Florensky on evolutionism -- "What is the differential equation?"

From At the Crossroads of Science and Mysticism, Lecture Four:

Renaissance culture also gave attention to the other principal form of being--time. The examination of the concept of time occurred later, and the fragmentation of being in time was performed later than the fragmentation in space: evolutionism came after mechanism.

Evolutionism does have a healthy seed--gentism, according to which an essence does not unfold in some single moment, and the spiritual meaning of an object is not exhausted by some single state, but exists in the totality of its states. But evolutionism errs when it states that this genesis is made up of infinitely small additions, so small that each separately can be considered not a creative act. ...

For example, let us consider the question of the origin of man. Evolutionism denies that there is a qualitative and fundamental difference between man and animals. But if this process occurs discontinuously, if man is descended from the apes, this theory loses its anti-religious character, since a qualitative change suddenly occurs. And if man was created from the dust of the earth by a special creative act, why not then allow in principle--only in principle--that man was created by a momentary addition of spiritual qualities to the ape?

What I am pretty sure Florensky is saying is that one need not take the creation story in the Bible literally to have a Christian worldview, but on the other hand he does insist on a "discontinuous" development of spiritual qualities. On the one hand, I suppose that science can't now and perhaps never will be able to address the important qualitative differences between man and the apes. For example, there will never be a fossil record of spoken language, so we will never know definitively when or how speech developed. On the other hand, Florensky (writing in 1920, mind you) could be taken as throwing his lot in with what might be called the "intelligent design" crowd. How else to interpret this statement, particularly with its wording about "creative acts"?

There's a very thought-provoking passage on how the differential calculus was absorbed into modern science:

For the immediate consciousness rest is opposite to motion, while the essence of science is the fact that we can study motion only by separating it into states as if of rest, with the result being the differential equation. The latter becomes the universal instrument of mathematics, and then of all science and the whole Renaissance epoch, since, to quote Kant, every science is a science insofar as it incorporates mathematics.

 He goes on:

What is the differential equation? Some sort of process is occurring, and we stop it and break it up into a series of instants and see it as if in sectional view. The differential equation is a general formula suitable for the sectioning and study of any process. With this method we are not concerned with the past, with what occurred earlier in time, with whether these are people or whether they are statues who suddenly started moving again after we had stopped them. Only the present is important for us here, not the past; but for many phenomena it is precisely the past that is important.

Writing in 1920, I suppose Florensky could simply not have known about all the modern developments in differential equations. Now it is commonplace to deal with integro-differential equations which were developed to take into account nonlocal interactions across both time and space. I wonder what he would say if he could have lived to see the era in which most differential equations do not involve continuous functions and Taylor series, but rather wild, mysterious functions and generalizations thereof.

Even today, one might think at first glance that Florensky is basically right in his description of differential equations, in that they are meant to break down a process into infinitesimal moments, each of which may be viewed as "not a creative act" but rather a blind obedience to some universal law. But even creative acts or subjective experiences can be modeled quantitatively. The whole use of optimal control theory to predict social behavior comes from the idea not that human beings follow mechanical laws but rather that they exhibit optimizing behavior, i.e. genuine acts of will. Florensky simply could not have seen this, since its development came only after his death.

Still, Florensky challenges me like no other thinker, perhaps because so few theologians know or write anything about differential equations! It would be naive to assume that mathematical objects appeared in a philosophical vaccuum. I should pay closer attention to how today's concepts are used (or could be used) to shape our world view.

To me, there will always be one fundamental discontinuity that cannot be ignored by any scientific theory, and that is the mere fact of existence. Between existence and non-existence there is no continuum. There can be no "probability" that the universe would come into being. Rather, its existence is pure impenetrable mystery. For me, this is basically the same thing as to say that God spoke the universe into being.

