Hyper Dimensional Philosophizing

[PixyMisa]

To not realize the difference between “our arbitrary creation of terms and definitions” and “physical reality” seems to be another blinder you are wearing.

What are you talking about? That's exactly what you're doing wrong.

Dimension is all about measuring something.

Nope.

The International System of Units which was developed was done so with a pretty large group of very educated people who looked at all our collective knowledge we have collected on describing our physical world and they made the decision to select 7 quantities and dimensions and call them the base from which all others would be derived.

Units. They defined, for pragmatic purposes, a standard set of basic units.

They took a chosen quantity of a chosen dimension and defined that quantity as the base quantity and that dimension as the fundamental dimension.

No.

From this all other dimensions they were defining could be derived, though you will find at some point an exception stated by them that there are in fact more dimensions than they list and that some of the dimensions they list can not be described by the 7 selected fundamental dimensions.

They didn't define dimensions, they define units.

But, in general, all the other dimensions they define units of measurement

They don't define dimensions at all. They do define units of measurement.

for are derived from the product of these 7 dimensions, each with an associated power.

These are not dimensions. This has been explained to you far too many times.

Take temperature: It is simply a measure of energy, a function of mass, length and time. You already have mass, length and time on the list.

Same applies for luminous intensity.

Quantity is just a number.

Current is not represented by anything else on the list, but it is a function of charge (a fundamental physical property like mass) and time.

I’ve been trying to find a good web page I can direct you to about this and believe I have found it. Ben Tilly, please look at the following links and see if you think they support what I am stating here.

http://physics.nist.gov/cuu/Units/bibliography.html
http://www.bipm.org/en/si/si_brochure/chapter1/1-3.html

The second page uses the term "dimension", but it doesn't mean what you think it does.

As far as Luminous Intensity being chosen as a fundamental dimension, in many ways how we chose to look at things is arbitrary, even if it is found to be a valid and provable way of looking at things.

You can choose arbitrary units, as long as they are consistently defined; that's fine. You can't choose arbitrary dimensions to represent the Universe, because the Universe actually exists and actually has a set of dimensions. You can, again, choose your co-ordinate system as long as that co-ordinate system can me mapped onto the Universe itself.

If Luminous Intensity is arbitrarily chosen as being a fundamental dimension, then the non-fundamental dimensions are derived from Luminous Intensity, not the other way around.

You can do that with a system of units, though starting with luminous intensity means that you have to exclude one of mass, length, or time, and it makes the maths hideous. Still doesn't mean the Universe has a luminous intensity dimension, of course.

If this choice works well for it’s intended use, helps us abstractly describe and understand our physical existence better and is found to be the best model for doing so, then choosing to accept and work the definition is an objectively wise choice.

Since none of that is true, no physicist on the planet considers luminous intensity as a dimension in the sense of space, time, mass and so on.

For the last time, the idea of extra dimensions is sound. Your choice of possible dimensions is based on a misunderstanding of what a dimension is.

You can't have a Universe where you have dimensions of space, time, mass and temperature, because temperature is just kinetic energy, i.e. the movement of matter. It's mathematical nonsense; a property cannot simultaneously be fundamental and derived.

 

[Jimbo07]

Ben Tilly,

Well put.

PixyMisa,

To not realize the difference between “our arbitrary creation of terms and definitions” and “physical reality” seems to be another blinder you are wearing.

Oppressed, I think that you don't recognize here that Ben Tilly and Pixy Misa's takes are amenable and yours is not.

I don't know what your background is, but your confusion between dimensional analysis and spatial dimensions suggests that it's not college. This is perfectly okay, but you must be willing to understand, as you yourself have put it, "a pretty large group of very educated people who looked at all our collective knowledge," have come up with working models.

...

Even if you don't plan on doing a full college education (and more people in society don't than do), depending on your math background, you may be very interested in introductory courses in physics and linear algebra. Introductory courses are fun, because they often outline what is still on the fringes of the discipline (especially if you get a good prof, who likes dropping 'teasers').

...

A problem that you are trying to solve can be said to exist in a "space" (not outer space, a "space"). That space has a dimension. That is, it has a number of independent parameters that, together, can define a point (or solution to a problem, say) in that space. This is immediately obvious to everyone in our typical outer space, or 4D spacetime. Notice the different uses of the word "space" to represent a couple of different, if related, concepts? It's the same with dimension.

In 4D spacetime, to solve problems specifically related to that "space's" geometry, the dimension is said to be 4, and the dimensions are referred to as (x,y,z,ct). Note that these can be easily translated to spherical or cylindrical coordinates. On the other hand, solving problems with 'dimensional analysis' essentially refers to a different problem space.

That is, different disciplines are using different definitions, at different times, of the word dimension. From one of the earliest links, the word dimension does not have a single, authoritative use across all of the maths and sciences. It's not the only word that suffers from this.

Please understand that this is not closed-mindedness on the part of dogmatic internet goons (except maybe in my case ). As Pixy Misa has pointed out, higher dimensionality to space time HAS been considered.

We've strayed far from the chance of any discussion of fiction, but we need to be on the same page for that, I think...

