what we may call "spiritual forces," because like physical forces they may oppose one another, conspire and perhaps combine into intermediately directed resultants ; but these spiritual forces cannot so conspire with or oppose the actual physical changes or motions of the moment as to "do work," but can only produce deflection or transference of an energy to whose potential they do not contribute.
I regard them as quasi-perpendicular to all physical forces : i.e. their action upon any physical atom is, in the above sense, always as if at right angles to its path, so that of course they cannot increase or diminish its kinetic or potential energy, except indirectly by deflecting it into new positions and conditions, where, however, all transfers of energy will still be made under purely physical laws.
(Here, and in what follows, we use the term "physical force" only in the sense of a push or pull exerted at a material point by attraction, repulsion, or vis inertiæ; and analogously, the term "spiritual force" : so that a group of agencies and phenomena, like electricity or intelligence, would not be called "a force.")
Even if the concept of quasi-perpendicularity, which perhaps has been already suggested by Maxwell and others, should rest upon nothing deeper than a metaphor or convention, yet it is the more presumably natural and helpful here because of its known value in Pure Algebra. Thus, the perfect symmetry between the relations of i (= ) to + 1 and to − 1 ; or of 1 to + i and − i, (i.e. that mutual independence of the two abstract units 1 and i which would seem so analogous to the independence of physical and spiritual forces), has led to the use of the "complex plane," with resulting methods of great power and beauty. On this plane every value of A + Bi is located at a point having longitude A and latitude B, as in the annexed scheme ; so that i is treated as quasi-perpendicular to 1.
In mathematics, this notion of quasi-perpendicularity, though as I think often implied, goes unnamed. It is very flexible : a translation and a rotation would be quasi-perpendicular, however their respective directions were related, and so would be the several parameters of a curve when they were regarded as a new system of variables.
Let us hold the concept in a correspondingly free way. Let it simply accentuate for us the fact that the ego does no physical work, but can only by hypothesis decree something as to the direction of work, while it may or may not connote for us anything that is geometrically more definite.
This quasi-perpendicularity appears to me the natural, and perhaps almost necessary, solution of other difficulties that have nothing to do with freedom, but only with the apparent dualism of mind and matter, and with their apparent interaction ; while it may also sufficiently suggest the deeper unity in which that dualism doubtless rests.
We do somehow receive impressions from the outer material world, and do, whether freely or as mere automata or channels of influence, produce impressions upon it ; while, on the other hand, we are aware of phenomena in ourselves, like intelligence, joy, gratitude, obligation, remorse, which seem to us essentially independent of space and matter, though they often have reference to the external world. Now I know of no other figure by which, so well as by that of quasi-perpendicularity, we can represent to ourselves this apparent independence and this apparent interdependence of the physical and the psychical. Our hypothesis may be held as hardly more than such a figure, and it still suffices for the present purpose : though I incline to think it is not merely a figure of speech.
Admitting in a general way such a solution, many curious questions of detail would remain which we cannot as yet adequately discuss ; nor need we, for the purpose of the present argument.
For instance, shall we think of the quasi-perpendicularity as mutual ; the physical forces exerting a merely directive effect upon the spiritual phenomena, as well as the spiritual forces upon the physical phenomena, and the law of conservation presumably holding in the spiritual as well as in the material system ?
Is there any spiritual force that involves the element of Time, or Inertia, and in virtue of which every system of spiritual forces must be in equilibrio just as a falling stone hangs balanced between the pull of gravity and its own resistance to further acceleration?
Again, must this quasi-perpendicularity be regarded as a mere convenient metaphor, or may it be an actual perpendicularity, the spiritual forces pulling in a space of their own, more or less like our known space ? In the latter case, are the two spaces coincident ? (Coincident perhaps, yet not necessarily coextensive. Our familiar space, if "positively curved," may be said to coincide absolutely with another having just half or double its extent, and yet each space to be complete and perfectly symmetric, two points of one space being at every one point of the other.) Or does the spiritual include the other as that includes a given plane or line ? Or is every line and every plane of one space perpendicular to every line and plane of the other ?
