Mandelbrot Antennae
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I’ve heard it called “the most complex” mathematical object, but that’s a hard title to earn, let alone hold. It’s complexity does have attractive and fascinating aspects, though. For most, its visceral visual beauty puts it miles ahead of the cool intellectual poetry of Euler’s Identity (both beauties live on the same block, though).
For me, the cool thing about the Mandelbrot is that it’s a computation that can never be fully computed.
Last Friday I ended the week with some ruminations about what (higher) consciousness looks like from the outside. I end this week — and this posting mini-marathon — with some rambling ruminations about how I think consciousness seems to work on the inside.
When I say “seems to work” I don’t have any functional explanation to offer. I mean that in a far more general sense (and, of course, it’s a complete wild-ass guess on my part). Mostly I want to expand on why a precise simulation of a physical system may not produce everything the physical system does.
For me, the obvious example is laser light.
I’ve been on a post-a-day marathon for two weeks now, and I’m seeing this as the penultimate post (for now). Over the course of these, I’ve written a lot about various low-level aspects of computing, truth tables and system state, for instance. And I’ve weighed in on what I think consciousness amounts to.
How we view, interpret, or define, consciousness aside, a major point of debate involves whether machines can have the same “consciousness” properties we do. In particular, what is the role of subjective experience when it comes to us and to machines?
For me it boils down to a couple of key points.
Philosophical Zombies (of several kinds) are a favorite of consciousness philosophers. (Because who doesn’t like zombies. (Well, I don’t, but that’s another story.)) The basic idea involves beings who, by definition, [A] have higher consciousness (whatever that is) and [B] have no subjective experience.
They lie squarely at the heart of the “acts like a duck, is a duck” question about conscious behavior. And zombies of various types also pose questions about the role subjective experience plays in consciousness and why it should exist at all (the infamous “hard problem”).
So the Zombie Issue does seem central to ideas about consciousness.
In one of the more horrific examples of virtual personal enslavement in the service of philosophy, another classic conundrum of consciousness involves a woman confined for her entire life to a deep dungeon with no color and no windows to the outside. Everything is black, or white, or a shade of gray.
The enslaved misfortunate Mary has a single ray of monochromatic (artificial) light in her dreary existence: She has an electronic reader — with a black and white screen — that gives her access to all the world’s knowledge. In particular, she has studied and understands everything there is to know about color and how humans perceive it.
Then one day someone sends Mary a red rose.
After a weekend of transistorized baseball, it’s time to get back to wandering through pondering consciousness. I laid down a few cobblestones last week; time to add a few more to the road. Eventually I’ll have something on which I can drive an argument.
There are a number of classic, or at least well-known, arguments for and against computationalism. They variously involve Pixies, different kinds of Zombies, people trapped in different kinds of rooms, and rock walls that compute. (In fact, they compute rooms that trap Pixies. And everything else.)
Today I’m going to ruminate on the world’s most unfortunate file clerk.
Moving on from system states (and states of the system), today I’d like to fly over the landscape of different systems. In particular, systems that are — or are not — viewed as conscious.
Two views make this especially interesting. The first holds that everything is computing everything and — under computationalism — this includes conscious computations. The second (if I understand it) holds that anything that processes input data into some kind of output is conscious. (I’m not clear if the view also sees an input-output system as a computer.)
So I want to explore what I see as major landmarks in the landscape of systems that… well, about the only thing we can probably all agree on is that they do something.
Over the last three posts I’ve been exploring the idea of system states and how they might connect with computational theories of mind. I’ve used a full-adder logic circuit as a simple stand-in for the brain — the analog flow and logical gating characteristics of the two are very similar.
In particular I’ve explored the idea that the output state of the system doesn’t reflect its inner working, especially with regard to intermediate states of the system as it generates the desired output (and that output can fluctuate until it “settles” to a valid correct value).
Here I plan to wrap up and summarize the system states exploration.
I left off last time talking about intermediate, or transitory, states of a system. The question is, if we only look at the system at certain key points that we think matter, do any intermediate states make a difference?
In a standard digital computer, the answer is a definite no. Even in many kinds of analog computers, transitory states exist for the same reason they do in digital computers (signals flowing through different paths and arriving at the key points at different times). In both cases they are ignored. Only the stable final state matters.
So in the brain, what are the key points? What states matter?
In the last post I talked about software models for a full-adder logic circuit. I broke them into two broad categories: models of an abstraction, and models of a physical instance. Because the post was long, I was able to mention the code implementations only in passing (but there are links).
I want to talk a little more about those two categories, especially the latter, and in particular an implementation that bridges between the categories. It’s here that ideas about simulating the brain or mind become important. Most approaches involve some kind of simulation.
One type of simulation involves the states of a system.
