Leibniz v. Newton: Handbags at dawn.

[uwot]

I'm grateful to Ginkgo for prompting me to revisit Leibniz; I can't remember why anymore, but never mind. This from Leibniz by G. MacDonald Ross OUP 1984:
"Leibniz held that it was not enough to formulate mechanical laws to describe and predict the behaviour of physical systems. A genuine science also had to explain the phenomena by postulating underlying mechanisms and powers of which perceptible motions were the results."
That in a nutshell is the difference between Empiricism and Rationalism. Empiricism doesn't care about the story behind the events, and while I describe myself as an empiricist, I do like a good story. Leibniz's idea was that 'monads' (atoms of a sort) are:
"nothing other than the receptive capacity of things, or their 'passive power' as he called it. Matter just was the capacity to slow other things down, and to be accelerated rather than penetrated (capacities which ghosts and shadows lack)- in other words, inertia or mass, and solidity. So, taking into account 'active powers' such as kinetic energy, Leibniz reduced matter to a complex of forces. In this he was anticipating modern field theory, which treats material particles as concentrated fields of force- an anticipation duly recognised by its founder, the Italian mathematician Ruggiero Giuseppe Boscovich (1711-87)"
Like I say; the most likely cause of all the phenomena that give the impression of a universe made of stuff, is some stuff the universe is made of. The problem with Newton is that (thanks to Hypotheses non fingo) he is reduced to asserting that the cause of gravity is the gravitational force, which doesn't explain anything.

[bobevenson]

I have to side with Leibniz since Newton frittered away most of his time on alchemy.

[Ginkgo]

I have to side with Leibniz since Newton frittered away most of his time on alchemy.

Newton couldn't make a crust out of alchemy so he turned to physics.

[bobevenson]

I have to side with Leibniz since Newton frittered away most of his time on alchemy.

Newton couldn't make a crust out of alchemy so he turned to physics.

He was an alchemist until the day he died, and devoted most of his writing to the subject.

[Ginkgo]

I have to side with Leibniz since Newton frittered away most of his time on alchemy.

Newton couldn't make a crust out of alchemy so he turned to physics.

He was an alchemist until the day he died, and devoted most of his writing to the subject.

Yes, that is correct, but in the interim he managed to put together three volumes of the most important works ever written up until that time.

[uwot]

Well there's alchemy and alchemy. The 'scientific' hypothesis goes back to Anaximander, but was supported by both Plato and Aristotle:
“Our own doctrine is that although there is a matter of the perceptible bodies (a matter out of which the so-called 'elements' come-to-be), it has no separate existence, but is always bound up with a contrariety.” (Aristotle: On generation and corruption.)
The idea is that there is some 'stuff' that the elements, earth, water, air and fire are products of; the 'contrarieties are hot and cold, wet and dry, so fire is hot and dry, air (steam) is hot and wet, water is cold and wet and earth cold and dry. The theory was that everything in the world could be created by manipulating those qualities. To the more mystical alchemists, the 'stuff', quintessence, aether, the philosopher's stone, was given magical properties. Others were more practical.
Leibniz worked for the Duke of Brunswick-Luneberg, amongst others. One of his duties was to test the claims of various alchemists. It was through this work that he met Heinrich Brand, the discoverer of phosphorous, for instance.
"It seems that Brand was working from an old alchemical text that hinted that the philosopher's stone was to be found in the dregs of the human body. He took this literally, tried distilling urine, and produced phosphorous." (Leibniz: G.MacDonald Ross.)
You can, and people did, discover useful things by heating and mixing things, it's just that the underlying causal explanation is wrong. Today scientists are much more reluctant to nail their colours to any metaphysical belief, they are more positivist, pragmatic, instrumentalist, Copenhagenist or any other version of empiricist; thanks in part to the influence of Newton:
“Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power … I have not been able to discover the cause of those properties of gravity from phenomena, and I offer no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy … To us it is enough that gravity does really exist, and acts according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.”
You don't need to know why something works to know that it works. The irony is that Newton's own alchemical beliefs were fruitloopery of the finest order, a fact he was very keen to hide from the royal society.

[mickthinks]

I have to side with Leibniz since Newton frittered away most of his time on alchemy.

Philosophy Now Forum presents: Bob Ad-Hominems-for-Every-Occasion Evenson!

[WanderingLands]

You don't need to know why something works to know that it works. The irony is that Newton's own alchemical beliefs were fruitloopery of the finest order, a fact he was very keen to hide from the royal society.

But then you'd run the risk of committing such fallacies as circular reasoning, which as you have presented in your OP, is exemplified in Newton's reasoning that gravity is caused by the gravitational field. That, and it also stifles the curiosity inside the peoples' minds to make since of life in general. Thus, I'd say that we should take heed of what Leibniz is saying regarding the underlying mechanics of the Universe.

[uwot]

But then you'd run the risk of committing such fallacies as circular reasoning, which as you have presented in your OP, is exemplified in Newton's reasoning that gravity is caused by the gravitational field. That, and it also stifles the curiosity inside the peoples' minds to make since of life in general. Thus, I'd say that we should take heed of what Leibniz is saying regarding the underlying mechanics of the Universe.

I entirely agree, that's why I did philosophy rather than science. I have said several times that I am prepared to entertain any story that isn't contradicted by the observable facts. It could be the case, as Descartes suggested, that all the evidence of my senses is planted there by an evil demon. It could be that everything is ideas in the mind of god, as Berkeley believed. Perhaps the universe is holographic, as David Bohm thought. Maybe Nick Bostrum is right and we live in a simulation. Who knows? Maybe Greylorn Ell has nailed it, or Yon Yalvin, or Gustav Bjornstrand or even, Cor Blimey Riley, you.
Everybody has some version of reality that they hang their epistemological hat on, even hard nosed scientists. Max Planck made the observation that new theories don't really replace old ones, it's just that the people who believe the old theories die. Einstein famously said that god doesn't play dice, despite the overwhelming evidence that (assuming there is a god) yes, he does.
I think I have said before that, in my opinion, it is mental weakness to insist that your personal version is correct. It is a lack of adaptability which in mild cases leads to conservatism, but in people who have it bad leads to intolerance, hatred and violence. So, yes, let's take heed of Leibniz, but tragically, people go to war, because they are too stupid or scared to admit they might be wrong.

[Ginkgo]

You don't need to know why something works to know that it works. The irony is that Newton's own alchemical beliefs were fruitloopery of the finest order, a fact he was very keen to hide from the royal society.

But then you'd run the risk of committing such fallacies as circular reasoning, which as you have presented in your OP, is exemplified in Newton's reasoning that gravity is caused by the gravitational field. That, and it also stifles the curiosity inside the peoples' minds to make since of life in general. Thus, I'd say that we should take heed of what Leibniz is saying regarding the underlying mechanics of the Universe.

That wasn't Newton's reasoning in relation to gravity. Newton didn't know what caused gravity so he avoided postulating a cause because he didn't know how gravity worked. He did know gravity was probably a force of some type that could be explained with mathematical precision. The type of precision that allowed a man to land on the moon, but not precise enough to explain the orbit of Mercury.

It was left up to Einstein to explain the cause of gravity.

[uwot]

It was left up to Einstein to explain the cause of gravity.

I don't often disagree with Ginkgo, but this is the sort of ontological assumption that someone of their philosophical sophistication ought to be alert to. What Einstein did was to postulate that gravity could be expressed as the stretching of 4 dimensional 'space-time', by matter or energy, in a way that is analogous with the stretching of a rubber sheet, by a heavy ball. As it happens, I'm working on a piece on exactly this topic at the moment; here's a bit from an early draft:

The model of warped spacetime that Einstein used to explain the behaviour of objects in gravitational fields is sometimes illustrated by analogy with a rubber sheet. If we imagine a sheet that is stretched completely flat, then a marble placed on it will stay where it is; if the marble is rolled, it will move in a straight line. If, on the other hand, there is a weight on the sheet, the sheet will not be flat, it will dip and a marble placed on the sheet will roll downhill towards the weight. A marble that is rolled across such a sheet, will not roll in a straight line, but will be deflected as it rolls around the rim of the dip created by the weight. If it is going too slow, it will not have the ‘energy’ to climb up the slope and will spiral into the dip created by the weight. Much faster and it will achieve the escape velocity, the amount of energy it needs to climb out of the dip and continue on its way. At a certain speed, the amount of energy is enough to stop the marble falling into the dip, but not enough to climb out, so the marble goes into orbit around the weight.
Any dip in the rubber sheet caused by a weight, can be thought of as a ‘field of force’, no matter how far from the weight, the rubber sheet will slope, however slightly, towards it; a marble placed anywhere on the sheet will start to roll towards the weight. In space, of course, there is no rubber sheet, but the gravitational fields of influence clearly exist and the equations that Einstein devised, based on the idea that mass warps space-time in an analogous way, describes what we can see happening, at least within the solar system, very accurately.
Whether the rubber sheet represents material reality is almost beside the point; it represents mathematical fact rather well. If the points on the sheet are plotted on a graph (turn it upside down for simplicity) the x axis represents field strength and the y and z axes distance; the closer to the weight, the greater the attraction. It doesn’t actually matter what you think causes the force of gravity, a point made by Isaac Newton:

Then it goes into the hypotheses non fingo. If you haven't seen the images of warped spacetime, I imagine it's because you live under a rock, but here's one anyway http://www.bing.com/images/search?q=ein ... edIndex=51

There are versions of Quantum Mechanics that postulate 'gravitons' as the medium of the force, rather than warped spacetime. I particularly like the idea that gravity is essentially refraction, I would, I made it up myself, but I have no idea which, if any, of those hypotheses is correct. For all I know, it's angels pushing stuff together, whatever; the maths works.

[Ginkgo]

I don't often disagree with Ginkgo, but this is the sort of ontological assumption that someone of their philosophical sophistication ought to be alert to. What Einstein did was to postulate that gravity could be expressed as the stretching of 4 dimensional 'space-time', by matter or energy, in a way that is analogous with the stretching of a rubber sheet, by a heavy ball. As it happens, I'm working on a piece on exactly this topic at the moment; here's a bit from an early draft:

Hi uwot

Actually, alertness is not one of my strengths so I didn't think it through. I am actually trying to avoid the implications of my last paragraph.

I guess it depends on the stance we take in relation to scientific realism when it comes to this question. Saying curved space time is a mathematical construct doesn't tell us a lot, other than (as you point out) the mathematics works. In a similar fashion when we talk about gravity at the Planck scale we are only talking about the predictive power of the maths and the model we choose.

Your point is well taken because I don't really want to try and explain my way out of causation in relation to ontology and science. Actually, I don't think anyone wants to tackle that question. Anyway that's my excuse and I am sticking to it.

[Wyman]

It was left up to Einstein to explain the cause of gravity.

I don't often disagree with Ginkgo, but this is the sort of ontological assumption that someone of their philosophical sophistication ought to be alert to. What Einstein did was to postulate that gravity could be expressed as the stretching of 4 dimensional 'space-time', by matter or energy, in a way that is analogous with the stretching of a rubber sheet, by a heavy ball. As it happens, I'm working on a piece on exactly this topic at the moment; here's a bit from an early draft:

The model of warped spacetime that Einstein used to explain the behaviour of objects in gravitational fields is sometimes illustrated by analogy with a rubber sheet. If we imagine a sheet that is stretched completely flat, then a marble placed on it will stay where it is; if the marble is rolled, it will move in a straight line. If, on the other hand, there is a weight on the sheet, the sheet will not be flat, it will dip and a marble placed on the sheet will roll downhill towards the weight. A marble that is rolled across such a sheet, will not roll in a straight line, but will be deflected as it rolls around the rim of the dip created by the weight. If it is going too slow, it will not have the ‘energy’ to climb up the slope and will spiral into the dip created by the weight. Much faster and it will achieve the escape velocity, the amount of energy it needs to climb out of the dip and continue on its way. At a certain speed, the amount of energy is enough to stop the marble falling into the dip, but not enough to climb out, so the marble goes into orbit around the weight.
Any dip in the rubber sheet caused by a weight, can be thought of as a ‘field of force’, no matter how far from the weight, the rubber sheet will slope, however slightly, towards it; a marble placed anywhere on the sheet will start to roll towards the weight. In space, of course, there is no rubber sheet, but the gravitational fields of influence clearly exist and the equations that Einstein devised, based on the idea that mass warps space-time in an analogous way, describes what we can see happening, at least within the solar system, very accurately.
Whether the rubber sheet represents material reality is almost beside the point; it represents mathematical fact rather well. If the points on the sheet are plotted on a graph (turn it upside down for simplicity) the x axis represents field strength and the y and z axes distance; the closer to the weight, the greater the attraction. It doesn’t actually matter what you think causes the force of gravity, a point made by Isaac Newton:

Then it goes into the hypotheses non fingo. If you haven't seen the images of warped spacetime, I imagine it's because you live under a rock, but here's one anyway http://www.bing.com/images/search?q=ein ... edIndex=51

There are versions of Quantum Mechanics that postulate 'gravitons' as the medium of the force, rather than warped spacetime. I particularly like the idea that gravity is essentially refraction, I would, I made it up myself, but I have no idea which, if any, of those hypotheses is correct. For all I know, it's angels pushing stuff together, whatever; the maths works.

What is it called when you are thinking of a subject, or learn something new, and it appears before you several times thereafter in a cluster - something like deja vu. And like deja vu, you think it is just coincidence or the fact that in the past you just never noticed it or weren't focused on it, but there is a superstitious 'feel' to it. Anyway...

I watched a couple Feynman lecture videos on the relation of math to physics and also on models of gravity. I was already familiar with Einstein's general relativity (as a non-physicist; but like uwot said, I don't live under a rock). I was playing with my kids recently on our trampoline and tried explaining gravity to a seven year old while sitting in the middle and rolling a ball around. I was reading Wittgenstein's Investigations and working on the relationship between rule following and meaning, which is favorite subject of mine (theory of knowledge) especially as it relates to mathematics. Anyway again...

Then I read this thread. It seems that models, or interpretations of rules - and I call mathematical laws of physics 'rules' - are an important, but neglected, subject matter of philosophy, mathematics, logic and physics. Feynman, in the lecture I watched, was(among other things)pointing out the psychological relationship between models and rules. Whereas the spacetime and gravitron models both employ mathematics and reach the exact same results, the models stimulate the mind in different ways. For instance, would Einstein have developed the mathematical rules he did if he had not reconceptualized gravity - i.e. developed a new model? Or did newly discovered rules lead him to the model? These questions involve the role of models in the development of knowledge - epistemology.

The next subject, that uwot and gingko are touching on, is ontology. A model assigns mathematical terms meaning. The terms refer to elements in the model and the model is supposed to represent reality. It sounds easy, but there are tremendous problems when one tries to explain the relationship 1) between the terms of a rule and the model and 2) between the model and reality. Mathematics is concerned with 1) and largely ignores 2).

Wittgenstein is clearly trying to hash out both 1) and 2) in the Tractatus and the Investigations.

So uwot - I agree with everything you have said and I hope you read the above in that light. However, I disagree with the 'whatever; the maths works.' I disagree in the sense that the only reason for philosophy (setting aside ethics, perhaps) lies in the notion that it is important to have an answer as to why the math works. Philosophy is concerned with the relationship between rules, models and reality in a way that physics is not.

The intersection of rule, model and reality (knowledge) that seems to happen again and again in mathematics and physics is still an unsolved mystery after several thousand years of science and philosophy. It (knowledge, that same busy intersection) also seems to involve the intersection of ontology and epistemology, as well as psychology and physics. Isn't such an important intersection a worthwhile subject of study in it's own right?

