Math and Science: Dehumanizing?

An interesting article reviewing Harper's magazine (I tried to get to the original article, but no such luck without money, and I just so happen to be a student) article "Dehumanizing: When math and science rule the school" -- link to CJR, I got this via Symmetry Mag.



I have no problem with liberal arts studies -- in fact, I encourage them and enjoy them myself. The problem I have with the above is: In what way are the sciences dehumanizing? If the point is more to speak up in favor of a liberal arts education, I would be in full support. But it strikes me as particularly silly to claim that math and science are dehumanizing, setting them up as some sort of Human anti-Human dichotomous interaction where one or the other wins out, and we have to set out to find the mean between them. Was I always as interested in math and science as I currently am? Far from. But I was also a 19 year old wanna-be artist. I would expect someone in the humanities, whose grown up a bit, to realize that the conflict between the two isn't intrinsic to the subjects, but a skewing of national culture values being directed towards the things that have "Practical" value or economic returns, which is something that scientists also have to deal with.

Because they are useful...

I ran into an interesting paragraph today. It stated the equation F = ma is used because... it's the fundamental equation in classical mechanics, and it helps to describe a lot of physical phenomena. Essentially, because it is useful. This was described in conjunction with a correlative equation in quantum mechanics that I can't begin to explain, so I'm not typing it out. There was a similar statement made in my Heat and Thermodynamics class that I'm taking: It claimed that Energy was THE fundamental concept of all of physics, and as such, evaded definition. This all brought home to me how much the philosophy of science is seriously influenced by Descartes and all the early modern philosophers: I've personally read that fundamental things escape definition being propagated by Descartes, Locke, and Hume. This shouldn't come up as much of a surprise, seeing as Descartes laid down fundamental work for calculus, and Hume is credited with seriously developing the philosophy behind the scientific method (Taking empiricism to its logical conclusions and inadvertently making a reductio ad absurdum argument for the existence of induction as a separate logical system, in my humble opinion). But this still surprises me.

The process of first principles in logical systems is arational, granted. But the idea that we use concepts in science simply because they are useful for describing the physical world seems, to me, to be a bit off from the idea that we are, indeed, understanding the physical world. I'm fine with stating that science only describes things in useful ways, and that is why we use them, but this description really gives little reason why we would choose one scientific explanation over another, or why even differing disciplines would, indeed, come to the same conclusions. I mean, by this, I could essentially adopt Aristotelian teleology in my description, claim that it's useful for understanding, and stand back satisfied with that use. However, just try and publish a scientific paper today where you ascribe purpose to your explanation, and I sincerely doubt it'll fly. To me, it seems that the "use" approach for validating the logical beginnings of scientific descriptions falls flat. I think the reason for this statement is to cut down the number of assumptions one has to make in making scientific pronouncements (which I would claim is a good thing) -- but unless there is some other validation method, I'm thinking that we are indeed still assuming that our minds are interpreting truth about the physical universe, but we're post hoc attempting to erase the fact that we're making this assumption.

So, sure, they're useful, and that's great. Maybe I'll change my mind when I realize there are other criteria that can be applied to first principles. However, I think it's a far more elegant solution to just admit that we're making something up that sounds like it might be right, then validating it empirically, and assuming all the while that our minds have some connection to the truth of the universe.

The Photoelectric Effect

You cover this topic in your first semester of Freshman chemistry. But at the time I have to say that I failed to grasp the weirdness (and pure scientific genius) of Einstein's nobel prize winning experiment dealing with the photoelectric effect. I don't pretend to be able to condense a good 50 years of scientific inquiry into one blog post, so I'm just going to focus on the single part of the photoelectric effect that I seriously missed in Freshman chem, and am only now beginning to grasp in Physical Chemistry.

The energy of an electron ejected from a metallic surface depends not on how much light is hitting said metallic surface, but rather how often the light hits the metallic surface. To illustrate this odd phenomena, suppose a ball being hit by another ball (in a perfectly elastic collision for ease of explanation):

Now, in mechanics (and if you're familiar with pool) we would expect the ball to hit the other ball, stop, and for the second ball to continue in motion, like so:

This would happen no matter how hard we shoved the original ball. As long as there was still kinetic energy in the initial ball when it hit the second ball, then the second ball will be sent away. This is somewhat still the case with regards to the photoelectric effect, but not exactly. The photoelectric effect deals mainly with light waves and electrons. The electrons are in a metal, which if you've ever opened anything electronic, you'll notice that it's filled with metal wires. That's because electrons easily move through metals, which is why metals can carry a current. This also makes the electrons easily knocked away from the metal by a source of energy like, say, light.


There's one more very important thing to consider -- at the time of this experiment, light was thought to be a wave (For some very good reasons, explained at Built on Facts). The energy transmitted from light was thought to be dependent upon a given light beams "Intensity", which was determined by the wave's Amplitude. This is important because the electrons held in the metal have 1) a certain amount of energy they need to absorb in order to knock whatever force is holding them in place away, as well as 2) however much more energy is added to the electron to get it moving. However, when Einstein flashed both bright and dim lights on his sheet of metal, there was no change in how many electrons were ejected. This means that the amount of energy from a light beam was not dependent upon its intensity. Further, there was a given Frequency where electrons were no longer ejected. So, the energy from light must be dependent upon how frequent each wave hit the metal, as opposed to how many waves hit the light in a given time. To illustrate this:






In these two drawings, the light with one "wave", but more frequency (illustrated by the shorter wave lengths, as all light travels at a constant speed) has a GREATER amount of energy than the drawing on the left with four "waves" hitting the metal plate all at the same time. Now, in everyday life, supposing you throw four balls at an equal amount of Force at a target and they all hit at the same time, you're going to transfer all of the energy in each of those those balls into the target at the same time -- which will give you a greater overall impact. If you were to throw them separately, but more frequently, the net energy transfered to the target would be the same, but the impact would be 1/4 of the initial example each time you threw the ball. In the case of the light waves, not only is the energy transfer greater with frequency, but so is the overall impact! This is completely contrary to everyday intuition (which is fine, as physical systems aren't actually supposed to do anything. we just observe what they do, then describe them). This all ALSO resulted in confirming a separate experiment by Planck that stated the same thing, but came from different angles -- which gave further support that the energy in a light wave is not dependent upon intensity, but instead on frequency. The end all equation to this all was:

E = hν

Where E is energy, h is a physical constant (called Plank's Constant), and nu (ν) is the frequency of a given wave.


