
Deiymiyan
I AM
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Mathematical Explanation...
#1838650  08/21/03 09:46 PM (14 years, 9 months ago) 


In terms of mathematics, how far have we come?
We add and subtract... multiply and divide... create scenarios of probabilities... comb trough permutations... Algebra... Geometry... Possible subatomic interactions...
All of these physical possibilities...
And Calculus puts it all into motion. Our fourth dimension... Time related events.
Is there any form of math that goes beyond rates of change?
What about division by zero... Does that have any significance yet? So far, a calculator will not give a good answer.
Are there any math gurus out there who might, perhaps, shed some light concerning the kinds of current limits math has reached?

Dei Gratia de integro,
Veni Vidi Vici:
In Nomine Domini..

pattern
multiplayer
Registered: 07/19/02
Posts: 2,183
Loc: Canada
Last seen: 3 years, 3 months

Re: Mathematical Explanation... [Re: Deiymiyan]
#1838767  08/21/03 10:17 PM (14 years, 9 months ago) 


I'm inclined to say that artificial intelligence is the height of mathematical expression. Certainly not the most complicated or complex, but it does reveal some limits.
 man = monkey + mushroom

kaiowas
mndfrayze'speppet urme
Registered: 07/14/03
Posts: 5,498
Loc: oz

Re: Mathematical Explanation... [Re: pattern]
#1839064  08/21/03 11:56 PM (14 years, 9 months ago) 


i took 4th level calculus (differential equations, D.E.) and linear algebra last year. differential equations dealt with rate of change with respect to many variables. Linear algebra on the other hand dealt with techniques on simplifiying and sometimes even solving systems of equations (ie. 4 equations are related and you find out how). I'm no guru, but that shit was mind expanding. Especially when representing four variables in the 3d plane (without any of the variables being held constant). basically an equation in four dimensions (four variables) is represented as a 3d object. We then apply either cartesian (sp?) or spherical coordinates and look at the rate of change over the surface area of the equation represented. dunno if that made any sense or not, though I'm trying
now onto dividing by zero. you can't divide by zero, because even though 0 exists, if you divide by it you will miss other solutions. This is a neat concept. In a D.E equation dy/dx=a*y, y=0 is a solution (dy/dx is the infinitesimal rate of change of y with repect to x ie the differential; y is a variable and a is a constant). why is y=0 a solution? well looking at both sides of the equation 0*a=0. if y is zero then dy/dx is zero. so 0=0. so say you want to find the constant "a" (finding constants is very impotant in physics). in order to do this you need to divide by y. now y is a variable (could be any number), but you already know y=0 is a solution, therefore you have to account for it, or else you can't find "a." Therfore when you divide by y, a sidenote must be written (for all other y not equal to 0 in this case) where is this going? in caluclus you would find an equation for the general solution (the nonzero solution). in this example the general equation (whic is the solution to the DE) is y=C*e^(a*x). you would then graph this solution alongside with the zero solution. what happens is that the two solution equations NEVER cross, and this is why you have to account for zero. so how do you know which one is actual solutions (since we have two or three for one DE)? easy, it depends on your starting point. if you start at 0, then you will use the resulting solution of the D.E equation that used y=0. if not, then you use the other one. this is why we need to look at everything, and the limit of dividing by 0 is very useful. hope that gave a couple of good points in my rambling
 Annnnnnd I had a light saber and my friend was there and I said "you look like an indian" and he said "you look like satan" and he found a stick and a rock and he named the rock ooga booga and he named the stick Stick and we both thought that was pretty funny. We got eaten alive by mosquitos but didn't notice til the next day. I stepped on some glass while wading in the swamp and cut my foot open, didn't bother me til the next day either....yeah it was a good time, ended the night by buying some liquor for minors and drinking nips and going to he diner and eating chicken fingers, and then I went home and went to bed.senior doobie

SkorpivoMusterion
Livin in theTwilight Zone...
Registered: 01/30/03
Posts: 9,954
Loc: You can't spell fungus wi...

Re: Mathematical Explanation... [Re: kaiowas]
#1839136  08/22/03 12:25 AM (14 years, 9 months ago) 


I......HATE.........MATH... It gives me Aneurisms Fuck Math MAth Sucks I HATE MATH!!!!!!!!!!!!!!!!!
 Coffee should be black as hell, strong as death, and sweet as love.

trendal
tangential derivation
Registered: 04/17/01
Posts: 20,638
Loc: Ontario, Canada

Re: Mathematical Explanation... [Re: Deiymiyan]
#1839326  08/22/03 02:12 AM (14 years, 9 months ago) 


A good place to look for cuttingedge mathematics is in String theory. One of the biggest hurdles yet to be overcome in string theory is mathematics which we don't understand yet.
Calabiyau shapes seem the most interesting to me at the moment
Look, here's a 2D representation of one:

Once, men turned their thinking over to machines in the hope that this would set them free.
But that only permitted other men with machines to enslave them.

MindTrap
Disembodiedvoice
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Re: Mathematical Explanation... [Re: trendal]
#1839332  08/22/03 02:14 AM (14 years, 9 months ago) 


or Chaos Theory

trendal
tangential derivation
Registered: 04/17/01
Posts: 20,638
Loc: Ontario, Canada

Re: Mathematical Explanation... [Re: MindTrap]
#1839344  08/22/03 02:18 AM (14 years, 9 months ago) 


Chaos theory lead me to an entirely different explanation of life.
Life, just as any large chaotic system, might obey the laws of chaos theory and thus order springs from the disorder.

Once, men turned their thinking over to machines in the hope that this would set them free.
But that only permitted other men with machines to enslave them.

wavesoflight
Stranger
Registered: 01/29/03
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Last seen: 14 years, 8 months

Re: Mathematical Explanation... [Re: trendal]
#1839346  08/22/03 02:19 AM (14 years, 9 months ago) 


WOW, that shape is nuts! I wish I were more into math. I only understand it on such a superficial level. My cousin is going back to school to get his degree and then Ph.D in it and he definitely speaks on a different level than me because he's studied it pretty intensively now for a few years.
Edited by wavesoflight (08/22/03 02:20 AM)

MindTrap
Disembodiedvoice
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Re: Mathematical Explanation... [Re: wavesoflight]
#1839349  08/22/03 02:21 AM (14 years, 9 months ago) 


The God equation.
We all know the answer is 42. It's figuring out what that damn equation is that's so difficult.

Faaip_De_Oiad
as above, so below
Registered: 05/29/01
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Re: Mathematical Explanation... [Re: wavesoflight]
#1839359  08/22/03 02:24 AM (14 years, 9 months ago) 


math frys my brain too, though I wish I could do more with it.
try n wrap your head around this one...........
infinity minus one......
WTF!?!?!?!??!?!?!?!?

trendal
tangential derivation
Registered: 04/17/01
Posts: 20,638
Loc: Ontario, Canada

Re: Mathematical Explanation... [Re: wavesoflight]
#1839361  08/22/03 02:24 AM (14 years, 9 months ago) 


Don't think that you have to go to school to learn a thing...

Once, men turned their thinking over to machines in the hope that this would set them free.
But that only permitted other men with machines to enslave them.

kaiowas
mndfrayze'speppet urme
Registered: 07/14/03
Posts: 5,498
Loc: oz

Re: Mathematical Explanation... [Re: Faaip_De_Oiad]
#1839368  08/22/03 02:27 AM (14 years, 9 months ago) 


inifinity minus one is just that. most of the time there can be a simplified solution when infinity is the variable (as it appears lots of times in physics). lots of times looking at one less than infinity shows can present a lot of information on how the curve (equation on a graph) moves. hehe I love math (such a nerd )
 Annnnnnd I had a light saber and my friend was there and I said "you look like an indian" and he said "you look like satan" and he found a stick and a rock and he named the rock ooga booga and he named the stick Stick and we both thought that was pretty funny. We got eaten alive by mosquitos but didn't notice til the next day. I stepped on some glass while wading in the swamp and cut my foot open, didn't bother me til the next day either....yeah it was a good time, ended the night by buying some liquor for minors and drinking nips and going to he diner and eating chicken fingers, and then I went home and went to bed.senior doobie

wavesoflight
Stranger
Registered: 01/29/03
Posts: 24
Last seen: 14 years, 8 months

Re: Mathematical Explanation... [Re: kaiowas]
#1839389  08/22/03 02:37 AM (14 years, 9 months ago) 


That talk about infinity just made me laugh, I could feel my brain trying to grasp that. Couldn't.

