Numbers!

[james blunt]

In that case, not any more than any other idea. Ideas are physical processes in brains.

Yes, ideas are a part of the neurological process. Some ideas are thoughtless though .

 

[james blunt]

But as you said, Numbers can be reached by trial and error , therefor, i ask, did you arrive at the conclusion that you are 45 by counting 44+1 ot by trial and error?

I arrived at that by my existing subjective education , trial and error is not the same as recording history and that I was 44.
Trial and error is more how many buckets it would take to fill a 30ltr container ,obviously we would get a result of the buckets capacity ,

 

[youknowme]

That which has physical existence .

In that case they are just as real as any other word.

If a writer writes a fictional story about an old sun-washed grain barn in a golden field of tall grass with a broad breach-heavy apple tree near by, then none of those things are actually real. However, if a writer went to a location like that which actually exist, to write about what she saw then she would be writing about things which have a physical existence. Such is the case with numbers, sometimes they are used to describe things which may not exist, and sometimes they are used to describe thing that physically exist.

 

[ChristineM]

I arrived at that by my existing subjective education , trial and error is not the same as recording history and that I was 44.
Trial and error is more how many buckets it would take to fill a 30ltr container ,obviously we would get a result of the buckets capacity ,

If you know the size of the bucket its not a problem. The bucket i use most is 6litre capacity, in which case is 5 buckets. If you dont know the size of the bucket you are venturing guessing which is not mathematics

 

[james blunt]

In that case they are just as real as any other word.

If a writer writes a fictional story about an old sun-washed grain barn in a golden field of tall grass with a broad breach-heavy apple tree near by, then none of those things are actually real. However if a writer went to a location like that which actually exist, to write about what she saw then she would be writing about things which have a physical existence. Such is the case with numbers, sometimes they are used to describe things which may not exist, and sometimes they are used to describe thing that physically exist.

Sometimes a story can be foretold by the preceding knowledge . It's elementary to consider quantifiable events and to try place value to it .
It extends from bartering values , the worth , perhaps pound for pound .

 

[james blunt]

If you know the size of the bucket its not a problem. The bucket i use most is 6litre capacity, in which case is 5 buckets. If you dont know the size of the bucket you are venturing guessing which is not mathematics

No , if it took 10 buckets to fill the 30 litre bucket , you would know the bucket was 3 litres in capacity without having previous knowledge of the buckets capacity .

 

[ChristineM]

No , if it took 10 buckets to fill the 30 litre bucket , you would know the bucket was 3 litres in capacity without having previous knowledge of the buckets capacity .

After the fact. It is a simple matter of counting.

There are several other ways to calculate it

 

[james blunt]

After the fact. It is a simple matter of counting.

There are several other ways to calculate it

Of course , I'm always calculating things , like now from example I am presently working with a set of finite numbers and playing with probability number theory . People may sometimes refer to this as gamblers fallacy but I understand the intricates of finite and infinite probability .

 

[Polymath257]

No , if it took 10 buckets to fill the 30 litre bucket , you would know the bucket was 3 litres in capacity without having previous knowledge of the buckets capacity .

When you say something like this, you are making a number of additional assumptions that other effects are irrelevant.

For example, in pouring the 10 buckets into the 30 liter bucket, the act of pouring will increase the temperature of whatever is being poured, so it will expand. In that case, each of the small buckets would end up being *less* than 3 liters.

Now, in this case, the temperature increase and expansion is very small, but that is why we can use the approximation of simply dividing 30 by 10 to find the capacity of the smaller bucket.

There are many other possible physical effects that can be relevant for even simple scenarios like this: for example, if we alternately pour water (H2O) and ethyl alcohol (C2H5OH), and we pour 5 buckets each (for a total of 10 buckets) and fill a 30 liter container, the small container again will NOT be 3 liters. This time, the small bucket will be slightly *more* than 3 liters. Why? Because water and alcohol have the property that a mixture has a smaller volume than the sum of the two initial volumes. And this is can be a significant effect.

Mathematics is a *language* we can use to model the real world. But we need to test to determine which parts of that language actually give valid results in the real world and when.

 

[Heyo]

How real are Numbers?

As I expressed some time ago (5 Planes of Existence) numbers are not real but they are also not mere constructs. They belong to the realm of Platonic Ideals.

