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OfflineDeiymiyan
I AM

Registered: 04/17/03
Posts: 656
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Mathematical Explanation...
    #1838650 - 08/21/03 09:46 PM (14 years, 4 days 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?


:crazy:

   


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Dei Gratia de integro,

Veni Vidi Vici:

In Nomine Domini..



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Offlinepattern
multiplayer

Registered: 07/19/02
Posts: 2,183
Loc: Canada
Last seen: 2 years, 5 months
Re: Mathematical Explanation... [Re: Deiymiyan]
    #1838767 - 08/21/03 10:17 PM (14 years, 4 days 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.


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man = monkey + mushroom


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Invisiblekaiowas
mndfrayze'speppet urme
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Registered: 07/14/03
Posts: 5,498
Loc: oz
Re: Mathematical Explanation... [Re: pattern]
    #1839064 - 08/21/03 11:56 PM (14 years, 4 days 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 :smile:

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 non-zero 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 :smile:


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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


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InvisibleSkorpivoMusterion
Livin in theTwilight Zone...
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Registered: 01/30/03
Posts: 9,946
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Re: Mathematical Explanation... [Re: kaiowas]
    #1839136 - 08/22/03 12:25 AM (14 years, 4 days ago)

I......HATE.........MATH...
It gives me Aneurisms
Fuck Math
MAth Sucks
I HATE MATH!!!!!!!!!!!!!!!!!
:mad:


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Coffee should be black as hell, strong as death, and sweet as love.


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InvisibletrendalM
King of Asides
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Registered: 04/17/01
Posts: 19,978
Loc: Ontario, Canada
Re: Mathematical Explanation... [Re: Deiymiyan]
    #1839326 - 08/22/03 02:12 AM (14 years, 4 days ago)

A good place to look for cutting-edge 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.

Calabi-yau shapes seem the most interesting to me at the moment  :smirk:

Look, here's a 2-D representation of one:
 


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OfflineMindTrap
Disembodiedvoice
Registered: 08/02/02
Posts: 349
Loc: It's all in your head...
Last seen: 12 years, 7 months
Re: Mathematical Explanation... [Re: trendal]
    #1839332 - 08/22/03 02:14 AM (14 years, 4 days ago)

or Chaos Theory


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InvisibletrendalM
King of Asides
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Registered: 04/17/01
Posts: 19,978
Loc: Ontario, Canada
Re: Mathematical Explanation... [Re: MindTrap]
    #1839344 - 08/22/03 02:18 AM (14 years, 4 days 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.

:wink:


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Offlinewavesoflight
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Registered: 01/29/03
Posts: 24
Last seen: 13 years, 10 months
Re: Mathematical Explanation... [Re: trendal]
    #1839346 - 08/22/03 02:19 AM (14 years, 4 days 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)


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OfflineMindTrap
Disembodiedvoice
Registered: 08/02/02
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Re: Mathematical Explanation... [Re: wavesoflight]
    #1839349 - 08/22/03 02:21 AM (14 years, 4 days ago)

The God equation.

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


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OfflineFaaip_De_Oiad
as above, so below
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Registered: 05/29/01
Posts: 1,947
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Re: Mathematical Explanation... [Re: wavesoflight]
    #1839359 - 08/22/03 02:24 AM (14 years, 4 days 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!?!?!?!??!?!?!?!?


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InvisibletrendalM
King of Asides
Male User Gallery

Registered: 04/17/01
Posts: 19,978
Loc: Ontario, Canada
Re: Mathematical Explanation... [Re: wavesoflight]
    #1839361 - 08/22/03 02:24 AM (14 years, 4 days ago)

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

:wink: :wtf:


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Invisiblekaiowas
mndfrayze'speppet urme
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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, 4 days 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 :smile: (such a nerd :frown:)


--------------------
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


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Offlinewavesoflight
Stranger
Registered: 01/29/03
Posts: 24
Last seen: 13 years, 10 months
Re: Mathematical Explanation... [Re: kaiowas]
    #1839389 - 08/22/03 02:37 AM (14 years, 4 days ago)

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


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OfflineMalachi
stereotype

Registered: 06/19/02
Posts: 1,294
Loc: Around Minneapolis.
Last seen: 8 years, 2 months
Re: Mathematical Explanation... [Re: wavesoflight]
    #1839464 - 08/22/03 03:16 AM (14 years, 4 days 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 2-d 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. :smile:



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The ultimate meaning of our being can only be fulfilled in the paradoxical leap beyond the tragic-demonic frustration. It is a leap from our side, but it is the self-surrendering presence of the Ground of Being from the other side.
- Paul Tillich


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InvisibleMystical_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, 4 days ago)

This is the extent of my mathmatical knowledge:

Teacher - What is pi?
Craven - mmmm...pie... *drools*

too much  :spliff:  I guess 


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


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InvisibleMerkin
neep.
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Registered: 07/04/03
Posts: 27,537
Loc: Ass Flavoured Pie Factory
Re: Mathematical Explanation... [Re: Mystical_Craven]
    #1839672 - 08/22/03 06:43 AM (14 years, 3 days ago)


This is the answer :> to your question


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Wheels of cheese wheeels of cheeeeese!!!


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Offlineneutralizer
Spiritual beinghaving a Humanexperience
Registered: 06/17/03
Posts: 635
Loc: This Planet Earth
Last seen: 10 years, 6 months
Re: Mathematical Explanation... [Re: Merkin]
    #1839849 - 08/22/03 10:06 AM (14 years, 3 days ago)

So, where does "the answer is 42" come from? How did we find this answer without ever knowing the question?


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There are things known, and there are things unknown, and in between are the doors - Morrison


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OfflineRhizoid
carbon unit
Male

Registered: 01/23/00
Posts: 1,728
Loc: Europe
Last seen: 1 day, 10 hours
Re: Mathematical Explanation... [Re: Deiymiyan]
    #1839884 - 08/22/03 10:22 AM (14 years, 3 days 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 pre-20th 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 public-key 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 non-zero and B is zero. Extending the numbers to include solutions for the last case won't be of any help for the multi-solution case.


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InvisibletrendalM
King of Asides
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Registered: 04/17/01
Posts: 19,978
Loc: Ontario, Canada
Re: Mathematical Explanation... [Re: neutralizer]
    #1840079 - 08/22/03 11:40 AM (14 years, 3 days ago)

A race of higher-dimensional 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 higher-dimensional beings don't know what the question is.

But the answer is 42.

:smile:

Or you could read some Douglas Adams work  :wink:


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OfflineGazzBut
Refraction

Registered: 10/15/02
Posts: 4,770
Loc: London UK
Last seen: 1 month, 7 days
Re: Mathematical Explanation... [Re: Faaip_De_Oiad]
    #1840101 - 08/22/03 11:46 AM (14 years, 3 days 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!


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Always Smi2le


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