Information, Spinoza’s “Idea” and The Structure of the Universe

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Ideas as Information

This is a difficult post to write, particularly because the ideas it addresses are just plain large. And these large ideas have such permeating ramifications, both towards Spinoza philosophy and contemporary Science it is indeed very difficult to do any justice to them. Instead it must be taken as a kind of rough draft, a sketch, of what may be conceptually possible when bringing the philosophical concepts Spinoza employed into contact with the Information. The thoughts here must be taken as provisional conjecture, but this is not to say that I do not find the comparisons offered here to be valid. Rather, I suspect strongly that what Spinoza was talking about, the relationships in the world that he was attempting to systematize, are very much the same ones that Science today talks about when thinking in terms of information.

All this comes into view with Tom Stonier’s radical Scientific proposal that Information is an essential component of the Universe, found in his speculative book Information and the internal structure of the universe: an exploration (1990). I’ll cite at length from his work below to present the core of his ideas about information, but first I need to make a conceptual leap which will make future thoughts of my application of Stonier’s ideas more clear.

Stonier’s abstraction on the left, Spinoza’s on the right:

Matter = Extension

Energy = Conatus (striving)

Information = Idea

I don’t want to justify these equalizations, but rather just let them remain as starting points, at least until Stonier’s vision of information is made more clear. I will say that the first of these seems obvious. What we mean usually by matter is precisely what Spinoza is attempting to describe through the Attribute of Extension. The second of these is both instinctively appealing but also has some difficulties in translation, mostly due to the much debated theoretical role conatus plays in Spinoza’s philosophy. Perhaps though in reading conatus as energy in the specific context of information theory important aspects of Spinoza’s conatus thinking may come into relief. And lastly, most importantly, the third of these, the equation of 21st century information with 17th century Spinozist idea, is the keystone of the entire comparison, and hopefully will reveal as much about what Spinoza was thinking, as about what he was trying to describe.

But now let us present Stonier’s idea that “information” comprises the universe just as much as matter and energy does.

Information is Real

Stonier spends much of his time hewing out a concept of elemental information from the concept of “energy”, leaving “matter” to remain relatively self-evident. It is in particular the way that we are able to see energy as existing in different forms yet to remain an objective measure of how things are composed, that provides the footing for how information is to be conceived. Much of what Stonier argues is that some of our energy descriptions are better handled as information transformations:

Just as there exist different forms of energy – mechanical, chemical, electrical, heat, sound, light, nuclear, etc – so do there exist different forms of information. Human information represents only one form of information..human information itself, maybe stored and communicated in a wide variety of ways and represent many different forms (9)

Right of the bat we have a very important idea, and one that communicates itself quite well with Spinoza’s notion on the limits of human thinking and epistemology. What we commonly refer to as “meaning” which is ever context bound, is only a form of information, just as mechanical energy is just a form of energy. The ideas we have as human beings are not reducible to the meaning of their expression in language. Rather, as Spinoza sees it, the ideas we have are rather best seen as dispositional relations to really only one thing, the whole of the Universe. The ideas we have are informational or organizational states, what Stonier will call “structure”. Let me quote at length what Stonier describes as the “heart of the concept”. I quote at length both because Stonier’s book is not accessible on-line, and also because he does a pretty good job of expressing himself on what he means:

Information and organization are intimately interrelated.

From this axiom we derive the following theorems;

1. All organized structures contain information, and as a corollary: No organized structure can exist without containing some form of information.
2. The addition of information to a system manifests itself by causing a system to become more organized, or reorganized.
3. An organized system has the capacity to release or convey information.

Let us examine the above theorems, beginning with the first. Any physical system which exhibits organization contains information. Information organizes space and time. The definition of the term “information” becomes analogous to the physical definition of the term “energy”: Energy is defined as the capacity to perform work. Information is defined as the capacity to organize a system – or to maintain it in an organized state. As we shall discuss later, it becomes impossible to perform “useful” work without an input of both energy and information. Conversely, all work brings about a change in organization, hence information.

Organization is a reflection of order. A structure or system may be said to be organized if it exhibits order. Order is a non-random arrangement of the parts of the structure or system. Randomness is the opposite of order, keeping in mind that certain forms of apparent randomness exhibit significant order, eg, a perfectly uniform distribution. For this reason, the terms chaos and disorder are preferable. Any quantitative analysis of information must be based, at least in part, on measuring either the order, or the chaos of the system.

Analyzing the information content of a chaotic system is made more problematical by the fact that a system may only appear to be chaotic: That is, such a system actually is responding to a simple algorithm – the apparent unpredictability reflects the fact that trivial variations in initial conditions may have a major impact on the system’s final behavior.

Organization and information are, by definition, closely interlinked. However, they are different: One cannot have a shadow without light, but a shadow and light are not the same thing. A shadow is the manifestation of light interacting with an opaque object. Likewise, organization is the manifestation of information interacting with matter and energy.