 

[ChristineM]

As I expressed some time ago (5 Planes of Existence) numbers are not real but they are also not mere constructs. They belong to the realm of Platonic Ideals.

And that is"one" post that tells it now it is ;-)

 

[ChristineM]

As I expressed some time ago (5 Planes of Existence) numbers are not real but they are also not mere constructs. They belong to the realm of Platonic Ideals.

So what about real numbers?

 

[Heyo]

And that is"one" post that tells it now it is ;-)

It would make communication about so many things so much easier if everyone would simply accept my proposed classification. (At least for me ;-)

 

[Heyo]

So what about real numbers?

"Real" in "real numbers has a different meaning from the philosophical real. It also is dependent on the language. German differentiates between "real" and "reelle Zahlen". So, a "real" number is as much real as a "blue" note in a piece of music has a visible colour.

 

[ChristineM]

"Real" in "real numbers has a different meaning from the philosophical real. It also is dependent on the language. German differentiates between "real" and "reelle Zahlen". So, a "real" number is as much real as a "blue" note in a piece of music has a visible colour.

I work by definition, not philosophy, identifying numbers as real has always thrown my understanding of real.

 

[Jayhawker Soule]

The map is not the territory.

 

[Polymath257]

As I expressed some time ago (5 Planes of Existence) numbers are not real but they are also not mere constructs. They belong to the realm of Platonic Ideals.

That is an interesting classification scheme. My basic issue is that I think the Platonic ideals are actually constructs in your system.

In particular, I see numbers as constructs and not something 'necessary'.

Overall, I see mathematics as a sort of very elaborate game. We have the rules of the game (rules of deduction) and a starting point (the axioms) and we can tell when the moves made are legitimate (a sequence of moves is called a proof). In this formal system, we construct aspects that correspond to our intuitions about a wide variety of things, numbers being one.

But, there are many, very different ways to go about these constructions and what is important is not usually the details of the construction, but rather that the interrelationships be maintained. Two different constructs that are 'isomorphic' are equally good at showing the structure.

And, the construct of (natural) numbers has a structure that allows enumeration. That is why it is useful. The extensions to such things as the rational numbers or the real numbers increase the utility of the systems in forming models of our perceptions. But they are still, ultimately, constructs that we use to simplify our thinking, not something that exists independently of ourselves (not 'necessary').

Even logic has variants, including paraconsistent logics, versions without the law of excluded middle, etc.

 

[Heyo]

That is an interesting classification scheme. My basic issue is that I think the Platonic ideals are actually constructs in your system.

In particular, I see numbers as constructs and not something 'necessary'.

Overall, I see mathematics as a sort of very elaborate game. We have the rules of the game (rules of deduction) and a starting point (the axioms) and we can tell when the moves made are legitimate (a sequence of moves is called a proof). In this formal system, we construct aspects that correspond to our intuitions about a wide variety of things, numbers being one.

But, there are many, very different ways to go about these constructions and what is important is not usually the details of the construction, but rather that the interrelationships be maintained. Two different constructs that are 'isomorphic' are equally good at showing the structure.

And, the construct of (natural) numbers has a structure that allows enumeration. That is why it is useful. The extensions to such things as the rational numbers or the real numbers increase the utility of the systems in forming models of our perceptions. But they are still, ultimately, constructs that we use to simplify our thinking, not something that exists independently of ourselves (not 'necessary').

Even logic has variants, including paraconsistent logics, versions without the law of excluded middle, etc.

I fear I can't prove to you that numbers aren't constructs and my best argument boils down to incredulity. But there are hints that it might be true. 1. Numbers (and mathematics) have been discovered independently multiple times. 2. Mathematics is always done in principally the same way. There seems to be only one mathematics. 3. Maths is strangely connected to the real world. Formulas fit well to explain things, even when the mathematical formula was thought up long before the phenomenon that it explains was discovered. 4. There seems to be no other system that is both usefull and consistent to do maths. Sure, we have invented alternative number systems and operators but they have to obey the same rules on higher levels of abstraction.

And I think it makes sense to make the distinction for practical reasons. What I have listed as constructs are things that are easily changed through consent. Ideals aren't. An insight some lawmakers should have had before trying to pass a bill to fix pi at 3.14.

