Saturday, March 17, 2012

New Aristotelians according to Connolley

A piece here by William Connolley gives me a chance to write about something today.  He says that 'with the success of science' the idea of 'abstracting problems', i.e. abstraction, isn't difficult. He considers the example of a ball moving on a surface, which requires the idea of a perfect sphere on a perfectly flat surface, 'ignoring friction'. This takes us straight away to Newton's laws of motion, such as the law that the ball moves in a straight line unless deflected or stopped by some force, and so on.

He claims that the ancients, such as Aristotle, were unable to make that abstraction. "They were still trying to understand the whole world as it was".
...It was "obvious" to them that the first and most obvious property of moving objects was that they stopped moving once you stopped pushing them. An ox-cart rumbling down some rutted muddy path stopped when the oxen stopped pulling it; that was obvious, and the study of such was so mired in the nitty-gritty reality of the world that precious little progress was made until Galileo abstracted (I know, I know, I simplify: Oresme etc worked on the problem too and got some of the way there; but again, only by picking on simpler examples).
Sorry, but that's quite horrible.  The ancients such as Aristotle were well used to abstraction.  Aristotle, as is well known, was profoundly influenced by Euclid and the abstract world of geometry, you know, perfect circles, spheres, lines, planes and so on.  As was Plato before him, of course, who was so impressed with abstraction that he constructed a quasi-religious theory about it.

To get Newton's laws abstraction may be necessary, but not sufficient. The crucial part of Connolley's example is the 'friction' bit. We have to 'ignore friction'. Yes, but what is friction?  Well, as we observe it with our own eyes in the natural world, it simply is the tendency of bodies in the sublunary world to slow down and stop.  An ancient philosopher could easily have abstracted away friction, after all, that's exactly what Euclid did.  There is no friction in Euclid's geometry, nor is there gravitation.  But there's nothing in that abstraction that tells you what friction really is.  The ancients thought that bodies slow down because that's what they naturally do, just as we think that bodies are naturally attracted to each other by gravitational force (which we still don't understand, except as some Aristotelian essential characteristic of matter).

The capacity to abstract is nothing to do with ancient science.  In fact, the problem was too much abstraction. By contrast, a little more observation and attention to the actual world would have done the trick. As I observed here and elsewhere, it was Buridan's observation of milwheels and ships, plus a spell in an armchair, that led him to reject Aristotle's theory of impetus.  Forget abstraction.

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9 Comments:

Blogger Belette said...

Hey, c'mon man, at least spell my name right. That's disrespect.

6:17 pm  
Blogger Belette said...

> An ancient philosopher could easily have abstracted away friction, after all, that's exactly what Euclid did. There is no friction in Euclid's geometry

I think you're wrong. Euclid didn't abstract away friction, because he never considered any problems of dynamics.

Have another go?

6:20 pm  
Blogger Edward Ockham said...

Oops, now correct. I have always typed it correctly before, in my defence.

>>I think you're wrong. Euclid didn't abstract away friction, because he never considered any problems of dynamics.

Why do you think that 'never considered problems of dynamics' implies 'didn't abstract away friction'?

I would have thought it was the other way round. If you are considering bodies without consideration of their dynamic properties, i.e. considering a sphere inasmuch as it is any sphere, without regard to whether it is light, or heavy, or moving, or not moving, or coloured red or gren etc, then you are precisely considering it abstractly.

Perhaps I am misunderstanding the meaning of the word 'abstract' here? What do you mean by 'abstract'?

6:51 pm  
Blogger Belette said...

Thanks for the correction, I'm happy now.

Unless there is some corpus of works by Euclid with which I'm unfamiliar, I think you've entirely misunderstood the situation.

Euclid never considered any problems of physics at all. All his work was pure geometry. It wasn't even what nowadays we'd call "statics" (http://en.wikipedia.org/wiki/Statics), it was pure geometry. So it certainly never made it to kinematics (http://en.wikipedia.org/wiki/Kinematics) and it certainly never ventured into dynamics (http://en.wikipedia.org/wiki/Analytical_dynamics).

So problems of friction were simply irrelevant to Euclid. They weren't abstracted away; they were never there in the first place.

Geometry itself represents an abstraction of the real world, that is correct. But as far as I can see the antient-Greek physics-types never followed the geometry-types down that road. That is the failure I'm talking about.

7:27 pm  
Blogger Belette said...

> just as we think that bodies are naturally attracted to each other by gravitational force

That is a correct description of Newtonian theory, but not of GR. There isn't really a "gravitational force" in GR, it is more a question of geometry (full circle ;-). But I'll admit to not fully understanding GR.

Amusing insight (that I learnt discussing Fictitious force on wikipedia): in conventional dynamics, the Coriolis force is "fictitious": it is a change-of-coordinates force; you can transform to a coordinate system in which it isn't present. But in GR, you can do the same for gravity.

8:14 pm  
Blogger Edward Ockham said...

>> I think you've entirely misunderstood the situation. Euclid never considered any problems of physics at all.
<<

I put it to you sir that you have entirely misunderstood the situation.

Right, Euclid never considered any problems of physics at all. that is to say, using my understanding of the word 'abstraction', that he considered bodies in abstraction from any of their physical properties.

8:04 am  
Blogger David Brightly said...

If we think of abstraction as a process of forgetting accidental properties and concentrating on essential ones then it's clear that the ancients could never have arrived at Netwon's laws because they thought of the slowing down of moving sublunary bodies as essential. Once friction is seen as accidental it can be abstracted away. But we have to wait for the medievals for this development.

8:09 am  
Blogger Edward Ockham said...

Yes quite. It's still odd why they took so long to spot that it was an accidental effect, when you think of all the considerable evidence for it. E.g. slipping on ice, smooth objects rolling further and so on.

9:32 am  
Blogger David Brightly said...

>> It's still odd why they took so long... <<

Well, is it though? My impression is that well into the middle ages and beyond thinkers were in thrall to Aristotle. Was there an alternative on offer? And the counter evidence is tiny in comparison to the overwhelming everyday evidence that earthly motion peters out. Smooth horizontal surfaces of any size, eg, ice-sheet covered lakes, weren't readily available to the denizens of the mediiterranean seaboard or places further east. Besides, there's no tradition of experimentation until we get to Galileo and his inclined planes.

10:39 am  

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