The pessimistic induction and Descartes’ evil demon

The pessimistic induction (PI) says something like this: Previous scientific theories have been wrong, so we shouldn’t believe what current science tells us. But let’s modify that with an “optimistic induction” that there is continuity through theory change (the wave nature of light survived the abandonment of the ether theory…) and our methods are improving. The PI then seems to be saying something like this: It might be the case that this or that particular theoretical entity will be discarded some time in the future. Well, this “might” claim looks a lot like Descartes’ evil demon argument for radical scepticism.

Descartes’ argument says that you might be being tricked by a powerful evil demon. The upshot is supposed to be a radical scepticism about the reality of the things we think we see. So I see a table, but I might be being tricked, so I should not believe the table exists. But obviously this brand of radical scepticism is not the orthodoxy. Why? Because another way to approach the evil demon is a kind of “fallibilism” that holds that I should believe that what I see exists, while accepting that I might be wrong, I might be being tricked by this demon.

In much the same way, I think the right approach to the PI (as moderated by the optimistic comments made above) is to say that the right approach is a “fallibilist realism” which says that while I can be confident that some element of current science will be discarded, on the whole I should believe in theoretical entities.

I think this picture fits nicely with scientific practice as well. Doing science whilst not endorsing the reality of the entities one deals with seems difficult. I mean, if I were a scientist and I didn’t believe in electrons, I’d find it difficult to theorise about them… Or to put it another way, if I were a young creationist, I would not become a paleontologist. (OK, cheap shot. Sorry). The point is that on the whole, scientists will believe in what they study, but will of course accept they might be wrong.

So this point seems obvious enough that I’m surprised I haven’t read about it before. I’m interested in hearing about any precedents of this position in the literature.

The end of time…

This New Scientist article made me wonder about time. The latest super-clocks are sensitive to differences in height (actually differences in gravitational field) small enough that their accuracy would be affected if they were placed on a slightly lower table, for example. This is madness. Maybe we’ve reached a point where time doesn’t really mean all that much any more. On those kind of scales, at that sort of precision, maybe time just stops being a useful concept. Like the length of a coastline stops being a useful concept when you measure it too accurately. (Because it’s a fractal). Or temperature; if you keep zooming in, you reach a point where the “temperature” of the volume becomes meaningless – if you zoom in enough that the volume contains maybe one atom or even no atoms, then surely temperature is unhelpful. Perhaps the same thing happens to time when we start trying to subdivide it into 10^-18ths of a second or whatever it is they are doing…

Here’s another article on time where some people seem to be reaching the same conclusions… I’m not sure these articles will be available – I’m on the campus network and they might have some sort of subscription to the magazine…

Titanoboa – Weighs a tonne and eats crocodiles

I just read about the Titanoboa. This is a snake that lived soon after the Dinosaurs died out. It was huge. I don’t think that quite does justice to it. It has been estimated that these things weighed upwards of 1,100kg and were 13 metres long. That’s a snake taller than your house weighing as much as your car! This thing was a metre wide! HUGE! The craziest part was that these things probably ate crododiles. Let me say that again; it ATE CROCODILES! You could not make up something like that up.

Brief thoughts on global warming

I was in the pub yesterday and the topic of global warming came up. Here are some quick points motivated by that discussion.

• Given the variety of environments the Earth has presented in its past, given the range of temperatures etc that have obtained on the Earth at some point in its history, the differences that even the most alarmist climate change advocates throw about are pretty darn small. That’s not the issue. The issue is that this tiny change is catastrophic from the point of view of human survival.
• The question is not really “Have humans caused global warming?” but “Is the warming phenomenon real and is it harmful to our survival?” And if the answer to that question is “yes and yes” then the next question is “What can we do about it?” The question of carbon emissions etc. causing global warming is only an issue insofar as it gives us an account of a mechanism that might be warming the world. And knowledge of that mechanism might help us to deal with the problem. If carbon emissions are contributing to warming, and if the warming is a threat to our survival, then cutting emissions might slow or stop the process thereby prolonging our survival.
• The idea that global warming is going to end all life on Earth is pretty ludicrous. If they had shoulders, certain extremophiles would be shrugging them right now. I’m sure Pyrococcus furiosus are no strangers to nonchalance.
• I think real action on global warming is going to be driven by financial incentives. Eventually a confluence of factors including improved renewables technology, depletion of oil reserves and increased demand for energy will cause some kind of renewable energy to become significantly cheaper to produce and distribute than fossil fuels are to extract and refine. Until that day, things will continue pretty much as they are now.
• That’s not to say I’m a climate change sceptic. I turn of the lights when I leave the house, use public transport, I take the train rather than fly*. But I’m a cynic and a fatalist when it comes to humanity’s capacity to change without big big shocks forcing the change. Which I guess was sort of the message of The Day the Earth Stood Still…

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* turning off lights saves me money on my electricity bill, I don’t have a license, so I have no alternative to public transport and anyway who’d drive round central London? I take the Eurostar because I don’t believe the plane is faster or more convenient once you factor in time spent in security, being there 2 hours in advance travelling to Stansted, travelling from “Brussels South” to the centre of Brussels etc.
And while it may be possible to get flights cheaper, the Eurostar experience is a good deal less unpleasant than the god-awful Ryanair. And anyway, Ryanair isn’t that much cheaper most of the time. Also no baggage weight limit on Eurostar. But despite all that my intentions are to do those little green things I am capable of doing (as long as the don’t inconvenience me too much or cost me anything).