It is important to emphasize the conceptual necessity for an abstract term such as “information”. Information is a quantity which may be altered from one form to another. Information is a quantity which may be transferred from one system to another. This is not true, at least to the same degree, for the more concrete terms “order”, “organization”, “pattern”, or “structure”. The matter parallels the difference between the terms “energy” and “heat”. Energy is being capable of being transformed from one form to another, as well as being transferred from one system to another. In contrast, the limitations of the less abstract concept “heat” (a quantity directly perceptible to our physical senses), cannot explain how heating a boiler causes a locomotive to move, or a light bulb to light up in response to the electricity generated by a steam turbine.

Likewise, “information” maybe transformed from one form to another, as for example, when dictating a manuscript: Patterns of sound waves end up transcribed as words on a printed page. It’s easy to understand that the information was transformed via the stenographer and printer, from the spoken to the written word. It is not clear how the oscillating molecules of air comprising the sound pattern end up as apparently unrelated patterns of dye molecules on a printed page. The matter becomes even more mysterious when one eliminates the human intermediaries and speaks into a voice-to-print device. The structure of the phonemes making up a word is not the same as the structure of the printed syllables making up the same word. The information content, however, may be considered the same for both.

Information, like energy, is an abstract quantity. Communications engineers have recognized since Hartley’s time, over half a century ago, that information may be treated as an abstract quantity. What the present work proposes is more than that, viz, that information, like energy is a physical reality.

To be more precise, heat (involving uncorrelated photons in a crystal or randomly moving molecules in a gas) is the product of the interaction between matter and energy. Structure is the product of the interaction between matter and pure information. Energy, in pre-relativity physics, was considered as the more abstract quantity which, when added to matter, manifests itself as structure (organization).

As will be discussed in a later chapter, such a conceptualization of information leads to a different quantitative definition from that of the communications engineers. Such a definition also differs from the standard dictionary definition which defines information as, for example: knowledge, news, or what is told. Dictionaries go on to define knowledge as all that is, or maybe known. Knowing is defined as: recognizing, perceiving with certainty, being aware (of), being acquainted with. There are other, more specialized meanings provided by dictionaries, but the gist is that information is either a form of knowledge, or equivalent to it. Dictionaries define knowledge and information purely in implicitly human terms. This is in marked contrast to the principle that information is a property of the universe – that it comprises the “internal” structure of the universe.

Human information may involve the perception of that “internal” structure. Every time scientists define a constant such as the gas constant, Avogadro’s number, Boltzmann’s or Planck’s constant, etc, they have discovered another aspect of the organization of the universe. Each such discovery represents the human perception of the information contained within physical systems.

Aspects of human information systems, including the terms knowledge, meaning, significance, intelligence, etc will be explored in a future work, Beyond Chaos. The present work is concerned with the physics of information systems – systems whose reality is independent of human perception and which therefore transcends it.

To sum up: All regular patterns contain information. The mathematics of chaos had demonstrated that even apparently highly irregular patterns, may be the product of some rather simple algorithm which underlies the chaos. To the argument that what we are really talking about is “patterns” and “organization”, the answer is that “information” is a more abstract generalization which, in the long run, one needs in order to measure it by some universal measure such as “bits”. It becomes as difficult to measure quantitatively a pattern or a structure in terms of bits without the aid of the abstract concept “information”, as it is to measure in joules the output of light by a lamp without the more abstract concept of “energy”.

Information is an implicit component in virtually every single equation governing the laws of physics. (25-28)

The first thing that needs to be addressed if we are to make a successful comparison between Stoniers concept of information and Spinoza’s notion of Idea is the thought that information can be “transferred”. I think that this is related to the way in which we view energy as some form of primal substance that can be poured into (or drained out of) various containers. I’m not sure how helpful this image is in either the case of energy or information. The addition of energy to a system is a transformative one. The system itself is changed. And I think Stonier is onto this with his idea that information itself, when added, changes the structure of what it is added to. There is, therefore, something of competing images here, images that have to do with how we view the boundaries of things. From a Spinozist point of view, therefore, when Stonier says:

The addition of information to a system manifests itself by causing a system to become more organized, or reorganized.

An organized system has the capacity to release or convey information.

I think it is better said that an organized system has the capacity to improve the organization of (the adequacy of the ideas of) systems outside of it. Information does not pour out of a system, into another, but rather communicates itself, interactively, through the improvement of the organization of things beyond it. In this way the physical object of a book does not “release or convey” but rather through interaction, re-organizes the materiality of the reader. Key to changing the metaphor we use to describe informational relations is to see that when there are such interactions nothing is being passed back and forth, but rather what is involved is the substantive change in the relational capacities of each distinct thing, in the context of something larger than each (be it a larger system, or the Universe itself).

Stonier in his re-imagining of information uses the concept to address itself to the problem of entropy. He works to show that entropy is not strictly equivalent to “heat” (which is one of its manifestations), a difference that actually marks out the need for an information science as structural changes in matter do not exclusively follow heat changes. As such he places organization and heat at odds to each other (heat, the move towards randomness, works against the move towards organization), but energy and information are actually part of a triangle of universal elements:

The application of energy expresses itself as heat which causes particles (molecules, photons, plasmons, etc) to vibrate and to move at random. In contrast, the application of information causes particles to be bound into fixed patterns and ordered motion. In that sense, heat may be considered as the antithesis of organization.

If heat is the antithesis of organization is heat, and by implication, energy the antithesis of information, that does not preclude the possibility that energy and information may interact to provide a mix which might be viewed as “energized information”, or alternatively as “structured energy”. INFORMATION and ENERGY must not be viewed as the opposites of a bipolar system, rather, they must be considered as the two angles of a triangle, with MATTER comprising the third (74-75)

This is problematic to a Spinoza/Stonier comparison, and I think Spinoza actually helps out here. Stonier wants to see something like a crystal at very low temperature as possessing an ideal of information, a structural coherence with very little entropy (heat). I think that this is a mistake in his visualization. Because I view the conatus as equivalent to energy, actually all things that exist possess both informational structure (what I want to call informational or ideational lean towards the Universe), and also the energy (tendency) to maintain that lean (entropy will be handled at another time). In fact the informational and energy dispositions are mutual expressions of each other. The introduction of heat (randomness) is actually an informational transformation from the outside. Instead of thinking of information as merely the internal structure of a thing, it is both the internal and relationship organization of a thing.

We can see this on the most fundamental level in examples of “energy” transfer, reconfigured to reflect exchanges of information. Stonier uses the classic of billiard balls: 

…consider two billiard balls, one red, one white, rolling along on a billiard table at equal speed. The red one is moving in a north-easterly direction, while the white one is moving in a south-easterly direction. Let them meet in such a way, that the collision results in a reversal of direction: The red one now traveling south-east, while the white one travels north-east.

The question that one may ask is whether the two balls exchanged energy, or whether they exchanged information. Certainly the collision, involving a glancing blow, seemed not to affect appreciably the energy content of the system as a whole. Nor did the energy content of the individual balls appear to be affected appreciably since they continued moving at virtually undiminished speed. What was altered however, was the direction…To restate the question: Is the conservation of momentum a reflection of the fact that the two bodies merely exchanged information? (81)

Instead of seeing energy as conserved and “transferred” between objects, one can also describe such an interaction as an exchange of information. In fact, I suggest it is not the exchange of information so much as the informational re-orientation of each. The ideas of each ball, its informational properties, has changed through interaction. We can see the foundations of Spinoza’s panpsychism wherein each thing “thinks” (is made of ideas that make a difference in its capacities in the world).

Stonier himself provides an interesting example of the primary dichotomy he would like to set up between heat and organization, with an implicit tension between energy and information, that if warm-blooded mammalian brains. This is more than a mere exception I would suggest, but rather points to the problem of Stonier absolute contrast between energy and information itself. As he writes of the mammal and heat (randomness):

Present-day biological systems, with minor exceptions (eg, certain chemosynthetic bacteria), obtain their energy from the sun. Light, as we shall discuss later, is a form of energy with a high information component. In general, biological systems eschew heat – either as an energy input, or as a product. When heat is generated, it is the by-product of metabolic reactions and usually reflects an inefficiency in the system. The one clear exception is the production of heat to maintain efficiency of advanced metabolic systems operating in highly organized environments. To maintain the very high levels of structural information in the system, the changes in entropy associated with changes in temperature must be kept to a minimum. The most advanced information processing system known is the mammalian brain. When the temperature rises only slightly above a critical threshold (as with a high fever), the system begins to fail as the individual hallucinates. A relatively slight drop in temperature, on the other hand, leads to narcosis. Thus even relatively minor (heat-inducing) changes in entropy, change the delicate organization of the system so as to interfere with effective information processing.

Therefore, in the one exception where biological systems do produce heat and utilize heat, the function of the added heat is not to provide energy, but to maintain a stable temperature so as to minimize externally induced entropy changes. In other words, heat is used to help stabiliize organization – it is the one instance where the controlled application of heat constitutes an input of information. (66-67)

As I have argued elsewhere when considering Spinoza as a Chaoplexicist, Is Spinoza a Cyberneticist, or a Chaocomplexicist?informational increases cannot be seen solely in terms of an internally defined relation, for instance the structure of crystal. Instead they have to be read as edge-riding properties at the border of chaotic distributions. For instance there cannot be any such heat/organization polarity. If the Universe achieve a degree zero state it would not have reached a state of maximum information. Instead, the heat (randomness) use by mammalian lifeforms is not an exception, but an expression of the informational transformations that make up the structure of the Universe. Organization is best not seen in contest with Energy, but rather Energy expressions are necessarily informational ones. Even a purely random, equilibrium distribution is informational. And information increases (what for Spinoza would be increases in the adequacy of ideas) are not expressed sheerly as “structure” but rather the ability to bestride structure and chaos. This is precisely what lifeforms do with “heat”, not eschewing it, but surfing it.

