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The boundaries of things
Posted: 24 June 2007 11:27 AM   [ Ignore ]
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After listening to a podcast where the hosts interviewed a physicist on causation, I was inspired to talk about a certain point made in the show with those who are interested.  To listen to the whole podcast, or to fast foward to the point where I have transcribed click here

The whole show is pretty good, but it gets very interesting at at the 26:00 mark, and it is from that point in the show that I transcribed for the sake of discussion.

Here it is:


Kevin:  All things have boundaries.  Now do you believe that those boundaries are created by consciousness?

Richard Healey:  That’s a tricky one.

Kevin:  For example, generally speaking we say a tree ends where the bark is, and with the outer layer of cells on the leaf, for example.  But we don’t necessarily have to draw the boundaries there, we could draw the boundaries somewhere else.

Richard:  Yes.

Kevin:  It’s the same with all things, isn’t it.

Richard:  Yes and no – there are better places of drawing the boundaries and worse.  There’s no correct way of drawing the boundary to a tree, and indeed if you press hard enough there’s no correct way of drawing the boundary to all kinds of objects, like you and me, or an apple, or an automobile.  They don’t have well-defined boundaries.  And yet there are very bad decisions as to where to draw the boundaries and quite acceptable ones.  I take this to be a typical case of vagueness: all terms, all the ways we divide things up using our language and thought, are to a certain extent vague, and yet the vagueness is not such as to permit arbitrary delineations of boundaries around objects.  But let me just pursue this a bit further, because I think when you look at what science says about this, it’ll get much more interesting; in particular what quantum mechanics says about the existence of boundaries.  Typically, the picture of a supposedly solid object that would emerge from quantum theory would be one which described that object in a rather abstract way, in terms of a wavefunction or, actually, a density matrix; and if you asked, where does the object finish, where is its spatial boundary, there will be no unique answer forthcoming from that quantum mechanical representation of the object.  Indeed, there would be a nonzero probability of finding bits of that object arbitrarily far away from where you think the object is.  Of course those probabilities would be minute, but there would be no way in the theory to draw a well-defined boundary.  So quantum mechanics, it would appear, would permit one to draw boundaries outside of the range of acceptable boundary choices in our ordinary language.  My car might have a boundary which extends way beyond my garage – even when my car is supposedly in my garage.

Kevin:  The boundaries change, don’t they, depending on what’s practical at the time.  For example, when you’re driving along a freeway at 120 km/h, you might want to extend the boundary of your car quite a bit further than if you’re only travelling at 10 km/h on your local street.  In your mind, the car extends further.

David:  It depends on how you conceive of the car.  If we conceiving of it in terms of heat, or electromagnetic radiation, then we’d have a different conception of the boundaries of the car.

Richard:  But they wouldn’t typically be useful conceptions for your auto mechanic.

David:  No, but if we’re thinking of it in terms of a heat object, for whatever purpose, then maybe we would.

Kevin:  I think these are the same problems that we’re finding on the quantum level: when we use different instruments to measure things – of course we’re using different instruments because we have different purposes – then different things appear to us.  Because we have a different purpose.  So to me there’s a consistency there.  I mean, it’s said a lot that the quantum realm is non-intuitive.  But that doesn’t sound right to me, because things are going to change if you have different purposes, and if you measure them in a different way.  That seems altogether intuitive to me.

Richard:  I suppose the way of reconciling the claim with what you just said is that most people don’t have purposes, and are not familiar with purposes, that would make it relevant to think of things that way.

Kevin:  That’s a very good point, because if you’re not fully conscious of what your purpose is, then not very much will be intuitive.  Everything’s going to seem mysterious, because you’re not going to understand what you’re doing.

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Posted: 24 June 2007 11:30 AM   [ Ignore ]   [ # 1 ]
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Richard Healey: And, if you ask well, where does the object finish? Where is it’s spatial boundary? 

There would be no unique answer forth coming from that quantum mechanical representation of the object, and indeed there would be non-zero probability of finding bits of that object arbitrarily far away from where you think the object is.

What does he mean by ‘there would be non-zero probability of finding bits of that object arbitrarily far away from where you think the object is? 

And the part where he says: of finding bits of that object arbitrarily far away from where you think the object is - is he saying: “of finding bits of that object arbitrarily far away from where you think the object ‘ends’?

