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 futant462
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 The orgin, end, and evolution of Mathematics 
#4396225 - 07/12/05 02:44 PM (18 years, 9 months ago) |
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As I've been delving deeper and deeper into the chaotic depths of mathematics more and more, I've come to look at the whole field from a different angle, which has led me to some interesting observations and insights. The foundation of the argument requires 2 axioms:
1) Mathematics has always existed, before humans, before the big bang, yada yada, and merely lacked a formal system or languange in which it could be discussed or communicated.
2) The establishment of the base-10 unit system set up the rest of mathematics as humanity knows it today. With the establishment of this, regardless of our understanding at the time, the basis of addition, algebra, calculus, number theory, etc already 'existed', it was simply up to us to 'discover' it.
This came from a viewpoint I have adopted that all of mathematics is merely a game, in which you can represent information formally, as long as you obey certain rules that cannot be violated without destroying the validity of the argument. The point of the game is, as I see it now at least, to learn all the rules. I find it fascinating that all knowledge of mathematics to this point has existed forever, and was in a sense innevitable to discover upon the onset of the base-10 unit system.
Also, has anyone heard any arguments as to other methods of formalizing the language of nature that would be more effective than base-10, I have often wondered if there is a better system of representing this information that would be simpler/more intuitive, perhaps with different rules?
just throwin some thoughts out there, hoping some others will fan the fire.
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"no drug, not even alcohol, causes the fundamental ills of society. If we're looking for the source of our troubles, we shouldn't test people for drugs; we should test them for stupidity, ignorance, greed, and love of power.?
-P.J. O'Rourke
What is a Quantum Particle?
The Dreams that stuff is made of!
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 moog
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Registered: 02/15/05
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Re: The orgin, end, and evolution of Mathematics [Re: futant462]
#4396847 - 07/12/05 05:21 PM (18 years, 9 months ago) |
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Well I see mathematics as a way to describe and play with the components of a system that has to be derived from the system itself. So like, you say mathematics existed before the 'big bang'? I don't think mathematics as we now know it could have existed then except as being able to describe the properties of the singularity or whatever existed "before" the big bang. What I'm saying is, mathematics exists to describe a system as soon as a system exists, as an inherent set of properties of that system. Sort of like the laws of physics came as a result of the existence of the universe, and we use them to describe and predict things within the universe. In the absence of the system in which they're used, the rules don't exist and thus there'd never be any cause for them to be discovered.
"Also, has anyone heard any arguments as to other methods of formalizing the language of nature that would be more effective than base-10, I have often wondered if there is a better system of representing this information that would be simpler/more intuitive, perhaps with different rules?"
You could take the rules inherent in each individual system and then convert them to another system, but that would needlessly complicate things, I think. Base-10 simplifies things by using a standard measurement from system to system. Take for instance a certain kind of tree, say a maple tree. The tree could be considered a system with it's own laws or rules or mathematics, in terms of how the tree looks, how it grows, how it reacts, et cetera. Converting the rules of a tree to the rules of a certain type of bacteria, would be extremely counterintuitive and difficult.
If there's a simpler way of representing infromation from system to system, you'd have to go "higher" and consider things in a broader perspective, perhaps even out of the realm of our own perception. I think that's why the base-10 method has worked so well, because we can apply it to almost every system we know of in the physical world. But there are other systems that can't be modeled mathematically or scientifically, at least according to humanity's current level of knowledge. Like, how would you predict an emotional reaction using mathematics? One might say this is absurd. But as long as a reaction isn't random, it can be modeled with mathematics. It's just that in some systems we're missing knowledge of how to do that.
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Diploid
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Re: The orgin, end, and evolution of Mathematics [Re: futant462]
#4396896 - 07/12/05 05:34 PM (18 years, 9 months ago) |
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I think you misunderstand what a number base is. It's just a way of labeling quantities.
In base 10, the number 7 is prime.
In base 2, the number 111 is prime.
Both represent exactly this many: * * * * * * *
Every property that applies to * * * * * * *, applies to it in any base you chose to operate in. The base is only a system of symbols that make representing quantities more convenient than one notch for each unit.
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Republican Values:
1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.