Now... OK... admittedly, here's where things are still shady for myself... but the photoelectric effect also demonstrates the dual nature of light: That light exhibits both wave-like and particle-like features. The best formulation I can come up with here is that, supposing we have a wave, like above, and we know the frequency that the wave needs to be at in order to knock electrons loose (as frequency corresponds to energy). We set that frequency to just above what is required to detect electrons being knocked loose. Now, we spread that light beam out with a lens over an entire metallic surface. What is observed? Whether the light is spread out or focused on a single point, the same number of electrons are ejected. If we had a wave, the entire wave would be spread out over the surface, and we would then also have less energy transferred to the plate, and we would expect electrons to not be knocked loose. However, since we still observe electrons not only be knocked loose, but the exact same number of electrons being knocked loose, we have to conclude that light energy comes in packets. And THAT is the beginning of quantum (meaning "piece") mechanics.

Holy. Fuckin'. Shit.


(apologies for any bungling to actual history of this discovery, or even misrepresentation of the theory. Really, I'm just beginning to grapple with these concepts. Someday, this stuff'll make even more sense)

Conceptual Question of the Day

Classes started today. Also, I think I'm going to try to treat this more like a traditional blog, which means more frequent updates with less thought out content. Sweet. Though I'd like to also throw in some good content when I feel I have the time. For now, however, my semester is lookin' hella busy, and I don't think I have the time to write an end-of-the-week recap of my thoughts on science. Instead, I'm just blundering along and pushing out junk, hoping that something sticks to the inner walls of knowledge.


So, of all the questions I raised to myself today, this is the one I remember as the most interesting: Suppose a ball is coming towards you. You do not know the origin of the ball. Before the ball looks like it's going to hit, how do (or can?) you distinguish between a) a ball coming towards you, and b) a 4 dimensional "sphere" entering the familiar 3 dimensions.

Teaching Experience, 1

Let it be known that I want to be a teacher. It isn't what I want to do when I first graduate, but it is what I want to become in the end. So, I try to explain things to people as well as keep up on my philosophy of teaching. The other week I had a good teaching experience, and have recently read Whitehead's "Aims of Education", which has me thinking about teaching in general. The experience went like so:

My brother visited me. He has recently graduated from High School and is currently working some low income jobs before he goes to college. In conversation he made a comment where he felt uncertain about evolution. I asked what, and specifically he thought that random mutation was an odd concept. Particularly, he found it difficult to believe that random mutation could create viable species over time, because he found the idea of "Random" to be arbitrary, and he thought that if a species mutates that it would be more likely to die. I explained what "Random mutation" actually meant -- not that it just happens, that there are explanations for the mutations, but the causes are out of anyone's control and therefore are labeled "random" -- and that he was completely correct in his assumption that a mutation is more than likely kill an animal. It was only in the rare cases where a mutation actually helped a species pass on its genetic code and survive better than its peers that the mutation is passed on. I also noted that there was more to speciation than random mutation, such as sexual selection or dramatic geographic separation, etc. Later we visited my campus' museum of rocks, and the museum of stuffed birds. We saw fossil records of now extinct species, and stuffed animals of species still alive. Later we visited our towns' zoo. Once we reached the zoo, my brother would comment about certain features of an animal, how these features helped that animal survive, and essentially out-compete other animals in certain ways.

So, in an afternoon, he had the groundwork of a theory given to him, and then he was able to make deductions from that theory about actual animals that he experienced. I'm sure Rousseau would be proud right now, but I'm a little uncertain about Dewey (of whom I am a large admirer of). My brother obviously learned something, and started applying that knowledge to what he saw in the everyday world. Which is awesome, and for a passing incident where I hadn't really prepared anything of the sort and we were just hanging out, very awesome from my perspective, as he's grasped the foundations accepted by the scientific community. These are all important. However, as teaching should be about process, what I taught him was not the process of science. He learned how to make logical conclusions from a given framework of knowledge. Which is, in fact, a fantastic skill, and of great use in the scientific method. However, there was no induction that occurred -- we didn't have a large sampling of animals from which we induced the hypothesis of natural selection, but rather, we walked amongst the animals looking for positive confirmation of a generally accepted hypothesis. This is all well and good, but it's not scientific, and it's not teaching the scientific method, but rather the analytic method.

But then there's the practical side of things: Most places have access to zoos. But do they have access to wildlands that easily show speciation? We could substitute in photographs, but that would certainly not be what Whitehead would agree to, as he's seems to be more of a mixture of a Romantic/Utilitarian educator. I don't know if I agree with him entirely, but I certainly saw something awesome occur while we visited the zoo -- the application of accepted theory, and the acceptance of accepted theory. It wasn't the whole method of science, but analytics is certainly an important part of science. Perhaps the scientific method, as a whole, could be spread out amongst the various sciences? Leave the Null-Hypothesis to the physical sciences, as physical objects are in easy supply to any school budget?