Incomplete information

It’s now autumn – on Saturday, even though the temperature was still felt August warm, the vernal high tides shouted the new season as they flushed out the late summer seaweed blooms. The boy and the dog and I walked down a few days ago to the boat landing, and the cresting tidal water was lapping happily above the edge of the marshland, eroding it as we watched, and the dog was both happy to easily get into the water and disappointed that there was no beach to roll on to dry off. 

Two days later, we walked along the beach, standing a few feet higher than we were used to, looking down at the tidal bore churning up the lower boundary of the estuary. The same tides which had washed away the red kelp had deposited a massive pile of new sand, forming a prominent ridge that dropped steeply back into the ocean on one side, down into a strange sandy valley in front of the dune bluff filled with tide pools, but that made the two of us feel like we were walking on a mountain ridge, the ocean off to the right and the dry ground above the dunes level to us off to the left on shore on the other side of the vale. The dog was rather excited to find the remains of dead bluefish to roll around in, which had come in with the new sand; this made for an unpleasant car ride home, at least for the boy and me. 

Both at the town landing and on the beach, the boy and I talked about how the water was rising each year – even in his short lifetime so far, he’s noticed it – but we also talked about how beautiful the whole thing was. The dog, had she had the power of speech, I’m sure would have said similarly sublime things about the fish. But it was easier to talk about sea levels rising on the Maine coast than it was to talk about its beauty, or beauties, in any form.

In fact, I think beauty can’t be spoken of; it is the signal quality of beauty, or more broadly, of what is the aesthetic in this world. When we experience something that extends beyond our ability to exchange that experience with someone else in immediate terms (beyond simple words like “beautiful” or “smelly” or “sublime”), it enters the realm of aesthetics, and when it is the result of human artifice, the realm of art. This might seem uninteresting, but we live in a world dominated by information theory, and the concept of something which can not be exchanged without loss of fundamental meaning (as opposed to that which is subject to potential loss of meaning) is an extremal case in information theory. It deserves some consideration.

“Information theory” is both a means of expressing the transmission of “information” from a source to a receptor, over a mechanism which inevitably risks some loss of quality, and a way of looking at the physical world. Both are children of Claude Shannon, a noteworthy polymath who evolved the transmission theory while thinking simultaneously of signal degradation across wire networks and thinking about cryptography. Others then subsequently realized that his concept of information transfer also held when considering the realization of information about quantum particles in motion upon measurement, measurement being directly analogous to the “receiver” function in information transmission. Implicit in both of his expressions of “information”, however, is the idea that there is completeness which is accessible: there is a “true” message being transmitted from Bob to Mary, and there is a fully coherent version of a transmission function that exists instantaneously prior to measurement.

But let’s look at the simple version of his theory: a message (“Hello world”) is being transmitted over a mechanical (or digital, or whatever) bridge, which today we’d call a network, from an originating source to a receptor. The source is by definition a human being (or a device constructed and programmed by a human being, which for these purposes is the same thing) and the receptor is also a human being. The problems Shannon recognized – and which he then quantified – involve signal and message decay. The decay could come from outside of the experiment: cosmic rays bombarding the wire over which the message is transferred. Or, because some nasty person taps into the wire to read the message, it could come from decay due to measurement and rebroadcast. 

Separately, Shannon quantified the concept of encryption in preserving the privacy of transmission, and faced the challenge of trying to transmit information about the message – its encryption key – in a way that the nasty person couldn’t first intercept and use to read the message before the intended receiver got it. Encryption depended, though, on an unambiguous transmission message, a point Shannon assumed to be the case – indeed, he is aware of the fact that reliability of the original message – the idea that it is complete prior to transmission – is a postulate of his approach to information theory as a construct.

When we think about how we actually communicate, however, the idea of an unambiguous transmission quickly becomes absurd. Even the simple message “Hello world” is fraught; now, fifty years or more after it was first used to give birth to a live instance of C as a programming language, the two words should inspire a wealth of computer scientist nostalgia, and the use of the phrase is, within computer science at least, used to signify a foundational or existential concept, something that should spark in the receptor the idea that “big things will follow”. The first time it was used, however, it was meant to imply a birth, something innocent and without guile. The programmers were excited to invent a new language, but they were also aware of the limitations and simplicity of the initial release of C into the world. They were hoping for the outcome which, ultimately, did occur – the C kernel is at the heart of nearly every computing device in existence today. But in 1973, it was just some grad students deking around.

But transmitting “Hello world” doesn’t say anything except the raw words, and the specific flavor of meaning that a transmitting entity means to evoke when she sends those words is impossible to fully quantify – and thus impossible to transmit. The concept that Shannon sets up, indeed, is much more data-free than we normally describe: it only transmits the letters of the words. It depends on the sender and receiver understanding the same language, in which “Hello” is a personal informal greeting and “world” is a word denoting the entirety of instant lived existence – which is a lot of loading in and of itself – but the meaning of “Hello world” at the transmitter cannot and will never be fully received by the receiver.

I’d like to propose the notion that aesthetics is simply that personalization which exists at the point of transmission of a concept, and its comparable but always unequal counterparty, the personalization applied by a receiver to any received message. This 
“information” is not equivalent to the encryption key used and exchanged between a sender and receiver to maintain privacy. Rather, this is the extraneous information which exists at each end of the transmission mechanism, in the office of the transmitter and the console of the receiver. 

