Foundation for Integrated Education
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January 8, 1951Dr. F.L. Kunz, Executive OfficerThe Foundation for XntefXwtad iducaticn,KOOE 1605<!2Q iiaat ltfnd StreetNew York 17, N.Y.Dear Dr. Kunz!Thank ycu for your readinesstc prepare a paper for the seconcl symposium. The paper should be betweenten and twenty average printed pagesin length. Any topic closely relatedtc the problem cf al truism, especiallythe techniques of altruization, whichlies within the field of your interests,would be suitable.I have just asked the SeaccnPress to send you a copy of the firstsymposium by first class mail.TTith best wishes in thisnew year, I amCordially ycurs.
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J ^ , H1LLANDALEV- U/h"} ( If L . PORT CHESTERNEW YORKJ^KJ* "NtfMajLsLW*! <3tt»»-w- ~ ,t*aa «—■* <K =7=* ^^^ -v- u^-A Ai-*
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Sorokin_IX_F_7_040
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THE HC.L2 OP A BIOL03ICAL FIZLL JHEOBT IB EHUCATI-j::*Four.dati nr. for Intogr;I.Bie general education movement was prompted in this country principally by the disparity between modern man's 'material achievaiients andhis social, moral, economic and political competence. Through it,higher learning was to-do its part in arresting the deterioration ofsociety by correcting over-emphasis upon vocationalism.From the beginning of the movement it.was clear that contemporaryknowledge is too vast and too complex to be taught as a whole at thedescriptive-and-operational level. Hie criteria required to controlthe inevitable sampling have been arrived at in practice by arbitratedopinion and administrative fiat, necessarily, for lack of a philosophical consensus. Ths outcome for the most part was the now familiarpattern of selections from physical science, social studios, andhumanities.From the early days of the movement It was also evident thatmere slices of learning were inadequate. To counteract specialization'seffects by encouraging the student's interest in many or all major aspects of learning, is to commit ourselves to offer knowledge more andmore as a meaningful whole. This task is also Impossible of performancewhen confined to the descriptive-and-ojierational level.Secular colleges do not possess an official philosophy. Indeed,except to some degree in the exact sciences, there is no body of approved, consolidated, far-reaching, concepts collected and taught.Hence for any conceptual interknittin,'; that might be done to encouragephilosophical insight, the teachers of the general course became responsible. Under such conditions a quickening of Interest in thestudent may be affected, if the copses chance to be well devised, andif tha instruction is inspired.But effective conceptual integration of subject-matter, constituting the beginning of an authoritative philosophical consensus fora given campus or for this confused country, is not likely to beachieved by this procedure in any reasonable time. In fact, it willbe my purpose to try to show that a consensus will be impossible untila certain hiatus of knowledge is filled in. Since the true alternativeto authoritarian indoctrination (which as a nation we repudiate) is a" Read before the American Association for the Advancement of Science,Section Q (Education), December 28, 1950, at a symposium sponsored bythe Foundation for Integrated Education.
