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Sunday, February 28, 2010

Buoyancy and Atmospheric Gasses

Why does an iceberg, say, float on water? Water and ice are the same material, but the solid form is less dense than the liquid form.



This, however, doesn't happen in an orbital freefall condition though because there is no gravitational field to define which direction is up and which direction is down.



According to a Newtonian physical model, there needs to be a change in momentum, an impulse, to cause the less dense object to slide through the denser object at a faster rate, this occurs in the presence of a gravitational field which provides that impulse because gravitation is a body force related to mass which thereby acts on the denser object more than it acts on the lighter object.



That is at least part of the cause of buoyancy, however that doesn't exactly explain all of it though. Buoyancy is also statistically related to the principle that a less massive object, perhaps a soccer ball for example, will be knocked higher into the air than a more massive object, perhaps a bowling ball, assuming that the same amount of impulse (force integrated over time) is provided to the objects, perhaps by a kick of the foot. Statistically speaking, more massive objects have more mass inertia than the lighter objects do, and so the same amount of energy will drive one higher than the other.



On the molecular scale of collisions, every collision is like different masses being kicked around against each other. Statistically, the lighter masses should end up higher than the heavier masses provided that the same amount of impulse is given to all of them. Unfortunately for the model, the Earth is an open system and thereby is exposed to the light from the sun, so different molecules will absorb different wavelengths and get different levels of impulses than other molecules do.



So you can therefore get the paradox of more massive molecules going higher than a lighter molecules as you go up.



Sources:

Water P-V-T

Gas Absorption Spectrum

Saturday, February 20, 2010

Geo-Pattern 1

Fourier Analysis and Linear ODE's

Fourier Anylisis (where omega, w = 2pi/T)


Specific Fourier Waveforms


0th and 1st order differential equations


2nd order differential equations


Note - This tailor approximation method can be used for simplifying things for obtaining approximate numerical solutions for given input functions


nth order linear ODE's and transfer functions


Rules for Laplace Transforms


Laplace Transforms for specific functions


Special differential equation forms


Note - People who like this post will also like The Best So Far

- Sources
Pictures 1,3,4,6 are my personal notes
Pictures 2,5,9 taken from Wolfram's Mathword
Pictures 7,8 taken from Laplace Transform Tables

Friday, February 19, 2010

Religious Mythology vs Naturalism

Well, the majority of religious stories are people's dreams, history mixed with myth, hallucinations, incorrect hypothesis about nature, metaphorical parables and such. No real scholar takes religious stories as factual. Religion represents about 6000 years of human imagination, the Bible Torah and Koran represent a biased interpretation of history localized in the Middle Eastern Semetic regions of the world whereas the 8-fold Path and the Vedas represent biased Asian history. There are many other similar legends by many other cultures throughout human history.  When you look at history for what it really is, you realize that every culture had stock in making themselves look great, and hence religious traditions embellished on the specialness of their own native people.

Studying it all from an unbiased context you should see that is true, perhaps you don't realize this, but a large driver in the successes and failures of cultures spreading was geography and resources and certainly not the validity of the religious traditions of the surviving cultures which determined this.

It is the naturalists whom realize the world for what it truly is, based on evidence. There is no evidence for any kind of life after death, no evidence for reincarnation, of becoming an avatar, or anything like that and therefore naturallists tend to reject supernatural beliefs.  Rather, for the here and now naturalists realize that we should love ourselves, obtain intellectual enlightenment via studying maths and sciences, get a nice home with a nice garden, earn plenty of money, innovate to make the world a better place, make friends and acquantences, raise a family, and then when it's all over your material self gets recycled by nature while your ideas and innovations, your genes, memes, and temes go on evolving for however long causality will allow them to.  If you really believe however, that you're going to get an eternity of intellectual enlightenment AFTER you die, then go ahead and believe that, but there is no evidence for it.

Thursday, February 18, 2010

Why Do People Laugh at Creationists?

Here is the first video of a 32 video series. There is some good information about what creationists believe, and how that correlates negatively to what actual science has shown to be true.

Wednesday, February 17, 2010

Random Number & Triangle Fields



The following "Random Number & Triangle Fields" that I did up on MS Excel shows something neat about the mathematical parameters of controlled chaos. (each time you save the Excel file it generates a completely new image)

Tuesday, February 16, 2010

Monday, February 15, 2010

Napoleon Hill - Accurate Thinking



-On a side note-

It should be mentioned that inductive reasoning (including science itself) should be under constant revision, in a bayesian sense, to accomidate and explain all the outliers to a theory or generalization, and that using inductive reasoning somebody could easily draw the wrong conclusion for lack of enough data.

It should also be mentioned that deductive reasoning can be incorrect via initially assuming a false premise, perhaps based on incomplete inductive reasoning or erronious misinformation, or by the utilization of faulty logic to arrive at a conclusion.

However, generally, with more accurate logical (deductive) and objective (inductive) scrutiny comes more accurate thinking.

Sunday, February 7, 2010