4) We need a smaller, less-intrusive government.
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crunchytoast
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Re: The orgin, end, and evolution of Mathematics [Re: Diploid]
#4397274 - 07/12/05 07:10 PM (18 years, 9 months ago) |
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my take on math: it's invented. like, 2+2=4, true, but it takes human creativity to describe the reality of 2+2 equaling 4. so in one sense 2+2 does not equal 4 until someone says that it does... if that makes any sense.
IOW the properties of the reality arise with the description. whereas the reality itself just is.
that's because in my mind, calling reality a system with latent and manifest properties is like pretending humans don't have an active role in creating math.
Quote:
Like, how would you predict an emotional reaction using mathematics? One might say this is absurd. But as long as a reaction isn't random, it can be modeled with mathematics. It's just that in some systems we're missing knowledge of how to do that.
i would argue that spinoza did this in the ethics many centuries ago
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"consensus on the nature of equilibrium is usually established by periodic conflict." -henry kissinger
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trendal
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Re: The orgin, end, and evolution of Mathematics [Re: futant462]
#4397355 - 07/12/05 07:34 PM (18 years, 9 months ago) |
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Also, has anyone heard any arguments as to other methods of formalizing the language of nature that would be more effective than base-10, I have often wondered if there is a better system of representing this information that would be simpler/more intuitive, perhaps with different rules?
Most (all?) of the 'constants' we measure in nature are not whole numbers in the base-10 system. In the 'perfect' descriptive theory the constants should, intuitively, all be whole numbers.
?
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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.
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futant462
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Re: The orgin, end, and evolution of Mathematics [Re: trendal]
#4397610 - 07/12/05 08:39 PM (18 years, 9 months ago) |
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ya, that's sort of what I was getting at in the alternate base example. i.e. is there possibly a way in which we could notate mathematics so that the calculations actually wind up being more intuitive or logical in a sense.
Moog, you said that before the big bang or before the universe as we know it the laws of physics or math would have not existed, but that isn't necessarily true. Take for example this reality right now, and then zap all matter in the universe out of existence in an instant. Now just because there is no matter anymore does not mean that the laws aren't still there, there is simply nothing for them to act on. Almost makes me wonder if there is a similar phenomenon occurring right now that we are unaware of, acting on some piece of our reality that we are completely oblivious to.
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"no drug, not even alcohol, causes the fundamental ills of society. If we're looking for the source of our troubles, we shouldn't test people for drugs; we should test them for stupidity, ignorance, greed, and love of power.?
-P.J. O'Rourke
What is a Quantum Particle?
The Dreams that stuff is made of!
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vampirism
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Re: The orgin, end, and evolution of Mathematics [Re: futant462]
#4397905 - 07/12/05 10:28 PM (18 years, 9 months ago) |
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Quote:
ya, that's sort of what I was getting at in the alternate base example. i.e. is there possibly a way in which we could notate mathematics so that the calculations actually wind up being more intuitive or logical in a sense.
just using purely whole numbers works. Modular math is useful for a lot of things.. Computers describe everything at the hardware level in whole numbers.
Quote:
Now just because there is no matter anymore does not mean that the laws aren't still there, there is simply nothing for them to act on
The problem with this is that math is *only* an abstraction from reality. There is no way for math to supersede reality because math is based off of reality. There *are* no laws, just useful standards of processing information.
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crunchytoast
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Re: The orgin, end, and evolution of Mathematics [Re: vampirism]
#4398099 - 07/12/05 11:11 PM (18 years, 9 months ago) |
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that's an interesting question- could you use base e or base pi? what would that look like? is that like how fractals can have fractional dimensions (now i really dont know what i'm talking about)
dang math is cool
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"consensus on the nature of equilibrium is usually established by periodic conflict." -henry kissinger
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SneezingPenis
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Re: The orgin, end, and evolution of Mathematics [Re: futant462]
#4398984 - 07/13/05 07:28 AM (18 years, 9 months ago) |
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Pinback
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Re: The orgin, end, and evolution of Mathematics [Re: moog]
#4398986 - 07/13/05 07:29 AM (18 years, 9 months ago) |
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Base 10 (probably) has worked well because we have ten fingers. Makes it easy to count.