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democratically achieved consensus which gets its force from the worth andreasonableness of a common educational experience, our present frustrationis dangerously stultifying.The specific cause should be a matter of primcry national concern. Ifit can be determined, we must then caa if wa can correct it. To this weIt is necessary at the start to be clear upon nae point at least: Thehope for a meaningful and enduring World consensus lies, broadly, alongline3 of reason and philosophy and, specifically, along lines consonant withscientific standards, This dees not moan that "hat wo now accept as established knowledge is enough, but that the basic positive metr.ods used toachieve present accepted science are good, and the results acceptable, aafar as they go. There are bound to be prematura erroneous personal conclusions as to the constitution of man and the nature of the universe, and therelations of these two, based on present limited science findings. Thesefaulty deductions are to be charged a~ainst their hasty pronulgators, notagainst basic scientific attitudes and methods.As befits a high-ranking cultural discipline, science has many techniques. Of these one group, namely, those of exact science, has importantprior claims over all others, if insight is to be an object. For exactscience gets its authority from the internal mathematical and logicalstructure, and is thus by its very nature philosophical in character. Inaddition it gives us effective and increasing master;' over nature, andthus proves out as a species of realism. Exact science is therefore coinof the realm for a world society.The exact sciences of matter and energy are well structured, and display year by year a progressively improving internal authority. The generalconsensus they offer derives from the content itself. In fact, progressin structuring them has been so conspicuously accelerated this century thata general field theory may presently be taught, comprehensive of all majormaterial phenomena. However, the subjects, matter and energy, are insen-tients, hence the values obtained are in the learning experience not inThe situation we have just noticed, typical of ihysics, chemistry andastronomy, is almost exactly reversed in social studies and humanities.These have little or no meaning when divorced from values, but at presentare only loosely structured,life sciences, as such. Man is rooted in life, first, and experiencesmatter only secondarily. In life sentience appears, making occasion forvalues, since without pleasure and pal", values do not even a>"ise.And now we confront a puazle. ihe centralmost subject of biology isorganisation. Yet the singular fact is that despite life's importance tous, and its opulence of forms, the mathematical and logical over-all structuring of biology is rudimentary when conxared with that of ->h,vsics andchemistry. This state of affairs is known to all. Because of it, lifehas frequently been interpreted philosophically in terms of mechanism bythe unscientific device of ignoring or postponing discussion of the specialsubject matter: sentience, organisation, and self-directed functional form.Tills has led to conceptual impoverishment. The alternative has been aninadequately structured vitalism which attends to unique subject matter,but does not greatly enlarge the sovereignty of the exact sciences.-2-
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So long as we remain content with samples of '3io"-lelge in general education, loosely knit with a few principles, we can live with this failurein biology to offer a general structuring comparable in exactness, 3cope,and acceptability to that of physics. But If we look upon general educationas the authoritative moans to stimulate culture and insight, the Cunceptualhiatus under notice is intolerable. All manner of substitutes may be offeredin lieu of the extension of structuring from physics through biolssy towardman and society. But wa would do wall, I think, to recognize these as beingin part what they are: improvisations necessarily substituted for thephilosophical lag in the life sciences.The ideal way out of our frustration is clear, tfa are required tobring the life sciences up level with those of matter and energy not byraductionism, but by api lying basic exact science ntathodJ through wt biology. In contemporary terns this means a biological field iheory whichembraces life-data inside and outside the scope of physics and chemistry.Thiti implies In turn that Mophysios and biochemistry are not enough.Oiganisms are sentient and display psychic activity. There is thereforea subject v;e cannot neglect, biopsychology. Many creatures are self-sustaining functional forms rich In symmetries and asymmetries, some apparentlyexplained mechanically, others inexplicable. Xiatover their rationale,they provide a special topic, bio-esthetics. Organisms nave a unicue relation to space (functional morphology) and to timefevolution, the oppositeto entrop)^'). A space-time for life would Iisve to account for these fewspecimeus~of topics, and for many others, If social studies and fee humanities ore to be demonstrably linked in a valid fashion with the exactsciences of matter and energy to make an intelligible valued whole.= considerations are1. ;ihat factors, hitherto not exploited singly or as wMoles by biologists,are at hand and suitable for the structuring of life-sciences?a. If the suggestions along that line which follow seen to have promise,can they be formulated in a program of research? That is, can the problemsbe stated in a way that suggests specific inquiries into parts of the subject, which may in turn be significant to the whole?3. What practical set-up end procedures are implied, additional to presentfamiliar practices in ths advancement of biolcgical knowledge?k. What would a sustained, systemaiic, and sufficient program cost?5. Would an accelerated effort be worth-.rtiiilrll tfa may have confidencethat biological science will eventually achieve an over-all structuring..This last question is intended to suggest th.-.t special efforts might haverapid results of particular importance to society during the present timesof confusion.The first question alone calls for immediate answer. There would bono point in concentrating attention on the well-known need to improve theover-all structuring of biology unless there were reasons to believe thatsomething fresh can be suggested. The time left may therefore be devotedentirely to a few items which promise at least the beginnings of a biological field theory. Our account here must necessarily be in skeleton-3-