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Posted: 24 June 2007 11:57 AM   [ Ignore ]   [ # 2 ]
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Well, I’m no physicist (!), but if an object’s position is described as a probability distribution for the position of its constituent atoms, the distribution might extend much farther than the apparent boundaries of the object at the normal scale at which we live and view it. So there is a possibility (tiny, as he says) of some atom that in some sense is part of the object actually having a position far beyond what we would perceive to be the boundaries of the object.

But as usual, I’m not sure the descriptions appropriate at a quantum level have any meaning at our normal scale of existence. Sure, apparently solid objects are composed of much mofre empty space than actual matter, but a baseball will still break your nose if it hits you hard enough, so the practical utility of such a description is arguable.

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Posted: 24 June 2007 01:35 PM   [ Ignore ]   [ # 3 ]
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The problem here comes partly from the general Shroedinger equation and it’s application and partly from wave-paricle duality.  In the first, we can describe something that doesn’t really exist called an orbital using the wave function (E*Phi=[h(cross)divided by 2*mass]*the sum of the partial differentials of phi(r)with respect to the components of r along the axes x,y and z, all multiplied by the hamiltonian) added to potential energy distribution function.  This wavefuntion (phi) has a real part and an imaginary part (phi*) which is displaced from (out of phase with the real part) ie. it is complex.  If the amplitude of phi(particle) is phi(x) at some point x, then the probability of finding the particle within the lienar region x+dx is a squared funciton (comprised of the real part times the imaginary part) over the range (dx) ie. probability = (Phi*)*Phi.dx.  This is asymptotic, meaning there is a finite but non-zero probability of finding the particle right over the other side of the universe! When we talk of “integrating over all space”, in fact we tend to limit it to sensible ideas of the volume in which the probability density values are reasonably significant.  The other point is Max Born’s clarification of wave particle duality, whereby he explains that a particle (be it electron or photon) can be considered to act as a carrier wave (i.e a component whose position is distributed) and a carried particle whose postion can be anywhere within that distribution at any one time.  Ergo, an electron that is part of an atom of your car could be right over the other side of the universe right now, but it almost certainly isn’t so try not to lose sleep over it.  I hope I have managed to give non-physicists a reasonable gist without being overcomplicated.


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Posted: 24 June 2007 01:50 PM   [ Ignore ]   [ # 4 ]
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Incidentally, an ancient philosopher (I forget which one) once said that all matter was composed of the boundary and the infinite.  This is annoyingly difficult to refute, but utterly unhelpful.

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Posted: 24 June 2007 01:59 PM   [ Ignore ]   [ # 5 ]
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Well, vagueness is an eternal issue with anything that is not pure mathematics. And all boundaries in the physical world are vague.

The separate question as to whether human concepts “carve nature at its joints” (in what I believe is Plato’s words) is a separate one, but equally interesting. It basically boils down to the metaphysical question as to whether there are so-called “natural kinds”, or whether all “kinds” are human created.

My own feeling (FWIW) is that there are such things as “natural kinds”, and that part of the job of the sciences is to discover what they are. Epistemologically speaking, we should take it that the natural kinds are those kinds that are used in the natural sciences to describe nature.

So, for example, there is no natural kind “jade”, since scientists discovered that the human concept “jade” actually mapped onto two entirely distinct geological types, “jadeite” and “nephrite”. Jadeite and nephrite are natural kinds. “Jade” is simply a human fiction, cobbled together by their artificial conjoining.

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Posted: 25 June 2007 11:28 AM   [ Ignore ]   [ # 6 ]
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Boundaries, even in physics, and especially when they are vague, are not part of the material world.  You have to remember that when we talk about “a tree” we are already talking about a fiction, an object of thought that describes some part of the world for our convenience.  Likewise, when we use the concepts of “jadeite” or “nephrite”, these are human fictions just as much as “jade” is.

Concepts, like “boundary”, and boundaries we use, are tools.  The concept of “boundary” that we use to limit physical bodies in daily experience fails when it is misapplied, as at the atomic scale.  Atoms, as we have come to describe them most usefully for our purposes, do not have boundaries, and so things made up of atoms cannot have boundaries that obtain at the atomic scale.  This is not because of any incompatibility or contradiction in reality, only because of incompatibilities in our models of reality.

Let’s say that you punch someone in the face.  Your defense can be “I never touched him”, and you could prove beyond a shadow of a doubt that no atom that made up part of your body actually made contact with any atom that made up part of his body.  You would still go to jail, because the law uses a different model for reality than physics.

