Hegel does maths

While browing the Dictionary of Philosophy, on my way towards Hobbes, I stopped at Hegel, and noticed a comment about his “orbits of the planets”, something to the effect that the view that he proved, from first principles, that there are seven planets, is an error of translation. Odd, I thought: Hegel I know little about, other than a vague disrespect and a lack of interest in finding out more. But I didn’t know he was up to astronomy or maths; and… he isn’t. You can read it here if you like.

It looks to me like nonsense, along the lines of the modern french philosophers stuff that Sokal shredded. Lots of it is words that could mean anything; the first obvious error is in his analysis of book 1, section II, prop 1 of the Principia, which Hegel thinks shows that both the arcs and the areas are proportional to time. This is wrong, clearly: in an elliptical orbit, the body moves faster at apogee, and traces out less arc in unit time than when at perigee. Or if you prefer the geomerical view, in an elliptical orbit the arcs *must* be smaller when the radii are larger, because the areas remain the same. There follows some confusion about the physical meaning of the parallelogram of forces… he seems to think that the mathematical resolution represents some physical reality. Hegel appears to be following the failed Greek idea of deducing the world from pure though, disdaining tedious experiment: Perhaps philosophy itself can deduce a priori what the experimental method, which assumes the name of philosophy, tries to discover with false and fruitless success from experiments, seeking therein with a sort of blind enthusiasm after the shadows of true philosophical concepts in sense perceptions. This doesn’t seem likely, when Hegel manages to decide that the tangent to the ellipse represents centrifugal force (I may have got that wrong because the entire thing is so badly garbled its hard to understand. I *think* it may partly be the standard “does centrifugal force exist”, garbled, but its hard to be sure). On the plus side, he notices that in the famous application of the law of centripetal force to the motion of the moon and to the planets with their satellites, there is no reference to any relation between the masses. Clearly this gravitation law is a law merely of the phenomenon of motion and not a force law at all but alas he misses his chance when he decides It would be tedious to discuss the distinction. Fairly soon after he discovers that law can be inverted which says that the gravitation force stands in inverse ratio to the square of the distances, so we can say instead that it stands in direct ratio to the square of distances. How he got there I don’t know, but we may as well skip lightly onwards from this point.

Ah. Suddenly I’m at the end. The seven-planets stuff is just the standard attempts at numerology to find a pattern in the planets orbits which isn’t there (he should have stuck to his first sentence: relations of planetary displacements, which appear to be a matter of experience alone); he certainly doesn’t say there are only seven, assuming the translation is honest. What a let down.

A brief googling doesn’t point me at any interesting commentaries on this text. Is it now regarded as uninteresting juvenilia, to be quietly ignored? In conclusion I suppose I should note that being wrong about area A doesn’t mean you’re wrong about area B: Hobbes, who I was heading for, made any number of embarassing maths errors, which don’t touch Leviathan.

[Update: Gauss wasn’t impressed – see comments -W]

Arctic Sea Ice Retreat: When Will the Arctic Ocean be Ice-Free During Summer?

Asks climatematters@columbia. But they ask it in a way that suggests they think the trend is going to be steep. So I offered them the standard bet. We’ll see.

Meanwhile, anyone interested in whether 2009 is likely to be a record can get some action over at ipredict (thanks Gareth). I’ve bought some; current price is about 0.23. I’m not really sure what a fair price would be; I have some buy orders in. Its quite educational.

The world is no warmer than it was 30 years ago?

Every now and again, its nice to be reminded that no matter how irritating the overenthusiasm of the greenies can be on occaision, the real wackos are on the septic side. If you can’t cope with the long words at [[Global Warming]] then you can always look at the pretty pictures. Or maybe you like numbers?. More probably, you like sticking your head in the sand.

I’m sorry, but this kind of nonsense is just tedious. The world is getting warmer. You can argue about just how fast, and there is certainly a lot of room to discuss how much of a problem this is and how best to deal with it, but try to avoid arguing with basic reality. If you’re really naughty, you may end up on CNN.

[Update: lots of exciting fighting in the comments, but things are getting lost there. In particular, M offers us a bet, but its terms are obscure as is who its directed at. So I’m pulling it up here, and am interested in taking it up, if it can be clarified. As I understand it, M is offering If you think the naughties were normal, you should be quite willing to bet that the temperature over the next 5 years will average significantly above the average for 2002-2007. $1000 says it won’t. But he hasn’t defined “significant”. I take it that is *isn’t* prepare to bet $1000 that the 2008-12 average won’t simply be higher than 2002-2007 (why is he using 6 year periods but talking about 5 year averages?). Assuming he isn’t, I’m interested in the bet, provided we can agree a meaningful definition of “sig”, and… we know who he is. You can’t expect known people who can’t run away to put up against an anon, who can cut-n-run.

More update: we negotiated over the terms of the bet, and came close, but only at the expense of taking the bet down to $100, which is trivia. At that level, we’re only doing it for reputation, which is meaningless for an anon. So no bet -W]

Iron fertilisation

Nurture notes some controversy over LOHAFEX. We’re taken aback by this flagrant disregard of international law, says someone I’ve never heard of.

Well, my reading of COP 9 Decision IX/16, Section C (Ocean Fertilization), paragraph 4 is that it says it requests Parties and urges other Governments, in accordance with the precautionary approach, to ensure that ocean fertilization activities do not take place until there is an adequate scientific basis on which to justify such activities, including assessing associated risks, and a global, transparent and effective control and regulatory mechanism is in place for these activities; with the exception of small scale scientific research studies within coastal waters. So since it is merely a request or an urge, its not law (LOHAFEX news also makes the assertion that the document is not legally binding).