Florensky on philosophy

"Psychologically, it is natural for people to say that everything is very simple. This is opposite to the sense that begot philosophy--the sense of wonder. To be a philosopher is always to perceive reality as something new, as something that is never boring or stale. The adventure of the spiritual life consists in the fact that everything is renewed, first is one's consciousness and then outside oneself. The one essential thing is to transform all of reality. We must die and forget everything that seemed boring and stale, and when we awaken, all will be renewed for us; it will be beautiful and eternally joyous." -- Pavel Florensky, At the Crossroads of Science and Mysticism

I think this is my new mission statement for life. For context, this is actually part of a critique of modern thought. The quote continues:

"And to some degree this actually happened. The second part of Faust represents spiritual renewal after suffering. Its beginning is depicted in hues reminiscent of the sky, an approximate vision of the primordial creature, in contrast to the task of Renaissance culture--not to wonder at anything." 

 This book is a gem, absolutely necessary for anyone thinking about building a Christian worldview.

Florensky on community

From Letter Eleven in The Pillar and Ground of the Truth (scripture references in original):

Equal love for all and each in their unity, concentrated in a single focus of love for several, even for one in his separation from the general unity; disclosure before all, openness with everyone, together with esotericism, the mystery of the few; the greatest democratism together with the strictest aristocratism; "absolutely all are the elect" together with the elect of the elect; "preach the gospel to every creature" (Mark 16:15; Cf. Col. 1:23) together with "neither cast ye your pearls before swine" (Matt. 7:6); in brief, agape-philia--such are the antinomic dualities of the Good News. The power of the Gospel is accessible to all, does not need an interpreter. But this power is also thoroughly esoteric; not one word in the Gospel can be understood correctly without the "tradition of the elders," without the interpretation of spiritual guides, successively handing down the meaning of the Gospel from generation to generation. The Book clear as crystal is at the same time the Book with seven seals. All are equal in a Christian community and, at the same time, the whole structure of the community is hierarchical.

"Antinomic dualities" are at the heart of all of Florensky's theology, so it's important constantly to stress where this is coming from. Truth itself is not found apart from love, and love is found in self-denial leading to self-revelation, which is fully reflected in the Triune existence of God and more specifically in the incarnation and cross of Christ. Everything leading to the Truth, then, has an antinomical structure, consisting of two opposites which cannot be reconciled by the rational mind, but in fact reinforce one another to the spiritual mind. That is the starting point.

Here Florensky shows, as he always does, how essential this antinomical structure is to Christian life. Community itself consists thrives on a contradiction between the essential equality of all members and their essential inequality. Choose one or the other, and you'll get it wrong. Only by embracing both aspects of community, and allowing them to reinforce one another, can you fully understand--and, more importantly, experience--community.

Likewise, community has an antinomic structure in that it is both collectivist and individualist. Jesus came to call a people to himself; yet he also had disciples set apart, whom he called friends--one, in particular, called "the disciple whom Jesus loved." Jesus loves all of us, but this phrase refers to only one person in all of human history. The experience of community cannot be merely collective and abstract, but also must be concrete and personal. That is the tension. It cannot be resolved by reason, but only by love. Indeed, love finds genuine expression by embracing this tension.

From mathematics to theology

[T]heology is, for all its modesty, in an exemplary way a free science. This means it is a science which joyfully respects the mystery of the freedom of its object and which, in turn, is again and again freed by its object from any dependence on subordinate presuppositions.

--Karl Barth, Evangelical Theology: An Introduction

In modern usage, science is the study of a particular object or range of objects. Physics takes as its objects the most basic or "fundamental" objects of the empirical world, e.g. particles, energy, forces. Biology takes as its objects all living things, though it is not at all times clear what this means. Economics may take as its object particular markets, e.g. the housing market or the automobile industry, or it may take that grand object which Hayek liked to call the "catallaxy." In all cases, the amount of knowledge we can obtain about something is often inversely proportional to the level of complexity with which we are dealing. This is how it is usually described: physics studies the most simple objects, chemistry studies one level of complexity higher (i.e. compounds of the most basic materials), biology studies another level, psychology and neuroscience perhaps another level higher, environmental science and ecology another level still, and finally the social sciences: sociology, economics, and political science.