The third alternative seems untenable ; for, admitting it, how could a spiritual force produce even a deflective effect in physical space ? But the other two remain, and the second may fall in with such purely physical speculations as W. W. Rouse Ball's, who seeks to obtain both Newton's law and certain results of spectrum analysis from the virtual hypothesis that our known space, lying like a plane in a larger space, can vibrate in the fourth direction. [Messenger of Mathematics 21, p. 20, June, 1891.(Although this volume of the Messenger has evidently not yet been digitised, a similar, more popular essay by Ball on the subject may be found in his Mathematical Recreations and Essays.)]
It remains now to notice briefly, from the standpoint of mathematics, certain supposed difficulties of the Free Will hypothesis.
We are told that the Determinist theory is forced upon us : ---
And again, it is natural to assume a symmetry and reversibleness of relation between Past and Future which does not really exist, and thence to conclude that if one be fixed, the other must be so too. This argument is not that "from Causation," yet one seems to suggest the other. Now, however it be to the philosopher, Past and Future are not alike to the scientist. Even if physical causation be considered as reversible, many of the cycles of actual change are not. These cycles move in fixed directions, and not backward, even when they bring events and successive individuals or systems around to nearly the old conditions. And besides, there are changes going on which, as far as science can yet see, never will be unmade or offset by any cycle : for instance, the progressive residual concentration of mass and diffusion of heat, and the unceasing loss of "motivity." Thus neither from moment to moment nor yet in the long run is the relation of Past to Future a reversible one.
But if the objection merely means this, "Since every effect or phenomenon has a cause, and this cause has a cause, etc., thus giving an infinite number of steps of causation between the effect and its first cause, therefore free volition cannot be a cause, for this infinite number of steps between it and its observed effect must take an infinite time," --- if this be the supposed difficulty, then I think it turns upon the same fallacy as does the story of Achilles and the tortoise. We are told that he could not catch the tortoise, because while he ran 100 rods it crawled one ; and while he ran that one it crawled 1/100 ; and then 1/10,000 and so on -- Thus analyzed, the process did indeed require an infinite number of steps, but then these steps grew so rapidly shorter and shorter that the sum of all their lengths was finite, and might have been microscopic. Very likely it is as true in our problem as in that of Achilles, that one may rightly either introduce the infinite series or not : i.e. we may say "Everything is caused," and so bring in the infinite series, or say "Volition is its own cause " and stop there, replacing the series of steps by its resultant or quasi-sum.
So with character: if it be the joint product of environment, heredity, and volition, then in the long run it may seem to result mainly or wholly from environment and heredity, for the reason that volition (unless guided by principles whose development is, itself, largely due to environment, etc.) is like dice-throwing, now this way and now that, so that its net result varies nearly as the square root of the number of cases that have come up, while the result of a steady pull from heredity or environment varies as the number of cases.
It would seem then that the analogies of physical and mathematical science are not unfriendly to that old faith in freedom to which the conscience and common sense of the race have substantially held ; and if we cannot now hold to it in the old simple way, this is mainly because the world as known to us is so much larger and more complex than as known to our fathers.
We cannot do or become at once just what we would : the ego can act effectively only through, or as part of, an intricate mechanism, and perhaps much that it seems to initiate is mere ideo-motor reaction. Yet I think its directive agency does tell in making results to be somewhat other than they would have been, and thus gradually moulding character and environment, and the heredity of those who shall come after. Moreover, the effect upon the inner character may be more rapid than upon the apparent character and the environment : for if there be a certain element of earnestness, making the inner results fairly constant as to direction, these results should tend to accumulate proportionally to the number of occasions, while the effects of environment upon the inner character would be more conflicting and so would follow more nearly the law of the square root.
Thus, though development has taken the place of sudden creation in our new world, it may still be that we do, little by little, create our own characters, and not merely the character of the race.
J. E. Oliver.