If we ignore that niggle, it comes down to whether the experiment fits under the exemption of with the exception of small scale scientific research studies within coastal waters. Its definitely a scientific study. “small scale” is a near meaningless term, but 20×20 km sounds pretty small to me – smaller than an ocean GCM grid box, anyway. And 20 tonnes is not a lot, either. OTOH it doesn’t look like they are going to be coastal: the pre-cruise booklet says they haven’t decided exactly where to do it, but it will be in an upwelling eddy in the Polar Front region north of South Georgia. Scientifically restricting things to coastal sites appears completely pointless – probably the text of the resolution at this point is some meaningless politicians bodge. The Indians assert that such experiments were to be restricted to coastal waters was perhaps an aberration, which has since been amended which sounds like wishful thinking to me; if there has been an amendation, no-one knows where it is.

Conclusion: seems fair enough to me. Don’t think the whingers have got a leg to stand on (or maybe they have one leg out of four to stand on, but thats not good enough to stop you falling over).

[Update: there is a whole blog about IF, but its badly out of date -W]

Sea absorbing less CO2, scientists discover?

So says The Grauniad. It seems eerily familiar to me, and the The shift has alarmed experts, who blame global warming almost seems like a parody. Torygraph tags along.

Oh yes, here we were and here.

The new study says The results showed the amount of CO2 absorbed during 1999 to 2007 was half the level recorded from 1992 to 1999. This is all very well, but it cant be global, or it would be obvious in the atmospheric CO2 levels. And it isn’t.

Don’t believe a word of it, guv (part 2)

Ahem. So previously there was a lot of hype and confusion and not much paper. Now that has changed, with Reconstructing sea level from paleo and projected temperatures 200 to 2100AD by Aslak Grinsted, John C. Moore & Svetlana Jevrejeva.

Which says:

We use a physically plausible 4 parameter linear response equation to relate 2000 years of global temperatures and sea level. We estimate likelihood distributions of equation parameters using Monte Carlo inversion, which then allows visualization of past and future sea level scenarios. The model has good predictive power when calibrated on the pre-1990 period and validated against the high rates of sea level rise from the satellite altimetry. Future sea level is projected from IPCC temperature scenarios and past sea level from established multi-proxy reconstructions assuming that the established relationship between temperature and sea level holds from 200-2100 A.D. Over the last 2000 years minimum sea level (-19 to -26 cm) occurred around 1730 AD, maximum sea level (12 to 21 cm) around 1150 AD. Sea level 2090-2099 is projected to be 0.9 to 1.3 m for the A1B scenario, with low probability of the rise being within Intergovernmental Panel on Climate Change (IPCC) confidence limits.

(This abstract is a bit confusing. We use a physically plausible 4 parameter linear response equation to relate 2000 years of global temperatures and sea level. doesn’t mean what it appears to say. They only have 150 (or 300) years of sea level and T together; the 2000 years comes from using the resulting relation to reconstruct sea level over 2000 years. And the results (of the sea level reconstruction) must be dubious, because they earlier say We will, therefore, restrict the use of equation 2 to a relatively short period dominated by sea level rise, and (according to their results) this isn’t true of the last 2 kyr).

OK, so this a now comprehensible: we have some trust in the IPCC model projections of temperature, but we reckon their SLR estimates are too low because they don’t take into account ice sheet melt (see-also RC). So rather than try to model it, which we can’t, we’ll just look at the historical T-SLR relationship and project it into the future. This is a reasonable idea, and Rahmstorf did it in Science in 2007 and defended it. He only did 1880-2001; I’m not sure why he picked that period, it can’t be because he doesn’t trust he HS, perhaps he doesn’t trust the early sea level records.

Grinsted et al. believe that doubt has been cast on the assumptions of Rahmstorf, thought I’m not quite sure why. They do 1700-2007, by use Moberg or the Jones and Mann T reconstruction, and the Amsterdam SL record. Assuming I’m reading their table 2 right, when using only the historical data (1850 onwards) they get basically the same answer (0.32m – 1.34m) as Rahmstorf (0.5m – 1.4m) for SLR to 2100. Which isn’t too surprising, as its a very similar method. Using the longer record from 1700, they get 0.91m – 1.32m from the Moberg reconstruction, or 1.21 – 1.79 from J&M; but the J&M fit isn’t good (fig 7) so they prefer the Moberg version.

Using the 1850-2007 data only, the response time comes out at ~1 kyr. Which doesn’t sound right: I doubt you can determine such a long timescale from a short dataset. As indeed they notice: The simple conclusion is that the calibration time series is too short relative to the response time. Inclusion of the additional pre-1850 data clearly favors faster response and a higher sensitivity (aτ-1) than instrumental observations alone. For Moberg, the response time is much shorter: ~200 years. I wonder if that interacts with Hansens stuff at all? OTOH if you took the response time from the whole Holocene dataset (~2.5 kyr) then SLR at 2100 comes down to ~0.6m.

So where do we end up? Hard to say. The answers are compatible with Rahmstorf, but they effectively reject the Rahmstorf stuff because they don’t believe the response times when restricted to the shorter period. “Don’t believe a word of it” is no longer a fair response; its a reasonable piece of work, though I’ve no idea if its right or not. Boiled down, it amounts to “we’ll probably get more SLR from the ice sheets, but we don’t know how much yet”.

ps: Daniel says, play The Codex of Alchemical Engineering. So do I.

pps: To warm the cockles of Broons heart: when told that VAT was down to 15% from 17.5% D’s first response (having first checked what VAT was) was “oh cool, so I can buy more stuff!”

[Update: Of course, We’re all going to die -W]

[See-also: Aslak Grinsted. Recent global sea level acceleration started over 200 years ago? may also be of interest -W]