guest post by David Spivak
The idea that’s haunted me, and motivated me, for the past seven years or so came to me while reading a book called The Moment of Complexity: our Emerging Network Culture, by Mark C. Taylor. It was a fascinating book about how our world is becoming increasingly networked—wired up and connected—and that this is leading to a dramatic increase in complexity. I’m not sure if it was stated explicitly there, but I got the idea that with the advent of the World Wide Web in 1991, a new neural network had been born. The lights had been turned on, and planet earth now had a brain.
I wondered how far this idea could be pushed. Is the world alive, is it a single living thing? If it is, in the sense I meant, then its primary job is to survive, and to survive it’ll have to make decisions. So there I was in my living room thinking, “oh my god, we’ve got to steer this thing!”
Taylor pointed out that as complexity increases, it’ll become harder to make sense of what’s going on in the world. That seemed to me like a big problem on the horizon, because in order to make good decisions, we need to have a good grasp on what’s occurring. I became obsessed with the idea of helping my species through this time of unprecedented complexity. I wanted to understand what was needed in order to help humanity make good decisions.
What seemed important as a first step is that we humans need to unify our understanding—to come to agreement—on matters of fact. For example, humanity still doesn’t know whether global warming is happening. Sure almost all credible scientists have agreed that it is happening, but does that steer money into programs that will slow it or mitigate its effects? This isn’t an issue of what course to take to solve a given problem; it’s about whether the problem even exists! It’s like when people were talking about Obama being a Muslim, born in Kenya, etc., and some people were denying it, saying he was born in Hawaii. If that’s true, why did he repeatedly refuse to show his birth certificate?
It is important, as a first step, to improve the extent to which we agree on the most obvious facts. This kind of “sanity check” is a necessary foundation for discussions about what course we should take. If we want to steer the ship, we have to make committed choices, like “we’re turning left now,” and we need to do so as a group. That is, there needs to be some amount of agreement about the way we should steer, so we’re not fighting ourselves.
Luckily there are a many cases of a group that needs to, and is able to, steer itself as a whole. For example as a human, my neural brain works with my cells to steer my body. Similarly, corporations steer themselves based on boards of directors, and based on flows of information, which run bureaucratically and/or informally between different parts of the company. Note that in neither case is there any suggestion that each part—cell, employee, or corporate entity—is “rational”; they’re all just doing their thing. What we do see in these cases is that the group members work together in a context where information and internal agreement is valued and often attained.
It seemed to me that intelligent, group-directed steering is possible. It does occur. But what’s the mechanism by which it happens, and how can we think about it? I figured that the way we steer, i.e., make decisions, is by using information.
I should be clear: whenever I say information, I never mean it “in the sense of Claude Shannon”. As beautiful as Shannon’s notion of information is, he’s not talking about the kind of information I mean. He explicitly said in his seminal paper that information in his sense is not concerned with meaning:
Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem. The significant aspect is that the actual message is one selected from a set of possible messages.
In contrast, I’m interested in the semantic stuff, which flows between humans, and which makes possible decisions about things like climate change. Shannon invented a very useful quantitative measure of meaningless probability distributions.
That’s not the kind of information I’m talking about. When I say “I want to know what information is”, I’m saying I want to formulate the notion of human-usable semantic meaning, in as mathematical a way as possible.
Back to my problem: we need to steer the ship, and to do so we need to use information properly. Unfortunately, I had no idea what information is, nor how it’s used to make decisions (let alone to make good ones), nor how it’s obtained from our interaction with the world. Moreover, I didn’t have a clue how the minute information-handling at the micro-level, e.g., done by cells inside a body or employees inside a corporation, would yield information-handling at the macro (body or corporate) level.
I set out to try to understand what information is and how it can be communicated. What kind of stuff is information? It seems to follow rules: facts can be put together to form new facts, but only in certain ways. I was once explaining this idea to Dan Kan, and he agreed saying, “Yes, information is inherently a combinatorial affair.” What is the combinatorics of information?
Communication is similarly difficult to understand, once you dig into it. For example, my brain somehow enables me to use information and so does yours. But our brains are wired up in personal and ad hoc ways, when you look closely, a bit like a fingerprint or retinal scan. I found it fascinating that two highly personalized semantic networks could interface well enough to effectively collaborate.
There are two issues that I wanted to understand, and by to understand I mean to make mathematical to my own satisfaction. The first is what information is, as structured stuff, and what communication is, as a transfer of structured stuff. The second is how communication at micro-levels can create, or be, understanding at macro-levels, i.e., how a group can steer as a singleton.
Looking back on this endeavor now, I remain concerned. Things are getting increasingly complex, in the sorts of ways predicted by Mark C. Taylor in his book, and we seem to be losing some control: of the NSA, of privacy, of people 3D printing guns or germs, of drones, of big financial institutions, etc.
Can we expect or hope that our species as a whole will make decisions that are healthy, like keeping the temperature down, given the information we have available? Are we in the driver’s seat, or is our ship currently in the process of spiraling out of our control?
Let’s assume that we don’t want to panic but that we do want to participate in helping the human community to make appropriate decisions. A possible first step could be to formalize the notion of “using information well”. If we could do this rigorously, it would go a long way toward helping humanity get onto a healthy course. Further, mathematics is one of humanity’s best inventions. Using this tool to improve our ability to use information properly is a non-partisan approach to addressing the issue. It’s not about fighting, it’s about figuring out what’s happening, and weighing all our options in an informed way.
So, I ask: What kind of mathematics might serve as a formal ground for the notion of meaningful information, including both its successful communication and its role in decision-making?