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Contemporary physics is concerned, first, with energy; second, withthe quantum series, which begins in the non-pictorable atomic world, andappears in the range of aided and unaided vision as molecules and crystals;and, third, with the relation of energy to these particulates, massed upas matter.To give rational wholeness to Physical phenomena, two major concepts areintroduced, under realistic necessity: force fields and space-time. Because they are not directly perceived, fields are held by some to be butconvenient fictions. For present purposes they will be conceded reality,and space-time will be allotted at least those properties which naturalmotions require as background. Vie shall assume that if space-time isuseful to explain motion in ghysics, it should be found appropriate alsoto biology, wherein, however, its features are to be determined by thespecial ordered changes which occur in living nature.Contemnorary biology also has much to say about energy and quanta.The latter appear in living cells in such form as genes, protein and othermolecules and micellae generally, and as crystals, both those occluded incalls and also engendered therein and built uu as cellulose walls In plants.While the cell is alive, these particles earn' electric charge patternswhich change or disappear at death. In higher organisms especially, thermaland other physical and chemical uhenomena are also subject to living control. Within limits, then, the directive role of life and the functlon-alism of form seem evident. Nevertheless it might be reasonable to believethat the directive role ia only apparent, not real, that life is only anepiphenomenon, and hence that the electromagnetic field theories can presently be extended to account for living creatures.But biology offers important novelties In space-and-time activitieswhich lie far beyond the present boundaries of physics and chemistry.It is these which force us to look for a special field theory appropriateto biology. Reproduction exemplifies these imperatives. It allows organisms to go on aa specific funcUo-.al forms in space and adaptlvely asmeaningful unbroken causal series for long ages of time. This is singularin itself. But more: Sverything required to effect this seems to bepassed along as a potential in the genes and germ plasm. There Is nothingequivalent to this recognized outside biology, as that science is atpresent daflned.It is difficult to see how we can avoid the notion that there is anappropriate special space-time ground which provides the properties displayed in these and other familiar but unique features of life. It may betechnically difficult to establish the existence of the necessary detailsof the required field structure within a single free-living cell, wherewe may suppose that the contents and the activities are all significant.But if the germ cell be held to be the abstract of the adult organism,then the kind of content and motion in the cell, namely, streaming ofprotoplasm, metabolism, mitosis and meiosis, can be considered as workingout and stating itself in development and growth, metamorphosis and mutation.Ihis is tantamount to saying that living motion, in the strict sense, issul generis, and that is why the end result is a self-proportioned form inspace, ongoing by repetition in time.
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The present proposal, then, is that the essential methods of modernphysics are to be developed In studies of life to suit the data, taken intheir entirety, as befits the standards of exact science.The~method indispensable to successful description of fields and space-time is mathematics, In the usual categories of geometrical principlesand attendant or additional equations. We require a field geometrically sostructured as to account for the symmetries and asymmetries and the behaviour of living forms, Hie results must embrace palaeontology, genetics,cytology, morphology, taxonomy, and every other department of the lifesciences, and it must lead to acceptable systematisation of them.The magnitude of this proposed undertaking may seem much mora formidable than the task which Michael Faraday and others created for JamesClerk Maxwell and his successors. But there are features which giveenc ouragement,In the 1101061081 field if there is one the test objects are given.The very opulence and diversity of life provides that thousands of aspectsof Its geometry are ready at hand for study. Already many hundreds ofparticular studies contributory to the structure of the life-field areknown, such as principles of phylotaxy, cotyledon-leaf-and-plant-part groups,specificity of chromosome numbers, shapes, sizes and behaviour, growthproportions, relations of organ masses to body weights, and so on.A suitable geometry is also available in advance. Just as appropriategeometries were at hand for Relativity.The Euclidean character of the microcosm generally, and of quanta inparticular, is fairly well established; and biological forms depend on afine world. Certainly at the point where the molecules of pure substancesarrange themselves upon space-lattices as crystals, we have Euclidean space-fillers.The geometry we seek cannot be confined to the three dimensions ofspace, and time taken separately, the system to which D'Arcy Thompsonlimited his interpretation of the geometry of life in his book Of growth& Form (Macmillen, 19H2). We need a space-time geometry, because livingsystems are in incessant motion. 3ut this need also can be satisfied frommathematics at hand. The four-dimensional Euclidean regularities havabeen studies by Alicia Boole Stott, H. P. Manning, and many others. Recently they have been reviewed and consolidated in The Polytopes. by H.S.M,Coxeter (Hethuen and Co., London, I9U9).We therefore proceed to make a specific suggestion concerning thepossible role of these four dimensional analogues of the familiar regularconvex polyhedra.In three dimensions, Euclidean geometry provides us with five regularconvex polyhedra, or six, if ire count the sphere as a polyhedron with aninfinite number of sides. Since the tetrahedron is self-reciprocal (thatis, has a vertex opposite to the center of each face), they come In reciprocal couples. The dodecahedron and the icosahedron are mutually reciprocal, as are the cube and octahedron. The five regular figures constitute the three dimensional regular convex space fillers.
