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Nait
08-07-2004, 06:30 PM
How far has mathematics progressed in the world of Eizon?

I have no idea. But I'm willing to find out.

On a side-note, Zhem uses base-six, my favourite, and IMHO, the best base there is. Screw decimal, screw duodecimal, screw octal, hexadecimal and binary, hexal is the way to go.

If only because you can count up to 35 with your hands (that's 55 in hexal ), and 1 / 3 = 0.2 :D

-N-
08-07-2004, 06:55 PM
I can count up to 60 with both of my hands. Using the lines and creases in between each finger, as well as the subsections of each finger, thumbs included.

Anyways, I don't know - I saw your taxes, but has the concept of money and taxes even developed yet? Without the idea of "percent", taxes would be very difficult to implement - aside from a "hard tax" of a certain value.

The Department of Mathematics doesn't feel like re-deriving all the ancient Greek theorems either.

Nait
08-07-2004, 06:58 PM
Percents be damned!

After all, percents are just 1/100 - that's why I talked mostly in fractions. *_*

And BoB screwed up and said I could play it like it's a few hundred years after the rift. >:o

And I have some ideas for money. Tax-tokens and such.

-N-
08-07-2004, 07:00 PM
But are we assuming private ownership is an existant concept? I mean, BoB listed out the types of government we all have, but not any of the types of economic systems that we have...

Nait
08-07-2004, 07:05 PM
Well, I don't see what mathematics has to do with taxes anyway. >:o

I was thinking of mathematics extended from pseudo-sciences, like astronomy from astrology. Astrology is the study of fate, in many ways - which could lead to some statistical thinking. Or, if you concentrate on the part of astrology which defines the human itself, and not fate, you could get early psychology.

Mathematics from numerology or astrology or something else isn't so far fetched.

Loony BoB
08-08-2004, 12:39 PM
I dunno. How far had maths progressed during the medieval times? I imagine the Ingmarians would be the most advanced in that area because for some reason it's always the desert-dwelling people who lead in astronomy and mathematics. That and they were the leading engineers in Aiyon.

Nait
08-08-2004, 12:46 PM
I don't really believe that desert = astronomy and mathematics. The Twin Floods weren't always such a complete desert - and what about the astronomers of India, China, Mezoamerica? The Arabs were at the top of the game of mats in medieval times, but I'm sure there were reasons other than "desert-dwelling". For example their calendar, which is based on watching the moon - and which requires some mathematical prowess - could have given them the motive. And much of their stuff was also borrowed, given down by the Greeks and Indians.

Loony BoB
08-08-2004, 12:55 PM
But they were never as precise and accurate with their ordeals as the Egyptians/Arabs and particularly the Aztec (and Inca?).

I'm just saying that they would be more likely to advance that stuff than others would, not that they actually will.

Nait
08-08-2004, 01:00 PM
I don't know.

http://en.wikipedia.org/wiki/History_of_mathematics

Commerce, jometry of land and astronomy.

Proxy
08-09-2004, 07:49 AM
I hate math -_-;;

-N-
08-10-2004, 03:01 AM
Geometry:

Let's just assume that Euclidean geometry has been flushed out to its limits, ant there exists the concept of a Cartesian coordinate system.

Calculus:

The concept of approximating curves as a series of lines and analyzing them has begun. (Elementary calculus). Advanced differential equations have not yet been reached. Matrix algebra has not yet been conceived.

Metamathematics:

Number theory, set theory, and any form of analysis or metamathematics has not yet been conceived.

Everyone down with that?

Nait
08-10-2004, 10:31 PM
Geometry:

Let's just assume that Euclidean geometry has been flushed out to its limits, ant there exists the concept of a Cartesian coordinate system.

Calculus:

The concept of approximating curves as a series of lines and analyzing them has begun. (Elementary calculus). Advanced differential equations have not yet been reached. Matrix algebra has not yet been conceived.

Metamathematics:

Number theory, set theory, and any form of analysis or metamathematics has not yet been conceived.

Everyone down with that?

Nait not understand. Please, Neel speak slow. Nait understand, Neel speak slow.

crono_logical
08-10-2004, 10:33 PM
Just assume people can count :p

-N-
08-11-2004, 02:51 AM
Nait not understand. Please, Neel speak slow. Nait understand, Neel speak slow.:exdee:

Okay, I'll go slow, but be warned, it'll be long.

Geometry.

Euclidean geometry starts with the following five postulates.
1. For any two points, there can exist a straight line in between.
2. Lines can be extended forever.
3. You can create a circle given two points and a plane. (This is how a compass works.)
4. All right angles equal one another.
5. This is a crazy one - if a line intersects two other lines, and if on one side of that cross-line the angles created do not add up to 180 degrees, the two other lines intersect (and are not parallel).