 

[Polymath257]

I fear I can't prove to you that numbers aren't constructs and my best argument boils down to incredulity. But there are hints that it might be true. 1. Numbers (and mathematics) have been discovered independently multiple times. 2. Mathematics is always done in principally the same way. There seems to be only one mathematics. 3. Maths is strangely connected to the real world. Formulas fit well to explain things, even when the mathematical formula was thought up long before the phenomenon that it explains was discovered. 4. There seems to be no other system that is both usefull and consistent to do maths. Sure, we have invented alternative number systems and operators but they have to obey the same rules on higher levels of abstraction.

Your 1 and 2 seem to be linked. But I would claim they are false. A good example is that of a ratio. The ancient greek notion was *quite* different than the modern one. We tend to think in terms of fractions, while the ancient view was one of proportionality, which did not allow addition, and only limited multiplication. There was also a fundamental difference, in the ancient mind, between number (which was discrete) and magnitude (which could be continuous). Now, we see these as different aspects of the same thing.

So, I would dispute that there is only one mathematics. We have grown to the place that multiple previous ideas of mathematics are subsumed into the modern one, but that is a pretty recent development.

The 'unreasonable effectiveness of mathematics' in its application to the real world also somewhat sweeps the difficulties aside. My view is that math is a very expressive formal language. What that means is that if we need to express ourselves in some way, we *invent* new math to meet the challenge if it is not already developed. You seem to focus on the cases where the math was both previously developed and useful. But there have been many aspects of math with only limited utility in forming models of reality and many models that are not on a mathematical foundation.

As for there being only one consistent useful mathematical system, that is quite far from being the case. Any system we choose would have to satisfy certain requirements (say, the development of calculus) to maintain utility, but there are many different ways to put the basics on an axiomatic foundation. Modern math, for example, is ultimately based on set theory. But there are those who attempt to do similar things with category theory or using different versions of logic.

And I think it makes sense to make the distinction for practical reasons. What I have listed as constructs are things that are easily changed through consent. Ideals aren't. An insight some lawmakers should have had before trying to pass a bill to fix pi at 3.14.

Once again, I see it as similar to trying to change the rules of chess. You can do so, but you are then playing a different game. the value of pi is pretty far up the hierarchy from the axioms, so its like trying to change how some midgame strategy can be done as opposed to changing the actual rules.

 

[Heyo]

Your 1 and 2 seem to be linked. But I would claim they are false. A good example is that of a ratio. The ancient greek notion was *quite* different than the modern one. We tend to think in terms of fractions, while the ancient view was one of proportionality, which did not allow addition, and only limited multiplication. There was also a fundamental difference, in the ancient mind, between number (which was discrete) and magnitude (which could be continuous). Now, we see these as different aspects of the same thing.

I don't see ancient maths as different, only as less developed. And Greek maths was already pretty sophisticated. Proving the irrationality of the root of 2, the basics of calculus (Zeno) and applied maths like calculating the circumference of the earth that their thinking couldn't have been too far away from modern maths.

So, I would dispute that there is only one mathematics. We have grown to the place that multiple previous ideas of mathematics are subsumed into the modern one, but that is a pretty recent development.

The 'unreasonable effectiveness of mathematics' in its application to the real world also somewhat sweeps the difficulties aside. My view is that math is a very expressive formal language. What that means is that if we need to express ourselves in some way, we *invent* new math to meet the challenge if it is not already developed. You seem to focus on the cases where the math was both previously developed and useful. But there have been many aspects of math with only limited utility in forming models of reality and many models that are not on a mathematical foundation.

We can discover new branches of mathematics but they are still based on the same principles and they fit into the system without contradictions (mostly).

As for there being only one consistent useful mathematical system, that is quite far from being the case. Any system we choose would have to satisfy certain requirements (say, the development of calculus) to maintain utility, but there are many different ways to put the basics on an axiomatic foundation. Modern math, for example, is ultimately based on set theory. But there are those who attempt to do similar things with category theory or using different versions of logic.

And they would still follow the same function. Take one step back and they look the same.

Once again, I see it as similar to trying to change the rules of chess. You can do so, but you are then playing a different game. the value of pi is pretty far up the hierarchy from the axioms, so its like trying to change how some midgame strategy can be done as opposed to changing the actual rules.

Not chess, GO. You can play it on a small board, on a large board, you could play it on a hexagonal grid, you could make it 3D. As long you hold to the basic rules, it's still GO.

Btw.: Stephen Woodford is on your side but he doesn't explain why in this clip: