Chaos Theory January 29, 2009
Posted by pjd4891 in Mathematics, Metaphysics.3 comments
Chaos Theory's Mascot
In today’s class, we discussed how fluid dynamics is not researched thoroughly even though it is one of the most important fields. It is applicable for a wide variety of disciplines. Ocean flow could be mapped more accurately, which has a direct correlation to world temperature, air flow, and pressure. Turbulence has chaotic properties. Since turbulence is so chaotic, can we even accurately map ocean flow?
Turbulence
The Coastline Problem was formulated by Mandelbrot in the 1960′s. We discussed this in class. If you keep zooming into the coastline, the length will approach infinity. As you zoom in, the coastline appears more jagged, because you are focusing on smaller and smaller particles. What is the smallest particle we can focus on? Is there anything smaller than a quark? Chaos theory says you cannot have infinite accuracy, so the must be something smaller than a quark.
The Fractal Fern
These fractal examples appear chaotic, but when you make a small change (zooming in), it shows massive changes.
Wikipedia defines a fractal as:
- It has a fine structure at arbitrarily small scales.
- It is too irregular to be easily described in traditional Euclidean geometric language.
- It is self-similar (at least approximately or stochastically).
- It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
- It has a simple and recursive definition.
The Julia set is an interesting example as well:
We discussed that chaos theory states that we cannot accurately understand the universe. Chaos theory questions science at the core. Since we cannot make accurate predictions, what is the goal of science? How can we achieve the goal of science?
All through school, we are taught simplified versions of natural events. I do not believe that mathematical functions exist for all natural events. I think we can get closely model the flow of the ocean, but not completely accurately. There will always be factors that we will have no way of predicting or testing. Life is not supposed to be predicted and science tries to do just this. It tries to rid human lives of emotion in order to give an objective view of how the world works. While science has shown progress throughout time it may be progressing towards something that may not be the correct answer. But then this also gets into the problem with the idea of what is correct and what isn’t. I think science has no self analytical skills in certain circumstances and that it may not see the error of its ways.
At What Point in Development do Humans Become Conscious?, Part 1: Societal Ramifications January 26, 2009
Posted by ews8704 in Philosophy of biology, Philosophy of mind.4 comments
Societal Ramifications
The question of when we develop consciousness is, naturally, very loaded . If we are conscious in the womb, for instance, can abortion ever be moral? On my search for materials on nascent consciousness, I even ran across a book that insisted all expecting mothers should stay at home, lest they pass the toxic stress of the working world on through the placenta and trouble the fetus.
Underdetermination January 26, 2009
Posted by ebrister in Nuts and Bolts.Tags: Duhem, holism, underdetermination
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We read an excerpt from Duhem’s The Aim and Structure of Physical Theory (1906) which introduced the notion of underdetermination of theory by evidence. The underdetermination thesis holds that individual statements cannot be empirically confirmed or disconfirmed by a single observation. This thesis upholds holism: that our theories are composed of collections of statements which are evaluated as a whole. Disconfirming evidence can be dealt with by making any number of changes to this collection of statements.
Duhem writes:
In sum, the physicist can never subject an isolated hypothesis to experimental test, but only a whole group of hypotheses; when the experiment is in disagreement with his predictions, what he learns is that at least one of the hypotheses constituting this group is unacceptable and ought to be modified; but the experiment does not designate which one should be changed.
This challenges two common beliefs about how science works.
1. We cannot give a complete logical reconstruction of scientific reasoning which makes a conclusion seem to have been compelled by evidence. This is obviously the case for induction from evidence because it’s possible to generalize from a limited set of observations in any number of ways. But it’s also true for deduction; say, along Popper’s lines. Due to underdetermination, we can’t make a conjecture, deduce the results we ought to see, and then know for sure which part of the theory has been falsified when the deduced prediction is disconfirmed.
2. If we have two theories that are empirically equivalent except for giving different predictions as to the result of a crucial experiment, then running that experiment ought to give us the ability to choose between them. However, the problem is that this assumes that there is no overlooked alternative theory–that the two we are choosing between are the only two possible explanatory theories. This is why Duhem says:
Unlike the reduction to absurdity employed by geometers, experimental contradiction does not have the power to transform a physical hypothesis into an indisputable truth; in order to confer this power on it, it would be necessary to enumerate completely the various hypotheses;…but the physicist is never sure to have exhausted all the imaginable assumptions.
The class’s opinion last week seemed to be that understanding underdetermination was straightforward. I would like to point out, though, that the implications of the thesis are far-reaching and still of contemporary interest. For instance, here is the program for a conference this March on underdetermination.
Gödel’s Incompleteness Theorems January 23, 2009
Posted by Greg in Mathematics, Philosophy of mind.4 comments
Blah balha
–Evelyn Brister
I’d like to hit two main points in this blog post. First of all, I’d like to discuss Gödel‘s second incompleteness theorem a bit; second, I’d like to see if I can start an actual argument about the philosophical implications of these theorems.
(more…)
Introduction: At What Point do Humans Develop Consciousness? January 22, 2009
Posted by ews8704 in Philosophy of biology, Philosophy of mind.3 comments
Wired Baby
I first remember thinking about the nature of consciousness when I was 4 years old. Back then, I knew I was a big girl: my parents and teachers kept telling me so. I also knew that, before a girl is big, she is little. Yet I had no memory of being a little girl. (more…)
Levels of Natural Selection January 21, 2009
Posted by tcb1370 in Philosophy of biology.Tags: biology, evolution, gene, group selection, natural selection
2 comments
There are many theories about the question of “At What Level Does Natural Selection Operate”, but I’ve chosen to focus on just three mainstream theories.