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Seuss
Error: divide byzero
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Re: The orgin, end, and evolution of Mathematics [Re: vampirism]
#4399086 - 07/13/05 08:45 AM (18 years, 9 months ago) |
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> Computers describe everything at the hardware level in whole numbers.
This is misleading, if not wrong. Computers represent everything at the hardware level as a bit in one of three states: on, off, or unknown. (The unknown state, used by tri-state logic devices, is typically used to implement shared busses.)
A floating point number, is represented by two whole numbers, not one. One number holds the mantisa while the other holds the exponent of the floating point number.
Even integers are not simply represented by a 'whole number'. Signed integers strip the top bit and use it as a sign bit to indicate positive or negative. Thus the 8-bit number 10000000 (binary) can have the value of 128 (decimal) or the value of -128 (decimal) depending upon how it is used.
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futant462
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Re: The orgin, end, and evolution of Mathematics [Re: vampirism]
#4399199 - 07/13/05 09:38 AM (18 years, 9 months ago) |
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Golly, the world sure is a complicated place huh?
Quote:
Morrowind said:
The problem with this is that math is *only* an abstraction from reality. There is no way for math to supersede reality because math is based off of reality. There *are* no laws, just useful standards of processing information.
I was speaking more on the fact that reality does in fact have laws that we can speak in terms of. Simply removing the elements that those laws act on does not equate to removing those laws themselves, they merely have nothing to act on, so they become inconsequential to the system at that point, but that does not mean the cease to exist, for if those elements were reintroduced into the system, they would immediately begin acting again as if nothing had happened.
Whether the same can be said about math is a topic of debate still I suppose, but I tend to lean towards yes.
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"no drug, not even alcohol, causes the fundamental ills of society. If we're looking for the source of our troubles, we shouldn't test people for drugs; we should test them for stupidity, ignorance, greed, and love of power.?
-P.J. O'Rourke
What is a Quantum Particle?
The Dreams that stuff is made of!
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OldWoodSpecter
waiting
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Re: The orgin, end, and evolution of Mathematics [Re: futant462]
#4399229 - 07/13/05 09:51 AM (18 years, 9 months ago) |
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how do you say "polinom" on english? polynome or something?
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I descend upon your earth from the skies
I command your very souls you unbelievers
Bring before me what is mine
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Seuss
Error: divide byzero
Registered: 04/27/01
Posts: 23,480
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Re: The orgin, end, and evolution of Mathematics [Re: OldWoodSpecter]
#4399298 - 07/13/05 10:28 AM (18 years, 9 months ago) |
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> how do you say "polinom" on english? polynome or something?
Polynomial? as in x^3+2*x^2+5 ... a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power.
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Just another spore in the wind.
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OldWoodSpecter
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Re: The orgin, end, and evolution of Mathematics [Re: Seuss]
#4399305 - 07/13/05 10:32 AM (18 years, 9 months ago) |
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yea
for example second degree polynom(ial?):
3*x^2 + 2*x + 5
do you also call them second degree, third degree etc?
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I descend upon your earth from the skies
I command your very souls you unbelievers
Bring before me what is mine
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futant462
Somewhat Human
Registered: 07/02/05
Posts: 24
Loc: Boston MA
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Re: The orgin, end, and evolution of Mathematics [Re: OldWoodSpecter]
#4401727 - 07/13/05 09:51 PM (18 years, 9 months ago) |
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yup, that is the correct terminology I do believe
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"no drug, not even alcohol, causes the fundamental ills of society. If we're looking for the source of our troubles, we shouldn't test people for drugs; we should test them for stupidity, ignorance, greed, and love of power.?
-P.J. O'Rourke
What is a Quantum Particle?
The Dreams that stuff is made of!
|
Seuss
Error: divide byzero
Registered: 04/27/01
Posts: 23,480
Loc: Caribbean
Last seen: 2 months, 7 days
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Re: The orgin, end, and evolution of Mathematics [Re: futant462]
#4402569 - 07/14/05 06:26 AM (18 years, 9 months ago) |
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> do you also call them second degree, third degree etc
yes
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Just another spore in the wind.
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