Mathematics on Crutches

Does anyone else ever wonder why Integration works?

Or why division by zero is so complex, you have to use any method available to go around it?

Or why every definition of infinity is different?

Why is it that we build mathematical rules, laws, theorems, axioms, etc, but end up breaking our own rules in our own system?


My theory is that the mathematical black boxes are catching up with the modern world. We are forming ever-more complex problems with highly complex solutions (even if simplified). We must do this because our black boxes, our perfect theoretical worlds, are falling apart in a world (the real world) that needs faster and more efficient algorithms to solve practical problems.

We need to rebuild the foundation that our mathematics sits on. We need to solve the big problems, like some of those listed above. Many mathematicians and physicists of the past have not agreed what rules and/or laws actually govern our reality.

For example, Integration was built on the concept of Infinitesimals, but many famous mathematicians did NOT believe such units could exist;

i.e. a number X != 0 (not equal) is infinitesimal iff (if and only if) every sum X + X + ... + X, where X is an absolute value, and there are a finite number of terms, that sum is less than 1.

Without these units proven to exist, Integration exists only in Candyland. Of course, we have proven Integration to work in the real world, but we would have a more complete picture if we could understand the foundations of these processes and procedures.

Sometimes I feel like I'm the only one who believes our world is leaning on crutches.

Ever hear of entropy?

I'ts the theory that when you are born life is great and from then on
everything goes to hell in a handbasket.

It's the basics of chaos and the best math and physics people still
have a hard time writing equations to resolve it because they can't think backwards.

Everyone assumes that the longer time goes on the more organized things will be but it does not always hapen that way.

Just think of a perfect lake or pool of water, no waves and the surface looks just like a mirror.

Even though that lake looks perfect on the surface the water is flowing downhill to somwhere like a river with rapids or a waterfall.

Math equations can't explain these scenarios yet because they are too unpredictable and to complex.

Super computers are getting close to crunching the numbers but there is no way for us as humans to program those computers to recognize every scenario when we cant think of them all.

Just a thought,

kc0jfy

personally I have never thought 1 over zero should be a null ratio; it ought to be zero.

likewise, I don't believe in the reality of infinity. Nothing goes on forever.

I am by no means a mathematician but reading this post I could not help but think of the Chaos theory and Fractal Geometry:

Chaos Theory and Fractals

This subject was slightly popularized in the late eighties/early nineties in this book, where I mostly learned about it:

Chaos: Making a New Science

Protector, if you're familiar with Fractal Geometry I'd love to hear your take on it and how it relates to your post.

Originally posted by dr_strangecraft
likewise, I don't believe in the reality of infinity. Nothing goes on forever.

So you believe in the reality of Zero but not infinity???

What if they're both the same thing???
Like you said, "Nothing goes on forever."

Originally posted by mOjOm

So you believe in the reality of Zero but not infinity???

What if they're both the same thing???
Like you said, "Nothing goes on forever."

Wow, that's deep. lol.

A simple explaination for entropy: You can stack everything neatly and as clean as possible, but it's just going to get messed up again anyway.
Ie: Your house is dirty, so you clean it. But as soon as you do, the mess is just going to build up again. It's almost like it is magnetically attracted or something . Entropy is a law. You might as well leave everything messy and save yourself the work... that's how it likes to be naturally =).

Woo, Chaos theory as an excuse to be lazy.

Here's a fairly extensive site that may be of some interest-
members.lycos.co.uk...

There seems to be a problem. Many people still do not understand the meaning, the value, and the use of zero. In this day and age of high tech we still revert to this ancient myth that division by zero is some sort of error. Conceived and printed in the days when they thought the earth was flat, our early mathematicians created a mathematical error that has lasted for centuries and may last for eternity.

The guy has some interesting thoughts and goes into this topic in great detail. I remember having a vigorous argument with my 7th grade math teacher about this, although at the time, it was just about me being a posterior pain. Who knew I could've been right?

I don't believe in the materiality of "zero" either.

Our math is a logic, in case you didn't know.

And logic is merely a form of the Greek "logos," or word.

Our rules of "logic," and thus our math, are based upon nothing more or less than the grammatical rules of Attic Greek.