Group Level
Group selection is commonly referred to as “Multi-Level Selection Theory“.
D.S. Wilson defines group selection in this way:
Group selection promotes fitness of groups, relative to other groups in the global population. The levels of selection are not always in conflict.
It’s easy to fall into thinking about individual selection, when one is trying to imagine group selection taking place, but these following examples are sometimes used to differentiate between group selection, and the levels below it:
- Molecular reactions initially “competed” against each other, but eventually became cooperative and formed into simple cells.
- Simple cells once competed against each other for resources and eventually became complex cells working together.
- Multi-cellular organisms arose from groups of complex cells. We consider a multi-cellular organism to be one organism now, but it may have evolved as such because of the benefits to replication that groups of cells received when cooperating.
- Eusocial insects like bees, wasps and ants are groups that act as a single organism in some ways, and compete against other like groups. Note: This type of colony has actually evolved 11 different times independently. I find that to be very interesting.
Group selectionists also seem to use the idea of Koinophilia as evidence of their theory. Basically, by only choosing mates that have the most average characteristics of their population, a group can fend off selfish individuals from taking advantage of the group’s cooperation.
For more information on group selection, I would suggest this paper by D.S. Wilson and Elliott Sober: Re-introducing Group Selection to the Human Behavioral Sciences. Their main point is stated here in the abstract:
We show that the rejection of group selection was based on a misplaced emphasis on genes as “replicators” which is in fact irrelevant to the question of whether groups can be like individuals in their functional organization. The fundamental question is whether social groups and other higher-level entities can be “vehicles” of selection.
Gene Level
Gene level selection, also known as “Selfish Gene Theory” really seems to have been made most popular by Richard Dawkins, in his book “The Selfish Gene”. In this book, Dawkins explains the idea of replicators as the underlying cause of all evolution and describes the organism as a machine that perpetuates its replicators (in this case, genes).
He uses Evolutionarily Stable Strategies to show that most of the behaviors we see today in organisms can be explained by the way that replicators fall into certain patterns that do not allow other organisms to take advantage of them. These strategies may not be the most optimal in terms of overall benfit to the organism – for example, a strategy where an organism never fights another organism would be beneficial to everyone in the population – but they prevent a mutant aggressive organism from being born that would invade and inevitably spread through the population.
I found his paper Burying the Vehicle, to be very interesting because it refuted many of Wilson and Sober’s claims about ‘vehicles’ of selection. I think it can be summed up pretty well here:
Natural selection chooses replicators for their ability to survive in an environment that includes other replicators and their products. Sometimes cooperation among replicators is so strongly favoured that units coherent enough to be called vehicles emerge. But just because a vehicle may emerge at a given level, we have no right to assume that it will and I believe the evidence will show that at most levels it usually doesn’t. The question, “What is the vehicle in this situation?” may be no more justified than “What is the purpose of Mount Everest?” Ask rather “Is there a vehicle in this situation and, if so, why?”
Individual Level
Individual selection seems to be the most commonly accepted view of natural selection. Selfish Gene Theorists agree, in that since it is only through an individual that a gene may express its characteristic, the individual may rightly be thought of as the unit of selection.
For more information on the various levels of Natural Selection, I would take a look at the Wikipedia page Unit of Selection as a starting point.
Some authors and books I would suggest would be:
- Dawkins’ The Selfish Gene
- Frans de Waal – a primatologist who writes a lot about the origins of altruism
- Elliott Sober – a philosopher of science, who has an interest in biology
- PZ Myers – I can’t help myself. PZ is my favorite science blogger, so I have to include him. He’s done a few controversial things in the past to make his points, but he really knows biology. He is my daily source for information about evolutionary theory, so I would highly recommend him.
Zombies… Not Your Average Sleepwalker January 20, 2009
Posted by exk0730 in Philosophy of mind.6 comments
When I hear the word “zombie,” the first thing that comes to mind is a blood-covered, grunting, wobbling, decomposing corpse. Well I guess in magical lands and other universes, you could find one of these things. But there’s another connotation of “zombie.” The philosophical zombie. This type of zombie doesn’t grunt, and doesn’t wander around aimlessly trying to find some human to munch on. The p-zombie is a human, with some exceptions. It is physically indistinguishable from a human, yet it lacks conscious experiences, qualia, or sentience. When a p-zombie is poked in the eye, it will say “ow” and recoil, because it has the same behaviors as a human being, but it does not experience what that pain actually feels like. Zombie arguments tend to lend support for dualism by arguing against physicalist theories.
According to physicalism, all things can be explained by physical facts. If God created the world based on purely physical properties and laws governing the behavior of all things in that world, did God have to do something further to provide for human consciousness? If God did have to do something further, then it seems that physical properties must not explain everything there is about the world, suggesting that consciousness could not exist in a world of solely physical properties: a zombie world. It follows that if a zombie world is possible, physicalism is false.
The real question is: are zombies conceivable?
Gestalt Switch January 9, 2009
Posted by ebrister in Kuhn.2 comments
We discussed Kuhn’s comment that scientific revolutions require something like a Gestalt Switch: a scientist can’t operate in the old paradigm after having been converted to a completely different way of conceptualizing the world through the new paradigm.
In that discussion, I promised some images to illustrate a Gestalt psychology, such as the vase-face and duck-rabbit illusions which play on different perceptions of image and ground.
Trevor passed on a similar illusion of a figure spinning in two directions (which I, frankly, can’t see. Oh wait! Now I do!). The other illusions on this site are also cool!