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In a four dimensional region, required for space-time, analogues ofthe foregoing three couples all recur, and are joined by a fourth, namely,a polytope with 2h vertices, 96 edges, S3 triangular faces, and boundedby 2k regular convex octehedra. It is therefore self-reciprocal.Four dimensional space thus provides us with as many couples of reciprocal polytopes as there are kingdoms in nature.The accompanying plate lays out the series from point to polytope.(See following page)EXPLANATIO-' OF PLATERepresentative models of the four reciprocal couples of polytopes aredisplayed at the extremities of the figure above; five, if the sphere betaken separately. (For full discussion, and modelling, see The Polytopes.H.S.1I. Coxeter, liethuen, London, I9H9).To the right is the series point, line, square and cube-octahedron,ending with a correct perspective modal of the four-dimensional analogueof the cube. Above this figure are the numbers of its vertices, edges,square faces, and cubic cell boundaries, and below are the correspondingdata for its reciprocal, the four-dimensional analogue of the octahedron,which is bounded by 16 octahedral cells.Running vertically downward from the center is a series ending in amodel appropriate to the dodecahedron (and icosahedron) with the numbersof vertices, edges, faces and bounding calls also indicated.To the left runs the series appropriate to the ?U-hedroid. Sincethere is no regular three-dimensional representative here, a space isleft blank. The hexagon is its correct representative in the plane.Vertically upward is the series appropriate to the tetrahedron andpentahedroid.The suggestion is that the reciprocal nets connected with the terminalfigures constitute the basic field geometry, respectively, of crystals,plants, cold-blooded animals, and warm-blooded creatures, specialized inthe four geological eras. The assumption is that the life-field is geometrically totipoter.tial, and that the geometrical nets associated withthe analogue of the cube and octahedron came into play first, in theearth's crust, and remained in expression, to -;e joined by tho geometryappropriate to plants, both occurring in that kingdom. The structure ofthe field is thus displayed In natural forms progressively; and in eachhigher kingdom, cumulatively.