Malachi
stereotype
Registered: 06/19/02
Posts: 1,294
Loc: Around Minneapolis.
Last seen: 9 years, 18 days

Re: Mathematical Explanation... [Re: wavesoflight]
#1839464  08/22/03 03:16 AM (14 years, 9 months ago) 


I was briefly friends with this tiny vegan girl who was a math major... she held book club meetings at her apartment. first the republic, then a segway into math, flatland (really fun read) euclids elements. euclidian geometry = not my bag. I haven't even taken college algebra yet.. dread....
flatland was really interesting, it's about a 2d world. it's by a guy named Edwin A. Abbott, and it was written a looong time ago so you can get those super cheap dover editions. flatland it malachi's pick of the week, my full endorsement. pick it up at a library or bookstore near you.
 The ultimate meaning of our being can only be fulfilled in the paradoxical leap beyond the tragicdemonic frustration. It is a leap from our side, but it is the selfsurrendering presence of the Ground of Being from the other side.
 Paul Tillich

Mystical_Craven
mentally illpsychonaught
Registered: 06/16/02
Posts: 439
Loc: Earth

Re: Mathematical Explanation... [Re: Deiymiyan]
#1839472  08/22/03 03:21 AM (14 years, 9 months ago) 


This is the extent of my mathmatical knowledge:
Teacher  What is pi? Craven  mmmm...pie... *drools*
too much I guess

"Only those who risk going too far can possibly find out how far one can go..." T.S. Eliot

Merkin
neep.
Registered: 07/04/03
Posts: 27,537
Loc: Ass Flavoured Pie Factory


This is the answer :> to your question
 Wheels of cheese wheeels of cheeeeese!!!

neutralizer
Spiritual beinghaving a Humanexperience
Registered: 06/17/03
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Loc: This Planet Earth
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Re: Mathematical Explanation... [Re: Merkin]
#1839849  08/22/03 10:06 AM (14 years, 9 months ago) 


So, where does "the answer is 42" come from? How did we find this answer without ever knowing the question?
 There are things known, and there are things unknown, and in between are the doors  Morrison

Rhizoid
carbon unit
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Re: Mathematical Explanation... [Re: Deiymiyan]
#1839884  08/22/03 10:22 AM (14 years, 9 months ago) 


I have no clue what mathematicians are up to nowadays, and I doubt that they understand what most of it will be useful for. It can take a long time from the publication of some mathematical result to the first time it is ever used to explain something in some new scientific theory.
Of pre20th century mathematics, I know that all of the following branches have been very useful in science and engineering:
Algebra. Algebraic geometry. Differential calculus. Variational calculus. Fourier transforms. Vector algebra. Probability theory. Boolean algebra. Group theory. Number theory.
And I probably forgot something important in that list...
From the 20th century we also have Chaos Theory and Differential Geometry, although both have their roots in the 19th century.
Kurt G?del's Incompleteness Theorem is also a product of the 20th century, and in my opinion one of most important discoveries ever made. It has no practical usefulness in other sciences, but it affected the foundations of mathematics in a profound way, and thereby it also affected epistemology.
Group Theory and Number Theory were long seen as "pure" mathematics, meaning that it has no practical use. But group theory together with differential geometry is now at the core of particle physics, and number theory is the foundation of modern publickey cryptography.
As far as limits go, mathematicians have always tried to transcend limits by extending the range of the objects of discussion. The invention of zero is a famous example, and even "1" was once considered slightly controversial by some (you see why if you think of "number" as a thing that denotes a multiple of some single thing).
Negative numbers, rational numbers, real numbers, complex numbers, quaternions, octonions, vectors, tensors, and groups are all examples of such extensions. Mathematicians have become really good at this.
Division by zero is a different sort of limit, because of the way division is defined. Division is defined as the inverse of multiplication: A/B is defined as the solution X to the equation X*B = A. This has a unique solution when B is any number but zero, it has an infinite number of solutions when both A and B are zero, and it has no solutions at all when A is nonzero and B is zero. Extending the numbers to include solutions for the last case won't be of any help for the multisolution case.

trendal
tangential derivation
Registered: 04/17/01
Posts: 20,638
Loc: Ontario, Canada

Re: Mathematical Explanation... [Re: neutralizer]
#1840079  08/22/03 11:40 AM (14 years, 9 months ago) 


A race of higherdimensional beings once built a massive computer to answer the question of "life, the universe, and everything".
It spent millions of years searching for the answer.
In the end, it decided, the answer was "42".
The problem is, the higherdimensional beings don't know what the question is.
But the answer is 42.
Or you could read some Douglas Adams work

Once, men turned their thinking over to machines in the hope that this would set them free.
But that only permitted other men with machines to enslave them.

GazzBut
Refraction
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Posts: 4,770
Loc: London UK
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Re: Mathematical Explanation... [Re: Faaip_De_Oiad]
#1840101  08/22/03 11:46 AM (14 years, 9 months ago) 


Infinity 1 = infinity?
How about this one...
You go to a hotel with infinite rooms and ask for a room but the receptionist tells you all the rooms are full (infinite amount of guests!) how can you get a room in the hotel??
If any of you have read any Rudy Rucker and know the answer let the guys have a crack at it and dont reveal the answer! I must admit that I couldnt work this one out myself!
 Always Smi2le

