Sound and Fury

Today we celebrate the day St Patrick turned all the snake in Ireland into Guinness. Or something like that. Don’t let the church tell you St Paddy’s isn’t today. Just because it’s their holiday, doesn’t mean they can move it about…

Speaking of the church (Good link, good link…) here are some random thoughts on atheism. So the scientific atheist position seems roughly to be the following:

• You can explain everything with science.
• Specifically, you can explain religion by talking about memes, evolution and other such things.
• This is the best explanation of religion.
• The best explanation of religion doesn’t appeal to God.
• So shave the big man upstairs with Occam’s razor.

I think there is a subtlety in the Occam’s razor step that is often overlooked: this is a scientific explanation. It is good science not to believe in the existence of entities your theory doesn’t need. I think this scientific aspect of the Occam step is important.

So, what criticisms can we make of this? I think the Big One is the idea that we should be explaining religion with science. If you concede that, then you’re pretty much finished. But roughly speaking I agree with the argument. I just don’t quite feel pushes me all the way to outright denial of the existence of any deity. So I’d say I’m intuitively atheist, but philosophically agnostic.

I don’t really have a proper point.

I object to the accusatory letter the TV licensing authority people send me. My room is too small to comfortably house a television, and I really don’t need more distractions anyway. I’d be more than happy to pay a significantly reduced license for my use of BBC radio and the BBC website, but that isn’t on offer. And the fact that TVlicensing think I’m a criminal means I’m less inclined to even that reasonable idea… Today I got a “Things you need to know in case of prosecution” notice. It starts:

According to our database, your address remains unlicensed for you to use TV receiving equipment there, despite several requests for payment of your TV license fee.

Nowhere does it suggest that anyone has even considered the possibility I do not have a television. The only conditional statements are things like “if you are committing an offence…” or “if you are found to be breaking the law…” Nothing like “if you don’t have a TV, please disregard this notice, we apologise for the inconvenience and the insult caused by suggesting you are a criminal”

Actually, upon closer scrutiny there is some small print on the back that says if I don’t have a TV, I don’t need a TV license.

I wonder if Roger Scruton submits papers he reads to scrutony scrutiny. Heh. Oh dear… On an equally frivolous but philosophical note, this blog seems promising.

And another thing that annoys me more, the more I think about it. There are people trying to get me to give money to greenpeace. If I were going to give money to charity, greenpeace wouldn’t be the one I’d choose. First, green issues and ethical issues are in the news so much that it steals a lot of greenpeace’s thunder. Everyone is pretty much aware of the problem now. So I don’t feel obliged to give money to greenpeace so that they can “raise public awareness.” Second, I don’t want my money being spent on stupid things like sabotaging Japan’s whaling fleet. That’s not to say that I condone Japan’s actions, I simply don’t want to fund criminal activity, no matter how well meaning. Incidentally I think there are better ways to get Japan to stop whaling; encouraging Japan to fund more conservation efforts, encouraging less invasive “science” methods (let’s not forget Japan claims their whaling is for scientific purposes), publicising the extent of the whaling and its damage to the environment and so on. The Arctic Sunrise’s actions are petty and unhelpful in this arena.

So I’d rather give money to charities distributing leprosy treatments in poor countries or even to some research charity like cancer research UK or something.

Oh, and happy Pi Day!

I cannot spell the word license. Every time I typed it I had to look to see whether I’d got it right. I’ve been spelling it “lisence” loads. I wonder why that is. I have trouble with “exercise” too. I blame French.

Oh and one final thing, Donald Knuth’s Surreal Numbers should have been mentioned when I was talking about dialogues.

This started as part two of my list of web resources for students. But it has kind of devolved into a list of free stuff available online. Basically, as far as I can tell I got most of the good sources for philosophy online the first time round…

Here are some more sources for free stuff on the net.