Beware the angry monkey

I thought this was too funny not to mention.

I haven’t done a whole lot today. I spent a good long while just sitting here going “Yes, but what is a structure?” Which probably suggests I don’t quite have what it takes to be a structural realist. Shame.

I also spent rather too long trying to get LaTeX to play nicely with Kig. Now, kig can export pictures you have drawn as TeX files. But when you try and \include{thefile} in another file it messes up. So you can also export kig constructions as SVG files, which vector graphics software such as inkscape can transform into EPS, which is what should work with LaTeX. I haven’t actually tried this circuitous route to LaTeX picture perfection, because I don’t have any vector graphics software installed and I forgot to save my kig file of the nine point circle.

I have actually written a little bit today, and planned the next few weeks’ work. So it hasn’t been a totally wasted day.

I was thinking a bit more about my complaint about the kilo. I was wondering whether you could define a kilo in terms of the weight of a certain volume of a pure liquid, say water or mercury. But would that depend on the temperature and pressure? I don’t know. Or by making use of Einstein’s useful little mass/energy equivalence define a kilo as a certain amount of energy? A certain number of electron volts or some such…

Incidentally, I have started assigning tags as well as categories to my posts. This means that going through my old posts and tagging them could well become my displacement activity of choice…

yotta, zetta, exa, peta, tera, giga, mega… kilo?

All SI prefixes that are positive powers of 10^3 end in an “a” except “kilo-” I propose we change it to “kila-” because it won’t really make a difference to how people talk; a kilagram and a kilogram would be pronounced similarly by most people. What about people talking about “a kilo of rice” or whatever? Well, “kilo” can be adopted as a non-SI measure of weight much like “pound” or “ounce.”

Similarly, all SI prefixes that are positive powers of 10^-3 (or negative powers of 10^3) end in an “o” except “milli-” We should change that to “millo-” again with little or no need to alter how we talk.

Surely the Système International d’Unités is all about consistency. This is a a huge oversight on their part. Also, having a kilo, or kilagram, in Paris which is what we use to define what a kg is is quite unsatisfactory. If you want to know how long a second is, you look it up on wikipedia:

the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

You can get an atom of caesium 133 and do it yourself. With that measurement in place you can find out how long a metre is:

The metre is the length of the path travelled by light in vacuum during a time interval of ¹⁄_299,792,458 of a second. It follows that the speed of light in vacuum is exactly 299,792,458 metres per second.

You can procure a light source and a vacuum and find out how big a metre is.

But the kilagram, not so. If you want to know how big a kilo is, you have to go to Paris and weigh something against the International Prototype Kilogram. And while we’re at it, why does the SI unit have a prefix. That’s annoying too! I’m glad there are at least proposed future definitions. I don’t know if I’ve got my physics all backwards here, but here is perhaps another approach: Define a kilagram to be the mass a proton has when accelerated to speed X. Since distance and time are both well defined without recourse to an artefact like the IPK, this would put the kilo on the same level as them. This is an impractical definition, but no more impractical than counting osscilations in a caesium atom to measure a second or the proposed “counting atoms of carbon” approach to defining the kilagram.

Here’s a good quiz question: what do Liberia, Myanmar and the US have in common? They are the only 3 countries that have not adopted SI units as their primary method of measurement.

How cool is it that I can copy/paste text from wikipedia into wordpress and all the links automagically still work. That is really neat. Is that wordpress’ doing? Or wikipedia’s? Or firefox’s? Or Ubuntu’s? Whoever is responsible, you are now my heroes!

Science and maths exams are harder?

So apparently, science and maths exams are harder than arts subjects. Someone has done some research into differences between exam grades in science and arts subjects and found that “There were “substantial differences in the average grades achieved by the same or comparable candidates”.” This is really silly research. First, the average mark isn’t a very good indicator of the difficulty of the exam. Obviously, the difficulty of the exam contributes to the grades achieved, but the quality of teaching and probably several other factors also have an important effect. Secondly, I bet they found that the standard deviation in science subjects was much bigger too. It’s possible to do exceptionally well on more objective topics like chemistry and also exceptionally poorly. In, say, English the difference between a very good paper’s mark and a rather poor exam script will probably be smaller. And is a direct comparison of the type being made here even legitimate? “Easier” and “harder” are surely subjective and dependent on the individual pupils. Some people (myself included) found maths and science subjects at school to be fairly easy but struggled more with “soft” arts subjects. And the flipside is also true, some people who are gifted linguists for example might struggle with maths. So science and maths exams are harder for whom? I don’t think that comparing average grades across subjects and across pupils gives you any kind of meaningful conclusions.

