Reality as express through math.

[Chad]

Okay, I am wondering if there are any middle ground people here. As far and the issue of Mathematics is concerned.

I have noticed two distinct sub groups on this forum.

1)Hates mathematics and see no practical use for the subject in there life.

2)Romanticizes mathematics to the point were they believe that math is the natural language of the universe and therefore can explain everything.

Here is were I am at. I believe mathematics is a very well defined and beautiful language. It has logic and rules with out acceptations. This makes it one of the most useful languages known to the human race.

However, like every man derived Language it is nothing more that an expression of what humans experience reality to be. There is not secrete are mystical powers of mathematics. Its just a simple why to express complex concepts. Imagine trying to explain "one plus one" without using mathematical terminology. I am not saying it can't be done however 1+1=2 is just a much simpler way to look at this expression. From this expression you can understand so many different concepts. This is useful because you know that 1+1 will always be 2. This may get more complected when you realize that the functions normally aren't as clean as 1+1 however there are rules to deal with this and they also make intuitive since.

I wonder if anyone else here agrees with me.

My basic premise is this.
Math is useful
Math is simple
Math is beautifully logical
Math is not Mystical
Math is simply language to express observed reality and not useful for any other unknown aspects of reality.

 

[BigApplePi]

Imagine trying to explain "one plus one" without using mathematical terminology. I am not saying it can't be done however 1+1=2 is just a much simpler way to look at this expression. From this expression you can understand so many different concepts. This is useful because you know that 1+1 will always be 2.

You've raised a lot of great issues here. Let's try just the 1 + 1 = 2.

If one is going to conceive of one of something, what does that mean? It implies something is there having an identity and there is something more than that. We are talking quantity or counting. If we are counting, we are considering likenesses. That is, things are ordinarily different, but we are looking at only what they have in common. Before we go to any abstraction, let's look at apples. If you have one and then another, we define that combination as two apples. Adding is the combination of what we have considered together. So abstracting, 1 + 1 = 2 is the considering together of a likeness and another likeness.

That's a word definition in the real world. Not much mathematics. We may be talking symbolic logic if we are to go further into abstraction. Mathematics does have its foundations in philosophy as I've attempted here. If we skip foundations and go directly to math, we may talk about symbols such as "+" without regard to what they mean. We talk symbols and assume logical operations.

I will ramble on because there is more than one way to look at this. You say, "1+1 will always be 2." That is not any mystery if 2 is just the definition or shortcut for 1 + 1, just as 20 is the definition or symbol shortcut for 19 + 1.

If I recall, there is such a thing as "equivalence classes." If you look that up, things will rapidly get complicated, more so than you want to. In ordinary English I supposes it means if things are generally one way then each particular is going to be that way. Sometimes we can get another mathematical person on a forum who can explain it better, but that is mine.

Consider "two" pears. Then two pears will have the same "two-ness" as two apples. I'd better stop here.

 

[Chad]

You've raised a lot of great issues here. Let's try just the 1 + 1 = 2.

If one is going to conceive of one of something, what does that mean? It implies something is there having an identity and there is something more than that. We are talking quantity or counting. If we are counting, we are considering likenesses. That is, things are ordinarily different, but we are looking at only what they have in common. Before we go to any abstraction, let's look at apples. If you have one and then another, we define that combination as two apples. Adding is the combination of what we have considered together. So abstracting, 1 + 1 = 2 is the considering together of a likeness and another likeness.

That's a word definition in the real world. Not much mathematics. We may be talking symbolic logic if we are to go further into abstraction. Mathematics does have its foundations in philosophy as I've attempted here. If we skip foundations and go directly to math, we may talk about symbols such as "+" without regard to what they mean. We talk symbols and assume logical operations.

I will ramble on because there is more than one way to look at this. You say, "1+1 will always be 2." That is not any mystery if 2 is just the definition or shortcut for 1 + 1, just as 20 is the definition or symbol shortcut for 19 + 1.

If I recall, there is such a thing as "equivalence classes." If you look that up, things will rapidly get complicated, more so than you want to. In ordinary English I supposes it means if things are generally one way then each particular is going to be that way. Sometimes we can get another mathematical person on a forum who can explain it better, but that is mine.

Consider "two" pears. Then two pears will have the same "two-ness" as two apples. I'd better stop here.

My point is that mathematics as symbols is a simplification of larger consents that can not be completely understood without using mathematics terminology or symbols.

I am not confused about what math is and simply using mathematical terminology instead of the symbols isn't really explaining the reality of a situation not using math. Therefore, the conclusion can still be had that mathematics is just simple language used to understand farther complex concepts that we have no way of expressing with out numbers or other mathematics symbols/terminology.

I am not sure what you are trying to prove/argue here. I sounds like you are trying to teach me what math is which really isn't the question here and I don't understand why you would believe that I wasn't understanding what math is.

I understand that things get more complected when you start to realize that no to things are identical. However, using math is still simpler than trying to understand this reality without math. I am not saying math is away simple however, it is the simplest way to express some aspects of reality. This is why it is useful.

Calculus may not be simple however, it is much simpler to understand certain physical properties when you express them in Calculus therms.

Simply put Calculus based physics is my more intuitive than algebra based physics.
Calculus may be harder to grasp than Algebra however, understanding Calculus make understand many physical properties simpler.

I am not saying math is simple what I am saying is that math make communication simpler. As long as both people can understand the math than can intern understand the concept better. This is because as a language mathematics is far less open to interpretation than most language mediums.

Take English for an example. There is a rule that says that I always come before E unless its fallows C. This is a very wEIrd concept. In English there are exceptions for every rule and even exceptions the the exceptions. The simplicity to mathematics is there are no exceptions. There is only farther evolutions of the rules.

While it is completely possible that 1+1 may be closer to 3 than 2. Basically if you are rounding 1.49999999999999999+1.4999999999 your could still get 1+1=3. Because 1.4999999999+1.499999999 = 2.9999999999998 which rounds to 3 not 2. However, this is not actually an exception. In reality 1+1 will always =2 because 1.49999999999999 isn't actually 1 even if it rounds to (or is closer to 1 than 2.) This just means that in reality numbers are not normally as simple as 1+1. However, if you wish to be more concise you can be. All you need to do is look closer at the figure reality instead of rounding and making a guess.

 

[BigApplePi]

You are mostly right. I'll review your statements.

My point is that mathematics as symbols is a simplification of larger consents that can not be completely understood without using mathematics terminology or symbols.

Some larger concepts. One still has to learn the language and theorems leading up to larger concepts unless one takes the theorems on faith.

I am not confused about what math is and simply using mathematical terminology instead of the symbols isn't really explaining the reality of a situation not using math. Therefore, the conclusion can still be had that mathematics is just simple language used to understand farther complex concepts that we have no way of expressing with out numbers or other mathematics symbols/terminology.

Unlike spoken language the language is symbols built on symbols lower in the hierarchy of symbols.

I am not sure what you are trying to prove/argue here. I sounds like you are trying to teach me what math is which really isn't the question here and I don't understand why you would believe that I wasn't understanding what math is.

I got carried away. Sorry.

I understand that things get more complected when you start to realize that no to things are identical. However, using math is still simpler than trying to understand this reality without math. I am not saying math is away simple however, it is the simplest way to express some aspects of reality. This is why it is useful.

Okay, but math is more than that. Sometimes math is for other math. Sometimes math is more art than science because it is both.

Calculus may not be simple however, it is much simpler to understand certain physical properties when you express them in Calculus therms.

Simply put Calculus based physics is my more intuitive than algebra based physics.
Calculus may be harder to grasp than Algebra however, understanding Calculus make understand many physical properties simpler.

I am not saying math is simple what I am saying is that math make communication simpler. As long as both people can understand the math than can intern understand the concept better. This is because as a language mathematics is far less open to interpretation than most language mediums.

The symbols themselves are summaries of reality. In that sense, simpler. Understanding the symbols requires study.

Take English for an example. There is a rule that says that I always come before E unless its fallows C. This is a very wEIrd concept. In English there are exceptions for every rule and even exceptions the the exceptions. The simplicity to mathematics is there are no exceptions. There is only farther evolutions of the rules.

Good point. But we could say in English we have to list ALL the exceptions and those are part of the rules.

While it is completely possible that 1+1 may be closer to 3 than 2. Basically if you are rounding 1.49999999999999999+1.4999999999 your could still get 1+1=3. Because 1.4999999999+1.499999999 = 2.9999999999998 which rounds to 3 not 2. However, this is not actually an exception. In reality 1+1 will always =2 because 1.49999999999999 isn't actually 1 even if it rounds to (or is closer to 1 than 2.) This just means that in reality numbers are not normally as simple as 1+1. However, if you wish to be more concise you can be. All you need to do is look closer at the figure reality instead of rounding and making a guess.

Yes. We have to make sure we apply all the rules correctly.
++++++++++++++++++++++++++++++++++++++

Okay, I am wondering if there are any middle ground people here. As far and the issue of Mathematics is concerned.

I have noticed two distinct sub groups on this forum.

1)Hates mathematics and see no practical use for the subject in there life.