Booleian logic, the whole paradigm of constructing paradigms, is nothing more or less than using Greek grammar to describe truth:

A is true
If A is true, then B is false
C is false when B is true, and true when B is false.

C is true.

Therefore A is also true.

That is an example of Booleian Logic (and also of Greek grammar)

What I'm saying is, logic/math isn't set in stone. It isn't inscribed on an emerald tablet buried at the earth's core. It isn't inherent in the table of elements or something.

It's just a tool, created by humans, to help us explore the world.

I do believe in the concept of infinity, but not in the material universe. I believe infinity is actually an attribute of the Divinity. And divinity is not fully manifested in the material world. So, there's no un-ending-ness in our experience.

Likewise, zero is a mathematical concept, designed to make our accounting function in an easier style. Like the switch to arabic numerals from roman numerals. It merely adds flexibility to our system.

Especially economics, where we use it for counting money (another man-made, imaginary concept).

Is there ever zero leaves, zero planets, zero snowflakes? Of course not. every leaf is totally unique, as is every snowflake. We call them "same," so that we can pigeon-hole them into categories and count them.

By doing so, we are intentionally blinding ourselves to their unique qualities, in order to conceptualize them, count them, and charge interest on them.

Zero is an abstraction.

But then, I'm a Neoplatonist. I believe there are non-material universes that are just as "real" (if not more so), than this one.

The case is simply that we live in a physically biased culture.

When we say that something is irrelevant, we say it doesn't "matter."

We say it is "immaterial."

I believe that the Spirit is MORE IMPORTANT than "matter," than "material."

Is an idea somehow "unreal" because it is not material? Is communism unreal? What about poverty, or third-world debt, or Spousal abuse? Or justice? Or mercy? or Love?

Obviously, we humans are MOTIVATED by a lot of things that are "immaterial," that don't "matter."

Which is why I switched my major in my freshman year from physics to anthropology.

Originally posted by Cicada
I am by no means a mathematician but reading this post I could not help but think of the Chaos theory and Fractal Geometry:

Chaos Theory and Fractals

This subject was slightly popularized in the late eighties/early nineties in this book, where I mostly learned about it:

Chaos: Making a New Science

Protector, if you're familiar with Fractal Geometry I'd love to hear your take on it and how it relates to your post.

Fractal geometry, in my mind, relates more towards fractal dimensions. I know it also has its paws in Chaos Theory, but I think of chaos theory as complex systems more than funky looking patterns. Chaos Theory is being explored to better predict the weather and to better predict fluidic motion (like rushing water). I wouldn't be surprised if you start to see Chaos algorithms in the latest and greatest graphic cards to bring the newest games to life.

Fractal dimensions are an interesting concept and I certainly explore its possiblities in my personal research, but knowing what a fractal dimension is does not help you to learn what it does or how it has practical purpose in our lives.

Chaos is not necessarily hard to set up, but becomes complicated at an exponential rate, in my opinion. Plus, more complex algorithms take far more computation time.. and learning how to graph such things is no simple matter, either.

That all being said, I believe Chaos tends toward less entropy (less disorder), at certain intervals. For example, the swirling eddies in a current of water tend to use the same pathways when going around an object, e.g. a rock. Real world factors often balance out the Chaos so it appears more harmonious than chaotic. The problem with Chaos is what happens in between, where nearly indeterminate factors can throw your equation off or skew test results. Certainly, I am not skilled enough to say much more on the subject, but it does fascinate me.

Originally posted by dr_strangecraft
I don't believe in the materiality of "zero" either...

One point on zero is that was actually developed in India, or that general region (if I recall correctly) to calculate when a debt had been settled. Essentially, a negative number was a debt, so if all debts were settled, there was zero debt and two people were considered even. I have a source if you want more info.

Originally posted by dr_strangecraft
And logic is merely a form of the Greek "logos," or word...

True, but zero is not a Greek origination, nor is infinite if a remember correctly. Logic presents us with a set of steps to form a solution that cannot be proven false due to exhaustive cases. This means "one possible truth with anything else being false." Think about truth tables. They are exhaustive, so no case exists outside of what you are comparing. I believe this to be firm proof that some things are bound to be true or false, universally.

