Aristotle and the continuum

And now for something almost completely different. This all begins at History of the infinite where I said it might be fun to work out why his [Aristotle’s] “proof” that the continuum can’t be composed of indivisibles is wrong. This lead on to Aristotle against the continuum – reply (wherein you will find Aristotle’s proof that the continuum cannot be composed just of points, laid out reasonably comprehensibly). There is also The history of the continuum and Another argument against indivisibles (which is a less viable attempt via addition).

Anyway, to summarise: thinking about infinity is hard. Suppose we abstract A’s argument away from “the continuum” (whatever that is) to the real line (which is at least clearly defined) – and let’s say, just the real numbers between 0 and 1 (I’m using “real” in the mathematical sense of “real number“, not in the sense of belonging-to-the-real-world, of course. The first sentence of that linked article is a bit rubbish, though. Sigh). Then to restate A’s argument, we’re obliged to say “the real line is not made up of just numbers” (numbers == points). This is self-evident twaddle (how can the real be made up of anything other than numbers? It is them, by definition. Although if you want to be pedantic it also has an ordering and a metric), so the argument collapses in a heap (although it took me a while to realise this). If you want to, you can try to read through A’s original argument without the hints, and see where his argument falls down, but it isn’t necessary to do that in order to see that it is wrong.

Indeed the problem I’m having now is to see how his argument can ever have been believed, by him or by anyone else. It doesn’t help that from “continuum” I automatically go to “real line”, where his stuff falls over without you pushing it. So we have to try to think like him, and I think the key is to think geometrically not numerically (incidentally, I think the issue of rationals vs irrationals, or countability, is irrelevant here; A postdates the proof of irrationals, if that helps). And also you need to blur the line between the real-world and the maths-world; he is thinking, I think, largely in terms of the real world, albeit a slightly idealised real world. So he is used to thinking of lines, and of line segments, and of geometrical proofs in which those lines are marked by a few points. So he thinks of the line as a thing, to which you can add a few points, and then a few more, but obviously never by that process make the whole line.

If anyone out there has a way of stating his thinking in a way that makes any kind of sense, do please comment (I believe I may have turned on Captchas, don’t let that put you off).

[Update: NB found me, and I think that essentially resolves the problem, with:

points only come into (actual) existence for Aristotle when a division is made
between two line segments

That sounds correct, and explains the problem (together with his dislike of actual, as opposed to potential, infinities). So if you’re A, then given a line segment between two points, you can keep cutting it and keep finding points, none of which (of course) touch. And in your mind, therefore, you have a series of line segments spearated by points. What you can’t do is consider all possible cuts, because that kind of realised infinity is foreign to his way of thinking.

In which case, the final step is to go back and say, given that definition / idea, is his original proof valid? I think that, given that, his original result is valid, but vacuously so: he refuses to consider completed infinities, and a line, to be made of points, needs an infinite number of points, which he has ruled out, therefore a line isn’t made of an infinite number of points. But only because of his artifical restriction on the meaning of infinity.]

Global temperature response to radiative forcing: Solar cycle versus volcanic eruptions

Another one in the eye for the solarists. K. Rypdal, JGR VOL. 117, D06115, 14 PP., 2012 doi:10.1029/2011JD017283:

I show that the peak-to-peak amplitude of the global mean surface temperature response to the 11-year cyclic total irradiance forcing is an order of magnitude less than the amplitude of a cyclic component roughly in phase with the solar forcing which has been observed in the temperature record in the period 1959-2004. If this cyclic temperature component were a response to the solar forcing, it would imply the existence of strong amplifying feedbacks which operate exclusively for solar forcing, such as top-down mechanisms responding to the large variability in the ultraviolet part of the solar spectrum. I demonstrate, however, that the apparent cyclic component in the temperature record is dominated by the response to five major volcanic eruptions some of which incidentally took place a few years before solar minimum in four consecutive solar cycles, and hence that the correlation with the solar cycle is coincidental. A temperature rise of approximately 0.15 K over the 20th century ascribed to an increasing trend in solar forcing is more than offset by a cooling trend of about 0.3 K due to stratospheric aerosols from volcanic eruptions.

Or in other words, you can’t do attribution just by looking for cycles that you’d like to see in the records. That wazzock Scafetta springs to mind.

They even provide a list of Key Points:

* Solar cycle signal in global temperature is no more than 0.02 degrees K
* A 0.2 K periodic signal observed in phase with solar cycle is due to volcanoes
* Volcano cooling in 20th century more than offsets solar activity warming

Disclaimer: I’ve only read the abstract, but it seems clear enough.


* The 11 year solar cycle signal in transient simulations from the Whole Atmosphere Community Climate Model – not directly relevant, mind.

I am a red hot climate change denialist?

Strange – you might think – but not so bizarre that some people don’t think it. Here is the quote

William, given the article’s clearly supposedly-sceptical viewpoint, I did not expect my edit to survive but, 8 minutes! Wow, you are red hot! I note your track record of getting into trouble with Moderators over edit-warring issues, so will not be so foolish as to do the same with you myself. However, is there anything you would care to say in your defence that will prevent me from writing you off as a climate change denier?

Why does he call me “William”? I don’t know him, he doesn’t know me. Is he a foreigner? No, he is Britishor so he claims. But clearly not a well-bred one. I delicately suggested that he might get a clue (as the hip doodz say) from Conservapedia, but he doesn’t seem to have done so.

What has him so hot under the collar? The runaway greenhouse effect article. This has always been rather poor: largely because, as the article says, A runaway greenhouse effect is not a clearly defined term; and because it was edited by Andrewjlockley, who is part of the AMEG crowd. And because people keep confusing it with positive feedback. Our man wanted something less ambiguous, and there is a not-very-exciting talk page thread.

All this has odd echoes of last week’s tempest but Martin Charles Lack is not Andrew Judd – he seems to know when to back off, for one thing.

Largely irrelevant refs

* [[List of Viz comic strips]]. Check for “Captain Oats” – I still remember that one. I personally rescued Mickey’s Monkey Spunk Moped from redirection.
* No lessons learned from Climategate ? Fred Pearce and the New Scientist attack anti-nuclear book – this is a guest post at WUWT by Martin Cohe[n]. It contains refs to “Climategate”, therefore by WUWT standards it is publishable; but it is so laughably incoherent that even the regulars think it should be pulled. My comment.
* The Fireplace Delusion – meant to be about religion, but would fit the denialists, too. h/t Paul.