Aesthetics, seen through the lens of Shannon’s theory of information, is merely the instantaneous interpretation of the quantified information exchanged during a transmission exercise, happening twice: when the sender collapses their fulsome into transmittable form by stripping out their inarticulate aesthetic interpretations, and then again but differently when the receiver enriches the transmission with their aesthetic interpretations. There is no way to extract the persons of the transmitter and the receiver from the scheme, in the simple way in which Shannon does in his original brief formulation of his theory: even as like-willed individuals may design a mechanism to allow for rich data transfer, those same individuals cannot fully load the data with the entirety of the realm in which the transmitter will create the message, and in which the receiver will read it. Each will apply an independent sense, which is not just an analogy of aesthetics (the aesthetic of the artist in the transmission agent, the aesthetic of the viewer in the receiving agent), but which is a functionally complete definition of aesthetics in the presence of a formalized means of describing transfer.

Recognizing this, it should be trivial to also recognize that “art” – in its myriad forms – is really nothing more than overt loading of messages by transmitting parties; aesthetics, as most philosophy realizes, doesn’t require conscious acts of formation (crafts, engineered mechanical objects, and “naive” art, for example, are recognized as having an aesthetic even if their creators would object to the idea of a conscious creation of a form). But perhaps underrecognized in the Shannon formulation in this sense is the same active role on the part of the receiver. They are never a passive receiver of the transmitter’s signal: they always are interpreting it given the background of information (and accumulated history of past interpretation) that they have. This background cannot be fully expressed quantitatively – pick your source of proof for that: Gödel, Heisenberg, or Shannon are all lining up for duty – and thus ensure that the meaning of any information transfer can never be reverse transmitted – and, indeed, that our nefarious friend who intercepts the message will also never get “the full message”.

Information theory thus becomes something far more fraught than what Shannon intended: what it really reveals is the practical impossibility of reliably transmitting the full meaning of any message, due to the fundamental difference of informational interpretation that any two individuals will always have – and transmission always requires at least two individuals, and more if we introduce the nefarious interceptor. No complete information transfer is ever possible because of the unavoidable interpretation differences of the endpoints of the transfer mechanism. What emerges, however, is a realm of aesthetics – untranslatable and untransmissible alterations due to idiosyncratic understandings – that makes the world actually interesting, something beyond a mere computer program. 

There are broader implications as well, though. For example, Nick Bostrom has introduced what is to many a compelling notion that the world should be (statistically speaking) a computer simulation performed by a much more advanced civilization that we cannot comprehend. If we did live in a Bostrom simulation, though, it would be possible for my son and I to have an identical experience of the beauty of the tidal bore at Ferry Beach in Scarborough, because I could transmit to him a complete statement of my experience of the tides at a given moment. That is, computationally, our experience would be expressible in a complete form of code within the simulation; the simulation may be programmed to prevent the exchange of that specific kind of code between two elements within the game, but nevertheless, the full expression would be susceptible to complete expression. But we if interpret the world through a communications lens, it becomes readily apparent that, even if a complete transmission of my experience of a state of the world were possible, it would not be able to anticipate the way in which my son experiences the world, even at the same moment. In other words, it is impossible for a simulation to be programmed in which I could construct a complete transmission of state to my son, for anything. Every exchange involves artifice, interpretation, and judgment: in other words, the aesthetic frame. 

Beauty, in this sense, is not in the eye (or ear) of the beholder: the aesthetic sense (be it beauty or ugliness, in vision or in music or in form or in movement) is merely the unavoidable background out of which we try to send messages to our fellow travelers – and the unavoidable background into which we accept those transmissions. It is not noise – we’re not talking about the leakage of data in the mechanical system because of cosmic rays or faulty switches or wiretapping; it is endemic to any system of communications between individuals have the ability to apply non-standardized approaches to creating messages for transmission and for reacting to messages received.

I think Shannon had an inkling of this in his original statement of his theory back in 1945, but what he wrote was a practical piece, focused on building better code systems and understanding the decay function of mechanical systems in which the complete meaning of a transmission could be limited, for point of analysis, to the letter-order form of a simple sentence. But our world has stretched Shannon’s theorem to its limits in creating the internet, its underlying backbone of cryptography which ensures “message packets” are purely transmitted, and indeed in using information technology for the simulacrum of artificial intelligence, and in trying to create “aesthetic objects” out of information technology itself.

Taking Shannon’s theorem and assuming you have two Unix boxes as the sender and receiver, and maybe a third Unix box in Shanghai trying to intercept, and you have a workable theorem. But that’s not the world we live in (not even, really, in a cryptographic sense), and applying Shannon naively to a world in which we have discernable and incompatible individuals at each node quickly reveals the problem: we have ignored the constant creation of artifice, and incorporation of that artifice into both creation and interpretation and retransmission, in the operation of the system. We need to incorporate art and aesthetics into our quantized understanding of information – the price being a far higher level of uncertainty in interpretation (much as quantum mechanics has forced a recognition of probability into our understanding of physics) but the value being systems which recognize the fallibility of the transmission function even in normal operations (not just in regimes which assume bad actors intercept and interfere with transmission).

My son will never see the beach through my eyes, and I’ll never understand what he sees when he looks out over the estuary. Understanding that – and accepting that reality – is essential to me being the best parent I can be, but also, it’s essential for the boy to become the adult he needs to be in a world of complexity. The dog, on the other hand, will continue to try to find patches of dead fish to roll in. We’ll never understand that, either – even if the humans in the equation agree it’s pretty gross.