Clogging Your Intertubes...

Three Point Prowler: A Structural Analysis Program

2012-02-11T14:13:00.003-07:00

Written by Allie Jackson & Kyle Reeder
Colorado State University

Mineralic: A Mineral Identification Program

2012-02-09T23:38:00.003-07:00

Written by Kyle Reeder
Colorado State University
KReeder01@hotmail.com

Posterity and Induction

2012-02-03T01:12:00.001-07:00

Humans reason every day of their existence. Whether it is thinking about the weather or how to take a toaster apart, humans reason. Reasoning is paramount to the human condition. It is how we, as human beings, make inferences and arrive at conclusions according to what we observe. There are many types of reasoning that are included under the broad category of “reasoning.” One type of reasoning we use every day, completely unaware, is inductive reasoning. Inductive reasoning is a type of non-deductive reasoning that acts a basis for a majority of scientific developments. A philosopher by the name of David Hume questioned the justification for investing so much faith into induction; he believed that it is fundamentally flawed. There were a great many responses to Hume’s argument, one being the pragmatic solution which asserts that induction is necessary to human functionality. This response acts as a plausible solution to the problems of induction.

As mentioned earlier, induction is a type of non-deductive reasoning. The process of induction involves matter of fact, rather than relation of ideas. It concerns concepts which could conceivably exist in another manner. For example, a triangle’s angles adding up to 180 degrees is something we cannot visualize any other way. It is the relation of degrees to a triangle, and is absolute. Induction does not focus on necessity, but instead relies heavily on human observation. The principle nature of induction is the extrapolation of previously observed events to future events, or from the already observed to the unobserved. Induction has an inherent reliance on past experience: if a test has produced the same result 10 times out of 10 times, one can conclude the 11^th attempt will yield the same result. One can assume that if every orange they have seen is orange, then all oranges must have the same properties. Past experience acts as a credible source for the prediction of future events. Nearly all contemporary science is based on induction. The basic limitations of humanity force scientists to rely on inductive reasoning. One cannot observe everything in the universe, nor can one guarantee an absolute.

Hume’s argument stems from the justification of induction. His claim is that we have no feasible justification for believing induction. There is no proof that the past in any way impacts the events of the future. Induction cannot be proved independent of human experience because it pertains to matters of fact. When a glass is dropped, one can conceive the possible result that it will, in fact, not break, or perhaps not even fall. Consequently, induction must be proved on the basis of human experience. This becomes quite problematic because Hume explains that such proof is circular. That is to say, that the conclusion and premises are dependent on each other. A detailed explanation of this theory of circular logic present in induction can be easily presented in an example. For instance, Bill has performed experiment X 100 hundred times and has arrived at N result every time. He believes his 101^st attempt will also produce result N, because it has every other time. Joe insists that these prior events have no bearing on the future outcome and asks for a reason for Bill’s theory. Bill is using induction and Joe is utilizing Hume’s response. Bill says that every time he has encountered such a situation in the past (one relating to induction), induction has worked; so it will work in the present. Joe carefully asks Bill to examine his statement. Upon closer inspection it is clear that Bill is justifying the use of induction THROUGH induction. Circular logic is the only way to prove induction, and it is therefore invalid. Hume is stating quite simply that there is no justification for the use of induction and it should not be implemented in proper science.

Of the many responses to Hume’s argument, there is one in particular that both embraces and criticizes Hume’s logic. The main concept of this idea is the necessity of human function, of pragmatism. Nearly every aspect of our lives and theories is in some way rooted in the idea of induction. This view basically accepts that there is no true rebuttal to Hume’s argument, that he’s correct in his analysis of induction. However, because induction is so crucial to our everyday lives, we must, accept some standard. Nearly everything we say and do can be questioned due to the flaw of induction. So, while there may not exist some succinct refuting of Hume’s ideas, we still must use induction, for the sake of convenience. Simply put, life would be greatly more difficult without induction. Despite its shortcomings, it has been very successful in the past, and is required for much of our lives. One using Hume’s argument can easily defeat any statement which doesn’t have explicit empirical evidence. Consequently, we as a society must accept some standard believability for induction. I believe the aforementioned argument to Hume’s argument is remarkably successful. It accepts Hume’s claim that induction is unjustifiable but presents a unique concept that although the method of reasoning cannot be proved reliable without circular logic, it should still be used, out of convenience. We have arrived at a wall, so to speak, and the only way around it through being pragmatic. It is a realistic solution to the issues of induction raised forth by David Hume.

