Zan Huang

5.6 The limits of my language mean the limits of my world.

5.61 Logic fills the world: the limits of the world are also its limits. We cannot therefore say in logic: This and this there is in the world, that there is not. For that would apparently presuppose that we exclude certain possibilities, and this cannot be the case since otherwise logic must get outside the limits of the world: that is, if it could consider these limits from the other side also.

What we cannot think, that we cannot think: we cannot therefore say what we cannot think.

I. Lévi-Strauss and Calvino

There seem to be two modes of idea discovery. One, the idea arises out-of-distribution with respect to recorded knowledge about the world. Often representing a Copernican turn in understanding a subject, this mode requires a radical reencounter with existing paradigms through tacit knowledge found outside language itself1 and often creates new modes of thinking. Two, an idea simply arises from permutation of existing knowledge. These discoveries are the more common ones, and these specific ideas, though they may seem novel, are derivative and lie latent in the existing compendium. Often these two modes may occur concurrently.

It is important to ask why fundamental theoretical scientific or mathematical work that extends beyond a permutation exists, especially when our contemporary crisis is The Question Concerning Technology: questions such as the role of research when there are “automated researchers”2, and art when there is “the question of art generation”.

Many people are motivated to work on a sort of Ur-Solution through the means of practical engineering. We are seeing claims in the form of “if you scale and stabilize these techniques, scale the data involved and cover these technical potholes, then we will be able to solve this entire category of problem altogether”. This naturally leads to the question of “why do we care about theory or natural philosophy, when its theoretical problems can be treated as an engineering or industrial task?” There is also the group of people who do not believe that there was ever a theoretical task—that the Ur-Solution was an engineering trick waiting to be discovered all along. I will not answer this claim extensively here, but a clear difference between the two can be found in Lévi-Strauss’s distinction between the Bricoleur and the Engineer. A Bricoleur works in the set of existing concepts, rearranging them for new purposes or to new interpretations. An Engineer goes beyond this and works on a more fundamental level, often developing a new system of understanding upon raw materials3 to achieve a particular task or a new discovery. The distinction is not perfect.4 Obviously, we are all ensnared by existing language and existing systems of signs to the extent that we need to communicate and efficiently outsource certain mental processes. Bricolage is by and large more efficient.

This is also not to say that there isn’t any merit in Bricolage. Calvino’s idea in Cybernetics and Ghosts that our stories are but permutations is not completely wrong. In fact, they may even be automated, if we consider the role of the human to be one of interpretation and compilation. His take is strangely prescient. However, this cannot definitionally include what we brought up earlier as “outside language”.5 The limits of Bricolage are the limits of statistical distributions taken up by our language. Probably, this is one of the many fundamental divides between machine and human writing, though human writing itself is usually a combination of autoregression and the outside-language.6

II. Logarithms

What drives people to produce novel theoretical work? There are two primary and sometimes overlapping motivations for theoretical work. Either such theorizing is socio-economically relevant in a meaningful sense to the individual, or the individual producing theory is so teleologically driven by the work that it becomes ontologically relevant to the pursuant. We usually consider, in our culture, this second type to be an autistic obsession. We often find tropes for these sorts of people: think Isaac Newton, Grothendieck, or Gödel, and their many obsessions. I will not spend time discussing this second type of thinker, because they more or less naturally occur in the beautiful variance we find across human beings. I will spare the violence of explaining away things that simply are what they are. Again, we all have varying degrees of obsessions, some without any at all.

John Napier is a good example of the first type of theorist, whose invention of logarithms greatly extended the breadth of mathematical thinking.7 There really wasn’t anything like logarithms in the European world before Napier. Navigation charts relied upon astronomy, which required the ability to compute large products, divisions, and ratios. Logarithmic charts were a natural means to an end for these tasks. The word logarithm itself is a compound of logos and arithmos, ratio and number. Our modern conception of logarithms, if anything, loses this original motivational heritage. We usually meet them as inverses of one another:

These relations need not be circular. One can independently define \(\ln x\) by an integral, or \(e^{x}\) by a series, a differential equation, or a limit; the other then follows as its inverse. Either construction is already sufficient for us to carry modern mathematics, physics, and engineering. It is useful and has a rigorous definition. Napier didn’t have this apparatus, and I am willing to bet that most people who learned logarithms at some point in their lives do not sufficiently care or need to care about the origin of logarithms. Today, we take this inverse relation almost for granted, using the semiotic symbolic landscape of modern mathematical concepts. In fact, it’s a lot easier to think about the contemporary definitions than how Napier was conceptualizing this. We think of logarithms with integer bases as representing multiplicative ratios in the context of their reversal of exponentiation. And this gives us a conception of what it means for planets to orbit the sun, for money to scale, for populations to grow, and so on. In the context of a natural logarithm, it is just an inverse function for natural growth. Here is Napier’s definition from Mirifici Logarithmorum Canonis Descriptio:

The Logarithme therefore of any sine is a number very neerely expressing the line, which increased equally in the meane time, whiles the line of the whole sine decreased proportionally into that sine, both motions being equal-timed, and the beginning equally swift.

We find a similar parallel in Shannon’s information theory. The original paper is a mathematical study of channel coding and loss in communication. Although many of the terms in information theory can now be defined independently of the communication problem, there was an economic motivation there directly linked to the environment: in this case, the telecommunications research activity of Bell Labs that Shannon found himself in. The numerous extensions, reformulations, and reconceptualizations of information theory cannot hide its original purpose.

The examples are numberless. Carnot, the father of thermodynamics, was a military engineer focused on maximum capacity in efficiency of heat engines. Despite his theoretical abilities on abstract problems on top of his experimental prowess, Fermi still personally justified scientific advancement primarily through its ability to deliver technical and practical improvements.

The economic motivation that makes one produce new theory instead of Bricolage rests in whether the assemblage and permutation of existing components can adequately address a socio-economic need. This underlying cause for the occurrences of Engineers as opposed to Bricoleurs is the same, unless we are discussing people who like to formulate for the love of the game. In both cases, Engineers or Novel-Theorists think outside the symbolic order, outside common language. The difference between whether Engineers or Bricoleurs occur also rests upon whether there exist sufficiently pressing socio-economic problems to be solved that cannot be satisfactorily pieced together by existing cultural components, and whether that subject recognizes these problems and gaps (which implies some recognition of the socio-economic condition itself)—or in other words, recognizing the limits of one’s language and that which we cannot think of yet.

III. Exegesis

The motivational chain which drives fundamental discovery comes under threat when the economic superstructure parasitizes the base economy and when the tools which exist to obscure the real gaps created by the superstructure create a culture of automation. Automation cannot exist without the automatable structure. Automatable structure is congruent with an affixed language, or one that easily operates within the increasingly parasitized economy and omits the base realities upholding any socio-economic system. By effectively removing salience on real problems, only the ones that fit into the parasitic superstructure remain in the economy.

Superstructure is responsible for resource allocation and planning that may require secondary and tertiary operations. However, in this process, the financialized economy emerges through extraction in the process of allocation. Extraction implies a distillation process, by which extracted resources cannot remain in their original living form but must exist as a fungible and liquidatable asset (standing-reserve). Our natural philosophy and technological development are not immune to this process: consider here the rapid commercialization of the university.

Bataille’s excess normally creates economies of surplus, in which the excess of libidinal socio-economic capital flows into other great developments and mass rituals. A parasitized economy in which the affixed language overtakes all other forms cannot healthily channel this energy except into its own abstracted form. Recently, we see the emergence of religious techno-capital, a phenomenon which threatens its very base substrate. The hollow utopian aesthetics of modern techno-capital cannot reconcile with its own aftermath: the consequential cognitive-perceptual emptiness which fails to sustain any meaningful technological-scientific development on the base economy.