Dimensions

[sideshowbob]

Well, seems to me the following analysis seems to disagree with your perspective.

You have found a couple of specific examples. It's like saying 2x4 can not have length. But that in no way indicates that zero can never be a magnitude.

 

[Write4U]

You have found a couple of specific examples. It's like saying 2x4 can not have length.

No, it's like saying a 2x4 can not have zero length.

But that in no way indicates that zero can never be a magnitude.

According to the quote, magnitude can never be negative.
And

The zero vector (vector where all values are 0) has a magnitude of 0, but all other vectors have a positive magnitude.

seems to create all kinds of contradictions, when applied in a general sense.

 

[James R]

Write4U:

Nothing that prohibits something from occurring.

What prohibits something from occurring?

Perhaps I used the wrong term. I just read that the term "permittive" applies specifically to Electric transmission, which is another scientific convenience.

You're possibly referring to electrical permittivity. It's okay. You're still allowed to use the word "permittive" in other ways. You just need to be clear about how you're using it.

So to make it easier let's use the term "mathematically permissive".

I don't see how adding the adjective "mathematically" helps to clarify what you mean.

Without time or dimension, spacetime geometry and its mathematical permissions and restrictions does not exist and will allow the emergence of anything.

Without time or dimension, there is no spacetime geometry. Spacetime geometry is all about time and dimension (distance).

It is a permissive condition.
It is what allows the expansion of the universe itself.

Your claim is that "nothing" allows the expansion of the universe?

Nothing isn't a thing. It's literally "no thing"!

Look at some computer programming books.

Pass. I thought you might have some meaning in mind when you write things. If you can't/won't explain what you mean, I'm not that interested. A specific reference might suffice, possibly, but I'm surprised you can't just say what you mean in a short sentence or two.

Infinity cannot have a beginning.

What kind of infinity are you talking about? Infinity is a concept that can be applied to lots of different things.

Since you mention beginnings, perhaps you're talking about infinite time (?) Time could have a beginning and no end, which would be infinite time, wouldn't it?

Infinity is a timeless dimensionless condition.

Infinity is not a condition, as far as I'm aware.

I agree, but a condition is not a thing. A condition is an abstract quality and has no physical existence just as nothing is an abstract permissive condition.

So you're saying that our universe somehow came from an abstract quality that has no physical existence?

How could that happen?
----

Also, I note in passing that your reply to my previous post is very selective. Are you unable to define any of the other terms I asked you to define? Do you agree with the rest of what I wrote, including the objections I raised to your thesis?

 

[James R]

You mean that one definition of zero is: the number between the set of all negative numbers and the set of all positive numbers.

That would be one possible definition, albeit a rather clunky one.

The number itself has no value.

It has the "value" zero!

I cite the main definition that zero is: the arithmetical symbol 0 or 0̸ denoting the absence of all magnitude or quantity.

What a lousy attempt at a definition of zero! Where did you dig that one up?

At a pinch, "absence of magnitude" might squeak through the censors, but "absence of quantity" is about something other than numbers.

A temperature of zero degrees Celcius does not indicate an "absence of the quantity called temperature". Nor does it really indicate an "absence of all magnitude". The magnitude of the temperature is zero degrees Celcius! Zero specifies the magnitude of the temperature.

Maybe the author of this just got confused.

Adding 0 to a number leaves its same. 0 is called the additive identity and the property is called the additive identity property.

4 + 0 = 4

0 + 3 = 3

This is a better defintion. Zero is the additive identity in arithmetic. That is, zero is the number x, such that x+y=y+x = y for any number y.

Notice how zero is a number, just like 4 or 7 or -3.14159 or pi. It's not an "absence" of anything, though it can be used to quantify an absence of something.

If I have zero sheep, then there's an absence of sheep that are mine. But the number of my sheep is zero. If I add zero sheep to my existing flock of 7 sheep, I will have 7 sheep at the end of the addition process.

