Archive for the ‘nature of life’ Category

Additional thoughts on Zalamea’s book, and Pythagoreanism

August 18, 2013

Does Zalamea’s book offer us a new Pythagorean perspective? The mixture of his eidal, quiddital and archeal perspectives suggests to me a centrality of Mathematics that harks back to a Pythagorean viewpoint. Such a viewpoint is interesting to me, partly because it proffers a God with explicatory capabilities (the Universe is as it is because it conforms to Mathematics – or perhaps Mathematics is as it is because that’s how the Universe is): but, unless one can find a way to include ethics within Mathematics, it’s not at all clear that such a new Pythagorean perspective says anything about ethics. Indeed, perhaps it doesn’t say anything more than that the Universe is inextricably tied to Mathematics. And that is not really anything novel.

Yet the move away from a philosophy of Mathematics that makes Mathematics (in some sense) a tautology means that Mathematics and its philosophy is something more than just a human construction.

And perhaps there is still more: If I think of Zalamea’s quiddital Mathematics, I see the handiwork of God, whether in biology, or physics, or any other branch of science. But if I look at eidal or archeal Mathematics, I see possibilities that might or might not be in the actual Universe. I see connections between the possible workings of the Universe: perhaps we see into the mind of this Pythagorean God.

A Pythagorean God is not a deity that helps us directly to live our lives. It’s not a God in the usual sense in Abrahamic religions. A Pythagorean God is more in the background, more about the unity of the Universe, more about the underlying structure.

Zalamea and the Philosophy of Mathematics.

August 17, 2013

My holiday reading was F. Zalamea’s Synthetic philosophy of contemporary Mathematics, a recent (2012) translation of Zalamea’s 2009 “Filosofía sintética de las matemáticas contemporáneas”, translated by Zachary L. Fraser. I have to admire the translation first: my only other language is German, and I cannot imagine understanding the subtleties of this philosophical  book in anything except my native tongue. It’s readable, though it takes commitment, and some background in Mathematics (I have a degree in it, dating from 1973, but though I am an academic in Computing I really haven’t  studied Mathematics since then). I note that Tzuchien Tho describes the book as “dense bomb of a book” in his Almagestum Contemporarium.

I wish I had read this book earlier. Indeed, I wish it had been translated earlier. Why?

I’ve spent some time trying to understand Category Theory in the last few years, particularly as part of the INBIOSA project, which produced a book. The largest single element in that book  is the INBIOSA white paper, entitled  Stepping Beyond the Newtonian Paradigm in Biology: Towards an Integrable Model of Life: Accelerating Discovery in the Biological Foundations of Science. In this paper we (there’s 17 authors) discuss new ideas that attempt to move understanding of the foundations of biology towards something that might help to bring some mathematical  approach to the functioning of biological systems, towards something that might help explain living material in terms that aren’t just the biochemical equations, diffusion etc. As part of that we were looking for an approach that transcended the logical mathematics, used in what we were aware of the mathematical philosophy. One of our number, Ehresmann, was pointing us towards Category Theory, and certainly I , and presumably others too tried to understand what it was that Category Theory was really bringing to the area.

Now I’ve read Zalamea’s book I have a much better idea, not of the basics of category theory, but of why it was so important. It is a way of expressing how Mathematics works, of how Mathematics can be about Mathematics. Zalamea lights a way towards a new philosophy of Mathematics that brings together the constructive imagination of what he calls eidal Mathematics with the Physically based quiddital Mathematics, and the idea of Mathematics of mathematics in  archeal Mathematics (the italicised terms are Zaladea’s). He sees the recent mathematics of Grothendieck and (many) others as a revolution as important as Einstein’s in Physics, and sees this as requiring a related revolution in Mathematical Philosophy (or perhaps he sees this revolution as actually starting first, as he sees it based in the works of Lautmann who died in 1944, when Grothendieck was only 16).

Be that as it may, I think (and here I am but seeing through a glass darkly) that this different view of Mathematics can underlie a different view of biology. This richer philosophy seems to me to suggest that Mathematics can do more than describe the physical Universe: it can be the engine of that Universe, explaining how it operates. This is nothing new in Physics, but it is something new in biology. Can such a philosophy underlie a change in biology as critical as that of Einstein in Physics? Can it take the reductionist understanding supplied by systems biology, and show how this actually drives the biology? Can it go further, can we use the mathematics of Mathematics to understand how a Universe can become aware of itself? Can such a construction really help us to understand our construction of reality?

