Postmodernism and Mathematics

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ZackF

Puritan Board Graduate

PRINCIPLE #2: For every scientist, whether researcher, technician, teacher, manager or businessman, working at any level of mathematical competence, there exists a discipline in science or medicine for which that level is enough to achieve excellence.
That one has been bouncing around in my head for a few days. It reminds of an interview of a fairly well known software developer that I was listening to a few weeks ago. He avoided programming for years because he thought it involved difficult math and he hated math. Coding can indeed require advanced mathematics depending the program's function. In many cases, except for some very basic algebra, simple logic is often what is required. Along with the logic, perseverance in troubleshooting when the program just won't compile, run or run correctly are essential to success.

These idiosyncrasies can get bottled up in the term STEMs. That is why, thankfully, people are able to get into certain "STEM" fields without a degree. They have a computer and can make it work. Other examples are out there.
 

Jo_Was

Puritan Board Freshman
That one has been bouncing around in my head for a few days. It reminds of an interview of a fairly well known software developer that I was listening to a few weeks ago. He avoided programming for years because he thought it involved difficult math and he hated math. Coding can indeed require advanced mathematics depending the program's function. In many cases, except for some very basic algebra, simple logic is often what is required. Along with the logic, perseverance in troubleshooting when the program just won't compile, run or run correctly are essential to success.

These idiosyncrasies can get bottled up in the term STEMs. That is why, thankfully, people are able to get into certain "STEM" fields without a degree. They have a computer and can make it work. Other examples are out there.
I wouldn't even say that what EO Wilson is aiming for is that "computers" can do it (he grew up in an era in which "calculators" were still people!) but that there are fields where you don't need to be 100% on for certain skills, and rather than becoming expert at something you don't need all the time, you rather address those things as they come up. For instance, I work in ecology which, while it does have complex math and statistics, especially at certain population studies and scales, I can say a lot more with a lot less before I get to that point. Whereas something like phylogenetics or biochemistry require prerequisite skills in mathematics, statistics, and/or physics to really have that initial grounding! There's a higher threshold of background needed to get far in conversation.

STEM doesn't mean one is doing all of those things equally. Some HARD science tasks have very little TEM involved. Some HARD maths has very little STE involved. It's not like all are equally weighted across disciplines.
 

Logan

Puritan Board Junior
BTW, does anyone really understand what e^i(pi) means? I know it equals negative one, but it pretty much blows me away.
I was going to say that it's pretty complex :)

It has to do with several factors, one being that e^x is equal to its own derivative and leads to the unit circle, second being an imaginary exponent causing a rotation in the complex plane (perhaps most easily seen by Euler's equation, where e^i*x=cos x + i sin x, for proof I like the power series expansion of both sides of the equation).

The rotation forms a repeating unit circle in the complex plane.
e^i*0 = 1
e^i*pi/2 = i (pi/2 radians = 90 degrees, vertical in complex plane)
e^i*pi = -1 (pi radians = 180 degrees in complex plane)
e^i*3*pi/2 = -i (270 degrees in complex plane so purely imaginary)

Any exponent other than those four results in a complex number (e.g., e^i*pi/4 =0.707 + i0.707, which is still part of the unit circle and a distance of one from the complex plane origin).

At least, that's what it means to me but your truth might be different than mine!
 

Phil D.

Puritan Board Junior
e^i*0 = 1
e^i*pi/2 = i (pi/2 radians = 90 degrees, vertical in complex plane)
e^i*pi = -1 (pi radians = 180 degrees in complex plane)
e^i*3*pi/2 = -i (270 degrees in complex plane so purely imaginary)
And here I thought Hebrew was difficult ... :duh:
 

ZackF

Puritan Board Graduate
I was going to say that it's pretty complex :)

It has to do with several factors, one being that e^x is equal to its own derivative and leads to the unit circle, second being an imaginary exponent causing a rotation in the complex plane (perhaps most easily seen by Euler's equation, where e^i*x=cos x + i sin x, for proof I like the power series expansion of both sides of the equation).

The rotation forms a repeating unit circle in the complex plane.
e^i*0 = 1
e^i*pi/2 = i (pi/2 radians = 90 degrees, vertical in complex plane)
e^i*pi = -1 (pi radians = 180 degrees in complex plane)
e^i*3*pi/2 = -i (270 degrees in complex plane so purely imaginary)

Any exponent other than those four results in a complex number (e.g., e^i*pi/4 =0.707 + i0.707, which is still part of the unit circle and a distance of one from the complex plane origin).

At least, that's what it means to me but your truth might be different than mine!
My truth is the trimmed beard makes you look smarter.
 
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VictorBravo

Administrator
Staff member
(perhaps most easily seen by Euler's equation, where e^i*x=cos x + i sin x, for proof I like the power series expansion of both sides of the equation).
Last week, I actually spent a few enjoyable hours sailing those waters.

I'm glad for your truth. When I try to visualize it I end up corkscrewing through that complex plane and getting dizzy.
 
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