Okay, here’s a thought.

We all know that mathematics and human minds can create things that cannot exist physically in this universe. For example, two-dimensional objects, exponential horns that have finite volume yet infinite surface area, continuous energy levels, etc… There are many examples and we, as students of physics use them extensively. Yet they are definitely products of and are in existence in the universe that they cannot exist in physically.

So, let me wrap a question around it. What is it the real difference between physical existence versus conceptual existence when it requires something with physical existence to realize the concept?

Or put another way, the set of all things that have physical existence is a subset of those things that have conceptual existence, however conceptual existence is dependant on physical existence.

Comments?

 

BillO,

We all know that mathematics and human minds can create things that cannot exist physically in this universe.

No we can't. We imagine anything, but can only create a finite set things based on physical limitations and resources.

There are many examples and we, as students of physics use them extensively.

What are you talking about? Concepts, maybe?

So, let me wrap a question around it. What is it the real difference between physical existence versus conceptual existence when it requires something with physical existence to realize the concept?

That sounds like a contradiction. Why do you need a physical entity to imagine a conceptual idea, principle or process? For instance, the mathematical conceptions of summation, subtraction, multiplication, or division does not NEED any physical objects to be defined or imagined. Even though the concept can be applied usefully to physical objects.

Or put another way, the set of all things that have physical existence is a subset of those things that have conceptual existence, ...

Since one can conceive and imagine anything, that does not seem to be surprising or enlightening.

however conceptual existence is dependant on physical existence.[/

I believe I showed above that it is not so.

Comments?

With respect to what?

Ratch

 

That sounds like a contradiction. Why do you need a physical entity to imagine a conceptual idea, principle or process? For instance, the mathematical conceptions of summation, subtraction, multiplication, or division does not NEED any physical objects to be defined or imagined. Even though the concept can be applied usefully to physical objects.

I don't quite know why I'm responding to this, but Ratch, do you not consider yourself a physical object? Well, maybe your not.

You seem to have completely missed my point. Well done.

 

just a guess -

real

The other side of

What is it the real difference between physical existence versus conceptual existence when it requires something with physical existence to realize the concept?

is: ex nihlo, nihil fit.

 

I've been asserting for weeks that Ratch does not exist.

So, let me wrap a question around it. What is it the real difference between physical existence versus conceptual existence when it requires something with physical existence to realize the concept?

Before I attempt an answer, I want to be sure I understand the question. I will re-phrase the question, and await correction or confirmation. "Since I have to exist to imagine something, is there any degree of reality to the unrealistic things I imagine?"

 

BillO,

I don't quite know why I'm responding to this, but Ratch, do you not consider yourself a physical object? Well, maybe your not.

Yes, I do.

You seem to have completely missed my point. Well done.

Why thank you. I guess you did not explain yourself well enough.

Ratch

 

You seem to have completely missed my point. Well done.

Why thank you. I guess you did not explain yourself well enough.

Ah! Perception! The very thing which puts into doubt the existence of everything! (With possible exceptions, of course...)

You seem...

I guess...

But is there any truth, any objective reality, in these conflicting perceptions? Or in any perceptions whatsoever?

 

I've been asserting for weeks that Ratch does not exist.

Before I attempt an answer, I want to be sure I understand the question. I will re-phrase the question, and await correction or confirmation. "Since I have to exist to imagine something, is there any degree of reality to the unrealistic things I imagine?"

Not quite, but getting there. I assert that the things we imagine do exist. These thoughts and concepts are products of the universe. Even before pen is put to paper (so to speak) to record them in any transferable or storable form, they exist in our minds. Presumably in some configuration of our neurons and their supporting infrastructure and processes.

Very much they way the blueprints of a machine exist before the machine is built. However, the machine can be given physical form, whereas many of the concepts of our physical minds cannot.
My first thought was that these are errors but that is not quite right. Some of these concepts are used in our everyday understanding of the physical nature of the universe.

If we think of a set of all valid concepts C, such that the set P, of all concepts that can take physical form is a subset of C. Then how can H, a member of P, generate C?

Is this even possible unless C=P?

 

Why thank you. I guess you did not explain yourself well enough.

Ratch

That, so far, has been the bain of my life.

 

I'm sorry, but like Ratch I don't understand the question.

Is this a Hitchikers Guide to the Galaxy question?

Or are we talking Satre, existentialism, the sound of one hand clapping?

Or are we talking Godels theorem?

I can for instance posit a system that 3+3 =7.

Now I can't find such a system either in theory or reality.

 

This is much more a philosophical discussion than physics. I am moving it to the Off Topic section, where it may get better exposure.

Meanwhile, we await clarification...

 

I'm sorry, but like Ratch I don't understand the question.

Is this a Hitchikers Guide to the Galaxy question?

Or are we talking Satre, existentialism, the sound of one hand clapping?

Or are we talking Godels theorem?

I can for instance posit a system that 3+3 =7.

Now I can't find such a system either in theory or reality.

We are (I am) not really talking about any of the things you mentioned but the closest would be Godel’s Theorem.

On your system with 3+3=7, you could find it in theory if you were to create the theory around it. There is nothing in mathematics that would prevent that. It would then exist, be valid, but have no physical substance. Look up your theoretical algebra. You can create any number of systems that could have no physical meaning in this universe. You follow me?

Now, once you have adequately described that mathematics where 3+3=7 is a valid equation, where did it come from? It came from a physical object that is bound by the limitations of physical existence. Yet it is not.

I’m not talking philosophy here. This is not a “Where am ‘I’?” question, or a “Do I exist?” question or a "If there is no witness to an event, did it occur?" question. It is more along the lines of, what is it about the physics of this universe that allows a small piece of this universe, that we know as Studiot, to define another universe that does not or cannot physically exist in the terms of the universe that created it?

Here is another question, similar to, but not exactly like, the one I originally posed: How can the normal interaction of the fundamental particles and forces of this universe end up defining things that cannot be realized by the normal interaction of the fundamental particles and forces of this universe?

Or as my son put it: How can a piece of this universe, which is bounded by the laws of the universe it is in, define a universe where these laws do not apply.

BTW, I do not think we need to evoke deities or philosophy to address this.

 

There is a idea so powerful, that if you think of it fully in your mind, it will drive you insane, and erase all memory of it's existence from your mind. This is called the "Medusa Concept". I know it exists, but I deliberately do not allow myself to behold it, for obvious reasons. Be wary of it!

 

On your system with 3+3=7, you could find it in theory if you were to create the theory around it. There is nothing in mathematics that would prevent that. It would then exist, be valid, but have no physical substance. Look up your theoretical algebra. You can create any number of systems that could have no physical meaning in this universe. You follow me?

I follow this, but I don't agree that it exists in theory either, as it contains a logical inconsistency.

Consider the following sequence of constructs.

1) 3+3 = 7, with all the usual rules.

2) The space between mountains is defined as a valley. There exist two separately identifiable mountains without a valley between.

3) xdfpw[gko

Each statement becomes steadily more outlandish and less plausible until finally gibberish is reached. But can you refute (3). Do you even know what it means? Nothing in terms of our universe.

Here is another question, similar to, but not exactly like, the one I originally posed: How can the normal interaction of the fundamental particles and forces of this universe end up defining things that cannot be realized by the normal interaction of the fundamental particles and forces of this universe?

This is a much more interesting question. Here is a purely mathematical answer.

Consider the (vector) space of continuous functions, differentiable at all orders and all points.

The functions sin(nx), {n = an integer}, amongst others, form a basis for this space.

As such we can construct any continuous fully differentiable function from a series sum of sin(nx) functions using suitable coefficients. This are known as a Fourier series.

The point of comparison with your question is that our 'universe' here is the universal set of continuous functions. We can, however use infinite Fourier series to step outside and construct a function which is not a member of the universal set. (For example a square wave). This is a truly remarkable achievement as the fundamental requirement that adding any two members of the set begets a third is breached. I would say this is an example of your question.

 

There is a idea so powerful, that if you think of it fully in your mind, it will drive you insane, and erase all memory of it's existence from your mind. This is called the "Medusa Concept". I know it exists, but I deliberately do not allow myself to behold it, for obvious reasons. Be wary of it!

That, and a Pan-Galactic Gargle Blaster.

 

When you talk of things we can conceive of, but don't exist or aren't observed in our universe I think it is worthwhile differeentiating between those which could (might) exist, i.e.we can see no theoretical reason why not, such as a 20 foot brick or a bright green pigeon and those which we have a theoretical objection to such as a single brick wall twice the height of the Empire State, made of standard bricks and mortar. Our theoretical objection is not the enormous slenderness ratio but that any known standard brick at the bottom would be crushed. A more serious conjecture might be to seek solutions of the equation sin (x) = 3.

 

1) 3+3 = 7, with all the usual rules.

There in lays the problem - using all the usual rules. Look up groups and rings in abstract algebra. All you need o do is define a group where the binary operator is named addition such that 3+3=7 is valid and logical. A group in algebra is a set of elements and a binary operator such that:

1)The operator acting on two elements of the set results in an element of the set. So it is completely defined, and closed over the set.

2) One element of the set is an identity element. So if we call our operation #, there exists an element of the set e such that for any other element of the set x, e # x = x # e = x.

3) Every element of the set has an inverse element. If we take any element of the set p, there is another element q such that p # q = q # p = e.

2) The operation is associative. For any three elements of the set, (a # b) # c always equals a # (b # c).

So as a familiar example, [bold]I[/bold] is a group over [bold]normal[/bold] addition. The net of all this is that you can easily define a group where 3+3=7

This is a much more interesting question. Here is a purely mathematical answer.

Consider the (vector) space of continuous functions, differentiable at all orders and all points.

The functions sin(nx), {n = an integer}, amongst others, form a basis for this space.

As such we can construct any continuous fully differentiable function from a series sum of sin(nx) functions using suitable coefficients. This are known as a Fourier series.

The point of comparison with your question is that our 'universe' here is the universal set of continuous functions. We can, however use infinite Fourier series to step outside and construct a function [bold]which is not a member of the universal set.[/bold] (For example a square wave). This is a truly remarkable achievement as the fundamental requirement that adding any two members of the set begets a third is breached. I would say this is an example of your question.

I disagree Studiot. A Fourier series does not result in the exact function being modeled. It is more an approximation, albeit a good one.

For instance, take either a saw tooth or square wave function defined on the x-y plane where x is the independent variable and which are symmetrical around y=0. Each of these has discontinuities at which they are not defined and not differentiable.

However, the Fourier series for both of these converges to a well defined 0 at each of the points where the actual functions have discontinuities. Also, since each term in these series are differentiable at these same points, the summed series are differentiable.

The only way the Furrier series can be made look like the actual function is to artificially remove from the series’ domain the points that are discontinuous in the actual functions. That action alone, according to algebraic field theory, would be enough to remove the result from the original field.

 

1) 3 + 3 = 7

Only Ratch is allowed to split hairs and change other persons' definitions.

By the usual rules I simply meant that
3 and 7 are numbers (integers, rationals or reals as usually defined.)
If you wish to use another definition than 3 = 1+1+1 and 7 = 1+1+1+1+1+1+1, please state it.
That the operation + is defined in the normal way.
That the relation = is defined in the normal way.

I am comfortable with the four basic axioms of group theory so labelling your list G1 through G4

I note that if 3 is in your set, 7 must be in your set (G1)
thus -3 and -7 must be in the set (G3)
zero must be in the set (G2)
the result of 3 + 7 must be in the set (G1)
The result of 3 + 3 + 3 + 3 + 3......... must be in the set (repeated application of G1)

you can easily define a group where 3+3=7

So construct your group, showing all this

 

However, the Fourier series for both of these converges to a well defined 0 at each of the points where the actual functions have discontinuities.

You have missed the wood for the trees; I am trying to help your cause, not hinder it.

The important point is not what we call the function that the series converges to or what it might be similar to.
The point is that whatever we call it the 'function' is not continuous. It is only 'piecewise continuous' ; i.e. continuous on a series of alternate open and compact intervals.
It is easy to apply an epsilon-delta argument to the junction of these intervals, where f(x) may converge to zero in one of the adjacent intervals, but definitely something else in the neighbourhood of the junction in the other.


Here is a similar, but more concrete (well paper) example.

Consider the vector space of all (2D) sheets of paper. Any sheet of paper can be used as a basis for the set and any sheet of paper can be constructed by repeated edge glueing from a chosen basis sheet.

However if we rotate some sheets about an edge and glue we can construct a box, which is definitely not a member of the sheets of paper set.

 

I can for instance posit a system that 3+3 =7.

Now I can't find such a system either in theory or reality.

I believe it is called synergy, and there are lots of examples in the physical world where the net effect is greater than the sum of the the individual effects.

But, that may not be what you meant.

John