If we can classify mathematics as a science, it precedes even physics on this staircase of complexity. As John von Neumann said, "If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is." Mathematicians study the very simplest objects of all: those which can be defined precisely and axiomatically, and which therefore can be understood with absolute certainty.

Florensky on Eternal Punishment

I'm reading a second time through The Pillar and Ground of the Truth by Pavel Florensky. I usually don't reread books. This one just happens to have a certain draw for me, which may have something to do with the fact that Florensky is such an interesting yet completely unknown character.

Apparently it's all the rage these days to talk about hell. Rob Bell's book, Love Wins, provoked a lot of discussion among mainstream evangelicals, and has already produced a response book, Christ Alone. The Splintered Light Bookstore here in Charlottesville is now featuring on display no less than four books on the subject, including the two mentioned above, a book called Hell on Trial: the Case for Eternal Punishment, and (my personal favorite title), Hell Under Fire.

So what does Florensky have to say on the topic? In order to understand, one has to understand his underlying philosophy of doctrine. Religious doctrine is antinomic, meaning it contains contradictions within itself. Rather than being a sign of its weakness, this is precisely its strength: the thesis and antithesis strengthen one another, rather than diminishing or destroying each other.

With that in mind, here is an extended quote from TPGT, Letter Eight, which is entitled "Gehenna," summarizing Florensky's remarkable views on eternal punishment and carefully distinguishing them from other more prevalent views:

And so, we have described two series of progressively refined views. It is easy to remark that they hav eone and the same deficiency: they both rationalize the mystical process of punishment and purification, so that, according to the law of identity, sin is represented as either the very substance of the soul (the first series of views is of the "Protestantizing" variety) or as purely external in relation to the soul (the second series is of the "Catholicizing" variety). But neither view can be accepted. A man with evil will can in no wise be forced to change this will. But as long as he does not change it, he will not be reformed. Sin cannot be removed from a man without touching his inner essence (contrary to the second series). But, on the other hand, we cannot imagine a man who is absolutely and thoroughly corrupt, for this would mean that God's creation has not succeeded. The image of God cannot perish (contrary to the first series). Only one conclusion is possible from this, a conclusion which was drawn by us before, i.e. antinomy.

Thus, if you ask me, "Will there in fact be eternal torments?" I would answer "Yes." But if you were also to ask me, "Will there be universal restoration in bliss?" I would again say "Yes." The two are thesis and antithesis. I think that only the view expounded here satisfies both the spirit and the letter of the Holy Scripture as well as the spirit of patristic writing. But, being inwardly antinomic, this view requires faith and absolutely does not fit into the plane of rationality. It is both "yes" and "no." It is an antinomy. This indeed is the best proof of its religious validity.

Of course, I may be doing the reader a disservice, since by this point he should have already read through Florensky's lengthy discourse on the separation of the soul from the body, the separation of the self from the soul, and the utterly demonic nature of evil. It is only after one has plunged deep into the depths of his spiritual explorations that one can truly appreciate this man's rather simple, if intentionally contradictory, view of judgment. But alas, there is no time or space here to treat the entire letter.

Florensky on space-time

Toward the end of his life in a Soviet prison camp, Florensky had one last burst of creative insight:

"On 3 April [1936], Florensky directed a letter through Kirill [his son] to his teacher, Academician Vernadsky, in which he overcomes his anger at 'human stupidity' and tries to reformulate the cornerstone of his philosophy: the reality of time and space. Thought of by rationalists as an abstract way of organising our perceptions and by the sensualists as subjective delusion, for Florensky space and time are the key to understanding and

the most weighty proof of the reality of space-time is the fact of the existence of asymmetry in nature and of irreversibility in the temporal ... Asymmetry in time is irreversibility. To be is to be in time, to be in time is to be irreversible, that is 'historical'.

We cannot, as the cinema can, turn time around and have the splash before the dive. ... 'Physical space-time cannot be thought of other than as potentially immense in compass yet endowed with distinct content. And that leads to the assertion of the curvature of space-time'. Different sections of the curve have different surfaces: a rough surface wears more slowly, a jutting corner weathers faster. We cannot conceive of the border between the inner and outer body as flat. Thus time itself can be measured differently in different spatial conditions.

