Comments on: Continuous computing https://www.monomorphic.org/wordpress/continuous-computing/ Conceptual meandering Wed, 15 May 2013 10:43:07 +0000 hourly 1 https://wordpress.org/?v=6.4.3 By: Ingemar https://www.monomorphic.org/wordpress/continuous-computing/comment-page-1/#comment-36750 Wed, 15 May 2013 10:43:07 +0000 http://www.monomorphic.org/wordpress/?p=643#comment-36750 Are you saying that an continuous computer would be “closer” to the continuous nature in itself but that our digital computers are closer to our platonic idea of knowledge?

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By: johan https://www.monomorphic.org/wordpress/continuous-computing/comment-page-1/#comment-1180 Fri, 23 Jul 2010 09:03:03 +0000 http://www.monomorphic.org/wordpress/?p=643#comment-1180 Hi Soliptic,
(I moved your comment to this post since I assumed it was intended to be here. Somehow it ended up on the “Deletion” post instead.)
Thanks for your comment, and for the book tip.
The problem with your approach to equality would be identifying a particular continuous value. Maybe I misunderstand your suggestion, but I’ll just give my comments on what I think it is. My understanding is that we basically cannot measure or observe physical systems without affecting them – a device like a voltmeter changes the resistance in a circuit ever so slightly, measuring the speed of wind slows it down, and so on. This effect is sometimes very small, but the digital approach to circuits is basically a way of getting around it and getting reliable computation.
So if you decide to define equality as “pi is this particular continuous value here”, you would run into the problem of knowing when you are observing that value and when you’re not. And attempting to identify it using, say, a voltmeter, would change it slightly, unless you rounded off enough precision to compensate for those effects. But if you do, you will have some kind of digital system again, so the whole point is lost, I would think.
Of course we could accept that equality is inherently a “digital” operation. Two things in the real world are never said to be equal unless there is some degree of abstraction, some loss of precision.
Another approach might be to have the computer do symbolic algebra instead of working with numbers, so that it could reason about the calculations and say “these calculations have to have resulted in the same value”. This approach, again, seems to be inherently discrete.

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By: soliptic https://www.monomorphic.org/wordpress/continuous-computing/comment-page-1/#comment-1174 Tue, 20 Jul 2010 22:22:43 +0000 http://www.monomorphic.org/wordpress/?p=643#comment-1174 Firstly, I must say that I really enjoy reading your blog. I found it with a Google search for something I can’t presently remember, but I have been checking for new entries now and again for a couple of months. I even commented on on your blog exploring computer interfaces and their future.

This entry is particularly interesting to me, since I’ve often thought about the idea of a continuous computer. I don’t have the knowledge of formal computational theory as you do, however, so it was much more interesting reading your musings than regarding my own. As such, there are a couple of issues I’d like to get your input on.

Whenever I envision an analogue machine (the existence of which I was also unaware until you pointed it out) I imagine it’s implementation could be possible by — like digital machines — directly mapping voltages to mathematical values. For instance, an electronic component could hold a particular voltage between m and n, and m could be mapped to 1 and n mapped to 0, and every value in between could be subsequently interpreted appropriately as values between 1 and 0. Of course, I’m assuming voltage values could be accumulated continuously, as they are assumed to be in elementary circuit calculations.

I’ve also wondered whether the universe is continuous (as have many scientists and philosophers throughout the course of human thought). Can time and space be subdivided into an infinite number of fragments? I’m sure theorists have modern mathematical models that elucidate the answer far more clearly than I could comprehend. There’s a popular science book I read recently called “Programming the Universe” by Seth Lloyd, and he proposes an idea derived from information theory that says that the Universe is essentially a computer in itself, and from it’s humble origins as a singularity — or single binary value — the universe has been undergoing a process of “computational explosion,” requiring more and more precision to represent itself.

Finally, you show that a continuous machine creates a problem for equality comparison. But is this necessarily so? It’s true that the way equality is determined in our current computers is to exhaustively compare each value discretely value by value, but isn’t it possible that there’s another way to state equality? For instance, we could define pi as a particular continuous value in our continuous machine. We, as humans, certainly don’t need to compare f(x) operator g(x) to each digit in pi forever to understand that such an equality exists — we simply define it as such and derive the equality by deducing it.

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