Are mathematics' unsolvable problems caused by its foundations?

[druk]

I'm not a mathematician nor a mathematics student, so sorry if I'm writing nonsense.

I feel that mathematics solves many problems, but poses some that are unsolvable. So I've always wondered how this could be.

My answer: the foundation is completely wrong.

Take the zero: who was the "genius" who invented it? There is no such thing in the universe. You can't have zero apples. You either have "one" apple or you have "none". "None" can't be used to make calculations, because "none" means you don't have anything, and you can't use "anything" because, well, it's nothing.

Take negative numbers: same thing. You can't have -1 apples.

Take fractions: again, no such thing. You can't have 1/2 apple. Either you have 1 apple, or you have 1 "half apple". Once you divide a pizza, each slice is a new unit. You don't have 6 fractions of pizza, you have 6 units of "slices of pizza".

Same for infinity. There is no such thing. Even speed has an absolute upper limit. (Now that I think of it, speed has also some kind of lower limit, because your absolute speed can never be zero, as you will always be moving with respect to something. This agrees with my contention that zero doesn't exist.)

No wonder you encounter problems like division by zero, periodic numbers, determining pi, etc.

Thank you for your patience and your sense of humor, although I'll be waiting for serious answers.

Flame suit on.

 

[chroot]

Originally posted by druk
You can't have zero apples.

Of course I can. There are zero apples in my fridge right now. Not a single one.

You either have "one" apple or you have "none". "None" can't be used to make calculations

Why not? Jane has five apples; she gives Nate none. How many does she have left? Is this somehow an invalid question, which has no answer?

No wonder you encounter problems like division by zero, periodic numbers, determining pi, etc.

By "no wonder you encounter problems," I assume you mean "no wonder math exists" -- right?

Thank you for your patience and your sense of humor, although I'll be waiting for serious answers.

Thanks for your attempt to put us back in thousands of years before the birth of Christ.

- Warren

 

[druk]

Why not? Jane has five apples; she gives Nate none. How many does she have left? Is this somehow an invalid question, which has no answer?

Well (and I'm not willing to be a smarta%% here), you can't give what you don't have. Jane has 5 apples, not none. Giving Nate none means she didn't give him/her anything in the first place.

By "no wonder you encounter problems," I assume you mean "no wonder math exists" -- right?

I just can't understand that, having had time since thousands of years before the birth of Christ, man hasn't solved issues like determining pi, or division by zero, etc. This tells me that there's *gotta* be something wrong at the foundation of the system.
Perhaps we are trying to make it more and more complex, but we have taken a wrong turn somewhere and no level of complexity will let us solve those long-unsolved problems.
Doesn't it seem odd to you too?

 

[chroot]

Originally posted by druk
Well (and I'm not willing to be a smarta%% here), you can't give what you don't have. Jane has 5 apples, not none. Giving Nate none means she didn't give him/her anything in the first place.

I can confidently give you zero of anything you'd like. I'll even give you zero of that thing for free! Would you like zero sports cars? How about zero solid 24-karat gold mansions? I happen to have zero lying around here, just waiting to be given away. I'll put your name on zero of them.

The bottom line is that you said "zero cannot be used to make calculations." I showed you an example of using it:

Jane has five apples, and gives Nate zero of them. How many does she have left?

5 - 0 = 5.

Do you disagree with this answer? Do you feel this question has no answer?

I just can't understand that, having had time since thousands of years before the birth of Christ, man hasn't solved issues like determining pi,

How do you expect mankind to have completed an infinite task? Why are you not upset that mankind has not completed the similar task of counting all the integers? You seem to believe in the counting numbers 1, 2, 3... Why do you not feel it is a failure of mankind that no one has yet written all of them down? Does that mean the counting numbers are also useless and invalid?

or division by zero, etc. This tells me that there's *gotta* be something wrong at the foundation of the system.

Why on Earth do you think division by zero is a problem that should be solved? Think about it this way -- you multiply anything by zero, and it loses its identity. The numbers 7 and 8, after being multiplied by zero, both become zero. How can you tell the two resulting zeros apart? This is what division by zero would allow you to do -- to somehow say "this zero was once an eight, while this zero was once a seven." It makes absolutely no sense.

Perhaps we are trying to make it more and more complex, but we have taken a wrong turn somewhere and no level of complexity will let us solve those long-unsolved problems.
Doesn't it seem odd to you too?

