01.19.10

Aristotle’s Theory of TOPOS (Place)

Posted in Relativity, philosophy, physics, science at 12:22 am by nogre

[This is something I wrote before I had this blog, but I really like it and hope the readers here will find it interesting.]

The task of explaining Aristotle’s theory of place lies in the interpretation of this sentence: “Hence the place of a thing is the innermost motionless boundary of what contains it,” (Physics IV 212a20).  Now the idea of a motionless boundary for perceptible and obviously movable objects seems impossibly counterintuitive.  However, using Aristotle’s comments into the nature of place, we can understand how this theory extends beyond a simple boundary theory and into the modern era.

His discussion is started by making an observation:

The existence of place is held to be obvious from the fact of mutual replacement.  Where water now is, there in turn, when water has gone out as from a vessel, air is present; and at another time another body occupies this same place.  The place is thought to be different from all other bodies which come to be in it and replace one another.  What now contains air formerly contained water, so that clearly the place or space into which and out of which they passed was something different from both. (Physics IV 208b1-8)

Aristotle then makes some tentative moves into defining what could possibly fulfill the role of place.  First he discounts any idea that place could “be body; for if it were” he says, “there would be two bodies in the same place,” (209a6) and shows how this causes untold amounts of theoretical difficulty (ibid.).  Then he discusses how, as that which “primarily contains each body” (209b1), place could be viewed as the form or the matter.  Again he discounts either of these possibilities by noting that neither of them can be separated from a thing, whereas place may be.

The analysis turns at this point asking, “How many ways one thing is said to be in another,” (210a14) in the hopes of landing upon a useful interpretation of the notion of being-in.  Aristotle entertains the idea that a thing may be in itself, or more specifically, in itself “qua itself or qua something else” (210a27).  He gives the example of a jar of wine being in itself in virtue of the whole’s description in terms of its parts: the jar of wine is not reducible to a jar or some wine, but to their specific combination.  Hence that which is a subject may potentially be a container as well, as the jar is the container of the subject ‘jar of wine’.  However, he says this is impossible as no object is actually like this: the wine would have to be an equal part container, and the jar an equal part wine, else the whole of the ‘jar of wine’ will not be completely in itself.  It is in virtue of being different that the jar and the wine may come together, and hence he concludes that, “since the vessel is no part of what is in it (what contains something primarily is different from what is contained), place could not be either the matter or the form of the thing contained,” (210b27).

Aristotle then considers two sorts of boundary theories.  First, place is such that it is “some sort of extension between the extremities,” (211b7).  However, this sort of boundary exists independently of what is bounded and is permanent.  Insofar as anything moves, the place will change, and there will be two problems generated: 1. The boundary between, for example, the wine and air moving in a jar will be exactly coincident with the boundary between the air and wine, and each of these two boundary extensions will be partially coincident but must also be unique, and 2. There will be a place at the boundary of the displaced place, and so an infinite regress of places associated with previous places will be generated.

Finally Aristotle says, “place necessarily is… the boundary of the containing body at which it is in contact with the contained body,” (212a6).  Then, interestingly, he says, “Place… is rather what is motionless,” (212a17) and then, “Hence the place of a thing is the innermost motionless boundary of what contains it,” (212a20).  So how are we to make sense of containers that give us the boundaries but also do not move?

If we take our interpretation directly from the previous discussion of boundary, Aristotle seems to have made an awfully strange claim: place is a like a container that something perfectly fits in, and yet that container cannot itself move although what is contained therein necessarily can.  However, I would like to suggest taking him at his word in regards to place being necessarily a boundary.  It is necessarily a boundary of the containing body which is in contact with the contained body, but it is not sufficient that it be the boundary that most have in mind.  What has been missed by regarding the boundary as necessary and sufficient is the incorporation of Aristotle’s primary intuition into how we know place exists.

For us to notice any motion we need something stationary relative to the thing moving such that we may observe the motion as motion.  A stationary backdrop is necessary to view change.  Consider this example: it is a common experience to be sitting in traffic next to a bus.  When the bus starts to slowly pull forward sometimes it is possible to get the sensation that you have started to move backwards.  This sensation lasts until some other fact informs you that it was not you who were retreating, but the bus advancing.  In the first instance, the place that you inhabited was defined in terms of a stationary bus: any motion that occurred was relative to that fixed point.  When you realized it was the bus, and not you, that was moving, whatever it was that informed you that you were stationary became incorporated into the place.  Perhaps you saw a building and since it was not moving your senses of place and motion were reevaluated to accommodate this new information. Hence two different places were involved in this scenario: one corresponds to your (belief of) moving backwards and the other to the forward motion of the bus.  The first place has the innermost motionless boundary [illegitimately] defined in terms of the bus [since the bus was in motion], and the second has an expanded sense of place to include something motionless relative to both you and the bus. Place, therefore, not only encapsulates that which is moving, but also whatever is observing the motion and an independently stationary object.