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Posted: 26 June 2007 06:06 AM   [ Ignore ]   [ # 7 ]
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dougsmith - 24 June 2007 01:59 PM

So, for example, there is no natural kind “jade”, since scientists discovered that the human concept “jade” actually mapped onto two entirely distinct geological types, “jadeite” and “nephrite”. Jadeite and nephrite are natural kinds. “Jade” is simply a human fiction, cobbled together by their artificial conjoining.

But even in science aren’t the boundaries between kinds just lines drawn by what scientists agree to which each thing is similar to others in order to group them? To me that whole point was brought well home in the Pluto/planet debate. What distinct criteria we choose determines which rock is or is not a planet. As to jade I have a large collection, they are all very distinct pieces that only have similarities to the others where they can be grouped as jade. Certainly one can expect that a geologist will have a more sophisticated manner of differentiating, but wont that still be at a point (I assume chemically) either before or after things look very different?

My point being that we decide, but there is no evidence that either the jade or pluto either cares or agrees.

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Posted: 26 June 2007 09:25 AM   [ Ignore ]   [ # 8 ]
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Strictly speaking, the natural kinds used in the sciences are any kinds that are part of a natural law. If there are physical laws, there must be natural kinds which behave in accordance with those laws. Otherwise we would have no reason to believe that any regularities seen in the past would persist into the future. (Since object identity through time would be fictional).

Listening to Richard Feynman’s lectures, he certainly did believe that atoms existed, that light was a particle (a photon, with a boundary) that behaved rather strangely, but there you are. There is nothing in physics that would discount the existence of more-or-less vaguely bounded conditions for objects.

As for “touching”, the everyday concept of touching is what we use when we discuss “punching in the face”. And that concept clearly does not require the actual physical contact of the constituent atoms in fist and face. So by any clear standard of “touching”, a punch is a touch. All the rest is just sophistry.

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Posted: 27 June 2007 02:09 PM   [ Ignore ]   [ # 9 ]
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I’d hate to be the guy that tried to mug you!  A simple punch grab and twist manoeuvre would turn into a five hour existential debate.

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Posted: 28 June 2007 04:07 PM   [ Ignore ]   [ # 10 ]
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No, it isn’t sophistry at all.  It is two different models being used for two different purposes.  If you wanted to use the everyday version of “touching” in quantum physics, you would produce as nonsensical a result as if you use quantum mechanical concepts in describing events in court.

Feynman, like all good scientists, knew full well that his descriptions were not reality.  The models are based in reality, because they have to accord with observations of reality, but they are not reality itself, nor are they perfectly accurate representations suitable for all situations.

Perhaps we can think of it as something like a Rorschach test.  You see the blot because the blot and the paper it is on reflect light in different amounts.  Your eyes and brain are such that you perceive this difference as a shape.  You can then make of the shape what you will.  The same thing applies to seemingly less abstract bits of the material world - our minds isolate some perceptions, and objectify them, i.e., make objects of specific parts of the whole.  You may want to go with Plato and assume that when you isolate “a rock” from the rest of the universe that you are tuning into some eternal Form of “rockness”, but that is about as unscientific an attitude that you can take.  That is not to say, as some people mistakenly object, that the object does not behave as an object, or as the object that I conceive it as, only that I am the source of the reality of the object, as opposed to the reality of what it is I have objectified, which is independent of me or my conceptions.  For example, I may see a bat in an ink blot, but I am the one who has made that bat real as a concept - in the same way, however, I have made that ink blot real as an object to be interpreted as another object; what is that ink blot to a blind person?  It is nothing until someone who can objectify it does objectify it and thereby come up with a description of an object that can be communicated by means other than the visual.

There is no reason to believe that regularities observed in the past will be observed in the future.  But there is no reason not to believe so.  That is a question of absolute certainty, however, and what can you say you are absolutely certain of?  Probably not much.

“Object identity” already implies “through time”.  An identity is a relation, and in this case we can assume that it means a relation between the object now and the object at some other time.  But look at the Theseus Paradox if you want to have some fun.

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Posted: 29 June 2007 12:24 AM   [ Ignore ]   [ # 11 ]
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If you wanted to use the everyday version of “touching” in quantum physics, you would produce as nonsensical a result as if you use quantum mechanical concepts in describing events in court.

Feynman, like all good scientists, knew full well that his descriptions were not reality.  The models are based in reality, because they have to accord with observations of reality, but they are not reality itself, nor are they perfectly accurate representations suitable for all situations.