• John Baez has a great big list of free maths and physics texts available online. Be careful, there’s an animation on that page that crashes my browser.
• Project Gutenberg is a massive store of out-of-copyright texts in electronic formats. Lots of cool stuff available there.
• The Online Books page has lots of stuff on it. I don’t know if any of it is any good, though.
• Books about linux available online.
• Googling online free books gets you lots of hits. Most will probably be dubious however… Most search results always are…
• Here’s a book that looks interesting and is available for free by Alexandre Borovik of A dialogue on infinity fame. It’s called Mathematics under the Microscope.
• Another free book. It’s called God’s Debris and it is by Scott Adams of Dilbert fame. This one I have read. But I can’t really remember if it is any good…

Any suggestions as to other similar stuff is welcome.

I forgot to mention Cicero’s The Nature of the Gods which is kind of almost a dialogue. And while I’m linking to freely available stuff, The Elements is online for free. Read Digest and Be Impressed by the most successful maths textbook ever. 2000 years and still going strong.

“Read, digest and be impressed” I like that phrase. I shall use it regularly. Whether it is relevant or not.

I bought On the Shoulders of Giants today. I’m disappointed with the scope of it. It only contains work by Copernicus, Galileo, Kepler, Newton and Einstein. Not only is this a limited selection of people, but it is a limited selection of physics. To mention nothing of Aristotelian or Ptolemaic astronomy would be a big oversight if this were a book about astronomy. If it is a book about physics more generally, then that oversight can be forgiven, but then the absence of any work on quantum physics is inexcusable: surely the EPR paper and Bohr’s reply deserve a mention? Or extracts from Feynman’s popular science writing? Or Schrodinger’s  paper where he first describes his cat paradox? There is a lot missing from this collection, however you look at it. Maybe Hawking is setting himself up for a third installment of “Other people’s writing dressed up in a book with potted biographies by me and cover art by William Blake” which will cover quantum mechanics…

This is disappointing in the light of God Created the Integers. Look at the breadth of time and subject matter encapsulated in the writers from that volume: Euclid, Archimedes, Diophantus, Descartes, Newton, Laplace, Fourier, Gauss, Cauchy, Boole, Riemann, Weierstrass, Dedekind, Cantor,  Lebesgue, Godel and Turing. Even if this list has some disappointing gaps (Apollonius, Hilbert, Zermelo, Peano, Russell…) it is still a much better survey of the subject than Giants is of its subject.

I think what underlies this difference is an important differnce between maths and physics: the cosmological models that Copernicus overthrew are no longer useful at all. Copernicus was the first person whose work on astronomy is still relevant (OK, so Oresme and Burridan and maybe even some ancients suggested geocentric systems, but never mind them). In mathematics, older work is not superseded in the same way. The advent of non-Euclidean geometries did not invalidate or replace Euclid’s work. Mathematics is never proven wrong. It is only ever placed in a new bigger more general structure. That is probably due to the nature of the subject matter of maths as opposed to physics. Physics is about the world. Maths is..n’t. What maths is about is an open question, but whatever the answer is, it isn’t something which can contradict the results of mathematicians.

Probability is something I am interested in. I’m interested in the philosophical aspects of probability. When I was a maths student, probability didn’t excite me at all. But I am interested in the philosophy of probability and I wanted to write something more about it. My philosophy of physics essay was about one aspect of probability in science. But I’d like to look more at probability in general. I thought maybe of making it the topic of my postgrad seminar talk. It would be an interesting diversion from writing my dissertation. On the walk back from the bookshop today (dammit. I forgot to by the book I meant to pick up…) I was planning out how the talk would look in my head. It would have three sections… I use bullet points quite a lot in this blog, so perhaps I’ll use the ennumerate thing this time…