When Aristotle says, “First then we must understand that place would not have been inquired into, if there had not been motion with respect to place,” (211a12) he was not making an idle comment on the ‘discovery’ of the phenomenon of place.  Instead, he was beginning his analysis with the most important feature to be explained.  Galilean relativity holds fundamentally that motion can only be defined relative to some “system of coordinates” (Einstein p. 14), i.e. something motionless with respect to the moving object.  Although Aristotle did not have the benefit of Descartes’ mathematical works he still recognized the need for a reference system unique to each motion.

Now that the meaning of the ‘motionless’ criterion has been explained, what does ‘innermost’ mean if the boundary may include objects at a significant distance from the one we are describing?  The Earth is, in some sense, the place of all sublunary objects, but it is surely not the innermost boundary.  Again appealing to the exact phenomenon that Aristotle was dealing with yields the correct explanation: the motion of an object with respect to its place cannot be described by saying that the place of the thing is Earth.  Instead the innermost boundary should be the first boundary for which the description of motion and place of the thing make sense.  In the example of swirling wine in a jar (with the jar held steady but the wine still moving), the place of the wine can be said to be the jar because it describes the closest motionless boundary.  One might say that the place of the wine is equally on the table, or in someone’s hand, but both of these descriptions are related to motion other than that of wine swirling in the jar, and are really just shorthand for ‘the jar of wine is on the table, or in hand’ (consider, “The wine is on the floor,”: no swirling to be had).  The correct place of the moving bus example was the street, which could reasonably include things such as houses and other stationary objects, the most important one being the road.  Aristotle gives the ancient version of this, just before his final definition of place, in terms of the motion of a boat, such that it must be defined in terms of the whole river, which is taken as stationary (212a19).

One may think that I am being too charitable to Aristotle at this point because it may look that I have implied that the ‘innermost’ criterion of the theory will do all the work of translation between coordinate systems, which it does not seem to do.  However, Aristotle allows for the fact that we may treat a vessel such as a boat as a “transportable place” (212a14).  Hence we may allow for the things within a boat to have motion independent of a preferred fixed reference system.  This connection drawn between vessel and place gives the final aspect needed for a true relativity theory.  Historically the example of a boat on a river (212a19) is striking because Galileo uses the same example of a ship in his Dialogue Concerning the Two Chief World Systems (Salgado).

Commentary

Historically Aristotle’s theory of place has been treated as a simple boundary theory coupled with a few very strange statements that were assumed to be preliminary investigations into different methods of solving blatant paradoxes (King 91).  My suspicion for why this happened is twofold.  First, philosophy of place sounds like the most dry and uninteresting subject possible and hence it was not given its due study time over the course of history (after Aristotle that is).  Secondly, the modern formulation of relativity is given according to Einstein’s theory of Special Relativity.  Insofar as this is a theory of relative motion, it is easy to overlook the fact that it applies to objects without motion, things in place.  Aristotle’s formulation is none the weaker because of the way he cast his theory, but it is much more obscure to the modern reader, as Aristotle’s relativity is developed in a somewhat inverse way with respect to modern relativity.

Bibliography

• Barnes, J. ed. The Complete Works of Aristotle v.2, Princeton U. Press, Princeton 1995
• Einstein, Albert Relativity: The Special and General Theory Lawson trans.  Pi press, NY, NY 2005
• King, H. R., “Aristotle’s Theory of TOPOS,” Classical Quarterly #44 1950, pp. 76-96
• Salgado, Rob “Galileo’s Parable of the Ship” http://physics.syr.edu/courses/modules/LIGHTCONE/galileo.html Accessed 2/24/06

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12.31.09

Genetic Drift and the Uncertainty Principle

Posted in Relativity, biology, evolution, measurement, philosophy, physics, science at 4:48 pm by nogre

I have previously argued that the history of species must be treated like a evolutionary trajectory: we can only appreciate a species in a relative sense, just as we must evaluate physical trajectories relative to our own motion.

