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.

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.

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.

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.

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.

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.

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.

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.

Let me explain.

When practicing science we are ignoring, in part, at least three important things: time, space, and people.  Science is, in some respects, atemporal: we believe that if everything else is held the same, it doesn’t matter when we conduct our scientific experiments.  There is no scientific difference between an experiment performed this week and an experiment performed years ago; we can replicate the experiments of the masters and get the exact same results they did (within experimental error of course).

Secondly, science is, in some respects, separate from space:  we believe that if everything else is held the same, it doesn’t matter where we conduct our scientific experiments.  There is no scientific difference between an experiment performed in New York or in Shanghai; we can replicate experiments of scientists all over the world and get the exact same results they did.

Lastly, science is, in some respects, separate from particular people: we believe that is everything else is held the same, it doesn’t matter who is conducting our scientific experiments.  There is no scientific difference between an experiment that I have performed and one that someone else performs; anyone may replicate an experiment and get the exact same results as someone else.

This, among other reasons, is what makes science so great:  a scientific discovery will last beyond your life and your laboratory and can travel the world indefinitely.  Unlike a great performance (theater or sport, take your pick), it will be exactly replicable for all time.

Now, back to scientific methods being public.  If a scientific method is private, then it means that one or more of the three points listed above is being violated.  Either the experiment is limited to the people who performed it (only certain people can make it work), the experiment is limited to the time in which it was performed (it only worked that one time) or the experiment is limited to the place it was performed (it only works in my basement).  Once one of the three above points can no longer be ignored, then we have lost that which makes science so impressive.

Insofar as people are afforded the right to use language as they wish, I suppose it is acceptable for someone to call an experiment that violates one of the three above points science, or maybe, scientific.  I, however, hold that what is generally thought to be science necessarily requires that the above three points not be violated.