But zero has no magnitude.

You're confusing yourself again because you have such a surface level understanding of mathematics.

In science, we often write numbers in "scientific notation", which looks like this:
$$17.3 = 1.73 \times 10^1$$
$$5783.235 = 5.783235 \times 10^3$$
$$-1.7394 = -1.7394 \times 10^0$$
$$0.0018 = 1.8 \times 10^{-3}$$
If you like, you can refer to the "magnitude" of a number by quoting the power of ten in the standard scientific notation (which has exactly one non-zero digit in front of the decimal point). So, the magnitude of the number 5783.235 would be 3 (or, depending on how you want to say it, $$10^3$$).

Numbers that differ in their powers of 10 are said to different by "orders of magnitude". So 16000 is said to be 3 orders of magnitude larger than 16. Often this is used more loosely, by dropping the stuff before the power of 10. Thus the numbers 53 and 98 are both said to have the same order of magnitude, whereas 530 and 58 have different orders of magnitude, with 530 being larger than 58 by an order of magnitude.

Using this terminology we could write:
$$0= 0 \times 10^{51}$$ or
$$0 = 0 \times 10^{-23}$$
In other words, "zero" has no specific order of magnitude. Any power of 10 would do.

In nature zero is the absence of a property or (countable) value.

There is no "zero" in nature. Zero is a number, invented by human beings. Zero is not "nothing". Zero is not an "absence of something". It is a number.

Besides for purposes of this discussion, zero dimension means absence of dimension.

No. It means when we count the dimensions, we find that the number of dimensions is zero.

Generic universal mathematics are an inherent function of spacetime geometry.

Define "generic universal mathematics"?

How is this different from any other sort of mathematics?

This thread has been off topic for the last several pages about the meaning of zero, a mathematical symbol, which is only tangentially related to "dimensions" such as vectors and scalars.

Vectors are not dimensions. Scalars are not dimensions.
A vector space (which, by the way, is a mathematical abstraction) can have a dimension; the dimension is just a number. A scalar quantity can have a value, such as zero, which is just a number.

In mathematics, the dimension of a vector space V is the cardinality of a basis of V over its base field.

Pulling random quotes from the internet doesn't help your case.

The dimension of a vector space is a number.

Is dimension a vector or scalar?

It depends on the context in which you're using the word "dimension". It could be a scalar (a number), or it could be a more complicated concept (e.g. like a spatial dimension).
---

Class is over for today.

 

[James R]

Moderator note: Write4U has been warned for spamming his "universe is mathematics" religion to a thread where it is off topic. This follows previous warnings for the same behaviour.

Due to accumulated warning points, Write4U will be taking a short time out from sciforums.

 

[sideshowbob]

No, it's like saying a 2x4 can not have zero length.

Why can't it?

 

[arfa brane]

Is Mathematics real?

We should be careful in distinguishing what is mathematically real, and what is physically real, I think.
That mathematics in four dimensions appears to model the physical world is just a mathematical coincidence.
An unreasonably efficient one. Why the complex number appears to be involved in that efficiency is another coincidence, but without it physics would be, difficult.

Historically, mathematics kicked off because human observers wanted to understand stuff like the phases of the moon, planetary motion and whatnot. So the mathematics of all that must be real, in some sense.

 

[arfa brane]

Mathematical treatment of dimensions in computer graphics:

Mathematicians have discovered that many geometric concepts and computations can be greatly simplified if the concept of infinity is used. But the constraint is that we cannot treat infinity like a regular number.

[Without using] homogeneous coordinates, it would be difficult to design certain classes of very useful curves and surfaces. These curves and surfaces are very crucial in developing algorithms in computer vision, graphics, CAD, etc.

--https://prateekvjoshi.com/2014/06/13/the-concept-of-homogeneous-coordinates/

It's about simplifying things, or finding a least complex solution/algorithm. Amirite?