But what happens when we try to measure the very small in physics?  We find there is a limit to the precision at which we can measure, as given by the uncertainty principle.

This suggests that there may be some similar limit when it comes  to measuring small changes in species.  The more we try to pin down exactly what a species is, the less sure we will be about its future and the more we measure the direction the species is heading, the less sure we will be about exactly what constitutes that species.

If genetic drift is just another way of saying that we cannot pin down the exact genetic make-up of a species then drift may be considered to be an instance of the uncertainty principle.

and HAPPY NEW YEAR

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10.18.09

Monty Redux

Posted in epistemology, game theory, logic, philosophy at 6:37 pm by nogre

In the Monty Hall Problem a contestant is given a choice between one of three doors, with a fabulous prize behind only one door. After the initial door is selected the host, Monty Hall, opens one of the other doors that does not reveal a prize. Then the contestant is given the option to switch his or her choice to the remaining door, or stick with the original selection. The question is whether it is better to stick or switch.

The answer is that it is better to switch because the probability of winning after switching is two out of three, whereas sticking with the original selection leaves the contestant with the original winning probability of one out of three. Why?

The trick to understanding why this occurs is to view the situation not from the contestant’s viewpoint, but from Monty Hall’s. At the outset, from Monty’s point of view, the contestant has a one out of three chance of guessing the correct door. In the likely situation (two out of three) that the contestant chose wrongly, Monty then has to know where the prize is among the two remaining doors in order to open a door that does not reveal the prize. So Monty opens a door not revealing the prize and asks the contestant whether he or she would like to switch or not.

However, the contestant knows that in the likely (two out of three) situation that the initial choice was wrong, Monty had to know where the prize was in order to open the door that did not contain the prize. Since the contestant knows that Monty has to know where the prize is to make the correct choice, the contestant can (in this likely case) place him or herself in Monty’s shoes. At this point Monty knows that the remaining door is the one that contains the prize, and hence the contestant should switch.

If we consider the unlikely situation in which the contestant initially chose the door with the prize behind it, then this line of reasoning will not work. Imagine that Monty forgets the location of the prize every time the contestant guesses correctly. In this situation he can still open either of the remaining doors without ever ruining the game. From his perspective the location of the prize is unrelated to his actions; it played no part in his decision to open one door or another (he merely chose a door the contestant hadn’t).

So, in the one out of three case where the contestant initially selected the correct door, there is no way to deduce whether switching is beneficial based upon placing oneself in Monty’s shoes:  the situation where Monty has forgotten the prize’s location is indistinguishable from a situation in which he has not forgotten. Without any way to further analyze the situation and tilt the odds to over one out of three, the contestant should always assume that he or she is in the previous, more likely, situation and take the opportunity to switch.¹

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¹Imagine that the contestant has a guardian angel that will let the game run its course if the contestant switches doors, but will change the location of the prize such that if the contestant sticks with the original door the angel will make sure that the contestant wins four out of five times. Then the probability of winning while switching will stay at 2/3 but the probability of winning while sticking will be 4/5. If the contestant had some way of divining that this was happening, this would be a case in which further analysis would be of benefit.

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10.15.09

Climate Change

Posted in internet, philosophy at 12:31 am by nogre

This is a post for Blog Action Day 09!

If the climate changes rapidly enough, the human race is finished.  If the climate does not change quite that rapidly, we’ve got other problems.

For the sake of argument, let us assume that we are not beings in some religious pantheon, but are merely biological organisms of this Earth.  If the climate changes, i.e. if nature as we know it no longer exists, then how are we to think of ourselves?

For our entire history we have lived within a climate that is amenable to us.  Living in a new climate would be like living on an alien planet, without hope of returning to Earth.  The problem is:  we are not aliens, we’re Earthlings.  If we are not Earthlings, what are we?  Hence the problem of climate change is more than a problem of our survival, it is an existential problem of our species.

We don’t need any more existential problems, and since this is one preventable, lets do something about it.

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10.08.09

Sexual Reproduction, The Case for, Round 2

Posted in biology, evolution, fitness, philosophy, science at 7:24 pm by nogre

Let us assume that there are different kinds of adaptations.  Specifically, some are better than others in the long run:  some adaptations will only make a difference in an organism’s ability to reproduce viable offspring over a short period of time, whereas others will be beneficial for many generations.