These hypotheses, Florensky tells his son and through him his son's teacher, still out there and able to study and publish in the world of science, may be proved wrong tomorrow but will surely be proved right the day after and he needs to record them. So the free mind, struggling in the weary body amid the white mice, winter flies and billowing steam, still fought to communicate, to leave some trace..." (Pyman, p. 178)

If the Soviets had allowed Florensky to live, and if before his death he had been allowed to continue his own research, they might very well have had the philosophical counterpart to Einstein's general relativity.

Florensky on learning mathematics

In mathematics try not just to memorise what to do and how but take it in gradually, bit by bit, as though it were a new piece of music. Mathematics should not be a burden laid on you from without, but a habit of thought.

(From Avril Pyman's biography, p. 160.)

Language and Reason

Pyman discusses Florensky's attempt at "an answer to the eighteenth-century dispute between Church and Enlightenment as to whether language is God's gift to man or the creation of the peoples who speak it and the individuals who us it. Florensky's take of this dispute is conciliatory:

it is precisely in this contradiction, and in its extreme acuity, that language as eternal, steadfast, unchanging Reason, as pre-human Logos, is in fact conceivable as something at the same time infinitely close to the soul of each one of us, affectionately supple to the heart, personal in its every moment, its every movement and expressive of utmost individuality."

I see what Florensky's getting at here, but my suspicion here is that the Church and the Enlightenment were both wrong, and that even a conciliatory view of their positions is insufficient. I'm more convinced by a view of language as a cultural artifact, a "product of human action but not human design." I am a skeptic when it comes to language being so closely tied to "eternal, steadfast, unchanging Reason." There is a reason why words are so hard to define, why Socratic dialogs never reach firm conclusions. Language is grown; it does not transcend the created order, but is a product of the physical passage of time.

In other words, no matter how in tune we are with eternal truth, we still have no firm or final way to express this. "Out of the mouths of babes and infants..."

Florensky on Ontology

From Avril Pyman's biography on Florensky, quoting Florensky:

The basic self-awareness of humanity, that 'I live in the world and with the world', presupposes the existence, the real existence as reality, of both myself, humanity as such, and that which is outside myself, which exists apart from me or, more exactly, independently of human awareness ... In the act of cognisance it is impossible to separate subject from object; cognisance is at once the one and the other; more exactly, it is precisely the cognisance of the object by the subject, a unity, that is, in which the one can be distinguished from the other only in the abstract, yet at the same time the object is not obliterated by the subject, neither is the latter dissolved in the object of cognisance exterior to itself. Moreover, once unified, they do not engulf one another even though, while maintaining their mutual independence, they are no longer divided. The theological formula without confusion and without separation is fully applicable to the cognitive interrelationship of subject and object...

In other words, subjective and objective are analogous to the two natures of Christ--both bound up together as one, yet fully distinct. It is a paradox on which the pursuit of all knowledge depends.

Discontinuity

I read somewhere that the theory of functions had a profound impact on Florensky's philosophy. The assumption of continuity, for him, meant that the philosophy of the modern era was doomed to see everything in purely deterministic terms. The discovery of discontinuity, of functions that do surprising and almost incomprehensible things, signaled for him a turning point. The world was full of wonder again. Learning could be spontaneous, and the mind could leap forward in faith into the unknown.

There has to be something to this. When I teach calculus, I can't help but notice that students have the hardest time processing the definition of continuity--probably because they can't imagine discontinuity. Oh, sure, maybe a function jumps a few times here and there. Or maybe a function like f(x) = 1/x has a vertical asymptote. Big deal. For the most part in my beginning calculus class we deal with functions that are continuous everywhere they're defined, aside from maybe some removable discontinuities.

The definition of continuity is simply that the local behavior of a function f(x) near x = a is the same as the value f(a). The surprising thing to students is that this might not be the case. Take a function like f(x) = x^2, and obviously finding the limit is just a matter of "plugging in" the appropriate value of x. Discontinuity is jarring. It means the function doesn't behave the way one would expect. I find it necessary to hammer this point home for students, because otherwise they'll have a hard time perceiving that continuity is really an issue at all.

There is an intimate relationship between discontinuity and freedom of the will. To construct a continuous function one simply needs a general rule, e.g. f(x) = x^5 - 5. To construct a discontinuous function, one must dissect the continuum, picking out individual points of interest and declaring that a function behave differently at those points. It is this declaration by which a mind exercises its freedom of will. Even if it is silly or strange to do so, I may simply declare that f(5) = 0, even though for every other real number x I say f(x) = 2x. It is an act of will, a bold separation of chosen points from the rest of the continuum, an assertion that my word alone defines what a function is. Its local behavior may be perfectly continuous, and it may have a limit as x approaches 5. I am by no means bound by such trends.

One who is truly skilled at dissecting the continuum can do much more terrible things than making a function with a single point of discontinuity; indeed, it is not hard to define a function which is continuous nowhere, even though it is defined everywhere. I've given my students that problem as an extra credit assignment; I'm asking them to look it up and see if they can explain it to me. They won't be able to produce the example themselves, which is not a reflection on their intelligence so much as on the nature of mathematics. There are certain things one simply cannot imagine unless one has seen.

This is why mathematics is essential to a truly liberal education, and why I find it incredible how many educated people consider math a mere specialization totally closed off even to the average intellectual. There is nothing so liberating to the mind as being able to enter a world of pure thought, a world which is simultaneously the work of our own minds and beyond the mind's control. Every field in the humanities sounds to me to be obsessed with paradigms and paradigm shifts. Mathematics has no such discussions, because there is only one paradigm: discovery through creation. Mathematics is a creative act of will in the purest sense. "Let x be," and it is. What holds most people back from the world of mathematics is their unwillingness to take that leap of faith, to make that bold assumption of creativity, to step out of continuity with the world of the concrete and "practical" (concepts which any intellectual ought to address with suspicion). More than all the scientific applications, more than all the quantitative reasoning and critical thinking skills, mathematics has this one thing to offer the world: intellectual courage.

That is, of course, if one understands it the way, for instance, Florensky did.

Florensky on Creation

"Objectivity does exist. It is God's creation. To live and feel together with all creation, not with the creation that man has corrupted but with the creation that came out of the hands of its Creator; to see in this creation another, higher nature; through the crust of sin, to feel the pure core of God's creation... But to say this is to posit the requirement of a restored, i.e., a spiritual, person."

"'Nothing,' says St. Methodius, 'is evil by nature. Things become evil by the mode of their use...'"

"The body is something whole, something individual, something special."

"[T]he life of each of these organs--head, chest, and stomach--can be deepened by an appropriate training, and then a person becomes a mystic of the respective organ."

"[C]hurch mysticism is the mysticism of the chest.... If the chest is the center of the body, the heart is the center of the chest. And, since ancient times, the entire attention of church mysticism has been directed at the heart."

"A genuine Christian ascetic is distinguished from mystics of [the head] by restraint of a proud mind. He is distinguished from mystics of [the stomach] by inhibition of [lust]. All that a genuine Christian ascetic lives by arises in him not arbitrarily in one separate organ or another, but in the living center of his being, in the heart, and it arises there under the grace-giving action of the Holy Spirit, the Comforter."

"The genuine Christian ascetic is essentially connected with all of creation and does not despise anything that belongs to creation. But, in his case, in his feeling for creation, there is no lust. He penetrates deeply into the mysteries of heaven and earth and is not deprived of their knowledge, but, in his knowledge of the mysteries, there is no pride."

"Two feelings, two ideas, two presuppositions were necessary for the possibility of the appearance of science: first, a feeling and idea whose content was the lawlike unity of creation (in contrast to the caprice of demons...); second, a feeling and idea which affirmed the genuine reality of creation as such. Only these two feelings and ideas made it possible to pierce the reality of creation with a fearless, direct gaze, to approach this reality with trust, and to love it joyously.
Theologically speaking, it was necessary to introduce two dogmas in man's consciousness: the dogma of the Providence of One God and the dogma of the creation of the world by a Good God, i.e., the dogma of the giving of its own, independent being to creation. The providence of God and the freedom of creation form, in their antinomy, one dogma, the dogma of God's love for creation, a dogma that has its foundation in the idea of God as Love, i.e., the idea of the Triunity of Divinity. This antinomy, in all its decisiveness, is the foundation of modern science."

