A semi-mathematical theory of human to human communication

Part of a series of articles I’ll be posting over the next few days & weeks regarding thoughts from the past few years I’m only just getting round to writing about.

I believe many of the situations we face are generally of vastly complex nature and high dimensions, such that it is impossible for us to be able to see any situation in its entirety. All that we are able to perceive at any given time, is perhaps a tiny slice from a very specific perspective. And the best we can hope for, is to attempt to widen that slice by a tiny amount, and maybe even occasionally slightly shift our perspective. Unfortunately, contrary to popular belief, it’s not always being exposed to new ‘facts’ that helps us shift perspective — or at least, it’s definitely not enough. Instead we seem to need some kind of mental gymnastics to navigate to a new location inside our head, and gain these new view points. These mental gymnastics can often benefit from external nudging, and mental frameworks that act as structures around which we can build our thoughts. Traditionally this has been aided by natural language, evolved over thousands of years — but this isn’t always sufficient; and art for example is also critical to this end. I believe borrowing from other, more recent languages — such as computation — might also contribute to these mental frameworks.

In the spirit of the subject matter, doesn’t have to be read in any particular order:


Let’s assume for the sake of argument, that there is some kind of objective reality out there. This is of course, unreachable by us humans. The best we can hope to achieve, is to coat this objective reality in some kind of impenetrable shell of subjective human experience, and that is what we can try to perceive and learn about.

And then when it comes to communicating with each other about our experiences or ‘objective observations’, our default go to technology is natural language. Right now I’m using English, at times I’ll also often use Turkish. And already, just from two natural languages, I can see the differences in the way words have been assigned to the continuous landscape of human experience. Because language is discrete, it’s categorical. We take this immensely rich, high dimensional landscape of subjective reality, of meaning; and we literally butcher it. We carve it up into sections that we label with these inventions, technological artifacts that we call ‘words’. Surprisingly, this seems to work relatively well. Somehow we are able to communicate, exchange ideas, build culture and amass history. But I’m convinced it doesn’t work as well as we’d like to think. Perhaps related is the fact that a lot of this history that we’ve amassed consists of how we’ve destroyed other cultures, and why we thought it was appropriate to do so. And I’m even convinced that a lot of the social and political polarization which is on the rise today, is fueled by a failure in communication, perhaps more often than we might realize.


A mathematical theory of communication.

Some of you might be familiar with the above diagram. It is of course taken from the seminal 1948 paper in which Claude Shannon proposes what we now call ‘Information Theory’, one of the pillars upon which computer science — and in fact our entire digital civilization — is built upon. (The irony of talking about human-to-human communication, using a language invented for the human understanding of machine-to-machine communication, is not lost on me).

I don’t know about you, but I don’t think that I think in words. In my head, all of my thoughts feel to be more like amorphous clouds of ideas and concepts and connections and emotions and pictures and sounds and feelings and other things which I can’t really articulate. And they’re definitely not linear, but floating in a high dimensional space. And then, I squish those thoughts through what seems to me to be a kind of meat grinder; and out of the transmitter — i.e. my mouth — comes these words, linear, like a string of sausages. I find it really quite shocking how these words, just these flimsy little vibrations in the air, are somehow able to capture at least some of what I’m thinking. And once these words are out of my head and in the world, they are subjected to all kinds of noise and manipulation. I think we live in a time where we are unfortunately quite aware of the potential dangers that lurk in distorting words, whether it’s #fakenews or #alternativefacts etc. But I’m actually not going to dwell on this component too much, because I’d like to focus on other potential points of failure. So I’m going to assume for now, the situation where the words leaving my brain (i.e. that I’m typing on this page), are guaranteed to be reaching you without any interference (i.e. nobody hacks this website or the traffic reaching your computer). Because then we can agree that these sausages — my words — without any disturbance, do indeed reach your ears, or your eyes, or fingers, depending on mode of transmission. And then your brain explodes these words inside your head. And gives them meaning again.

To the universe, these words are meaningless, just arbitrary vibrations in the air, noise with a particular distribution. But to you, they somehow mean something. Interestingly though, I don’t know what exactly they mean to you. Even though we speak a common language, i.e. English; even though we share a vocabulary, and we (think we) share a dictionary, I don’t know how you’re unpacking what I’m saying. Because you only have access to these sausages to try and infer what I’m really thinking, you don’t have access to the thoughts inside my head. And that’s really a massive gap to fill, so you’re bringing everything you’ve ever seen, or heard or read to this decoding process. And unless I’ve read everything you’ve ever read, heard everything you’ve ever heard, lived everything you’ve ever lived; I am incapable of imagining what you’re taking out of what I’m saying right now. This is the difficulty of evaluating the performance of the listener’s (receiver) decoder.

And this is assuming that I have done a perfect job of squishing my thoughts through that meat grinder, to create a perfect string of sausages that truly represent what I’m really thinking inside my head. And that is highly unlikely. It’s a lot more likely, that these sausages are actually a very basic, crude, lossy representation of what I’m really thinking. And what really sucks is, while you only have these sausages to try and infer what I’m really thinking, when I look at those exact same sausages that came out of my mouth, I see the full picture! because I have access to the original thoughts that gave rise to them. So it can be quite difficult for me to see how you might ‘misunderstand’ me, to see how confusing my choice of words might be. This is the difficulty of evaluating the performance one’s own encoder.

So I think it’s good to assume the following, especially before resorting to quarreling:

  1. When you say something, it is quite probable that the words you chose might not actually be conveying exactly what you intended to convey — either not conveying what you wanted to convey, and/or conveying something that you did not want to convey (poor encoding).
  2. When a listener hears you say something, it is quite probable that they will unpack what you said in a way that is different to what you intended (poor decoding).
  3. When somebody else says something, they might not be aware that it is quite probable that that the words they chose might not actually be conveying exactly what they intended to convey (poor encoding)
  4. When you hear somebody else say something, they might not be aware that it is quite probable that you might unpack what they said in a way that is different to what they intended (poor decoding).

I’m not suggesting it’s impossible to communicate precisely with this clunky technology that we call natural language. Arguably, a poet is somebody who has mastered the art of navigating the rich, continuous, high dimensional space of subjective reality; armed only with these crude, low resolution, labels. A poet might not naively pick the first words that appear closest to the points of meaning that they seek. Instead, they are able to find very specific configurations of words, such that when these particular words are used together in a very particular order, they are able to transport you to very precise locations in that rich landscape of meaning, which might be otherwise inaccessible through more simplistic use of the same language*.

And this is one of the things that art tries to do too — through non verbal, alternative modes of communication — to take you to peculiar, difficult to reach locations in that rich, high dimensional space of meaning and subjective experience, often found only in the cracks between words.


*NB. This reminds me of when I first saw the classic PC DOS demo ATOM.exe (back in the age of dinosaurs), playing ‘analog’ audio through the 1-bit PC Speaker. It blew my mind, how could it be possible to get such sounds out of a speaker capable only of ‘on’ or ‘off’. And that’s how I found out about the clever hack known as pulse-width modulation, which gives you finer apparent control, resolution and precision than the system seems to be capable of by design.