Taking stock

So where have I/we been? And where are we going with Conservative tendency?

1. Interaction. I want the site to be more interactive, so, if you have an interest, please click on the followers gadget and/or comment or email me (engmar3 [at] gmail [dot] com). And thank you to those who have already shown their interest, and I hope you will continue to find the time to drop by.

2. The human condition. My interests are various but are centered around fundamental questions about the universe and our place in it. I see our situation in fairly bleak terms, actually - no religious comforts. Which is why social and intellectual comforts - a compliment, a probing question, a shared interest - are so very important.

3. Randomness. I'm interested in developing my knowledge of the philosophy of mathematics and logic, especially aspects of these subjects that may relate to fundamental questions. The various types and levels of randomness which appear to underlie physical processes is my current focus, as it has potential relevance to how we see ourselves and our lives.

4. Politics. My inclination is towards quietism, not activism; but I respect activists and those more politically engaged than I am at the moment. I think the long-term political trends we are witnessing are unfortunate - especially to the extent that they involve government-initiated solutions (or supposed solutions) to social problems. Generally it is a healthier situation if individuals and families work out their own solutions to their problems as far as possible.

5. The decline of the West. I am fascinated  by the rise and fall of civilizations, and there is an awful lot of rising (in the East) and falling (in the West) going on at the moment. Cultures must be underpinned by political stability and economic prosperity and arguably we are witnessing the last throes of a two-and-a-half thousand year cultural and intellectual tradition. What can be salvaged from the wreckage?

6. Minimalism. My conservatism is a minimalist conservatism - or perhaps my minimalism is a conservative minimalism! I seek out simplicity and clarity in matters of the mind and in aesthetics. I may try to develop this idea explicitly in the new year, but it is implicit in everything I write.

Through a crystal darkly

In previous remarks on randomness and computation, I mentioned the work of Gregory Chaitin, a mathematician and theorist who has written and spoken (he is a brilliant speaker) extensively for both specialist and general audiences. Chaitin's technical work is highly regarded, but his interpretations and extrapolations are sometimes a little idiosyncratic and he is inclined to sound a bit New Agey at times. (He is rumored to receive help in his thinking from a giant crystal!)

Paul Davies (a physicist and writer) is, by contrast, sober and restrained - even a little pedestrian by comparison - but he is a reliable guide within his areas of expertise. I recently came across a foreword by Davies to a book of Chaitin's essays* in which Davies gives his perspective on the significance of Chaitin's work and its implications for physics and our view of the world generally.

Chaitin (who had been obsessed from his childhood years with Kurt Gödel's incompleteness theorem) "greatly extended the scope of Gödel's basic insight," writes Davies, "and recast the notion of incompleteness in a way that brings it much closer to the real world of computers and physical processes. A key step in his work is the recognition of a basic link between mathematical undecidability and randomness. Something is random if it has no pattern, no abbreviated description, in which case there is no algorithm shorter than the thing itself which captures its content. And a random fact is true for no reason at all; it is true 'by accident' so to speak ... Chaitin was able to demonstrate that mathematics is shot-through with randomness ... Mathematics, supposedly the epitome of logical orderliness is exposed as harboring irreducible arbitrariness." (p. vi)

"[M]athematics contains randomness - or accidental, reasonless truths," Davies explains, "because a ... universal Turing machine [an idealized computer], may or may not halt in executing its program, and there is no systematic way to know in advance if a function is computable (i.e. the Turing machine will halt) or not." (p. viii)

But this limitation on what we can know or predict (known as Turing uncomputability) applies not just to mathematics and computers but also to scientific theories. On Chaitin's view, a scientific theory is like a computer program that predicts our observations (the experimental data).

Indeed, in the words of Paul Davies, " ... we may regard nature as an information processing system, and a law of physics as an algorithm that maps the input data (initial conditions) into output data (final state). Thus in some sense the universe is a gigantic computer, with the laws playing the role of universal software." (p. viii)

And if the laws of physics are computer algorithms, there will be randomness in the laws of physics stemming from Turing uncomputability. But, according to Davies, the randomness will, in reality, be "even more pronounced than that which flows from Turing uncomputability." (p. viii)

He points out that the real universe differs in a crucial respect from the concept of a Turing machine. "The latter is supposed to have infinite time at its disposal: there is no upper bound on the number of steps it may perform to execute its program. The only relevant issue is whether the program eventually halts or not, however long it takes. The machine is also permitted unlimited memory ... If these limitless resources are replaced by finite resources, however, an additional, fundamental, source of unknowability emerges. So if, following Chaitin, we treat the laws of physics as software running on the resource-limited hardware known as the observable universe, then these laws will embed a form of randomness, or uncertainty, or ambiguity, or fuzziness - call it what you will - arising from the finite informational processing capacity of the cosmos." (pp. viii-ix)