In asexual reproduction there is no mechanism for distinguishing between a short term beneficial adaptation and a long term beneficial adaptation.  This subjects long term beneficial adaptations to being potentially overshadowed by short term beneficial adaptations and genetic drift:  if a short-term genetic change  sweeps through a population, some adaptations can be wiped out.  This sort of (selected for or not selected for) genetic drift would be tempered if it were forced to go across the different biologies of the two sexes.

With sexual selection there is a mechanism for selecting long term beneficial adaptations over short term ones.  Long term beneficial adaptations will have to be good for both sexes:  if an adaptation is beneficial to both the male and female – individuals with significantly different biologies – then it is more likely to be  good for the entire species.  Short term beneficial adaptations may only be good for particular individuals or one sex, depending on the mutation.  This makes it less likely for short term, provincial adaptations (or drift) to last because they won’t be as effective across different the different biological make-up of the two sexes.

Therefore by distributing mutations across two different sexes – two similar but different biologies – long term beneficial adaptations can be selected for.

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10.01.09

Sexual Reproduction

Posted in biology, evolution, fitness, game theory, philosophy, science at 11:20 am by nogre

Say you are a single celled organism.  To reproduce you have to double your size and then you need to split yourself in half.  Repeat indefinitely.

Now say you are a single celled organism that has the option to reproduce sexually.  To reproduce you need to increase yourself to 3/2 your original size and find a similar mate.  Then you both contribute 1/2 to the new organism and repeat indefinitely.

Asexual reproduction requires you to double in size; sexual reproduction requires only a 3/2 increase.  Therefore the turn-around time for sexual reproduction is inherently shorter than for asexual reproduction (assuming there are viable mates readily available).

Is there a selective benefit to a shorter turn around time for reproduction?  If the species must constantly be adapting to a changing environment (that would be everyone), then having a higher rate at which new mutations (and thence adaptations) are introduced into the population is critical.

Secondly, given that there is enough food but it takes time to collect, I count more offspring for sexual reproduction:

In sexual reproduction, there is an additional child from the first generation of children (as compared to asexual splitting) created in the same amount of time: At the +50% mark #1 & #2 mate to create #5, and #3 & #4 mate to create #6.  Then, at the 100% mark (or plus an additional 50%) #1 & #2 mate to create #7, #3 & #4 mate to create #8, and, at the same time, the initial children #5 & #6 mate to create #9.  #9 is also one generation ahead of the offspring of asexual replication.

Now, to be honest, I’m confused.  I don’t think that anything above is particularly complicated.  However, Wikipedia does not note this as a benefit of sexual reproduction.  It actually says that asexual reproduction is much faster.  This makes me think that I must have made a mistake or else someone would have added it.

The going theory appears to be that since every organism in an asexually reproducing species can give off children, then there is twice the potential for offspring.  This completely ignores any struggle that an organism might have that would prevent it from reproducing, or that work can be split with a mate making it easier to reproduce.

My main assumptions are, among others, that there already is a significant population of organisms, the organisms are not too fussy about their mates (no significant waste of energy searching for a mate),  energy / work is being split with the mate, and that the limiting factor has to do with gathering food.  I can’t see how, if these (reasonable?) assumptions hold, sexual reproduction isn’t the dominant, winning strategy.

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09.29.09

A Priori Against Physicalism

Posted in biology, ontology, philosophy, physics, science at 12:54 am by nogre

I saw that Richard Brown is working to defend physicalism against a priori arguments.  He says that most (all?) arguments use the same intuitions found in the zombie-knowledge arguments.

This got me to thinking about a priori arguments against physicalism and I came up with something different:

If physicalism is, as Dr. Brown says, “… the view that only physical things exist. Physical things are those things that are postulated by a completed physics,” then I wonder who made physics king?  I’d have to assume that there is something within science that specifies physics as most fundamental.

However, science itself, or more specifically philosophy of science, is discipline agnostic.  There is nothing within the basic structure of science to specify physics as the foundation.  Maybe it is biology that is fundamental, maybe it is psychology, maybe something else; the point is that there is no a priori reason to prefer one over any of the others.  If there is nothing that distinguishes physics as a ground for the other sciences, then there is no reason that physicalism should be taken as a fundamental philosophy.

