Tag Archives: computer model

John Conway’s Life

Recently I mentioned that mathematician John Conway died last April. To his eternal disgruntlement, he is most famous for his “game” of Life — something he considered trivial and inferior to his real mathematical work. That fame is largely due to a Martin Gardener column in Scientific American — the most popular column the magazine had published up to then.

I said I wasn’t going to write about Life because it’s such a well-covered topic, but I thought I might whip up an implementation in Conway’s honor. (Went there; did that; videos below.) Getting into it made me realize Life connects back to my virtual reality posts.

So it turns out I am going to write about it (a little).

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Virtual Physics

Last time I left off with a virtual ball moving towards a virtual wall after touching on the basics of how we determine if and when the mathematical ball virtually hits the mathematical wall. It amounts to detecting when one geometric shape overlaps another geometric shape.

In the physical world, objects simply can’t overlap due to physics — electromagnetic forces prevent it. An object’s solidity is “baked in” to its basic nature. In contrast, in the virtual world, the very idea of overlap has no meaning… unless we define one.

This time I want to drill down on exactly how we do that.

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Virtual Walls

Last time we saw that, while we can describe a maze abstractly in terms of its network of paths, we can implement a more causal (that is: physical) approach by simulating its walls. In particular, this allows us to preserve its basic physical shape, which can be of value in game or art contexts.

This time I want to talk more about virtual walls as causal objects in a maze (or any) simulation. Walls are a basic physical object (as well as a basic metaphysical concept), so naturally they are equally foundational in the abstract and virtual worlds.

And ironically, “Something there is that doesn’t love a wall.”

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Virtual Mazes

First I discussed five physical causal systems. Next I considered numeric representations of those systems. Then I began to explore the idea of virtual causality, and now I’ll continue that in the context of virtual mazes (such as we might find in a computer game).

I think mazes make a simple enough example that I should be able to get very specific about how a virtual system implements causality.

With mazes, it’s about walls and paths, but mostly about paths.

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Virtual Causality

This is the third of a series of posts about causal systems. In the first post I introduced five physical systems (personal communication, sound recording, light circuit, car engine, digital computer). In the second post I considered numerical representations of those systems — that is, implementing them as computer programs.

Now I’d like to explore further how we represent causality in numeric systems. I’ll return to the five numeric systems and end with a much simpler system I’ll examine in detail next time.

Simply put: How is physical causality implemented in virtual systems?

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Physical vs Abstract

Maybe it’s a life-long diet of science fiction, but I seem to have written some trilogy posts lately. This post completes yet another, being the third of a triplet exploring the differences between physical objects and numeric models of those objects. [See Magnitudes vs Numbers and Real vs Simulated for the first two in the series.]

The motivation for the series is to argue against a common assertion of computationalism that numeric models are quintessentially the same as what they model. Note that these posts do not argue against computationalism, but against the argument conflating physical and numeric systems.

In fact, this distinction doesn’t argue against computationalism at all!

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Real vs Simulated

Indulging in another round of the old computationalism debate reminded me of a post I’ve been meaning to write since my Blog Anniversary this past July. The debate involves a central question: Can the human mind be numerically simulated? (A more subtle question asks: Is the human mind algorithmic?)

An argument against is the assertion, “Simulated water isn’t wet,” which makes the point that numeric simulations are abstractions with no physical effects. A common counter is that simulations run on physical systems, so the argument is invalid.

Which makes no sense to me; here’s why…

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Failed States (part 3)

This ends an arc of exploration of a Combinatorial-State Automata (CSA), an idea by philosopher and cognitive scientist David Chalmers — who despite all these posts is someone whose thinking I regard very highly on multiple counts. (The only place my view diverges much from his is on computationalism, and even there I see some compatibility.)

In the first post I looked closely at the CSA state vector. In the second post I looked closely at the function that generates new states in that vector. Now I’ll consider the system as a whole, for it’s only at this level that we actually seek the causal topology Chalmers requires.

It all turns on how much matching abstractions means matching systems.

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Failed States (part 2)

This is a continuation of an exploration of an idea by philosopher and cognitive scientist David Chalmers — the idea of a Combinatorial-State Automata (CSA). I’m trying to better express ideas I first wrote about in these three posts.

The previous post explored the state vector part of a CSA intended to emulate human cognition. There I described how illegal transitory states seem to violate any isomorphism between mental states in the brain and the binary numbers in RAM locations that represent them. I’ll return to that in the next post.

In this post I want to explore the function that generates the states.

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Failed States (part 1)

Last month I wrote three posts about a proposition by philosopher and cognitive scientist David Chalmers — the idea of a Combinatorial-State Automata (CSA). I had a long debate with a reader about it, and I’ve pondering it ever since. I’m not going to return to the Chalmers paper so much as focus on the CSA idea itself.

I think I’ve found a way to express why I see a problem with the idea. I’m going to have another go at explaining it. The short version turns on how mental states transition from state to state versus how a computational system must handle it (even in the idealized Turing Machine sense — this is not about what is practical but about what is possible).

“Once more unto the breach, dear friends, once more…”

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