Waves

2012-02-03T00:05:00.005-07:00

The interesting thing about waves to the apprentice physicist is the fact that the same wave equation (general form: ∂t^2 = ∂x^2 + ∂y^2 + ∂z^2) can be used to model so many different physical phenomena. The most prolific and congruent modelling is that of electromagnetic waves. One needs only a single equation to fully model every variety of colored light, radio waves, microwaves, UV, infrared, X-rays, and gamma rays; the only difference between all of these waves is their frequency and corresponding wavelength, because all of these propagating disturbances are fixed traveling the speed of light.

The most astounding equation to me in mathematics is the following:

c = 1/√(µ£)

James Clerk Maxwell stumbled upon the equation before mankind even knew what a radio wave was. The equation states that the speed of all electromagnetic waves is equal to one over the square root of the product of the magnetic & electric constants.

If you decompose the waveform of an incoming wave across an area, you will be left with component waves that when summed describe the 4-dimensional character of the incoming wave front. Let's call a set of waveform data "†".

† = [x,y,z,t]

While we may not know exactly what invoked † or where it was located, we do know the physics behind the propagation of an electromagnetic wave very precisely. Therefore, we can say that a source "¥" produced † through equation "ƒ" (where ƒ is the set of equation governing the motion of the wavefront in three dimensions through time):

Thus, ƒ(¥)=†, which is to say that if you input source ¥ into the equation ƒ, the result will be †.

Now, we know ƒ very well through prolonged study of physics and we can measure † using a spectroscope or various other devices. However, we can only know ¥ if we directly observe the source being created somehow.

What if we receive a dataset † and want to use ƒ to figure out what ¥ was? Well, we can't do that directly. Nonetheless, we do have ways of estimating ¥, which is really what all of physics is all about (using simplified models to make estimates of reality).

In mathematical terms, what we need is the inverse model of ƒ, which involves a branch of mathematics called inverse theory:

ƒ(¥) = †
ƒ'≈ ƒ^-1 ≈ 1/ƒ

ƒ'(ƒ(¥)) = ƒ'(†)
¥ = ƒ'(†)

The way we can do this is to make assumptions about ¥'s character and try to fit a model to † using a nonlinear least-squares fit. What we receive is called a non-unique solution, which means that there are an infinity number of ¥ that could have resulted in † based on governing equations ƒ.

These non-unique models are essential to modern exploration geophysics, in which seismic waves are modelled (really Blogspot, "modelled" is not a word?). When you detonate an explosive on the surface, seismic waves travel down into the ground. At each density or Young's modulus interface in the ground, waves are either reflected (given by a coefficient R, where 0≤R≤1) or transmitted (given by a coefficient T, where 0≤T≤1).

T + R = 1

If there are no interfaces, then T = 1 and there are no reflections. On the other hand, if there is an interface that produces R = .8, that means that 80% of the wave energy is reflected, forming an antiparallel wave front off of the interface, and T = 1 - .8 = .2, which means 20% of the wave energy continues through the post-interface medium.

Using inverse theory and a number of receivers, we are able to effectively model the subsurface using energy created by seismic sources. This is one branch of science that I am fervently interested in.

How Fast We Live

2012-02-02T00:21:00.003-07:00

Imagine with me a simulated reality (ƒ˚) constrained by parameters set by a technician.

The number of computations-per-second of the computer system that is hosting ƒ˚ limits the maximum speed of calculations, which then correlates to the maximum speed of time within ƒ˚.

It follows that if we create a pseudosentient being (§) within ƒ˚, constrained by the aforementioned parameters, the reality which § inhabits will propagate through time at a rate no greater than the limits of the system which is modelling it.

If we turn down the magnitude of the rate-of-change of time in ƒ˚, §'s thought processes will be slowed proportionally to the inputs the being receives from its artificial environment. In fact, § will not have any clue that we have altered the speed of time in the system.

Time could be constantly accelerating in ƒ˚ and the beings contained within would not have any possible means of detecting it.

As a corollary, consider your own life and the speed of time that you experience: how can you say for sure that time is moving forward at a constant rate? You can't.

Introduction

2012-01-30T20:51:00.004-07:00

If an outside observer were to peer into my life, they might notice the following things:

¬ introverted male cat owner
¬ honest, carefree individualist
¬ hard-working perfectionist
¬ beer-drinking, cigarette-smoking hedonist
¬ building a career in exploration geophysics
¬ prone to changing his mind suddenly
¬ creative & passionate intellectual
¬ rationalist, naturalist, secularist
¬ superior computer skills
¬ gun owner and knife fancier
¬ adventurer: hikes to remote areas alone

I have decided to start blogging again, because I miss having a place to compile the things I find on the internet as well as access to an outlet for my (supposedly) original thoughts when they come around.

I would be very happy and surprised if any of my old followers were still around! Please leave a comment if you are.