I've paraphrased these to sound okay. Basically, all geometry you learned in high school is derived from these five basic rules. So Euclidean geometry is basic stuff like "A line is one-dimensional, a square is two-dimensional", and stuff like "Angles inside a triangle add up to 180 degrees." Euclidean geometry takes place on a flat surface - a plane. It's pretty much intuitive geometry.

Non-Euclidean geometry takes place on curved surfaces, like spheres. There, the angles inside a triangle don't add up to 180 degrees. Since Euclidean geometry seems most intuitive (due to taking place on a flat surface), then I propose that it and all subsequent Theorems (such as Angle-Side-Angle, that stuff) have been derived. Hey, we gotta measure our land sizes somehow.

There's a lot of history surrounding Euclid's Fifth - many thought it should be a Theorem (a derived truth) rather than a Postulate (a starting truth). By denying the truth of Euclid's Fifth, non-Euclidean hyperbolic and elliptical geometries were discovered. I propose Eizon has not heard of such madness yet. Besides, I doubt GR (general relativity) has been discussed yet, and that's really the only application of non-Euclidean geometry, so there. :p

Calculus.

We can say calculus is in its nascent stages, as Eizonian scholars begin to study not only the phenomena around them, but how those phenomena change. Rate of change gives birth to the art of calculus. Rates of change are easy to calculate given a straight line (you just take the slope), but much harder of a curve. So some Metareason scholars in the Department of Mathematics got together, approximated a curve - they chose a circle - as a series of lines, and took the slopes of all those lines. They tried to use as many lines as possible. Lo and behold, what did they get when they looked at the slope data but a sine wave - the same functions covered in the trigonometric extensions of Euclidean geometry.

And from studying similar curves, their slopes, and then shifting their focus from the slope of the curve to the area under the curve, the scholars gave birth to the two Fundamental Theorems of Calculus, and I say that's where we stand so far. That gives scholars all over the chance to study truths about patterns in topology, give birth to chaos and reverse-chaos theories, invent imaginary numbers (Euler's Theorem), and discover governing differential equations behind natural phenomena.

Simplified: The groundwork for Calculus is set, but no more. What I have listed above is what can follow from these fundamental theorems. This gives other countries' scholars the chance to contribute to the growing wealth of Eizonian knowledge as well as put Metareason Academy at the forefront of such endeavors.

Metamathematics.

This is really high level stuff, as the prefix "meta" might suggest, so I say it just hasn't been thought about yet. Stuff like this involves the expression of mathematics, what truths can it express, and what truths does it not have the power to express. It involves really big words like "recursive set theory" that build on concepts such as "number theory" - the rules that govern properties of numbers, "set theory" - the same for sets, and so on. This would include Godel's Incompleteness Theorem.

Whew, well, there it is.

edit: SUPER SIMPLE VERSION: METAREASON ACADEMY OWNS MATH. :exdee:

Nait
08-11-2004, 10:01 AM
It's a language-problem. What's "calculus"? We never had "calculus" in school. >:O

EDIT:

Hey, leave something to the Academy of Zhem, too!

Shlup
08-11-2004, 10:16 AM
Nait just--I mean--Uh...

...:fpcry:

Nait
08-11-2004, 10:19 AM
Because I went to a Swedish-language school. Duh.

Shlup
08-11-2004, 10:33 AM
It's because you went to a Swedish-language school that you are absolutely insane?

Nait
08-11-2004, 10:47 AM
YOU UNDERSTAND


OH HAPPY DAY :whimper: :weep:


EDIT:

Neel: http://www.sunsite.ubc.ca/DigitalMathArchive/Euclid/byrne.html :cool:

-N-
08-12-2004, 02:51 AM
I went through all that trouble to explain all that stuff in my own words just for you, and you respond with a LINK? :mad2: No lower-level math findings and publications for you! :p

But seriously, there's a lot of room for growth. The biggest place for math to grow is in finding governing equations for how phenomena occur in the world. For example, governing DEs can be found for spring systems, spread and containment of infections, and so on.
Geometry is really basic stuff - that has to be nailed down, otherwise we can't even make maps. Hyper-geometry... well, once our society advances into existential crisis, we can introduce relativistic theories. :p
And provided sufficient research, you could literally reinvent Church, Tarski, Turing, and Godel's Theorems, except you can call them your own! Yay! :p Or maybe we live in a world were such theorems do not exist??? :eek:

edit: TOO MANY :p's!! I'M TURNING INTO CLOUT... glarble... gah... :x_x: