Is R real?

[untermensche]

I do not think you understood my point but no, models are not true or false in some reality aligned way. They are either useful or not. Their truth or falsehood is only meaningful wrt their ability to align with experience. Not sure how that makes any sort of claim about a subjective quality of humans as a species.

The behavior is called raging at the moon.

Lunacy.

What?

Claims of people being idiots because they understand that "real" is a honorific word without any importance is lunacy.

 

[Testy Calibrate]

What?

Claims of people being idiots because they understand that "real" is a honorific word without any importance is lunacy.

I did not claim anyone is an idiot though, did i?

 

[untermensche]

What?

Claims of people being idiots because they understand that "real" is a honorific word without any importance is lunacy.

I did not claim anyone is an idiot though, did i?

No. And nobody said you did.

The lunacy is not from you.

 

[Bomb#20]

If all the reals are really real, what is the first real greater than 1(or any other integer)?

Easy. 2.

 

[fast]

If all the reals are really real, what is the first real greater than 1(or any other integer)?

Easy. 2.

What about 1.001?

That’s a real number. It might not be a member of the set of all Real Numbers, but the question asks for the next real number, which would be 1.000001 if real numbers were confined to the millionth place, but that clause wasn’t in the question. There really doesn’t appear to be a specific numerical answer but instead an observation that something is wrong with the question in that it assumes a next number, which would be a good assumption had the question been about Real Numbers, which it isn’t.

 

[Bomb#20]

If all the reals are really real, what is the first real greater than 1(or any other integer)?

Easy. 2.

What about 1.001?

That’s a real number. It might not be a member of the set of all Real Numbers, but the question asks for the next real number, which would be 1.000001 if real numbers were confined to the millionth place, but that clause wasn’t in the question.

Sure, 1.001 is a real number greater than 1, but so is 2, and 2 is way older than 1.001. The question is asking for the first. Good luck finding a number bigger than 1 and older than 2. In fact, 2 is probably even older than 1 -- surely people would need to have known about 2 in order to have a reason to invent the concept of 1.

There really doesn’t appear to be a specific numerical answer but instead an observation that something is wrong with the question in that it assumes a next number, which would be a good assumption had the question been about Real Numbers, which it isn’t.

What's wrong with the question is that it assumes to be real a set has to have a "well-order"*, it assumes we know of a "well-order" for it, and it assumes if the set has more than one "well-order" we can identify one of them as special -- as somehow the right one to talk about.

You appear to be distinguishing between real numbers and Real Numbers. What is the distinction you're making?

(* "In mathematics, a well-order on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering.")

 

[fast]

Sure, 1.001 is a real number greater than 1, but so is 2, and 2 is way older than 1.001.

I didn’t see that one coming! Impressive!

My counter argument is complicated and messy but hinges on an acute distinction between numerals and numbers along with an acceptance that numbers are discoverables whereas numerals are inventions, but i’ll save that for another time and instead focus on the other thingy.

You appear to be distinguishing between real numbers and Real Numbers. What is the distinction you're making?

The thread is titled “Is R real?”

“R” (I believe) is short for “Real Numbers,” and given the content of his original post, it seems to me that the question can be more explicitly written as “are Real Numbers real?” I seriously doubt that “real” is being used in a single sense; otherwise, what else would a real thing be if not real?

My post recognizes the ambiguity and separates them out. One thing about labels is how infuriatingly misleading they are. For instance, the term “Imaginary Numbers” was named so to distinguish them from Real Numbers.” It makes sense, but it’s hideously misleading. Imaginary Numbers would have served us better by being labeled “Lateral Numbers,” for although they do not show up on the number line, they exist (picture them hovering over the number line). Hence, call them what you might, if they exist, they are anything but imaginary, but the label was chosen to contrast them from what was regarded as having a place on the number line and referenced as being real.

[r]eal numbers are real, and if a number isn’t real, then it’s not a number at all and thus imaginary, but both Real Numbers and Imaginary Numbers are real. They either exist on or above the number line. Even if that depiction is inaccurate, there’s a fundamental difference between something that has no home on the number line yet exists and a nonexistent.

The question “are Real Numbers real” has an answer, and the answer is yes, not so much because Real Numbers show up on the number line but because they are not imaginary—just as how Imaginary Numbers are also real despite not showing up on the number line—that they show up anywhere at all is good enough to show that they are not imaginary, be they dubbed as Imaginary Numbers or not.

 

[Speakpigeon]

Last nights long post disappeared TWICE, but to recap with much brevity: we should remain mindful of the distinction between the following four groups:

A) Real Numbers
B) Imaginary Numbers
C) real numbers
D) imaginary numbers

You should do brevity more often, we're so very over-busy nowadays.

The first 3 exist.

So, if Real Numbers exist, where are they?

And then how do we know they exist?

Now, remember this isn't what the OP is about, but maybe that's a necessary preliminary. The "real" question for now, is whether R can be taken as a good model of reality, for example of space and time.
EB

 

[Speakpigeon]

I do not think you understood my point

I understood what you said.

but no, models are not true or false in some reality aligned way. They are either useful or not.

I think I understood this point first time round.

Models are true or false.

And not because they may be useful or useless.

Their truth or falsehood is only meaningful wrt their ability to align with experience.

And how is that not what we normally mean by "true"?

true
adj. 1. a. Consistent with fact or reality

Not sure how that makes any sort of claim about a subjective quality of humans as a species.

Your claim, if only implicit, is that people who understand the notion of truth literally, i.e. in accordance to dictionary definition, are just plain wrong.

I think people who understand the notion of truth literally are correct.
EB

 

[fast]

So, if Real Numbers exist, where are they?

On the number line

And then how do we know they exist?

It’s another plane of existence, but rather than go down that road, consider what mathematicians think of numbers called real in light of numbers later called imaginary. That opens the door for the question how do we know they are real. If it should turn out that I’m mistaken regarding numbers as discoverables and numerals as inventions, they are not nonexistent.

Now, remember this isn't what the OP is about, but maybe that's a necessary preliminary. The "real" question for now, is whether R can be taken as a good model of reality, for example of space and time.
EB

That question seems lacking in some way. I’ve read and reread it several times. It’s a tool that can help us model reality, but for it to be a model of it itself doesn’t quite sit right.

 

[Speakpigeon]

On the number line


It’s another plane of existence, but rather than go down that road, consider what mathematicians think of numbers called real in light of numbers later called imaginary. That opens the door for the question how do we know they are real. If it should turn out that I’m mistaken regarding numbers as discoverables and numerals as inventions, they are not nonexistent.

All right, when you feel like it.

Now, remember this isn't what the OP is about, but maybe that's a necessary preliminary. The "real" question for now, is whether R can be taken as a good model of reality, for example of space and time.
EB

That question seems lacking in some way. I’ve read and reread it several times. It’s a tool that can help us model reality, but for it to be a model of it itself doesn’t quite sit right.

I fail to see what could be lacking in the question. Or in the expression of the idea that the set of Real numbers would be a good model for the continuity of space and time.

It's a question and it's a legitimate question, i.e. whether space an time, for example, are continuous in the same sense as the Real line is.
EB

 

[Testy Calibrate]

I understood what you said.



I think I understood this point first time round.

Models are true or false.

And not because they may be useful or useless.

Their truth or falsehood is only meaningful wrt their ability to align with experience.

And how is that not what we normally mean by "true"?

true
adj. 1. a. Consistent with fact or reality

Not sure how that makes any sort of claim about a subjective quality of humans as a species.

Your claim, if only implicit, is that people who understand the notion of truth literally, i.e. in accordance to dictionary definition, are just plain wrong.

I think people who understand the notion of truth literally are correct.
EB

That is why I used the example of Newton's dynamics. Are they true? And, yes, you did misunderstand my point. The fault, however, is probably on my end for not being clear. To say that the reals are or are not real depends on the context. That's because they are part of a model which is not the same thing as the objective reality which we model. Models have a recursive objective quality, that is, as a model is is objectively real, but the question of whether that reality is fully equivalent to the subject of the model requires the context.

 

[fast]

All right, when you feel like it.

That question seems lacking in some way. I’ve read and reread it several times. It’s a tool that can help us model reality, but for it to be a model of it itself doesn’t quite sit right.

I fail to see what could be lacking in the question. Or in the expression of the idea that the set of Real numbers would be a good model for the continuity of space and time.

It's a question and it's a legitimate question, i.e. whether space an time, for example, are continuous in the same sense as the Real line is.
EB

Mmm, maybe so. Perhaps not perfect but good.

The number line models continuity. It’s a construct that incorporates infinity, so even if there are (or aren’t)
bounds to space and time, the graph paper upon which we could draw the dimensions of a house is to the number line as is space and time to the drawing.

I think of space as boundless, and I don’t buy into the notion that time had a beginning, so why not, the continuity of the number line (lacking physicality as it might) does appear to model the continuity of both those other things, only one of which has a physical sense to it.

 

[WAB]

*deleted*

[I said something stupid]

 

[steve_bank]

Once again, real numbers as some kind of proof of the universe.

the reak number line is an abstraction. R is a subset of C complex numbers.

A complex number Z = a +-ib

Where a and b a re real numbers and i is sqrt(-1). ia is an imaginary number in three complex plane(y axis) and a is located on the real or x axis.

Magnitude of z =sqrt(a^2 +b^2). So is space infinitely divisible complex numbers? A real number is z = a +-i0.

So, the real number is a useful tool, but has no inherent relation to physical reality any more than a ruler.

A ruler is a real number line. As you divide it into smaller and smaller dimensions you end up with a limit set by disctrete atoms. There is no physical way to measure distance to an infinite resolution. And now Segway into the endless debate on infinity....

x,y,z used to define space is a useful abstraction. It allows us to locate a point in space relative to a reference point. Hadn't thought of it that way before numbers and coodinate systems are useful models, I'd say that is the best answer.

 

[steve_bank]

Real and Imaginary cause some confusion, historically poor choice of words.

They are just arbitrary tags.

You could say Unreal Numbers and Unimaginary Numbers and the math does not change.

 

[Speakpigeon]

I understood what you said.

I think I understood this point first time round.

Models are true or false.

And not because they may be useful or useless.

And how is that not what we normally mean by "true"?

true
adj. 1. a. Consistent with fact or reality

Your claim, if only implicit, is that people who understand the notion of truth literally, i.e. in accordance to dictionary definition, are just plain wrong.

I think people who understand the notion of truth literally are correct.
EB

That is why I used the example of Newton's dynamics. Are they true?

No, they are not. They never were. Scientists believed them true for a long time and now they believe otherwise.

And, yes, you did misunderstand my point.

No, I didn't. I responded to your claim that models are not true of false and I got that right.

Newton's model is false and always was. And yes, it was also useful and in fact still is, but that doesn't change the fact that it's false.

This falsifies your claim that models are not true or false.

The fault, however, is probably on my end for not being clear. To say that the reals are or are not real depends on the context. That's because they are part of a model which is not the same thing as the objective reality which we model. Models have a recursive objective quality, that is, as a model is is objectively real, but the question of whether that reality is fully equivalent to the subject of the model requires the context.

The thing is, I didn't even address that aspect of your post. How can you say I didn't understand it?

The question of whether models are true or false is distinct from and independent from (the reverse is not true) the question of whether mathematical abstractions are real. You are effectively conflating, as indeed many people do, the epistemological question of the truth of an abstract model with the ontological question whether the model is real, i.e. whether whatever is represented by the model has somehow the same essence as the model. A model need not be real in this sense, or "essentially true", i.e. true in essence, or "fully equivalent" as you put it, in order to be true simpliciter.

The OP concerns both questions, inevitably. Reality implies truth, if only because things are all true of themselves, but truth does't require and therefore doesn't imply reality. If the reverse was true, the notion of truth would be vacuous and people would be idiots talking about truth.
EB

 

[Speakpigeon]

So, the real number is a useful tool, but has no inherent relation to physical reality any more than a ruler.

A ruler is a real number line. As you divide it into smaller and smaller dimensions you end up with a limit set by disctrete atoms. There is no physical way to measure distance to an infinite resolution

I agree you can't measure space with a ruler. They've never been used for that. So, what happens to rulers is irrelevant and your comparison with R is only misleading and muddying. The OP concerns R in relation to space an time, not rulers and their relation to space and time.
EB

 

[Speakpigeon]

Real and Imaginary cause some confusion, historically poor choice of words.

They are just arbitrary tags.

You could say Unreal Numbers and Unimaginary Numbers and the math does not change.

Sure, but that's overlooking the reason people decided "Real" was an appropriate name. Intuitively, there is little doubt R seems a better model of real space and real time than N or even Q.

Changing the name wouldn't change this fact.

And whence comes the question.
EB

 

[Testy Calibrate]

That is why I used the example of Newton's dynamics. Are they true?

No, they are not. They never were. Scientists believed them true for a long time and now they believe otherwise.

And, yes, you did misunderstand my point.

No, I didn't. I responded to your claim that models are not true of false and I got that right.

Newton's model is false and always was. And yes, it was also useful and in fact still is, but that doesn't change the fact that it's false.

This falsifies your claim that models are not true or false.

The fault, however, is probably on my end for not being clear. To say that the reals are or are not real depends on the context. That's because they are part of a model which is not the same thing as the objective reality which we model. Models have a recursive objective quality, that is, as a model is is objectively real, but the question of whether that reality is fully equivalent to the subject of the model requires the context.

The thing is, I didn't even address that aspect of your post. How can you say I didn't understand it?

The question of whether models are true or false is distinct from and independent from (the reverse is not true) the question of whether mathematical abstractions are real. You are effectively conflating, as indeed many people do, the epistemological question of the truth of an abstract model with the ontological question whether the model is real, i.e. whether whatever is represented by the model has somehow the same essence as the model. A model need not be real in this sense, or "essentially true", i.e. true in essence, or "fully equivalent" as you put it, in order to be true simpliciter.

The OP concerns both questions, inevitably. Reality implies truth, if only because things are all true of themselves, but truth does't require and therefore doesn't imply reality. If the reverse was true, the notion of truth would be vacuous and people would be idiots talking about truth.
EB

Newton's model is not false. Wtf are you on about? Show me a single violation of thermodynamics. His inverse square law is not false either. It is merely imprecise at relativistic energy levels. The things you write are kind of idiotic.