The lower grades in science subjects is at least in part due to the dearth of properly qualified science teachers. As I said above, the quality of a teacher has a big impact on how well the students do in exams. And then there’s all the noise about dumbing down of exams; “maths exams are too easy” and so on. So what should we believe? Those who set the syllabus have the unenviable task of pushing the gifted kids, without leaving those who are struggling behind. But I think they should ignore all this noise in newspapers demanding easier/harder exams.

We are all going to explode tomorrow.

Today’s Guardian had a cool little special section about CERN. It is available here. I now have a false colour bubble chamber image as my desktop background. So the LHC hasn’t blown us all up yet, which is nice. If it ever does, I might feel the tiniest bit responsible, since I’m signed up to the LHC BOINC project…

In other news, the nine-point circle is my favourite fact about triangles. I will try and mention it and its relation to incircles and excircles in my dissertation. Hopefully with gratuitous use of diagrams drawn in Kig. If I can be bothered to learn how to get pictures to work in LaTeX… Another thing I’d like to do is learn how to write chapters as separate files and include them in some master file. For 15,000 words it’s hardly worth it, but it’ll be useful for next year. I’d also like to change the default font to Gentium, for no other reason than to make a move away from default LaTeX formatting…

Use and abuse of mathematical language.

I have complained about the misuse of mathematical language before. Philosophy of biology is a serial offender here. But I recently came across a really good use of maths concepts to convey an idea. In John Dupre’s paper Natural kinds and biological taxa he explains the apparent reasonableness of thinking of species as natural kinds as follows:

If it were possible to map individual organisms on a multidimensional quality space, we would find numerous clusters or bumps. In some parts of biology these clusters will be almost discrete

Now there is obviously no suggestion we do this. But it is a really neat way to get across the idea that members of a species really do have a lot in common, and it is fair enough to imagine species as being natural kinds.

Speaking of maths concepts in biology, I spent a while this afternoon thinking about the “sameness relations” Dupre uses to build classifications of animals. I struck upon the cool fact that if you demand that your relations be equivalence relations, then the classification will automatically have lots of nice kinds of consistency, because equivalence classes will always partition the space! I thought that was pretty cool.

Also today we were talking about the difference between Whitehead’s process philosophy and a more conventional ontology taking onbjects to be primitives. I started thinking of it in terms of category theory. So processes are arrows (maps morphisms whatever you want to call them.) and objects are objects. Now, I believe there is an alternative way of starting category theory which takes only the arrows as primitives, and defines objects in terms of special arrows: the identity maps. I then started thinking about taking just objects as primitives and defining arrows as ordered pairs of objects. (I don’t know if this is really legitimate…) So then I started thinking that maybe the two kinds of ontology weren’t really that different in that what you take to be basic doesn’t really matter. But maybe I was missing the point of the debate because category theory was clogging up my brain.

I also started thinking about logic and how some of the operators are interdefinable. So if you have NOT and then one of AND, OR and CONDITIONAL (and possibly BICONDITIONAL?), then you can define all the operators in terms of that. So normally you’d just take all of the symbols on board at the start. Because it doesn’t really make a difference in the end.

So I suppose my mind works in quite a mathematical/logical way. Does that make it strange that I dislike the misuse of maths language? Or does that make it more understandable? I don’t really know.

p.s. Dupre should have an accent and I could put in the logical symbols instead of AND etc. But I’m feeling lazy. Sue me.

Behold the duck

Behold the duck
It does not cluck
A cluck it lacks
It quacks

-Ogden Nash

I have spent much of today failing to write anything useful about Galileo’s Letter to the Grand Duchess Christina so I thought I’d write something here, just to reassure myself I am still capable of stringing the odd sentence together.

I bought a new razor recently, because I couldn’t find new blades for my old one. I succumbed to the mighty advertising clout of Gillette and bought a FUSION! razor. If you live under a rock, I’ll remind you that the FUSION! line of razors is advertised by Thierry Henry, Roger Federer and Tiger Woods. I don’t know which sportsman’s total lack of personality drew me to their product. All I know is that I now command the comfort of five blades AND the precision of one. Fear me. For I have experienced the miracle of FUSION!

Adam and Joe were talking about new holidays today on their BBC 6music radio show thinger. It was rather good and stuff. I’ll link to the podcast when it shows up (around 6 tomorrow, apparently). I didn’t text in any of the genius ideas I have had in the past. But theirs were specifically new days for sending cards on. Apparently they got the idea off the Apprentice. But I haven’t seen any of it this year. Or any year, for that matter.

I watched Any Given Sunday yesterday, because I’d picked it up at Borders for £2.99. Bargain! Anyway. Yes it was worth every penny of my three pounds. I also picked up The Talented Mr Ripley, Eternal Sunshine of the Spotless Mind and… some other film. All going for a song. Marvelous.