1. Discuss some of the terminology of philosophical work on probability. Different writers distinguish different numbers of types of probability and give them different but sometimes overlapping names. So I’d talk about what people mean by; objective, subjective, epistemic, ontic, chance, credence and so on…
2. Look at which of the extensions of these terms overlap or are contained in one another. Come up with my own classification of probabilities and associated vocabulary. This would probably take the form of different terms on different axes, because I think probability is more than a one-dimensional concept. (Does that make any sense? I might have to think about how to explain that some more…)
3. As well as terminology and concepts, there is the interpretation of probabilty. So I would finish by looking at which interpretations cause what kind of collapsing of concepts. If you’re a determinist, objective probabilities are going to have to collapse somehow. If you believe in GRW you can’t be a frequentist. (I’ve mentioned this point before I am sure…)

I’d take a realist, indeterminist position for most of the talk, because I think that will allow you to differentiate the most types of probability. Then to avoid criticism of the “theory-ladenness” of my characterisation, in the third section I’d look at the problem through different philosophical goggles. Wearing different philosophical hats.

This got me thinking about another awkward point. If you’re a realist about objective, physical probabilities, how do you guarantee they satisfy the axioms of probability theory? I can’t see how you do it. Even if you replace Kolmogorov with some other axiomatisation (Luder’s rule conditionalisation or whatever) you still have to explain why the probabilities satisfy that system. Since the probabilities will be inherently independent how do you do this?

Right I have to stroll back up to the bookshop before it starts raining again. I need to pick up On the Shoulders of Giants. Because it will look good on my bookshelf next to God Created the Integers and The Road to Reality. Because it will be a good source for my history of science essay.

I’m interested in the idea of the dialogue as a way of expounding philosophical ideas. So here is a list of some philosophical dialogues.

• Obviously, the daddy of them all; Plato’s whole oeuvre is roughly dialogue shaped.
• Berkley’s Dialogues between Hylas and Philonius
• Proofs and Refutations by Imre Lakatos. My favourite dialogue. It’s crazy! all the characters are named after Greek letters. It’s madness. But it’s really good. It gives you new perspectives on the history of maths. It also can kind of be seen as an allegory about the philosophy of science.
• Mary Hesse has a book called Models and Analogies in Science that has a dialogue between Duhem and Campbell. Have to admit I haven’t read it. But I did borrow the book from the library once to check it was there.
• Today I picked up Sue Blackmore’s Conversations on consciousness, which is basically dialogues between her and eminent philosophers and psychologists…
• Godel Escher Bach has many dialogues in it. They serve more as diversions and, again, as allegorical tools, rather than as the main expository tool. But they are still interesting and very clever.
• There’s Lewis Carroll’s original dialogue between Achilles and the Tortoise which served as the inspiration for Hofstadter’s GEB dialogues.
• Galileo used Salviati, Simplicio and Sagredo in his dialogues to discuss new sciences and new world systems. (Bizarrely Project Gutenberg has no results for galileo. Disappointing.)
• Schopenhauer has also used the dialogue.

I can’t think of any more dialogues for now. But I feel I’m missing some… Anyway, I think it is an interesting way of presenting an argument. I’d like to think more about what sort of discussions can usefully be presented in this form.

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So today I was reading Artificial Intelligence and Scientific Method and Gillies mentions that is a logical truth; a tautology in classical logic (but not in intuitionistic logic). I was interested by that and check that it is indeed the case by writing out the truth table. I didn’t bother to actually find a proof, but contented myself with the fact that the truth table + the fact that the propositional calculus is sound and complete is kind of a proof. Then I thought what are some other cool tautologies. Here are a couple I remembered.

Then I thought. Hmm. I’m a geek. But I’m still enamoured of this ability to put code in my wordpress posts so I thought I’d write about it…

So you can use code in wordpress posts. (Oddly, I can’t get \tex to display…[edit: use \LaTeX which I haven't seen before...]) That is cool and I thought I’d try it out.

I wonder if you can use Dirac notation

[edit, nope. not with \bra and \ket. you have to use |, \left, \right and > which just isn't the same...]

