Well, I was thinking about the last post a little more, and it occurred to me that I left out a very important limiting case. If the variables which make up the function being optimized are orthogonal, then we should get an interesting result. What this simplification amounts to is a function F which spans an N dimensional space (each dimension of the space representing an individual). It is trivial to prove in this case that the maxima of the overall function F would be obtained by maximizing each individual function f(x). I'll put an abbreviate proof here.
if F(x1,x2,...xN) = f(x1) + f(x2) +...f(xN)
then d[F]/dx1 = d[f(x1)]/dx1 and the same for all other variables
the extrema of the individual variables xi are dependant on the first derivative with respect to that variable
Since the extrema of F is dependant on the sum of all those individual derivatives, then clearly the maxima of F is achieved by maximizing each individual f
The only problem here is the income of one individual is in fact dependant on a great many things including the incomes of others in his profession, and the value placed on that persons work, which is inevitably dependant on the willingness to pay on the part of other members of society, which is in turn dependant on their incomes... you can see where this is going. This problem is clearly more complicated than I have made it out to be since the entire field of Game Theory is based on solving less complicated problems. Since I haven't read any recent literature on the status of Game Theory, I will not even try to bs my way through it. So, at least we have quasi dealt with one important objection to my previous post. I can clearly only address mathematical objections to the post since this is a topic which is at its heart a mathematical problem, which unfortunately evokes emotions in those who object to it.
It is best not to know your own limitiation since they can only limit your potential.
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Friday, April 04, 2003
So, I was reading an article about how unemployment has risen lately, and it got me thinking about the capitalist system. People have this notion that it is possible for us to get rid of the lower socioeconomic class and that all people can live comfortable lives. I am not completely convinced that that is true. In mathematics there is the same problem when considering optimization theory for multivariable systems. In order to achieve a absolute maximum for the function f(x1,x2..xN), it is not in general necessary to maximize each individual variable. An example of this is the problem of sphere packing, where one considers the optimal arrangement of spheres in a given volume and attempts to find the way to pack them so as to fit the most spheres in that given volume. This is a yet unsolved problem, but some very elegant recent work has shown that if you divide the volume up into smaller volumes and consider the packing of these individual volumes, and interesting relation is achieved. It is found that one does not have to optimize the filling of each individual volume, so if you can fit 18 spheres in one volume but only 16 in the adjacent volume, that does not automatically eliminate that arrangement from consideration. It turns out that optimizing the average filling of the smaller volumes is the determining factor for finding the absolute maxima for the function.
The problem is that I am not sure anyone understands what exactly is being maximized by the current capitalist system. Most certainly we are not optimizing the monetary status of each individual member of society. If that were our goal, then we would be part of a socialist society where everyone makes the same amount of money since in that case each variable is equivalent x1=x2=xN, and we have a single variable function. I guess what I am trying to say is that it may in fact be necessary to have some people living in poverty in order to facilitate others living extravagant lifestyles. I am not assigning a qualitative assessment for this situation, just noting that it is likely a mathematical inevitability.
The problem is that I am not sure anyone understands what exactly is being maximized by the current capitalist system. Most certainly we are not optimizing the monetary status of each individual member of society. If that were our goal, then we would be part of a socialist society where everyone makes the same amount of money since in that case each variable is equivalent x1=x2=xN, and we have a single variable function. I guess what I am trying to say is that it may in fact be necessary to have some people living in poverty in order to facilitate others living extravagant lifestyles. I am not assigning a qualitative assessment for this situation, just noting that it is likely a mathematical inevitability.
Thursday, April 03, 2003
You know what sucks... listening to yourself on a recording. So, I bought an electric guitar a week and a half ago just to mess around with. I decided to record myself and see what I sound like. The results were less than stellar.
Knockin on Heavens Door
Knockin on Heavens Door
So, as one might ascertain from my previous post, I have had phlebotomy clinic this week, which means I have to go to the hospital at 5am and draw blood from patients for three hours. So, we are required to wear scrubs (the blue pajama looking things that doctors wear) when we are there. Scrubs are not like normal clothes in that I don't feel the need to wash them regularly. I have been wearing the same pair day in and day out for four days now. I finally decided to wash them. They way I see it, scrubs are a lot like underwear... you can wear them for at least 4 days straight without washing.