I’m back from holiday now. I’m writing this before all the other work that running a University’ Department (well, Division) takes over from trying to think about what really matters. In reality, I’d like to spend a month re-reading Zalamea, and following up more of the references. Then talking to the other authors of the the INBIOSA white paper, and trying to integrate these ideas into it (one month seems rather conservative here). But rather than simply writing it in my notebook, I’m putting it on my blog, so I can try to discuss it openly.

Artificial Intelligence: are we nearly there yet?

May 2, 2013

Last night I gave a public lecture, at my University, with the title above. It went well: there were about 50 people, between about 11 and 75 in age, with some academics, some teachers, and quite a few whom I simply didn’t know. I spoke to my slides for about 45 minutes, then opened the floor to questions: and there really were a lot. I’m happy with the talk, I had been worried about it, for it’s a very different thing to be talking to a audience that’s come out in the evening, from lecturing to students. But this went well. Pitching it was an issue: how can one present material about artificial intelligence which fits all these people. I tried, and I think I succeeded. I had a very interesting discussion with a 17 year old lad at the end: I’d been saying that the concept of the AI Singularity was predicated in the concept of abstract intelligence – which is something I really don’t believe in. But he pointed out that there was nothing in  my argument to stop an embodied intelligence from building a more intelligent embodied intelligence, and that this could still be at the root of a positive-feedback intelligence loop. I couldn’t fault his logic. So now I’m not sure whether to worry about the singularity or not! Actually, Jurgen Schmidhuber thinks I should stop worrying and look at what’s already been done!

It took me a little while to work out why I was so pleased to have given the talk: then I remembered going to some public lectures in Glasgow University in the mid-1960’s, as a teenager, and really enjoying them. It is good to give something back!

Note: I’ve now written a 1000 word extract on AI, possibly for a newspaper – though it doesn’t mention the singularity. And now the Deccan Herald has published it!

Time and perceptual time

July 21, 2012

I’ve spent a lot of time (!) thinking about time in the last few weeks. Not that I’m serving time At Her Majesty’s Pleasure, as they say or anything like that, but on the nature of time, or rather on the nature of the neural construction of perceptual time. I even went as far as submitting a paper to the Artificial General Intelligence forthcoming at the end of the year in Oxford UK, about it. It’s one aspect of perception, and one that’s largely ignored.

To put it simply, perceptual time is related to physical time, but is different from it. In a similar way, perceptual reality is related to physical reality, but again, is different from it. The nature of these differences leads one initially into perceptual Psychology, but eventually into the murky realms of 1st person science, otherwise the realm of philosophy or perhaps theology. And that’s where it becomes tricky. But it’s still important, particularly for any system that would like to call itself sentient, or even (artificially) intelligent – hence the submission to AGI2012.

Yet there’s a huge set of possibilities there. Why the particular nature of human time perception? Earlier work suggests at least two levels of human perpetual time, one at about 40 to 50 ms, which might be thought of as an instant, and one at about 3 seconds, which one might think of as the “present instant” (discussed further in the paper). Is it different for other animals?

Is it the same for all humans? Might there be other entities out there with different views of time? our perhaps we already interact with other living entities with different view of time, like insects, or Gaia?

And if we met alien life systems would we even recognise them as such if their view of time was very different fom ours? Indeed, one might consider whole cultures and their view of the cultural present, which takes one into quite different areas of philosophy, and perhaps provides a novel perspective on the effects of the movement from oral additions, to written cultures, to the spread of mass literacy, to digital cultures and the spread of the immediate availability of huge volumes of cultural context. Perhaps for another day, perhaps for discussion with AKL!

Another issue is whether we would even recognise living entities elsewhere in the universe if their perceptual was sufficiently ddifferent from ours. But that’s matter perhaps for a story. Yet, particularly after finishing Mieville’s Embassytown, I was left wondering if the way forward for this line of reasoning was perhaps to try to write it as a story, rather than as a scientific paper: the ideas are not really suitable for a presentation with results and graphs, nor yet for a mathematical equational approach!

Memento Mori

March 16, 2012

I’m still marked as deceased. But I’m still not. However, the Marquis people have now promised to mark me as alive again. But it has certainly been a memento mori. Quite a few old friends have already gone (Scotland’s not famous for longevity), and I wondered if they know something I didn’t. perhaps, and perhaps not. And when I showed it to my DGM901 tutorial group this morning, they just laughed. Well, fair enough, and I did tell them I as trying to get it changed: I suppose to a 19 or 20 year old it is funny, but to me, well, yes, it has its amusing side, but also its serious side. What if i was to drop off my perch tonight? What have I missed? Do I have a bucket list (no!), though there’s things I’d like to do, though I do feel reasonably at peace with my immediate family (who are probably the only people reading this anyway). Ach well, bedtime. Hopefully, I’ll wake up in the morning, though one can never tell!