2)Romanticizes mathematics to the point were they believe that math is the natural language of the universe and therefore can explain everything.

Here is were I am at. I believe mathematics is a very well defined and beautiful language. It has logic and rules with out acceptations. This makes it one of the most useful languages known to the human race.

3)Math is both science and art. In the language of emotion, I'm cool to that.

However, like every man derived Language it is nothing more that an expression of what humans experience reality to be. There is not secrete are mystical powers of mathematics. Its just a simple why to express complex concepts. Imagine trying to explain "one plus one" without using mathematical terminology. I am not saying it can't be done however 1+1=2 is just a much simpler way to look at this expression. From this expression you can understand so many different concepts. This is useful because you know that 1+1 will always be 2. This may get more complected when you realize that the functions normally aren't as clean as 1+1 however there are rules to deal with this and they also make intuitive since.

That could be too simple an example to illustrate math.

My basic premise is this.
Math is useful - yes
Math is simple - sometimes
Math is beautifully logical - sometimes it is a grind
Math is not Mystical - the beauty has a mystery
Math is simply language to express observed reality and not useful for any other unknown aspects of reality. - false unless you count math itself as reality. Math is often used to observe math itself.[/quote]

 

[Chad]

You are mostly right. I'll review your statements.Some larger concepts. One still has to learn the language and theorems leading up to larger concepts unless one takes the theorems on faith.
Unlike spoken language the language is symbols built on symbols lower in the hierarchy of symbols.

I got carried away. Sorry.

Okay, but math is more than that. Sometimes math is for other math. Sometimes math is more art than science because it is both.

The symbols themselves are summaries of reality. In that sense, simpler. Understanding the symbols requires study.

Good point. But we could say in English we have to list ALL the exceptions and those are part of the rules.

Yes. We have to make sure we apply all the rules correctly.
++++++++++++++++++++++++++++++++++++++

3)Math is both science and art. In the language of emotion, I'm cool to that.
That could be too simple an example to illustrate math.

My basic premise is this.
Math is useful - yes
Math is simple - sometimes
Math is beautifully logical - sometimes it is a grind
Math is not Mystical - the beauty has a mystery
Math is simply language to express observed reality and not useful for any other unknown aspects of reality. - false unless you count math itself as reality. Math is often used to observe math itself.

[/QUOTE]

Okay that clears it up. I don't think that we personally disagree in our conclusion we both just wish to express these conclusions differently.

I understand the learning curve issues and the math explaining math issues. However, even when math is explain math it still comes down to some reality in the end no matter how many degrees of separations you have to take before you get there. The end result is a simplification of reality concepts.

What I mean by last concept is that math doesn't tell you the meaning of life or similar abstract consents its jut not the nature of math to do such a thing.

By not mystical I not saying its not beautiful logic however in the end this is all it is. its not some mystical force that can tell you answer to problems you aren't even looking form. Its a language system not an answer or math is not the answer it's a tool we use to find the answer.

 

[danielfang7]

Okay that clears it up. I don't think that we personally disagree in our conclusion we both just wish to express these conclusions differently.

I understand the learning curve issues and the math explaining math issues. However, even when math is explain math it still comes down to some reality in the end no matter how many degrees of separations you have to take before you get there. The end result is a simplification of reality concepts.

What I mean by last concept is that math doesn't tell you the meaning of life or similar abstract consents its jut not the nature of math to do such a thing.

By not mystical I not saying its not beautiful logic however in the end this is all it is. its not some mystical force that can tell you answer to problems you aren't even looking form. Its a language system not an answer or math is not the answer it's a tool we use to find the answer.[/QUOTE]

I agree, but I have some doubt about it as well. Mathematics tends to be viewed as a tool; especially if you look at simple examples such as 1+1=2. However, I think mathematics does much more than "simplify reality concepts".

For example, look at the work most theoretical physicists are accomplishing nowadays. Yes, I agree that in most cases math is just a tool, as the invention of imaginary numbers are used to solve complex problems that we simply can't solve with mathematics for four dimensions. However, math is providing us explanations, it is providing us answers as to why things are the way they are. Theoretical physicists are looking for a theory of everything (such as string theory, which would require additional dimensions), which in the end, would be determined through mathematics. Mathematics would then not be a tool that simplifies realistic concepts; it is something that lets us understand the unknown, and provide us with explanations and answers.

In most cases it is indeed a tool, but one must look at the bigger picture. Math provides us with answers, it provides us with explanations about unrealistic phenomena. Anyways, sorry for any typing errors or grammar issues, I'm typing this literally as thoughts come along in my head in class.

But overall, good point.