Downward Causation: Useful or Misguided Idea?

[Speakpigeon]

Except you will not get to infinity, you'll get to internal and external equilibrium pretty damn quickly.

Maybe. Maybe not.

The notion of pressure requires in practice a really, really huge number of molecules in the considered gas. Pressure is regarded as the average force of the impact of individual gas molecules hitting the considered surface. When you get down to one molecule, it's clear it's meaningless to talk of 'average' and therefore of pressure.

So, we're back to a thought experiment, where, unlike in the real physical world, pressure could be halved and halved again without limit. In this case, you achieve basically the same result as Banach–Tarski, except you accept the additional and unnecessary constraint of going through a pseudo-physical procedure. Unnecessary from the point of view the Banach–Tarski theorem, but useful I think to help us with our intuition. Still, Banach–Tarski doesn't add anything fundamental to our intuition about infinity. It's just a formally rigorous way to make the point, unlike our intuitions.

I even think you procedure is preferable. It suggests an algorithm to move from one set of balloons to the next. It could be made rigorous very easily. And the result would, again, be more intuitively convincing because the balloons of the successive sets are in effect identical from one set to the next.

Still, I take our basic intuition about infinities to be good enough. Like Banach–Tarski, the balloons may help us understand the quasi-physical quality of the paradox.
EB

 

[Speakpigeon]

To my limited brain (I will never understand the BT Paradox fully for example) maths (and probably logic) can 'do' certain things which appear to be intuitively 'un-doable' in the real world because they use concepts which we cannot intuitively grasp, or perhaps even grasp in any way and which may in fact be abstract (existing in thought only). Perhaps the best example, and the one that causes the most paradoxes (and is involved, I think, in the BT Paradox) is the very annoying example of infinity. So, a simpler illustration of a related paradox, than the BT one, I think, would be that if we cut an infinitely long string in half, we have two infinitely long strings. In fact, we could cut the string in half again, and half again, and in theory 'make' a very large number (an infinite number in fact) of infinitely long strings from just one.

You can cut an infinitely long string in half only once.

You start with a string going on to the infinite in both directions. Cutting anywhere, you cut it in half. Then you're left with half-line strings, and then there's nowhere to cut which would cut the two bits of string in two halves (identical halves). Instead, you cut to get one infinite bit (another half-line string) but also one finite bit of string. So, you always end up with two infinite bits. Only the finite bits get to increase in number. In effect, your experiment shows infinity doesn't increase through cutting.

So, it's also not quite the same result as with the balloons, since each balloons is an infinite set of points, so each time you double the number of balloons, you double the number of infinities.

Still, you would achieve the same result with the string as with the ballons if you take it to be not only an infinitely long piece of string, but also a continuous medium, possessing therefore an infinite number of points in each finitely long bit of string.
EB

 

[Speakpigeon]

Rather than testing each other’s psychic powers, how about everyone pauses a moment and reviews how their particular intuitions about what a concept fits in with the various definitions in the literature.

Me, it's something like that:

2. an idea of something formed by mentally combining all its characteristics or particulars; a construct.

I take concepts to be a mix of the analytical and the intuitive. Basically, you can create a concept by articulating two or more intuitive notions. You can do that from scratch, by combining two existing intuitive notions into some novel concept. You can also do the same to make up a concept as a more abstract model for an intuitive notion, in which case you're effectively "analysing" this last intuitive notion into an articulation of other, more fundamental or primitive, intuitive notions.

There will always be intuitive notions left within the concept, but you can do it again and again without any theoretical limit. The limit comes from our ability to intuit more fondamental intuitive notions. I don't think we could analyse a point as an articulation of more fondamental notions. Defining a point as an intersection of lines won't do here because lines are less fundamental than points.

Still, I think that's really the gist of what Euclide did and all that mathematicians and theoreticians do.
EB

 

[Subsymbolic]

The notion of pressure requires in practice a really, really huge number of molecules in the considered gas. Pressure is regarded as the average force of the impact of individual gas molecules hitting the considered surface. When you get down to one molecule, it's clear it's meaningless to talk of 'average' and therefore of pressure.

Ruby's original example was this:

Or, try this (I read it somewhere in relation to the BT Paradox). Take a balloon and fill it up with gas. So you have a balloon of a certain volume. Now decant the gas into two balloons, and you will get two balloons, each with half the volume of the original. But now reduce the surrounding air pressure by half and you will get two balloons each with the same volume as the original. And keep going. Decant again into 4 balloons and reduce the air density by half again. Voila, 4 balloons of the same volume as the first one. And so on, to infinity.

My response to this:

Except you will not get to infinity, you'll get to internal and external equilibrium pretty damn quickly.

Is perfectly correct and doesn't invoke reduction to a single molecule, merely reduction to equilibrium. This experiment would be perfectly doable in the lab, and relies on the fixed porosity of the physical elements. BT relies on the uncountable porosity of the elements and the axiom of choice. Not simply infinity.

So, we're back to a thought experiment, where, unlike in the real physical world, pressure could be halved and halved again without limit. In this case, you achieve basically the same result as Banach–Tarski, except you accept the additional and unnecessary constraint of going through a pseudo-physical procedure. Unnecessary from the point of view the Banach–Tarski theorem, but useful I think to help us with our intuition. Still, Banach–Tarski doesn't add anything fundamental to our intuition about infinity. It's just a formally rigorous way to make the point, unlike our intuitions.

While I'm unsure about how you get there, I assume you are accepting the point that there is something that can be done in Platonic spaces that supervene on the physical that cannot be done anywhere else, thus establishing that there are two determinisms: mathematical/logical and physical.

I even think you procedure is preferable. It suggests an algorithm to move from one set of balloons to the next. It could be made rigorous very easily. And the result would, again, be more intuitively convincing because the balloons of the successive sets are in effect identical from one set to the next.

Show me the rigorous proof that simply relies on an infinite set and I'll be convinced, until then...

Still, I take our basic intuition about infinities to be good enough. Like Banach–Tarski, the balloons may help us understand the quasi-physical quality of the paradox.
EB

I'm unsure that Ruby and you share a basic intuition about infinities: you think a string that is infinitely long can be cut in half once, he thinks an infinite number. I think I agree with you, as simply cutting gives a bounded end. However, I think he just worded an accurate intuition in an unfortunate way.

 

[Subsymbolic]

You can cut an infinitely long string in half only once.

You start with a string going on to the infinite in both directions. Cutting anywhere, you cut it in half. Then you're left with half-line strings, and then there's nowhere to cut which would cut the two bits of string in two halves (identical halves). Instead, you cut to get one infinite bit (another half-line string) but also one finite bit of string. So, you always end up with two infinite bits. Only the finite bits get to increase in number. In effect, your experiment shows infinity doesn't increase through cutting.

Stated as it is, no, but restarting it so as not to give a bounded end: 'you remove an infinite length of string from the middle of your infinite length of string' and all is fine. If it's real string you can tie the bits either end of the infinite piece of string you removed together, if it's imaginary string imagine a knot...

So, it's also not quite the same result as with the balloons, since each balloons is an infinite set of points, so each time you double the number of balloons, you double the number of infinities.

I'm not sure that this is the case. B-T relies not on multiplying the points, but in the uncountable porosity between them. It's a different idea.

Still, you would achieve the same result with the string as with the ballons if you take it to be not only an infinitely long piece of string, but also a continuous medium, possessing therefore an infinite number of points in each finitely long bit of string.
EB

The only point that is relevant to the thread is whether there are things you can do in maths or logic that you can't do anywhere else. If so then downward causation is easy to demonstrate. I think if we also want a thread in which we can all give ourselves headaches trying to get to grips with the implications of infinity and the axiom of choice, then that would be easy to arrange.

 

[Speakpigeon]

While I'm unsure about how you get there, I assume you are accepting the point that there is something that can be done in Platonic spaces that supervene on the physical that cannot be done anywhere else, thus establishing that there are two determinisms: mathematical/logical and physical.

No, I don't quite share your view as to supervening Platonic spaces.

I guess I'll have to get there somehow but not quite yet.

I even think you procedure is preferable. It suggests an algorithm to move from one set of balloons to the next. It could be made rigorous very easily. And the result would, again, be more intuitively convincing because the balloons of the successive sets are in effect identical from one set to the next.

Show me the rigorous proof that simply relies on an infinite set and I'll be convinced, until then...

I won't, promise.

Still, I take our basic intuition about infinities to be good enough. Like Banach–Tarski, the balloons may help us understand the quasi-physical quality of the paradox.
EB

I'm unsure that Ruby and you share a basic intuition about infinities: you think a string that is infinitely long can be cut in half once, he thinks an infinite number. I think I agree with you, as simply cutting gives a bounded end. However, I think he just worded an accurate intuition in an unfortunate way.

Yes, and so you do accept that Ruby and I share the same basic intuition on infinity (as indeed most people, I think). It's true infinity got people to argue a lot throughout history so they probably not quite shared the same intuitions but I would expect myself that there would be a large consensus with still a possibly vociferous and disgruntled minority having "original" views.
EB

 

[Speakpigeon]

My response to this:

Except you will not get to infinity, you'll get to internal and external equilibrium pretty damn quickly.

Is perfectly correct and doesn't invoke reduction to a single molecule, merely reduction to equilibrium.

Reduction to equilibrium? Sorry, I don't know what that means. Feel free to explain.

Rather, as I see it, at one point, there won't be enough gas molecules to go around the balloons so the balloons will just look deflated and pitiful, as if just full of vacuum within an outside vacuum.Think of the downcast American flag on the Moon in the Seventies.
EB

 

[Speakpigeon]

Stated as it is, no, but restarting it so as not to give a bounded end: 'you remove an infinite length of string from the middle of your infinite length of string' and all is fine.

Hold on! I have no idea how you even conceive of how to do that. No algorithm there, I think.
EB

 

[Subsymbolic]

No, I don't quite share your view as to supervening Platonic spaces.

I guess I'll have to get there somehow but not quite yet.

Show me the rigorous proof that simply relies on an infinite set and I'll be convinced, until then...

I won't, promise.

Still, I take our basic intuition about infinities to be good enough. Like Banach–Tarski, the balloons may help us understand the quasi-physical quality of the paradox.
EB

I'm unsure that Ruby and you share a basic intuition about infinities: you think a string that is infinitely long can be cut in half once, he thinks an infinite number. I think I agree with you, as simply cutting gives a bounded end. However, I think he just worded an accurate intuition in an unfortunate way.

Yes, and so you do accept that Ruby and I share the same basic intuition on infinity (as indeed most people, I think). It's true infinity got people to argue a lot throughout history so they probably not quite shared the same intuitions but I would expect myself that there would be a large consensus with still a possibly vociferous and disgruntled minority having "original" views.
EB

I don't know, I'll wait and see what he thinks.

I don't think intuitions have any place when talking about the varieties of infinities. Rigorous definition, sure, but intuitions?

Either way, I was using it to demonstrate an example of downward causation, not to get into a parallel discussion on the nature of infinities. If there's a counter argument to the B-T argument, I'm all ears, but beyond that, three non specialists discussing a particularly specific area in maths is not my idea of fun.

 

[ruby sparks]

While I'm unsure about how you get there, I assume you are accepting the point that there is something that can be done in Platonic spaces that supervene on the physical that cannot be done anywhere else, thus establishing that there are two determinisms: mathematical/logical and physical.

But wouldn't that assume the answer to the OP is yes? It would seem to be one thing to say that things can be done in maths which can't be done in the real world, but it seems to be going a step further to say that the former can determine the latter. Or perhaps you didn't mean that. Perhaps you would say that the two don't interact? In which case the answer to the OP would be no.

 

[Subsymbolic]

My response to this:

Except you will not get to infinity, you'll get to internal and external equilibrium pretty damn quickly.

Is perfectly correct and doesn't invoke reduction to a single molecule, merely reduction to equilibrium.

Reduction to equilibrium? Sorry, I don't know what that means. Feel free to explain.

Rather, as I see it, at one point, there won't be enough gas molecules to go around the balloons so the balloons will just look deflated and pitiful, as if just full of vacuum within an outside vacuum.Think of the downcast American flag on the Moon in the Seventies.
EB

Yep, that's what equilibrium looks like: the same pressure on the in and outside. By this process, a pressure tending towards zero on both sides.

 

[Speakpigeon]

So, it's also not quite the same result as with the balloons, since each balloons is an infinite set of points, so each time you double the number of balloons, you double the number of infinities.

I'm not sure that this is the case.

Well, I am, as long as we're talking about "ideal" balloons, possessing an infinity of surface points, which are not supposed to exist in the physical world.

B-T relies not on multiplying the points, but in the uncountable porosity between them. It's a different idea.

Sure, it is, but I was comparing balloons to strings, not balloons to Banach–Tarski.

Banach–Tarski doesn't create new points as seems the case with the balloons. It just rearranges them. It's in fact more like Ruby's string example except this one doesn't work.
EB

Ecological note - I can hear right now an actual woodpecker busy right outside my open window pecking at some bark somewhere. Can't see it, though.

First time I hear one inside Paris! As far as I know, until now they would only peck at trees inside a large park just outside Paris (Bois de Vincennes and Bois de Boulogne).

And there were not so many of them only a few years back.

Ah! Climate change, I think.

We're doomed.
EB

 

[ruby sparks]

At this point, I'm sitting on the 'no' side of an answer to the OP. Iow, no, the mental has no causal effect on the physical and no, mathematical objects and processes do not affect reality. Anyone on the 'yes' side?

Whether upwards, downwards or sideways is the correct way of thinking about it I'm not sure, but I'm fairly happy with thinking of mental (and mathematical) as 'higher', in terms of supervenience. And I'm thinking that mathematical is a subtype of mental, in that it's essentially mental. There are no numbers in the real world, for example.

 

[untermensche]

What is the objective model of consciousness that we use to make comments about it's abilities?

That is how scientific conclusions are made.

With models.

 

[Subsymbolic]

While I'm unsure about how you get there, I assume you are accepting the point that there is something that can be done in Platonic spaces that supervene on the physical that cannot be done anywhere else, thus establishing that there are two determinisms: mathematical/logical and physical.