Originally posted by dr_strangecraft
What I'm saying is, logic/math isn't set in stone...

Logic is largely believe to be set in stone and so is quite a bit of math. But many popular algorithms and formulas remain unproven to this day. However, they work in practical settings, which is all that matters sometimes.

Originally posted by dr_strangecraft
Especially economics, where we use it for counting money (another man-made, imaginary concept).

I don't think of economics as imaginary, but rather necessary for a society of two or more people. Any exchange of goods, or barter system, requires that we don't lose more physical resources than what we have--like that commercial where a cave man kept selling his teeth for goods, then had no teeth left to eat with (thus his death would result). So, in the physical world, economics is necessary to survive, thus making it solid (non-imaginary), but by no means having a solid logical base (no truth tables for Econ).

Originally posted by dr_strangecraft
Is there ever zero leaves, zero planets, zero snowflakes? Of course not.

By definition, yes. If you do not have a surplus of something, or a debt of something, you have zero of it. Which is just saying, "I do not have any leaves, planets, nor snowflakes."

every leaf is totally unique, as is every snowflake. We call them "same," so that we can pigeon-hole them into categories and count them.

Could you imagine not having a name for snowflakes or leaves. Or having to name every one something different? That just leads to enormous amounts of irrelevant information... like in Biology (ooooo, he takes a stab at biologists). The pigeon-hole principle is one of my favorites.

Originally posted by dr_strangecraft
But then, I'm a Neoplatonist. I believe there are non-material universes that are just as "real" (if not more so), than this one.

But wouldn't you also agree that because this one has the unique quality of physicality that it proves in every moment what can be real and finite? Either you have an apple or you don't... know what I mean?


[edit on 4-11-2005 by Protector]

Originally posted by yeahright
Here's a fairly extensive site that may be of some interest-
members.lycos.co.uk...

There seems to be a problem. Many people still do not understand the meaning, the value, and the use of zero. In this day and age of high tech we still revert to this ancient myth that division by zero is some sort of error. Conceived and printed in the days when they thought the earth was flat, our early mathematicians created a mathematical error that has lasted for centuries and may last for eternity.

The guy has some interesting thoughts and goes into this topic in great detail. I remember having a vigorous argument with my 7th grade math teacher about this, although at the time, it was just about me being a posterior pain. Who knew I could've been right?

Thanks for the post, but it is wrong. I have not read everything, as the author is long winded, but he has not shown any evidence of what happens in special cases, such as where one number is equal to a different number due to dividing by zero. He simply tries to explain everything away as equaling zero, which is just an assumption and not necessarily true at all. In all lower level mathematics, it appears that dividing by zero will result in zero or infinity, but alas, life is not so simple.

Edit: This website is terribly inaccurate and gives no formal mathematical proofs (because he/she can't since it is wrong) and tries to explain away the results as working because it is the foundation of mathematics, not rules like division (fractions) and the likes. Wow... terrible!

[edit on 4-11-2005 by Protector]

Originally posted by Protector

Originally posted by dr_strangecraft
But then, I'm a Neoplatonist. I believe there are non-material universes that are just as "real" (if not more so), than this one.

But wouldn't you also agree that because this one has the unique quality of physicality that it proves in every moment what can be real and finite? Either you have an apple or you don't... know what I mean?

Although the portion of the universe we can sense has physicality, I am not convinced it is unique. The argument about having an apple applies, but it may apply to non-material realities as well.

In regards to the ZeroByZero website posted earlier, I wrote an email to the person who runs the website and here is the response... WOW:

Why throw out a perfectly feasable mathematical equasion? You must be think that thousand year old mathematicians were better then modern ones. Mathematics is not like the bible. Most of our mathematics today is not older then the light bulb. They did not deal with industrial aplications. They had no idea or nuclear phisics. Super conductors or lasers. They were siple people who used simple math. Now you seem to belive that because something has been taught for a thousand years, then it must be right. Do you know how stupid that is. Most of our science today is a contradiction to what people thought a thousand years ago. If we listend to arguments like yours we would be living in the stone age.

If you dont research my work then bother talking to me. You waiste my time.

I don't even know how to respond to this crap. Any ideas?