There is nothing worse than the look of disappointment/anger in a patients eyes after you dig around in their cubital fossa for an entire minute with an 18 gauge needle only to come out without having drawn a single drop of blood. Without fail, as soon as you pull out, that area begins to bleed profusely onto the bed sheets reminding you that you were right there but still missed.
Tuesday, April 01, 2003
Alright, it is about time I got my thoughts on natural selection off my chest. People in general public seem to have varying degrees of misunderstanding of what natural selection means. Most educated people think that intelligence is the ultimate trait which must prevail above all others. This is manifest in the kind of self grandiosing perceptions that educated people have to distinguish themselves from the rapidly breeding lower classes. Other people think that intellect has put us above evolution and that we are not effected by it anymore. Neither of these could be further from the truth. Selection is based on the inherent instability of genetic structure which underlies all life on earth. Most mutations which a individual in a species acquires is a null mutation, in that it does not cause any structural or functional change in the organism. Only rarely does an organism, through the various forms or germline and mitotic mutation, acquire a functionally active mutation. This mutation can either help the organism or hurt the organism. Cystic fibrosis is an example of a single point mutation which is terminal to the organism as a whole and is therefore selected against. On the other hand, if a person were to gain a mutation which increased the enzymatic activity in their skeletal muscles myosin ATPase activity, then that person would be able to run faster and lift more than the rest of the species. So, the question still remains, what traits are in fact selected for? The answer is that it depends on what it is that allows that individual to out reproduce the others in its society. The higher the frequency of a particular set of genes is in a society (i.e. how many direct descendant of that one mutated individual there are), the more we can say that trait has been selected for.
Were does this get us? The problem isn't how to breed a society full of individuals that are genetically pure. Rather, it is important to have as diverse a genome as possible to allow the species to adapt to all possible selective pressures. The idea is that no matter what disease or environmental change comes along, there will be at least a small subset of the population that will be genetically equipped to adapt to that new evolutionary challenge. If a disease comes along that requires the gp120 surface receptor to gain entry to the cells (HIV), then any individual with mutations in that receptor will be selected for (there have been naturally immune individual identified in part of Africa). If we lose our ozone layer and are bombarded with UV radiation, then people with highly active DNA repair mechanisms and high melanocyte activity will win out. One important thing to note is that all these things are only important for the reproductive life of an individual (approx. ages 13 through 35). Once you have reproduced, nature doesn't care what the hell you do just as long as you don't out compete the reproductive members of society for life sustaining resources.
All of this is of course a testament to how well evolution has equiped us for survival since almost all life threatening diseases don't manifest until late in life once an individual has completed reproducing. This of course makes sense since we evolved in the jungles of Africa where the life expectancy is something like 25 years at best. Alright, I have babbled long enough...
Were does this get us? The problem isn't how to breed a society full of individuals that are genetically pure. Rather, it is important to have as diverse a genome as possible to allow the species to adapt to all possible selective pressures. The idea is that no matter what disease or environmental change comes along, there will be at least a small subset of the population that will be genetically equipped to adapt to that new evolutionary challenge. If a disease comes along that requires the gp120 surface receptor to gain entry to the cells (HIV), then any individual with mutations in that receptor will be selected for (there have been naturally immune individual identified in part of Africa). If we lose our ozone layer and are bombarded with UV radiation, then people with highly active DNA repair mechanisms and high melanocyte activity will win out. One important thing to note is that all these things are only important for the reproductive life of an individual (approx. ages 13 through 35). Once you have reproduced, nature doesn't care what the hell you do just as long as you don't out compete the reproductive members of society for life sustaining resources.
All of this is of course a testament to how well evolution has equiped us for survival since almost all life threatening diseases don't manifest until late in life once an individual has completed reproducing. This of course makes sense since we evolved in the jungles of Africa where the life expectancy is something like 25 years at best. Alright, I have babbled long enough...
Monday, March 31, 2003
Sunday, March 30, 2003
So, I am in a dance that the Indian medical students are doing at our schools multicultural show. You never realize how uncoordinated you are until you try to learn new dance steps. I think the only thing saving me is that my partner really knows the dance well, so I just pretty much follow her. It is going to rough though since we are only going to practice one more time before the show due to our impending Pharm exam. I am really glad that no one reads these posts because I didn't really tell anyone that I am doing this dance so I only make a fool of myself in front of my school friends.
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