The locus of this reasoning I believe is found between the two, conflicting theories of Information and its relationship to entropy. Shannon, famously, linked the information content of a message to the surprise factor of its distribution. So if you received absolutely random message (taken to be utterly entropic), its information would be at maximum. Stonier, because he is not dealing with messages, but states, but an absolutely random distribution as the minimum of information structure. Truth be told, the answer lies between these two. A distribution, when seen as a message and measured for information, carries with it its relational capacities found in the reader of that distribution. In keeping with Shannon, the work that must be done in application of informational decoding of a random message is very high, so the message contain maximum information. If one is surprised very little by a message, it is composed of very few differences that make a difference to the reader. Its information is low. With Stonier, a random distribution of gas molecules composes very few differences that make a difference to the observer, so the information is low, but the reader/observer and the system/message have to be taken as a whole. The antithesis between these two perspectives is in their framing. If for instance we were to play a game where the exact distribution of gas molecules in a box near equilibrium state provides clue the game’s aim, suddenly the box is brimming with information, differences that make a difference. In fact, real world information differences, organizational relations that make a maximum of differences in the world, are those that oscilate or rather surf between both Stonier concept of fixed, structural, very low energy information, and Shannon’s very high entropy notion of message information. Maximal information, as lived, rides between this balance between structure and chaos. It is as Spinoza says,  

E4p38 – Whatever so disposes the human Body that it can be affected in a great many ways, or renders it capable of affecting external Bodies in a great number of ways, is useful to man; the more it renders the Body capable of being affected in a great many ways, or of affecting other bodies, the more useful it is: on the other hand, what renders the Body less capable of these things is harmful.

To use a Stonier example, for a crystal at low temperature to be in a maximum state of information its constellations of elements would have to be in state in which they can effect or be affected in the greatest number of ways, and one is not sure that this is the case. Such a state is not just useful, I would say that it demarks the greatest adequacy of ideas , or informational orientation, as is historically possible. Part of this is because for Spinoza there is such thing as a state that has no information or organization.

There are additional difficulties to be handled in the equation between Spinoza’s “Idea” and Stonier’s “Information”, for instance the reality of entropy and the ultimately question of whether, or to what degree a “closed system” actually exists, has to be worked through. And there are several other aspects of Stonier’s theory that lend themselves to an elucidation of Spinoza’s thinking, for instance the way in which he re-reads changes in “potential energy” as changes in “information”, the moving of a system into a less probable state. These are things I cannot take up right here, hopefully in the future. It is more that Stonier’s view that information comprises an essential, transformational component of the Universe, just as energy and matter does provides a highly effective backdrop for understanding just what Spinoza means by Idea. What he means by Idea is Information. And it is precisely the distinction between human information and information as an abstraction that best brings out the differences Spinoza meant in both his epistemology and his ontology, the way in which there are distinct limits to what we know, but also that in knowing anything we are changing our informational relationship to both it and the world. Improving the Adequacy of our Ideas is perhaps best seen as improving our Informational organization of ourselves, thinking is position altering. And all things must be regarded as, in some sense, thinking.

I hope that this presentation has not be unfair to Stonier whose theory and book deserves much better treatment. I am not one who enjoys the detailed summaries of positions, and have used Stonier only as a peering into the possibilities of Spinoza’s thinking, both in terms of what he really meant, and how it might help us understand how things are. But Stonier’s theory is beautiful in its own right worth serious study for what he claims. My Spinozist adaptation is at best provisional.

“By mathematical attestation”: Spinoza’s Epiphanic Calculation

Just How Mathematical Was He?

I have been having an interesting conversation over time with Eric Schliesser at Leiden University who holds a minority position on the role mathematics plays in Spinoza’s position on what can be known. He strongly interprets Letter 12 towards a skepticism for just what mathematical calculation (and its attendant applied empirical observation) reveals. As Letter 12 attests, Spinoza regarded mathematics as a “product” of the imagination, come from our imaginary classifications of objects as wholly bound things – cut out from the cloth of Substance, if you will. I wrote on my agreement with this here Spinoza and Mechanical Infinities, but Eric really would like to push the interpretation so far as to restrict all of mathematical endeavours to the realm of the imaginary (the lowest forms of knowledge for Spinoza, the other two being the “rational” and the “intuitional”). This of course comes up against Spinoza’s rather obvious and profound use of mathematics as a model for philosophical investigation and even the higher forms of knowledge as both his method more geometico and his illustrations of higher knowledge both make use of mathematical forms as exemplary.

In large part I really am in agreement with Eric, in the most common Spinoza interpretations the mathematical has somehow risen far above the frame in which Spinoza intended it, but it makes very little sense for me to regard the “products” of imagination as imaginary itself – in the Emendation Spinoza speaks of the production of tools of intellection out of imaginary relations as a positive progression. Clearly mathematical description provides distinct causal understanding of the relations between things, and it is exactly in this vein that the empirical science observations of several centuries does provide a substantive remove from mere superstition, something that Spinoza firmly places himself against. It would seem that Spinoza’s true position lies somewhere in-between, not accepting Galileo’s thought that Nature is written in the language of mathematics, but also grasping that in mathematics (and observation, experiment) there are genuine increases in understanding, freedom, power, joy,  and ultimately for Spinoza, Being.

In this way mathematics is seen as:

1. Both a product of the imagination, and an aid to the imagination [Auxilia imaginationis] (Letter 12).

2. As such they are qualifiable as ens rationis which is what Spinoza calls them in letter 12 [eius modi Entibus rationis], something he is elsewise careful not to be blurred with ens imaginationis (E1App).

3. It should be admitted that Spinoza does not help things by just prior to distinguishing “number” as a  “things of this reasoning” in letter 12 to Meyer he refers to it as  “nothing more than thinking’s, or better imagining’s, modes” [nihil esse praeter cogitandi, seu potius imaginandi, modos] – he wants to straddle the line here and a little confusedly so.

4. But reading numbers as ens rationis (distinct from ens imaginationis), these, as Spinoza notes in the all important E2p49 asserting the collapse of volition into the concept of “idea”, are not ens reale (Cor. dem. [III. B (iii)], except when the latter is understood as an operant, an affirmation and an action.

5. The real and the rational abstraction that describes it are not to be confused. It is this final distinction that provides the skeptical element towards an ultimate mathematical reduction of Nature.

6. One has to live with the exegetical problem that while Spinoza in the Appendix of Ethics part I makes a strong distinction between things of the imagination, and things of reason, in letter 12 he oscillates, even within sentences, between things of (this) reason and something he undefinedly calls aids (auxilia) of the/to the imagination, never sure how he wants to describe Number.

Are Maths Only Imaginary? What Would that Mean?

By my understanding Eric places increases of power in mathematical description solely within the a “usefulness” category, all the while restricting them to the “imaginary realm”. While I really enjoy this outlier position, the very substantive nature of these increases in usefulness simply remains unexplained. And though this in part may be due to some inconsistency in how Spinoza treats the imagination (and the concept of order itself), I do think that Spinoza saw in mathematics (and scientific testing) genuine increases in the understanding of things, without acceding to the thought that mathematics genuinely reveals the eternal essences of things. For Spinoza we are, even the most scientific among us, like a “worm in blood”, not comprehending entirely the body and indeed the Universe we live in.

In this discussion there is an interesting, and indeed I think problematic sentence that at least provisionally I would like to retranslate. It is found in the Appendix of the first part of the Ethics, and in it Spinoza appeals to the very mathematical attestation by which we perceive or understand things of the world. He had just finished rebuffing two stages in thinking: addressed are those that feel that astronomically it is the motions of the heavenly bodies themselves that somehow compose [componere] a harmony, a harmony that God delights in; and then those that from this notion of celestial harmony then find that it is the disposition of the brain alone from which human judgment comes, something which results in a skepticism of knowing in general. One is left with either a physiognomic theory of differences of perceptions (there are as many different kinds of brains as there are palates), or presumably on the other end the “veil of ideas” of proto-idealism.

In contrast to this physiognomic skepticism, Spinoza turns to the very discernment of things [res]:

Res enim si intellexissent, illae omnes teste mathesi, si non allicerent, ad minimum convincerent.

I translate this literally because there is some disagreement in the major English translators on the meaning of Spinoza’s sentence (and I think that both of them are somewhat wrong):

For if things they would have been able to discern, those all by mathematical attestation, if they were not allured, at minimum they would have been convinced.

The two counter translations I provide here. Curley in some rather convoluted restructuring, attempts to emphasize the “all” as an accusative. All these persons would be convinced if they merely discerned things correctly. The things themselves would convince everyone. While Shirley, I think more correctly, places emphasis upon both Spinoza’s mode of argumentation, and mathematical attestation. Here they are:

“For if men had understood them, the things would at least convinced them all, even if they did not attract them all, as the example of mathematics shows.” (Curley)

“For if men understood things, all that I have put forward would be found, if not attractive, at any rate convincing, as Mathematics attests.” (Shirley)

There really is no support for Curley’s inventive transformation of “omnes” into a universal emphasis of agreements, though that may be implied. Really what Spinoza is saying is that indeed contrary to merely the physionomic understanding of judgments (and also a celestial orderliness model), distinct discernments of things have come via the testament of mathematical treatments. While Shirley’s translation grasps the general thought of this, Curley captures the very epiphantic nature of such intellection, it is through mathematical treatments that the very nature of “things” appears.

And the little caveat on the nature of how such men will be affected by such discernment is telling. Such fellows will be convinced, though they may be “attracted” to such an interpretation. Here Spinoza seems to be putting his thumb in the eye of those that disagree. There are it would seem libidinal investments in seeing the world other than the way in which it is most arguably so. There is also perhaps a commercial connotative association of liceo, “to buy, to put a price on, to value” which may not be far from Spinoza’s intention.

Teste Mathesi

So what are we to make of this “by mathematical attestation” [teste mathesi]. Clearly, it is by reason of mathematics that philosophers (and scientists) arrived at the notion of a harmony composed of celestial bodies in motion, a sense of harmony that for Spinoza ultimately lead to viewing the brain as the source of all human judgment; so it cannot be by mathematics alone that we come to discern things properly. And Spinoza has in turn used the geometic method in such a way that he seems to feel that he has, via such a mathematical attestation, produced a discernment of things. As Spinoza in Letter 12 strongly calls into question the ultimate knowledge available by mathematical measurement and calculation, there would seem to be only one more meaning remaining. Mathematical attestation is for Spinoza a revelatory one, one in which the coherence itself (what is calls elsewhere a different “standard of truth”) provides the conviction of discerment, but also one in which any mathematical description always remains merely an approximation, a rounding off of the edges. And these are the edges through which the epiphany of perception itself shows through. This is in keeping with my general sense that in that all the propositions found in the Ethics are linguistic expressions, none of them actually are adequate ideas. It is rather that the interaction with the Ethics itself, its real, material and ideational body, is to provoke, is to cause, a real material and ideational change in the reader, one which cannot be reduced to the arguments themselves.

In a certain sense, Spinoza’s very intellectual and physical experiences as a craftsman, the precise use of calculation when applied to physical substances in the service of gaining the desired effects is the very thing that would preclude any minimization of mathematics or the testing of experimentation. Craftsmanship is after all where abstracted calculation and experiential rule of thumb come most closely together. And by all testament, Spinoza was a superb and devoted craftsman.

In a modern sense, we might want to say that for Spinoza the Universe is not a linear mathematical thing, but that the coherences of cognitions and communications between things is at best brought out by linear mathematical treatments (those only known of the day), treatments that in the end must also then be compared with man’s own finitude as a creature. As a craftsman perhaps he not only understood the way in which calculation and figure could be used to control and shape material, but also understood the often unexpected, unique and eruptive form of material itself, the way in which the glass, bubbled and fogged as it is, defies the curve of optical imprint of the lens grinding form. For Spinoza there are always non-linear magnitudes within magnitudes, beyond any one boundary-making, linear abstraction. But this does not prevent mathematics itself to produce reductive epiphanies unto the relationship between things.

Some follow-up thoughts: Spinoza “Following the Traces of the Intellect”: Powers of Imagining

}∅{ The Full Set

The Full-ness of a Body

This is not what I intend to write on the Subject of Infinity, but it is a projective chain of thoughts. It is a tracing of a yet un-consolidated line of interpretation.

Fido the Yak presents a symbol/concept which – and I’m not sure of its origin or complete meaning – is quite intriguing in the light of my recent readings on Spinoza, the Infinite and mathematics. What I would like to call the Full Set. This is how Fido describes his imagination of it

}∅{ is like an in-cept, yet it emerges discursively as a response to the arche. How does it originate? Autopoietically? Or do we acknowledge that it is a con-cept with the arche? (Like its withness with the empty set.) I talk about }∅{ extemporaneously because the extemporaneous describes it. If you can be in a state of consciousness that includes nothing while excluding nothing then }∅{ can describe such a state of consciousness, or a goal of thinking, a guideline, better. Maybe you’d want it to represent an empty concept, I don’t know. I say now the }∅{ expresses the acknowledgment that the explanation never exceeds its explained, which is a way of saying it never accomplishes what it sets out to do, and that “foundation” is a metaphor—you may see why I call it “the breach.”

We are running in similar directions, but I prefer in my own thinking to not think of it as a breach, so much as a whole plenitude, close to Deleuze’s Full Body, the Body without Organs. (Here my thoughts proceed from his in-spiration, in perhaps an appropriation.) It is closely related to Spinoza’s notion of the Infinite as something that cannot be broken. So, in my hands, it would describe the infinite proximity between any two limits.

It emerges from Spinoza’s diagram of bound infinities, which proclaims that within any bounds there are an infinity of magnitudes which are themselves divisible:

It is important to see that for Spinoza these are magnitudes(and not simply points on an imaginary line, which are at best ab-stractions). As magnitudes, they are FULL. Now, if we are to play with symbols, the requisite symbol for Spinoza’s point about bound infinities would be something like }∞{, which is to say, between any imposed limits, there are an infinity of magnitudes buried. Also importantly, and somewhat divergent from Badiou’s concept of Count-as-one, the symbol should not be {∞}, because for Spinoza any (abstract) internal bounds already, already refers to, or references to some degree a determination that lies outside of it, as in his Letter 12 diagram…

The sub-section between AB and CD {}, already includes comprehension of the circle circumstance itself, }{. Or, the internal count-as-one (set), really is composed, determined by the bordering edges of something beyond it, as a mode of comprehension, consciousness itself.

Playing With Symbols

So, while Spinoza in Letter 12 seems to be presenting something of a }∞{ determination, what would be the intuition of the full set }∅{, which is our subject here mean? It is not that between any two abstract limits there is some sort of nothing, or emptiness (for Spinoza denies the ontological consistency of the void). It is rather that the act of distinction and limitation itself drives itself toward the impossibility of separation: as we enter into the infinity of magnitudes (let us start with Badiou’s count-as-one teeming/erupting with multiplicities) {∞}, we are pre-positedly forced both outward…}∞{…but also inward to the full set itself…}∅{…the way in which what lies between simply cannot be divided at all and remains unbroken. It is not the sheer multiplicity that lies between any borders (inside, or outside), but rather the implicition that there is no “gap”, the very fullness of Being, from which mathematics, figure drawing and set-making composes only an abstraction, an imaginary class. It is for this reason that for Spinoza rational thought leads ultimately to an Intuition of immanent wholes and a speed of thought. 

Or, if put another way, any conception of emptiness, or lack, or nothing {∅} (whether it be mere psychological wanting, or mathematical 0), diverges upon the fullness of being, showing itself to be a figment.