Originally posted by Protector
I don't even know how to respond to this crap. Any ideas?

I'd just copy and paste the following equation:

Let x=0.9~
10x=9.9~
9x=9
x=1

Therefore 0.9~=1

Originally posted by AkashicWanderer

I'd just copy and paste the following equation:

Let x=0.9~
10x=9.9~
9x=9
x=1

Therefore 0.9~=1

The problem is in line 3. If x is constant throughout your exercise, line 3 should read:

9x = 8.1~

That's where the error is.

Originally posted by dr_strangecraft

Originally posted by AkashicWanderer

I'd just copy and paste the following equation:

Let x=0.9~
10x=9.9~
9x=9
x=1

Therefore 0.9~=1

The problem is in line 3. If x is constant throughout your exercise, line 3 should read:

9x = 8.1~

First of all, 0.9~ multiplied by 9 does not equal 8.1~.

Second of all we arrive at line 3 by substracting 1x from 10x.

9.9~-.9~=9

[edit on 17/11/2005 by AkashicWanderer]

Originally posted by Protector
In regards to the ZeroByZero website posted earlier, I wrote an email to the person who runs the website and here is the response... WOW:

Why throw out a perfectly feasable mathematical equasion? You must be think that thousand year old mathematicians were better then modern ones. Mathematics is not like the bible. Most of our mathematics today is not older then the light bulb. They did not deal with industrial aplications. They had no idea or nuclear phisics. Super conductors or lasers. They were siple people who used simple math. Now you seem to belive that because something has been taught for a thousand years, then it must be right. Do you know how stupid that is. Most of our science today is a contradiction to what people thought a thousand years ago. If we listend to arguments like yours we would be living in the stone age.

If you dont research my work then bother talking to me. You waiste my time.

I don't even know how to respond to this crap. Any ideas?

I posted it originally as just a "hey check this guy out". Now you know what happens when you actually try to correspond with some of these colorful website types. Looks like he's not great at grammar or spelling, either. I advise you either back slowly away, or throw a doughnut to distract him, then run for it in the opposite direction.

Originally posted by AkashicWanderer
Therefore 0.9~=1

What is so absurd about this statement ?
0.9~ tends to 1 so saying that 0.9~=1 is very accurate. Also without such approximations where would you get any feasible solutions ?
It may not be exactly equal to but how would you answer 1- 0.9~ ? You would say 0 because you cant write the solution. The important thing is we KNOW that they are not exaclty equall beyond which it doesnt really matter.

I'm an engineer so in my profession I come across a lot of such mathematical approximations, they are a given. Imagine manufacturing a shaft of 0.9~ it is impossible. Also how would the metrology dept certify it ?

Originally posted by AkashicWanderer

Let x=0.9~
10x=9.9~
9x=9
x=1

Therefore 0.9~=1

I think I know whats wrong here;
The basic of multiplication is that when you multiply two numbers; every digit of the first is multiplied with the second. Here that is not possible especially in step 2.
Also if you reallly want to check, you could just add X ten times.
X+X+X+X+X+X+X+X+X+X=10X; if you do this you will realise that 10X is not 9.99~ but is a slightly different value which when subtracted with X again would give :
X=9(0.9~)/9 = 0.9~

That equation is right. 9.9~ = 10

Lim 10 - 1/n = 10, since 1/n = 0
n->oo

The notation 0.0~1, i.e. an infinite number of zeros before a one, is still considered to be a zero since it has an infinite number of zeros after the decimal point. Thus, you can't have 9.9~ + 0.0~1 = 10, since all numbers after an infinite sequence are ignored.

I'm not saying that that this logic is a smart thing to do in mathematics, but it is the current "way" to do things. Since our number line does not have a way to deal with nested sets, we have to live with the current logic, so we say that 9.9~ is 10.

Look at it this way, if you are infinitely close to kissing a girl's lips, you are kissing her lips. In all practical applications, you can never be infinitely close without contact. Thus, even adding more theory to this point of the mathematics is pretty pointless for humans. Anything less than 1/(2^70) is considered irrelevant in the life of the universe anyway.

Moral of the story: if it looks like a duck, waddles like a duck, quacks like a duck, just call it a duck.