"Only Christianity has given birth to an unprecedented being-in-love with creation. Only Christianity has wounded the heart with the wound of loving pity for all being."

"'Love of nature...But what about ascetism, the escape from nature?'--we can hear the objection of worldly people. In response, I affirm in advance that worldly literature has never understood the spirit of Christian ascetism.... This leads to a situation in which the substantial differences between Christian asceticism and the ascetism of other religions, especially the Hindu religion, are usually not recognized. ... [T]here is nothing more opposed than they. ... One despises creation, although it is involuntarily attracted by its evil, and attempts to acquire magical powers over it; the other is in love with creation, although it hates the sin eating away at it, and the ascetic does not need magical powers, because grace-endowed creation will remove the yoke of sin's heteronomy and will be able to live as it is in itself, in accordance with its originally given mode of being."

These thoughts, scattered throughout Florensky's chapter on "Creation" in The Pillar and Ground of the Truth, summarize for me the full meaning of science--this "being-in-love with creation." And it is only through a certain disposition--a "mysticism of the heart"--that one can truly enter into this kind of science.

That's my take on the relationship between science and religion.

Orthodoxy

Now that I've read Naming Infinity (which I mean to blog a bit more about, but I've been busy) I thought I'd dabble a little bit in Pavel Florensky's The Pillar and the Ground of the Truth, adapted from the very same thesis that Nikolai Luzin read on his journey to converting from atheism to Christianity.

The first letter of PGT, "To the Reader," contains some profound statements of what makes Orthodoxy different from Catholicism and Protestantism. Florensky introduces as a main topic this thing called ecclesiality--which he insists cannot be defined!

Ecclesiality--that is the name of the refuge where the heart's anxiety finds peace, where the pretensions of the rational mind are tamed, where great tranquility descends into our reason. Let it be the case that neither I nor anyone else can define what ecclesiality is!

After meditating on this for a little while, he briefly outlines what for him is the fundamental problem with both Catholicism and Protestantism:

Where there is no spiritual life, something external must exist as an assurance of ecclesiality. A specific function, the pope, or a system of functions, a hierarchy--that is the criterion of ecclesiality for Roman Catholics. On the other hand, a specific confessional formula, the creed, or a system of formulas, the text of the Scripture, is the criterion of ecclesiality for Protestants. In the final analysis, in both cases what is decisive is a concept.... But by becoming the supreme criterion, a concept makes all manifestation of life unnecessary.

And finally, he offers what he feels to be the strength of Orthodoxy:

The indefinability of Orthodox ecclesiality, I repeat, is the best proof of its vitality.... There is no concept of ecclesiality, but ecclesiality itself is, and for every living member of the Church, the life of the Church is the most definite and tangible thing that he knows. But the life of the Church is assimilated and known only through life--not in the abstract, not in a rational way.... What is ecclesiality? It is a new life, life in the Spirit. What is the criterion of the rightness of this life. Beauty. Yes, there is a special beauty of the spirit, and, ungraspable by logical formulas, it is at the same time the only true path to the definition of what is orthodox and what is not orthodox. [emphasis added]

...

That is why there is only one way to understand Orthodoxy: through direct Orthodox experience.... [O]ne can become a Catholic or a Protestant without experience life at all--by reading books in one's study. But to become Orthodox, it is necessary to immerse oneself all at once in the very element of Orthodoxy, to being living in an Orthodox way. There is no other way.

In short, my initial reaction is, "Wow."

It's no wonder so many people in the West are discovering Eastern Christian theology and finding it refreshing. To me, the emphasis on beauty as a genuine measure of orthodoxy is profound, and something in me tells me it's just what I'm looking for.

I wonder where Florensky will take me?