Very nicely put! I have tried to make this point, not nearly so clearly, in several threads.

You may want to go with Plato and assume that when you isolate “a rock” from the rest of the universe that you are tuning into some eternal Form of “rockness”, but that is about as unscientific an attitude that you can take.  That is not to say, as some people mistakenly object, that the object does not behave as an object, or as the object that I conceive it as, only that I am the source of the reality of the object, as opposed to the reality of what it is I have objectified, which is independent of me or my conceptions. 

Ok, I may have to call in a professional philosopher (or maybe just Alexander) to deal with this Gordian knot. Here’s what I think you are saying:
1) Our perceptions create objects out of reality which are representations, not the things themsleves.
2) As such, our representations cannot be said to be the true essence of the things (their Ideal Form).
3) However, this is not equivalent to saying the things we perceive have no intrinsic existence apart from our perceptions, for of course they do. We simply have to take our perceptions/concepts as the best available representation while still being careful not to confuse the representation with the thing itself.

If this is actually what you’re saying, I agree. If not, I’m confused.

confused

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Posted: 29 June 2007 07:38 AM   [ Ignore ]   [ # 12 ]
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The problem with the view that our perceptions create object is that this amounts to a form of Berkleyan idealism. To say that there’s some “thing in itself” (Kant’s ‘ding an sich’ IIRC) that is unknowable behind the human-created perceptions or concepts is just to obfuscate the matter.

When we discuss natural kinds, we aren’t saying that there is a “form of x” for every word “x” in the language. That’s a form of straw-man argument. We’re saying that there are certain regularities in our experience, and we believe that the best explanation of these regularities is that there is a sameness of the part of the external world responsible for that regularity. Not every word in the language picks out a lawlike regularity.

Then if we see a regularity over here that is similar to a regularity over there, we say that the best explanation of this similarity of regularity is that they both instantiate the same property or natural kind. To take one imperfect example, cats tend to give birth to kittens, and dogs to puppies. Is there some explanation of that odd regularity?

If we could not do this, we could not assert any sort of law of nature. Everything would be random. The assertion that there are no natural kinds just is the assertion that there are no laws of nature. As the predicates that take part in any law of nature are themselves natural kinds.

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Posted: 29 June 2007 10:56 AM   [ Ignore ]   [ # 13 ]
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Well, I’m not sure I follow exactly, but I do think we need to recognize that our perceptions of things are incomplete representations of the thing. FLowers look pretty to us at the wavelengths of light we can see, but they look quite different to bees who can see in the ultraviolet. At those wavelengths they evince patterns designed to guide the insects to the nectar sourece. So if we say the flower is as we see it and no more, we’re crediting ourselves with a more complete understanding than is warranted. I suspect this is true about many things, both sensory and conceptual, that have aspects to what they are we may not appreciate. It doesn’t mean there is no consistency or value to our understanding because it is, of course, based on properties the objects truly have. And it’s the best we have. But again, we need to recognize that it has limitations.

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Posted: 29 June 2007 01:27 PM   [ Ignore ]   [ # 14 ]
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mckenzievmd - 29 June 2007 10:56 AM

Well, I’m not sure I follow exactly, but I do think we need to recognize that our perceptions of things are incomplete representations of the thing. FLowers look pretty to us at the wavelengths of light we can see, but they look quite different to bees who can see in the ultraviolet.

Agreed 100%, Brennen. That’s why I revert to the “perceptions” (or, better, “observations”) of the sciences when talking about real objects and natural kinds. Scientific investigation tells us that colors are, basically, fictions of our visual processing. However, wavelengths of light are not fictions.

Science sharpens our observational abilities by many orders of magnitude, and allows us to better distinguish reality from mirage.

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Posted: 30 June 2007 05:42 AM   [ Ignore ]   [ # 15 ]
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Back when I was reading about how IBM spelled out its initials in gold atoms on a crystal lattice, it was also reported that they could only move the atoms an integer distance, IIRC, 10 x -35m, which is to say that any give atom is observed to be seen at say some multiple of that distance, ie, not a floating point measurement.

They are talking about a “pixel” of space. The ultimate boundary. Which is basically what 18th century Bengalese Saint Ramprasad says referring to the fact that you exist within a “projected matrix” out of the mind of Kali. Or whatever other name you choose to apply to the “supernatural” projection equipment.

Joseph Campbell makes the point that this primordial Goddess is *not* a personality like a god, with a divine plan.

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