But wouldn't that assume the answer to the OP is yes? It would seem to be one thing to say that things can be done in maths which can't be done in the real world, but it seems to be going a step further to say that the former can determine the latter. Or perhaps you didn't mean that. Perhaps you would say that the two don't interact? In which case the answer to the OP would be no.

I don't know, it seems pretty obvious to me that the result of a calculation done in maths (that can't be done anywhere else) can and will inform my thinking and thus my action, in the real world. I've used the example of being chased by Laplace's demon several times to make that point for B-T. So yes, I'm quite sure that the two do interact and that it is a prime facie example of non mysterious downward causation in which mental events (my calculation of an example of B-T in my head) being able to cause physical events, like behaviour.

 

[Subsymbolic]

Well, I am, as long as we're talking about "ideal" balloons, possessing an infinity of surface points, which are not supposed to exist in the physical world.

B-T relies not on multiplying the points, but in the uncountable porosity between them. It's a different idea.

Sure, it is, but I was comparing balloons to strings, not balloons to Banach–Tarski.

Banach–Tarski doesn't create new points as seems the case with the balloons. It just rearranges them. It's in fact more like Ruby's string example except this one doesn't work.
EB

Ecological note - I can hear right now an actual woodpecker busy right outside my open window pecking at some bark somewhere. Can't see it, though.

First time I hear one inside Paris! As far as I know, until now they would only peck at trees inside a large park just outside Paris (Bois de Vincennes and Bois de Boulogne).

And there were not so many of them only a few years back.

Ah! Climate change, I think.

We're doomed.
EB

The way things are going, we are certainly all doomed. As for the woodpecker, while it may be climate change, I suspect it's also the EU's very careful attitude to toxic chemicals in farming that has allowed bird populations to begin to revive. I was told only the other week that the 2013 regulations on neonicotinoids as pesticides due to the worries about bees has really helped songbird populations. This, of course, was in the context of our idiot politicians taking back control of their ability to inadvertently kill the birds and the bees without European interference.

Don't say anything. Just don't.

As for the balloons, I was talking about physical ones, but, talking about the other sort, I think my point is that, just as in B-T, you could take advantage of uncountable porosity and the axiom of choice rather that defining the balloons as having an infinite number of points.

 

[Subsymbolic]

At this point, I'm sitting on the 'no' side of an answer to the OP. Iow, no, the mental has no causal effect on the physical and no, mathematical objects and processes do not affect reality. Anyone on the 'yes' side?

Whether upwards, downwards or sideways is the correct way of thinking about it I'm not sure, but I'm fairly happy with thinking of mental (and mathematical) as 'higher', in terms of supervenience. And I'm thinking that mathematical is a subtype of mental, in that it's essentially mental. There are no numbers in the real world, for example.

Face it Ruby, anything that is symbolic, that is, becomes meaningful through intersubjective consensus, doesn't exist in the world in the sense you mean it. People often confuse something having intersubjective consensus with something that is objective. Numbers, Beliefs, you know...

Either way, I'll do it again:

mathematical objects and processes do not affect reality

I'm being chased by Laplace's demon. I decide that I'll calculate how many balls I can generate through a certain well known mathematical process following logical laws that I have discovered. If I can make one ball, I'll turn right, If I can make two I'll turn left. What will I do and why? What will the Demon do and why?

 

[Speakpigeon]

Where's DBT when we need him?!

That's at least treasonous felony or something.
EB

 

[Speakpigeon]

I suspect it's also the EU's very careful attitude to toxic chemicals in farming that has allowed bird populations to begin to revive.

Yep, that's what I think. But we're apparently also loosing some bird species due to lack of those little beasties they like to feed on.

Don't say anything. Just don't.

EB

 

[DBT]

How many times do you need to be told like a child that your logic sucks?

Saying the brain somehow and in some unknown manner creates consciousness does not tell us what consciousness can do to the brain.

You keep repeating this absolute nonsense I suppose because your mind is incapable of learning anymore.

Consciousness is a form of brain activity. Again, consciousness does whatever the brain is doing, nothing more, nothing less. That there are multiple feedback loops happening within the brain while conscious activity is taking place does not mean that consciousness has autonomy....as you appear to suggest.

You have no idea what consciousness is.

It is a completely unexplained phenomena.

Nothing is known about it objectively.

You have no grounds to make claims about what it can and cannot do.

There is reflexive brain controlled respiration and there is the ability to take a deep breath at will.

Rubbish. There is enough evidence to show that what effects the brain in turn effects its ability to generate consciousness, alcohol, drugs, physical trauma, chemical imbalance, etc, etc, etc.

All this has been pointed out to you numerous times, including studies, references and quotes. You can't face the fact that conscious brain activity equals conscious experience. The existence of multiple feed back loops and information input from multiple regions of the brain doesn't change the fact of brain agency, brain state and condition.