At this point the physicalist would want to find some grounds for the claim that physics is fundamental.  This is problematic though: nothing could be used from within physics because that would be question begging.  On the other hand, if we try to justify physics as fundamental by appealing to something outside physics, then isn’t that thing that provides the justification more fundamental than physics itself?  If we have to justify the claim ‘physics is fundamental’ by appealing to something even more fundamental, then physics is no longer fundamental because it needs an outside justification.  Therefore any justification for physicalism is inherently question begging or self-contradictory.

I know I haven’t disproved physicalism; at best I’ve indicated that justifications for it are bad.  And if any justification is bad, then the position is indefensible.  Since most philosophers don’t like to hold indefensible positions, perhaps this is sufficient.

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09.24.09

A Rabbit in a Forest of Mushrooms

Posted in epistemology, philosophy, wittgenstein at 11:32 pm by nogre

Today I was in a shop and a young mother came in with her stroller and a handbag with an image of a sleeping rabbit in a forest of mushrooms.  The rabbit had a thought bubble that read, “A rabbit in a forest of mushrooms.”

I told her I liked the bag… I don’t think she realized that it had reminded me of the last paragraph of Wittgenstein’s On Certainty:

676. “But even if in such cases I can’t be mistaken, isn’t it possible that I am drugged?” If I am and if the drug has taken away my consciousness, then I am not now really talking and thinking. I cannot seriously suppose that I am at this moment dreaming. Someone who, dreaming, says “I am dreaming”, even if he speaks audibly in doing so, is no more right than if he said in his dream “it is raining”, while it was in fact raining. Even if his dream were actually connected with the noise of the rain.

The rabbit had created a visible dream-thought bubble that had correctly identified his actual situation, though the rabbit was asleep.

Does the rabbit’s dream-thought count as justified true belief?  It may well be justified because the rabbit could be observing it’s surroundings within the dream (and those images could be connected to reality through memory), it is apparently true, and the rabbit believes it (according to the rules of thought bubble attribution).  So the dream-thought of the rabbit seems to qualify as Justified-True-Belief, but I don’t believe we normally count dream-thoughts as knowledge.

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09.17.09

On Charitability

Posted in language, metaphysics, ontology, philosophy at 7:45 pm by nogre

There is no such thing as a private reality.  By private reality I mean any portion of reality that you alone can experience, that no one else could possibly understand.

There is, however, reality that is yet unexperienced and unknown to you.  Others may have experienced it before you, like explorers who have been to a far away place.  If a philosopher is clever, it is possible that she found a way to imbue her words with such an experience.  Since there are no private realities, it is also possible that you may be able to extract those experiences.

The allure of philosophy is then the allure of the unknown, the exotic and unexplored.  To be charitable is to approach philosophy in search of some yet unknown bit of reality.

Under these circumstances it is futile to give specific instructions on how to be charitable; each of us must understand how to prepare ourselves for adventuring beyond the relative comfort of what we know.

If anything, have faith in yourself and do not make assumptions (even charitable ones) about what you are doing.

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09.14.09

Not quite Skynet

Posted in NYC, biology, evolution, game theory, internet, news, philosophy, products, random idiocy, technology at 10:33 pm by nogre

For those readers of mine, I’d like to open up a small opportunity.  Quite a bit of my time and effort has gone into revamping parts of the theory of evolution and I have previously mentioned here that I’ve taught myself to program and created a simulation.  Well, this isn’t completely true.

The short version is that I’ve made computers try to survive the real world.  By real world, I mean my program contains lots of little files that make decisions, and these decisions are about buying and selling stocks, based upon actual real-time data available on the internet.  The decision engines (or ‘orgs’, as I like to call them) that correctly predict the movement of the stocks make money and eventually replicate.  Those orgs that are unsuccessful at predicting stock movements lose money and die off.  The replication process is governed by genetic algorithms that include various mutations.

The short short version is that the program is a cross between a stock market program and a tomagotchi (digital pet).  You host a colony of organisms that survive by ‘eating’ (buy and selling) stocks; it acts as your own personal hedge fund.

Anyway, I could use a tester or two, so if anyone here wants to participate, send me an email.  I’ll get around to writing up more details about the program soon too.

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In other news,  I’ve finally gotten around to updating the NYC Area Philosophy Calendar.  Someone even sent me a nice email asking if I was still going to do it (before I got around to it.. busy busy) and another person even asked if they could start adding events.

Hmmm, interest in the calendar (it only took 2 years).  An actual object (program) that came from studying philosophy (original theory of biology, 2004.).  It’s taken some time but I feel like I must be moving up in the world.

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