[WanderingLands]

I entirely agree, that's why I did philosophy rather than science. I have said several times that I am prepared to entertain any story that isn't contradicted by the observable facts. It could be the case, as Descartes suggested, that all the evidence of my senses is planted there by an evil demon. It could be that everything is ideas in the mind of god, as Berkeley believed. Perhaps the universe is holographic, as David Bohm thought. Maybe Nick Bostrum is right and we live in a simulation. Who knows? Maybe Greylorn Ell has nailed it, or Yon Yalvin, or Gustav Bjornstrand or even, Cor Blimey Riley, you.
Everybody has some version of reality that they hang their epistemological hat on, even hard nosed scientists. Max Planck made the observation that new theories don't really replace old ones, it's just that the people who believe the old theories die. Einstein famously said that god doesn't play dice, despite the overwhelming evidence that (assuming there is a god) yes, he does.
I think I have said before that, in my opinion, it is mental weakness to insist that your personal version is correct. It is a lack of adaptability which in mild cases leads to conservatism, but in people who have it bad leads to intolerance, hatred and violence. So, yes, let's take heed of Leibniz, but tragically, people go to war, because they are too stupid or scared to admit they might be wrong.

I will agree that people have their own versions of what life is, and I'm certainly am not an exception to it, and I do agree that conflict is caused by imposing beliefs (though I am still not with you on conservatism). Still - doesn't hurt to know things, although it's not good to excessively obsess over it.

[Ginkgo]

Then I read this thread. It seems that models, or interpretations of rules - and I call mathematical laws of physics 'rules' - are an important, but neglected, subject matter of philosophy, mathematics, logic and physics. Feynman, in the lecture I watched, was(among other things)pointing out the psychological relationship between models and rules. Whereas the spacetime and gravitron models both employ mathematics and reach the exact same results, the models stimulate the mind in different ways. For instance, would Einstein have developed the mathematical rules he did if he had not reconceptualized gravity - i.e. developed a new model? Or did newly discovered rules lead him to the model? These questions involve the role of models in the development of knowledge - epistemology.

I could be wrong, but I think Einstein was pondering the speed of light when he suddenly realized that Newton was wrong in relation to gravity. I think he imagined a solar system that was suddenly hit by the disappearance of the sun. If Newton was correct then such an event would cause all the planets to immediately fly off into the cosmos. Conversely,Einstein realized that if the universe has a speed limit (speed of light) then this would not happen. well, not for about 8 minutes as far as our planet is concerned.

The next subject, that uwot and gingko are touching on, is ontology. A model assigns mathematical terms meaning. The terms refer to elements in the model and the model is supposed to represent reality. It sounds easy, but there are tremendous problems when one tries to explain the relationship 1) between the terms of a rule and the model and 2) between the model and reality. Mathematics is concerned with 1) and largely ignores 2).

Wittgenstein is clearly trying to hash out both 1) and 2) in the Tractatus and the Investigations.

Absolutely. I couldn't agree more.

What makes people come up with this type of stuff? For example, I just recently went back to Roger Penrose's first papers in relation to spin networks. This works date back to the early 70s. Nothing better to do with my time I guess.

It seems to me that Penrose was having a shot in the dark. He developed a very simplistic model to explain a very complex system. That is to say, simple compared to how complex such a system might be if it actually existed..

So we have a model of the universe on paper. A universe that may not resemble his model in any shape, way or form. The rest is pretty much history because many people have continued to develop and improve Penrose's theory in a variety of areas, not least of all quantum gravity theorists. Now we have people such as Smolin telling us that it just may be possible to devise a scientific experiment to show in an indirect way the existence of spin networks.

So uwot - I agree with everything you have said and I hope you read the above in that light. However, I disagree with the 'whatever; the maths works.' I disagree in the sense that the only reason for philosophy (setting aside ethics, perhaps) lies in the notion that it is important to have an answer as to why the math works. Philosophy is concerned with the relationship between rules, models and reality in a way that physics is not.

The intersection of rule, model and reality (knowledge) that seems to happen again and again in mathematics and physics is still an unsolved mystery after several thousand years of science and philosophy. It (knowledge, that same busy intersection) also seems to involve the intersection of ontology and epistemology, as well as psychology and physics. Isn't such an important intersection a worthwhile subject of study in it's own right?

Another very interesting comment Wyman.

You may well be correct, then again the universe may well be at its most fundamental level geometry and mathematics. If so, then we just have to works towards discovering it by putting the geometry together. Perhaps the maths is the reality, I am starting to think so.

Thanks for the posts guys.