Analog and Digital Intellect: Threshold Intensity, or Either/Or

 

Analogical Co-munications

I came across (now twice, but this time investigated) this wonderful collection of Deleuze-inspired writing and exhaustive explications, Pirates and Revolutionaries. Some of the very best stuff on the internet for instance on Spinoza’s concept of infinity. This article though on the difference between Analogical and Digital thinking is immensely clear and open-ended, for any of those who have not considered deeply the two modes of intellect. Below is one small snippet in a wide-ranging summation and positioning:

We will first address the research on animal communication that Gregory Bateson discusses in his Steps to an Ecology of Mind, a text that Deleuze cites when distinguishing analog and digital language. According to Bateson, the ‘messages’ that animals convey refer not to objects but to their social relations; for example, the cat’s mewing does not mean milk, but ‘dependence.’ A more compelling illustration is his story of a wolf-pack leader catching an inferior male who broke the code of hierarchies, and achieved coitus with a female, which involves being locked-in with her. Bateson explained previously how an adult wolf weans young puppies by crushing them down with its jaw. Then, in the case of the leader finding his subordinate infringing upon his mating prerogatives, instead of attacking, the leader simply crushed the male down as though weaning him. This communicates their social relationship by analogy: ‘just as a father is to a puppy, I am to you.’ In general, most animals normally convey their interrelations by means of such an analogical language, which consists of paralinguistic and kinesthetic expressions (body language) that communicate magnitudes of social relations (such as being more or less dominant) by means of analogous changes of magnitudes in bodily expression. Deleuze himself defines analogical language as one of relations, which consist of “expressive movements, paralinguistic signs, breaths and screams, and so on.

“Deleuze’s Analog and Digital Communication; Isomorphism; and Aesthetic Analogy”

Analogical/Digital Oscillation

What is interesting for my processes is that here in the treatment of the analog and digital I am finding the confluence of two divergent studies. Last month I found myself troubled by Hoffmeyer’s notion of the life-defining Digital and Analog concretizations of an individual, touched on in my review of Morten Tonnesson’s essay on Bio-morality Bioethics, Defining the Moral Subject and Spinoza. I very much wanted to write a piece on the kind of distortion Hoffmeyer was performing when reducing the individual into an almost entirely digital (DNA) state, a capacity he felt that was only something that living things could achieve. I had a strong intuition of what I wanted to say about what was problematical in this, but time and circumstance dragged me away.

My objection to Hoffmeyer stemmed from my Spinozist position of the parallel postulate that the order of things and of ideas is the same, and that, at least from a Spinozist position, it was nonsensical to say that an individual existed in primarily a digital state. If Spinoza is correct, one can never have a primarily digital state of an individual, as the material, bodily dimension follows it explicitly. At the time of my original intuition I simply roughly equated Spinoza’s “idea” with digitality. But in the long loop I’ve run into discussions with Eric Schliesser who is organizing a paper to be presented on Spinoza’s skepticism towards mathematical capacities to describe Nature (at first a counter-intuitional position given the mathematic-like forms of Spinoza’s reasoning, and his dependent use on mathematical examples). Our talks gave me to look closer at Spinoza’s letter 12 to Meyer (which Corry Shores does an incredible job of summarizing in cross-reference fashion, treatment I would like to return to). There, famously, Spinoza puts numbers and mathematics to be the products of the Imagination, the lowest forms of knowledge in his coming trinity of knowledges, found in the Ethics). There is no space/time here to go into these investigations, though it is good to mention that they touch on Badiou’s deep misreading of Spinoza and Badiou’s Ontology of Mathematics. It is enough to say that Spinoza denies the Substance itself cannot be discretely divided, and that even the discrete operations of which mathematics specialize fail at capturing the infinity of the taken-to-be finite modes. The order and connection between ideas (and things) is not a numerically ordinal connection. Mathematical discretions are imaginary constructs by Spinoza’s reasoning, as must be the digital reductions/abstractions that much of conceptual philosophy concerns itself with.

In this sense any digital abstraction of analog expressions/relations itself must be materialized. This makes Hoffmeyer’s digital/analog oscillations that are supposed to define life in further jeopardy, at least from a Spinozist perspective, for digital discretion does not even correspond to the notion of “idea” ordering. Rather, Spinoza’s take on infinities under which a maximum and minimum are known, turns digital processes into extreme analogical ones.

This leads me to minimize the entire latter portion of Corry Shores appreciation of Deleuze’s digital/analog analysis of modern painting, on Spinozist grounds. Even the most binary reductions are not “safe distance” processes, but rather are products of the imaginary under specific thresholds. They are felt in topographies, as any viewer can attest. The digital is always felt. The calculation is ever an impression on the material of the body seen through the discretion of its organized thresholds. One can see that there is a certain “faculative disorder” in the (digital) peak tracing of diagrammic representations, but, following Spinoza, these can only be analogical, which is to say continual, conjoinings. If Spinoza’s treatment of the infinite which disjoins the imaginarily discrete (mathematical) infinity from the real, expressive causal infinity, tells us anything, it is that diagrammic dis-organization and re-organization are imaginary processes which ever seek a continuity in the body itself, the body an infinite expression of magnitudes which press nestled upon each other. But unlike Deleuze’s pursuit of the chaotic elements (and this may only be an aesthetic difference), looking with the Intellect, as Spinoza would, is seeing-through these connections, not as bound, but as continually out-flowing and unitary. In this sense the ordering of numbers is a pale, imaginary imitation of the density of continuity in all things, a mechanism for our continual re-orientation.

