Speed blog
Ok, got to leave again really fast, here, so I'll type some quick things.
1) Think I got most of my two presentations for the ASA conference next week finished! Yessss!
2) Somehow, when I was making my ultra important list of previously-unmentioned-by-Ben blogs you should visit, I missed my own cousin's blog, www.myronmarston.blogspot.com which has some of the coolest pictures of China you will find around.
Add to that the fact that China blocks blogger, and yet... somehow he still manages. Could have something to do with his hacking skills.
3. I had a genius revelation this morning in the shower. Ok, so I'm flattering myself, but recently all my best thoughts have been coming to me in the shower. I don't know why (the other day, I suddenly realized how Delta-Sigma A/D converters worked, which had been a mystery to me for years). Today I was thinking about Taylor Series. No, wait, this is really cool -
So you know how you have functions, like "Sine" or "Cosine" or "e^x" or "x^2" etc...? And all of them curve and go up and down, etc. Point is, they are not straight lines. Well, if you zoom in close enough to any of these functions, at some point the function looks like a straight line. Pretty much most useful functions on the planet, for engineering math, can, if you zoom into any point on the function, be represented by a straight line. Some linear function of "x."
This is why, for example, you can say sin(x) = x, for small values of x. Because, the function sin(x) looks like the function y = x, for very small values.
If you zoom out a little farther, and you begin to see a little bit of curvature, you can represent the function by a square, some function of x^2, plus the original function. Zoom out farther, you can represent the function using your function of x, your function of x^2, and your function of x^3. This is called a "Taylor Series Expansion."
The reason this is so cool, is because the same principle can be applied to way more things than math. Almost everything, if you zoom in close enough, seems to look entirely different than if you zoom out. Newtonian physics seems to work for low speeds, but to get a more accurate picture, you need to zoom out and include a whole lot more speeds. Once you do that, relativity seems to surface. Zooming into the surface of the earth, everything looks flat.
I've heard a lot of people make arguments about science related things, based on "it's just so obvious" or "that's just so obviously wrong." I've heard this applied to the theory of relativity, evolution, big-bang, etc. Whether or not any of these are correct/true/whatever aside, an argument based on "this is so obviously true" or "this is so obviously false" is a very bad argument to make, when the scale of the subject is much larger than the observer. You can't include enough terms in your "Taylor series," so to speak. I.e. evolution involves a very long time. To get an accurate picture, you need to observe from a different vantage point. Same with relativity etc. That isn't to say it can't be done, but what is "obvious" in such cases is always only the first term in a series.
Ok, really got to go. Hope everyone had a really great Thanksgiving. Mine was good, though I wish I was at home for it, but I had a great time at Chad&Rachel's (from Penn State Christian Grad's) place, with a few other's from PSCG and around.
1) Think I got most of my two presentations for the ASA conference next week finished! Yessss!
2) Somehow, when I was making my ultra important list of previously-unmentioned-by-Ben blogs you should visit, I missed my own cousin's blog, www.myronmarston.blogspot.com which has some of the coolest pictures of China you will find around.
Add to that the fact that China blocks blogger, and yet... somehow he still manages. Could have something to do with his hacking skills.
3. I had a genius revelation this morning in the shower. Ok, so I'm flattering myself, but recently all my best thoughts have been coming to me in the shower. I don't know why (the other day, I suddenly realized how Delta-Sigma A/D converters worked, which had been a mystery to me for years). Today I was thinking about Taylor Series. No, wait, this is really cool -
So you know how you have functions, like "Sine" or "Cosine" or "e^x" or "x^2" etc...? And all of them curve and go up and down, etc. Point is, they are not straight lines. Well, if you zoom in close enough to any of these functions, at some point the function looks like a straight line. Pretty much most useful functions on the planet, for engineering math, can, if you zoom into any point on the function, be represented by a straight line. Some linear function of "x."
This is why, for example, you can say sin(x) = x, for small values of x. Because, the function sin(x) looks like the function y = x, for very small values.
If you zoom out a little farther, and you begin to see a little bit of curvature, you can represent the function by a square, some function of x^2, plus the original function. Zoom out farther, you can represent the function using your function of x, your function of x^2, and your function of x^3. This is called a "Taylor Series Expansion."
The reason this is so cool, is because the same principle can be applied to way more things than math. Almost everything, if you zoom in close enough, seems to look entirely different than if you zoom out. Newtonian physics seems to work for low speeds, but to get a more accurate picture, you need to zoom out and include a whole lot more speeds. Once you do that, relativity seems to surface. Zooming into the surface of the earth, everything looks flat.
I've heard a lot of people make arguments about science related things, based on "it's just so obvious" or "that's just so obviously wrong." I've heard this applied to the theory of relativity, evolution, big-bang, etc. Whether or not any of these are correct/true/whatever aside, an argument based on "this is so obviously true" or "this is so obviously false" is a very bad argument to make, when the scale of the subject is much larger than the observer. You can't include enough terms in your "Taylor series," so to speak. I.e. evolution involves a very long time. To get an accurate picture, you need to observe from a different vantage point. Same with relativity etc. That isn't to say it can't be done, but what is "obvious" in such cases is always only the first term in a series.
Ok, really got to go. Hope everyone had a really great Thanksgiving. Mine was good, though I wish I was at home for it, but I had a great time at Chad&Rachel's (from Penn State Christian Grad's) place, with a few other's from PSCG and around.
posted by tmm at
3:07 PM
3 Comments:
Myron's pictures of China are great, and a second for his blog.
Hooray, photos! Glad you had a good Thanksgiving meal. :)
[You also neglected to mention a certain blogging sister, who occasionally posts things just. for. you. and then isn't sure if you read them or not. (See: Thanksgiving photos and "elf in hat" series.)]
I would just like to point out that I did mention JupiterButtons in my additional recommendations.
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