There are, it seems, different forms or levels or randomness. The 'mild' form which - as chaos theory shows - is implicit even in classical, deterministic physics; the pseudo-randomness which can be generated by simple computer algorithms; the well-known randomness inherent in quantum mechanics; and perhaps the deepest levels of all stemming from proven features of idealized computers (Turing machines) and from seeing the universe itself as a giant computer - one with specific limitations on its processing capacities.

These are difficult (and to some extent speculative) ideas. But I think they are worth pursuing and may even have profound implications for how we see ourselves and our world.

It is, of course, impossible to draw definitive political or metaphysical conclusions from them, but, if the ideas are sound, there will be such conclusions to draw.

Let me just mention two thoughts which come immediately to mind: Chaitin's and Davies' notions are utterly incompatible with any political ideology which attempts to predict, plan and control human affairs; and they also appear to undermine perspectives which incorporate notions of a providential force operating behind the scenes and impinging on natural processes, historical events and/or individual destinies. 


* Thinking about Gödel and Turing: essays on complexity, 1970-2007 (World Scientific, 2007).

Of mice and men

Last night, as I was walking on a footpath by the river, I felt something softish roll under my left heel. It was a juvenile mouse (or some such rodent) which had fatally mistimed its dash across the path. It was still breathing, its body apparently split, with yellow stuff coming out. I didn't have the stomach to put it out of its misery and gingerly pushed it aside with the toe of my shoe and walked on.

Later in the evening, I chanced upon this passage, this cri de coeur, by Nassim Nicholas Taleb, with the section heading, "The world is unfair":

"Is the world that unfair? I have spent my entire life studying randomness, practicing randomness, hating randomness. The more that time passes, the worse things seem to me, the more scared I get, the more disgusted I am with Mother Nature. The more I think about my subject, the more I see evidence that the world we have in our minds is different from the one playing outside. Every morning the world appears to me more random than it did the day before, and humans seem to be even more fooled by it than they were the previous day. It is becoming unbearable. I find writing these lines painful; I find the world revolting." *


*The black swan: the impact of the highly improbable (Penguin, 2008), p.215.


[Something lighter next time. I promise!]

The randomness at the heart of reality

Is reality ultimately based on randomness? How one answers this question ultimately colors one's outlook (I suggest) in deep and subtle ways. Of course, there are many ways one could approach the issue and there are ambiguities in the question itself. But I am drawn to such questions as this (as a moth to a flame?) and, since I read and think about them, I might as well write about them here from time to time.

Here, then, are a few notes about Vlatko Vedral's view of the issue ...

Vedral draws a distinction between "classical superficial randomness" (e.g. coin tosses) and "quantum fundamental randomness" (see Decoding reality (OUP, 2010), p.163). Randomness approximates to unpredictability and much in our world appears random because it is impossible to predict in practice even if in theory one could do so using the methods of classical physics (if one had all the relevant data etc.). But the quantum world is different. No prediction can be made (even in theory) of certain quantum events. Quantum theory embraces randomness, and sees some quantum phenomena as random in a fundamental sense.*

We can think of scientific theories, Vedral writes (p. 166), as computer programs "with the output being the result of whatever experiment we are trying to model. We say that our theory is powerful, if we can compress all sorts of observations into very few equations."

But any theory will be finite and will (as Gregory Chaitin first fully realized within information theory) only produce a finite set of results. "In other words, there will be many experimental outcomes that could not be compressed within the theory. And this effectively implies that they are random." (p. 167)

Is the randomness in quantum theory due to the theory's incompleteness - our lack of knowledge of a more detailed deterministic underlying theory - as some people think? Or is "randomness inherent in the Universe, and therefore ... [an essential] part of any physical description of reality? Randomness could simply be there because our description of reality is always .... finite and anything requiring more information than that would appear to be random (since our description could not predict it)." (p. 167-168)

Vedral states what he sees as a "very profound conclusion" that this view implies: "that randomness in quantum physics is far from unexpected - in fact according to this logic it is actually essential. Furthermore, it would mean that whatever theory - if any - superseded quantum physics, it would still have to contain some random features." (p. 168)

To me it matters (or seems to matter) whether or not randomness is at the heart of things. Does it matter to you?

* I have revised this passage slightly in response to a comment.