I don’t really have a purpose in writing this. I seldom have the need to write formulae in this blog. Maybe I should write more formulae. Although I do dislike the use of mathematics to legitimise something that might otherwise be considered “soft.” A prime example of this is where you say that Organisms change as a function of their environment and themselves, and the environment changes dependent on the state of the environment. Then the following meaningless equations are used. Apparently to justify the proposition:

Ignoring the fact that I’m pretty sure that should read rather than (because they are clearly not supposed to be the same function…) and I believe that organisms affect how their environment changes, these equations mean nothing! What exactly is supposed to mean? Yes it’s obvious they are angling for “change in organisms through time” or something like that, but why not say that? Why shoehorn in some fancy looking maths? isn’t something that has time-derivatives in any meaningful sense. It’s purely an attempt to make the thing look more “scientific” which is crazy. There’s nothing unscientific about using words to express your ideas.

Anyway. That turned into a bit of a rant when it was supposed to me just testing out the LaTeX functions of wordpress…

I have edited this several times to make it all work. I don’t normally edit posts, but this is just a sandbox for my messing with messing…

I have added plenty more people to my list of births and deaths spreadsheet to reflect my new-found interest in the Copernican Revolution. I also added the odd mathematician, some philosophers of science and quite a few early quantum physicists. I have another spreadsheet of important or relevant dates, but it only has a couple of entries so far…

I still haven’t found a good way of representing this information as a timeline. It seems such a simple idea: taking a spreadsheet of dates and building a timeline from it. I’m surprised I haven’t been able to find any programs that do it. Any help would still be appreciated.

I’m normally insistent on using British English spellings. Axe not Ax. Utilise not Utilize. And so on. But I have no trouble writing “program” to mean a computer program. But I’d still insist on writing “television programme.”  I think this is something I picked up from David Miller last year. He made the same point at some stage in his notes for his Symbolic Logic course. Are we witnessing the birth of a new word, a splitting off from an old word? Some cross-pollination back across the Atlantic? If this is more than just me and my logic lecturer, I think it is an interesting linguistic quirk…

Writing down my thoughts about my research proposal was such a good idea that I’ve decided to write a little something about all the other things I’m up to at the moment. If nothing else, it will help me work out what I’m doing. First things first: I’m writing three essays for the three courses I’m taking this term. I shall say a little about each in turn.

History of Science. The course is focussed on the Copernican revolution, so I thought I’d look at the influence of progress in mathematics on the progress in astronomy. I’m aware that Ptolemy and Aristotle probably had a better knowledge of conics than did anyone afterwards in Europe up until the Eighteeth century. The works of Apollonius were translated from Arabic into Latin only in the 1700s. So Copernicus and Galileo didn’t have that stuff available. This might go some way to explaining why it took so long to get over the idea of orbits being circles… So that’s what I want to look at there.

Philosophy of Biology. This is the one I am least sure about. I don’t really know what I want to do. Possibly something about levels of explanation and abuses of language. I feel strongly that people use the idea of “fitness” where they really shouldn’t. As a statistical tool to assess differential population growth based on certain traits or genes, it’s fine. But when people start talking about a gene or trait “conferring a selective advantage” or “increasing fitness” then I start to feel uncomfortable. They seem to be creating an extra level of explanation that is vacuous and possibly misleading. I don’t know if this vague unease can be stretched out to five thousand words, though…

Scientific Epistemology and Methodology. This course is really very broad, and I have managed to pick an essay topic that is kind of outside of the scope of the course. I’m writing about robot scientists and what they can teach us about science. There isn’t really much written on this so I’m sort of a bit all over the place at the moment. I’m looking at robot science from lots of different philosophical perspectives.

The other thing I have going on at the moment is much more on the back-burner until I get these essays out of the way. That is my dissertation topic. I’m looking at structuralism and geometry. A lot of talk about structuralism in philosophy of maths is centred on discussing the natural number structure. I want to look at to what extent can we think of geometry as being structural. I’d also like to look at the relationship between structuralism and axiomatics.

So… that is what I’m currently pondering. That was useful to get it all written down at least in a cursory way…