No, what seems odd to me that you're content to feel there is such foul play afoot -- that there is some vast conspiracy in which all of us are simply hiding these "problems" of yours -- yet you haven't taken the time to actually learn even elementary math. Before you can competently critique a system, you're obligated to understand it.

- Warren

 

[ahrkron]

Originally posted by druk
Take the zero: who was the "genius" who invented it?

Somebody who noticed that it was much easier to write 4035 instead of keeping a bag with that many stones, or to add

 300
+105
----
 405

when tax paying people brought 105 more pieces of cocoa.

How would you add, subtract or multiply roman numerals? Especially if you need to account for the riches of a nation.

Take negative numbers: same thing. You can't have -1 apples.

But again, you need a way to represent decrements.

Or think about geometry and directions. It is definitely not far fetched.

Take fractions: again, no such thing. You can't have 1/2 apple. Either you have 1 apple, or you have 1 "half apple".

And how do you call the relation between the sizes of the "half apple" and the apple?

Again, if you think in geometry, once you select a unit length, what are you supposed to do when trying to measure something smaller? redefine your system? ... forever?

What is wrong with finding a way to consistently work with fractions of your unit?

 

[lastlaugh]

Well (and I'm not willing to be a smarta%% here), you can't give what you don't have. Jane has 5 apples, not none. Giving Nate none means she didn't give him/her anything in the first place.

Well 0 is valuable for equations especially for describing systems of forces in equilibrium.
Or Calculating extremum.
Or place holding
I agree a lot of funky stuff does happen around 0 but that is no reason to get rid of it.

 

[quartodeciman]

Yet one more retort.

If all you want to do is account for real and actual apples (or other valuables), then there still exists a perfectly good system of numbers, {1, 2, 3, ...} for dealing with just these. They haven't left town. These numbers are commonly called the "natural numbers" and they are still valid in themselves. Does that mean no other system of numbers is ever of any possible significance? Why?

Suppose I have no apples, while you have 5 of them. I borrow 2 apples from you so I can eat today. That leaves you 3 actual apples. I eat the 2 apples you loaned me while you eat none. Now there are three apples left from the original set, and you have them. Then you come back to me and ask for payback of 2 apples. "What apples? I have no apples now. I ate what I got from you. You have the only apples between you and me. That's the end of the matter." You might find that an unsatisfactory answer, but I told the truth. There are no actual apples for me to pay you. Worse, I might inherit 20 new apples. You think you have a claim on me for 2 of them, but I reply "What are you talking about?" Well, what you are talking about is not just actual apples, but debits and credits in apples, assets and liabilities, something beyond just inventories of actual apples. In short, you believe you have a claim on me. You deserve 2 apples out of my assets. It might help if we said for the record that I had -2 apples, then received 20 apples, but I am obliged to pay you 2 (and maybe interest), leaving a balance of no more than +20 - 2 = +18 apples clear. You can avoid the signed numbers through double-entry bookkeeping, but the computation with signed numbers works perfectly well too.

you can't give what you don't have

But you can give what you don't actually own. Think about short selling of stock market securities.

My last rejoinder-

No wonder you encounter problems like division by zero, periodic numbers, determining pi, etc.

There are problems in in mathematics, but these* aren't among them. At most they are problems in the minds of certain individuals.

Another example:

{1, 2, 3, ...} This is that set of natural numbers again, known since prehistoric times. Every natural number has an immediate successor. Call this the successor relation S. So S(101) = 102, S(5280)=5281, and so on. A reversed relation called the immediate predecessor can be defined. Call it P. So P(102)=101, P(5281)=5280 and so on. Of course, somebody is bound to pop up and complain that P(1) is impossible with these natural numbers. The person speaks truly. But what is called a problem is not a problem at all. The natural numbers were intended to be generated beginning with 1 as a seed. So moaning about P(1) is simply unimportant. Nobody promised in advance that the reverse relation P would apply to every natural number.

Now correcting for inclusion of 1/0 in the rational numbers takes something more expensive: selectively giving up some prior rules of computation. 1/0 + 1 = 1/0 = 1/0 + 0. But we can't subtract the 1/0 from each side and arrive at 1 = 0. Nobody promised division should apply to 1 by 0 in the first place. There is no problem with this.

---
*What are periodic numbers?