Spinoza, On The Immortality of the Soul

Controversially, the question of the immortality of the soul/mind arises in Spinoza’s writings, and with it the definition of personal identity. At one point he takes up thoughts about a poet who has, in an Altzheimer’s way, has lost contact with his person. In what sense is the poet still himself? To answer this, Spinoza argues for the existent essence of non-existent modes, a position which Deleuze sums as such:

“A mode’s essence is not a logical possibility, nor a mathematical structure, nor a metaphysical entity, but a physical reality, a res physica. Spinoza means that the essence, qua essence, as an existence. A modal essence has an existence distinct from that of the corresponding mode.” Expression in Philosophy (192)

Despite Deleuze’s assurance that this reality is not mathematical, Spinoza does take recourse to mathematical analogy to make clear his meaning, for instance (cited below), the existence of essence of an infinity of equal rectangles within the essence of a circle (Theorem 35, Euclid) which exist even if only one or even none exist modally.

 

So the essence of a mind is said to exist within the mind of God, eternally, despite its own limited duration. What this does is give the human mind a kind of eternity, an existence outside of the brief flicker of expression, but what this also does is place that eternal existence in relation to all other essences, of all other things, animate and inanimate, which are also produced by God/Nature. The human mind is eternal in essence as all other things are eternal in essence. But further, (as is shown in the note to EIV39 below), identity itself, our preservation of ourselves as ourselves in duration, is also not guaranteed, and is in fact likely an illusion of perspective. Just as his Spanish poet has died to himself, despite the continuity of his body, unable to recognize even his own writings, we too would only be an infinite series of eternal essences – slight modifications of a rectangle within its circle – defined only by our momentary consonance of parts – both ideational and extended. It is not so much that Spinoza has awarded undue eternity to the human mind, but rather has radically (categorically) undermined the basis upon which the human mind privileges itself to be unique among things in this world, given eternal life, but a life fused with all other things, capable as alien to its own “past” as akin to another thing. I list below relevant passages and definitions to this thinking:

EV29- The human mind cannot be absolutely destroyed with the body, but there remains of it something which is eternal.

(Proof) There is necessarily in God a concept or idea which expresses the essence of the human body, which, therefore is necessarily something appertaining to the essence of the human mind. But we have not assigned to the human mind any duration, definable by time, except insofar as it expresses the actual existence of the body, which is explained through duration, and may be defined by time – that is we do not assign to it duration, except while the body endures. Yet there is something, notwithstanding, which is conceived by a certain eternal necessity through the very essence of God; this something, which appertains to the essence of the mind, will necessarily be eternal.

EIV39note – …But here it should be noted that I understand the Body to die when its parts are so disposed that they acquire a different ratio of motion and rest to one another. For I dare not deny that – even though the circulation of the blood is maintained, as well as the other [signs] on account of which the Body is thought to be alive – the human Body can nevertheless be changed into another nature completely different from its own. For no reason forces me to think that the Body does not die unless it is changed into a corpse. And, indeed, experience seems to urge the opposite conclusion. Sometimes a man undergoes such changes that I should hardly believe that he was the same man. For example, I have heard tell of a Spanish poet who was struck by an illness; though he recovered, he remained so oblivious to his past life that he did not believe the tales and tragedies he had written were his own. He might have been taken for a grown-up infant had he also forgotten his native tongue.

EIp8 – By eternity, I mean existence itself, insofar as it is conceived necessarily to follow solely from the definition of that which is eternal. (Explanation) – Existence of this kind is conceived as an eternal truth, like the essence of a thing, and, therefore, cannot be explained by means of continuance or time, though continuance may be conceived without a beginning or end.

EIp24- The essence of things produced by God does not involve existence. (Corollary)… God must be the sole cause, inasmuch as to him alone existence appertain.

EIp25 – God is the efficient cause not only of the existence of things, but also of their essence.

EIIp8 – The ideas of particular things, or of modes, that do not exist, must be comprehended in the infinite idea of God, in the same way as the formal essences of particular things or modes are contained in the attributes of God. Note – If anyone desires an example to throw more light on this question, I shall, I fear, not be able to give him any, which adequately explains the thing of which I here speak, inasmuch as it is unique; however, I will endeavour to illustrate it as far as possible. The nature of a circle is such that if any number of straight lines intersect within it, the rectangles formed by their segments will be equal to one another; thus, infinite equal rectangles are contained in a circle. Yet none of these rectangles can be said to exist, except in so far as the circle exists; nor can the idea of any of these rectangles be said to exist, except in so far as they are comprehended in the idea of the circle. Let us grant that, from this infinite number of rectangles, two only exist. The ideas of these two not only exist, in so far as they are contained in the idea of the circle, but also as they involve the existence of those rectangles; wherefore they are distinguished from the remaining ideas of the remaining rectangles.