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III.When the series of reciprocal cou-les i3 referred to natural forms,immediate confirmations of their prcbable usefulness coma to light.Here ire have opportunity only to notice a conspicuous feature of theargument.Experts familiar with crystallography and structural chemistry haveestablished tie role of the cube a-id octahedron i;i tile geometry of theirsubject matter.* In general it may be said that these figures provide thebasic frame of reference for inorganic crystale, broadly, the mineral kingdom. Besides the foregoing positively established state of affairs, thereis a slgnlficrint negative statement which can be -nade rbout the geometryof this kingdom: the regular convex dodecahedron does not occur in inorganic crystals. The nearest npproxiza'ion is, I believe, one form ofpyrites, but the dihedral angles are unequal. In short, the overwhelmingevidence is for a basic cube-cc trhsdral geometry for the crystals.A few years ago the suggestion that inorganic crystals are la anysignificant sense a part of the life series might nrve sornded quitefantastic. But Pilliau Stanley's work on the tobacco mosaic virus maybe the beginn-ng of a new outlook, giving earlier data of relation ofcrystals to life fresh meaning: For crystals are occluded in many typesof living cells, for purposes which, I believe, remain obscure, Woodyplants engender within their ceils crystals which migrate to the wallsto build cellulose. Mo less significant is the fact that there are nowknown a few hundred substances of organic origin which display the opticalproperties of crystals when, in their pure state, they are held betwaancertain temperature ranges. The notion of living cells as aperiodiccrystals thus becomes part of a whole system.We have, thus, reason to put aside the idea that the bifurcation ofnature into living and non-living occurs when c-ystal cells give way toprotoplasmic cells. Instead we conceive of inorganic molecules andcrystals as indispensable to life, and as joining with organic moleculesin the fluid system of the cell to make possible the expression of awell- and consistently-structured field.Eie suggestion is that evolution is the sequential exploitationand display of the geometry of the life-field, from the simpler cube-octahedral systems of the inorganic, to the richer system of the dodoea-icosahedral system, both being unitedly displayed in plants; and so toanimal forms and tissues, where the field displays an*additional complexfrom the twenty-four hedroid couple.The contents of the cell are doubtless selectively maintained inaccordance with the geometric properties of the field appropriate tothe species, exercised through the specific numbers, shaving, sizes andbehaviours of the chromosomes and genes.Whore, then, is the bifurcation in nature between living and nonliving? I would be inclined to say that none is directly apparent, andprobably none exists. There are merely ordered systems of many magnitudes, among the largest being the whale, the greatest dinosaurs.
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sequoias, and beds of crystalline rocks, the series going down and vanishing out of sight as single cells and quanta. If there is a bifurcation,it is between the ordered end the apparently non-ordered, but in fact eventhis may be fictitious.We are facing the facts ihich surest that incrganic moleculna nndcrystals are the necessary basis of life, having come first presumablyin the evolution of the planet. We are but suggesting that *he mineralsystems display an internally consistent geometry based u>'on the cubeand octahedron, and thr.t this is in turn "art of a larger, closely-knit,geometric system, and that we are therefore impelled to inquire whetherthe rest of the kingdoms of nature exploit the rest of this geometricIn principle, there is nothing novel in the suggestion. If investigation justifies the concept, It will then be time to make some revisionsin our philosophy of life, and these we must expect. For if a problem hesremained for centuries before us, unsolved, we must conclude that thethinking which fra-nes it has had some defects. Changes in that thinkingmay require of us some considerable adjustments.Some of the features of that required new thinking are suggested tous by analogy from recent events in physics. It may turn out that thefield and not the cell is totipotential. In that case crystals of in-; to be regarded as very limited expressions of theOit, all that is left of the complex space-timei rational parameters, symmetries, and the like,issarily suppressed, because a static three-dimen-llsplay more. The evolution of protoplasm, then,of more of the field potential to exhibitl in a liquid medium. Thus the organic molecule can be in constant conjunction with the loiter orders of the fieldgeometry displayed by inorganic substances present.This kind of thinking implies a ro-definition of biology, as thescience of the self. Crystals are then merely self-forming and self-existent. Plants are self-sustaining sad solf-pcr-ietuating. Animalsdisplay self-motility and self-direction. Thus life becomes bothscientifically and philosophically the condition precedent to the appearance of self-conscious, moral, aesthetic ~an.The notion Implies that the field, besides having as its structurea consistent geometry of great interest, may also have a carrier featurewhich appears in living forms a.s sentience. As remarked ; bove. It isobvious that sentience is the root base of values, for without pleasureand pain, why should there be any occasion to choose a course? We wouldbe inclined to look upon the Just internal proportions which we callrational parameters as all that 13 left of an aesthetic and meaningfulwealth in the field. In short, the universe is indeed consistent,charged with value, snd human life has meaning. The purooss of thestudies here proposed is, in fact, that we may bring out of the realmof belief and into the realm of knowledge, good reason, teachable truth,about this intelligible universe.organ!■igiamay comilife field.InEveryt.iln;; else i3 nectsyelannot d!ievice which alltitself, ]t affords mo'
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