 

[Oppressed]

If you have access to a library look up the book "International vocabulary of basic and general terms in metrology". It might only be available in a technical library. You can also purchase it online.

This is the usual guide use for terms by the Bureau International des Poids et Mesures.

 

[Oppressed]

Jimbo07,

I completed my University Degree in Electrical Engineering with two minors, one in math and one in physics in 1997.

 

[PixyMisa]

Jimbo07,

I completed my University Degree in Electrical Engineering with two minors, one in math and one in physics in 1997.

Blink.

 

[Jimbo07]

Jimbo07,

I completed my University Degree in Electrical Engineering with two minors, one in math and one in physics in 1997.

Good.

Then you know that a set of N orthonormal vectors form the basis of a space of dimension N. This is true regardless of the space you are working in. In engineering mechanics these are your unit vectors.

You will also have performed 'dimensional analysis.' I have no idea from where the apparent confusion has arisen...

 

[Ziggurat]

To help us understand physical existence we have developed the convention of organizing physical quantities in a system of dimensions. The International System of Units has chosen 7 base quantities each of which is regarded as having its own dimension.

From these 7 dimensions which are sometimes referred to as fundamental dimensions, the International System of Units.

The symbol for the fundamental dimension of length is “L”
The symbol for the fundamental dimension of mass is “M”
The symbol for the fundamental dimension of time, duration is “T”
The symbol for the fundamental dimension of electric current is “l”
The symbol for the fundamental dimension of thermodynamic temperature is “Capital Theta”
The symbol for the fundamental dimension of amount of substance is “N”
The symbol for the fundamental dimension of luminous intensity is “J”

I did not make these definitions, a body of highly educated people did.

And you misunderstood them. The SI defines fundamental units, NOT fundamental dimensions. Most of these independent units are associated with "fundamental" dimensions (ie, meters are associated with length), but that is NOT true of amount OR luminous intensity. Amount is DIMENSIONLESS. It is a pure number, and numbers have no dimension. I've already told you that. Your persistence in ignoring this correction does not speak well for your comprehension skills.

Seems to me Luminous Intensity is a derived dimension, but I have not spent that much time trying to figure it out. I for one do not plan on arguing with the community of scientists, engineers and such who selected these seven dimensions as the base upon which the built the SI system of units and measurement.

Luminous intensity, as already mentioned, has dimensions which are derived from dimensions associated with other fundamental units. The Candela is considered a fundamental unit because there are aspects of the definition of the unit which make the unit independent of the other SI units, but the dimension is not fundamental. Units and dimensions are not the same thing.

The whole point of this thread is to discuss for fun the possibility of dimensions which have either not been solidly proven of not proven at all. It is an exercise of imagination and reasoning.

It is perhaps an exercise in imagination, but it is most certainly not an exercise in reasoning.

 

[Oppressed]

Jimbo07,

…and if I said Luminous Intensity was a dimension of space I would be wrong.

But that is not what I have stated. Space is part of our physical existence which we measure. In order to measure it, we have defined dimensions to do so. To measure space our most basic model uses 3 dimensions. When we measure space-time we use 4 dimensions.

But what constitutes a dimension is not just that of length and time. The dimensions of length are used to measure space but there are many other dimensions which are NOT used to measure space but are used to measure something else.

Ziggurat,

A very large body of very well educated people defined the list of dimensions as being “Dimensions”. You can follow some of the links I have previously given, contact them and explain to them they are wrong.

I quote: “
quantity dimension
dimension of a quantity
dimension
dependence of a given quantity on the base quantities of a system of quantities,
represented by the product of powers of factors corresponding to the base quantities
NOTES
1 The conventional symbolic representation of the dimension of a base quantity is a single
upper case letter in roman (upright) sans-serif type. The conventional symbolic representation
of the dimension of a derived quantity is the product of powers of the dimensions of the base
quantities according to the definition of the derived quantity.
2 Quantities having the same dimension are not necessarily quantities of the same kind.
3 In deriving the dimension of a quantity, no account is taken of any numerical factor, nor of its
scalar, vector or tensor character.
4 The dimension of a base quantity is generally referred to as ‘base dimension’, and similarly for
a ‘derived dimension’.
EXAMPLES
a) In the ISQ, where L, M and T denote the dimensions of the base quantities length, mass, and
time, the dimension of force is LMT –2.
b) In the same system of quantities ML–3 is the dimension of mass concentration and also of
volumic mass (mass density).
”

 

[Ziggurat]

Ziggurat,

A very large body of very well educated people defined the list of dimensions as being “Dimensions”. You can follow some of the links I have previously given, contact them and explain to them they are wrong.

I never said they were wrong, I said you were wrong. And I have no intention of digging through all your past links to refute every single instance that you misinterpreted one of your sources. What you have quoted in this post does not contradict anything I said.

 

[Oppressed]

I have checked and confirmed through multiple resources to make sure that I am right.

http://physics.nist.gov/cuu/Units/bibliography.html

This site will give you links through which what I have said can be verified.

You can state I am wrong all you like, but I pull my information from 6 years of University level education, 10 years of professional engineering experience and references from the majority consensus of scientists and engineers around the World.

 

[calebprime]

I have checked and confirmed through multiple resources to make sure that I am right.

http://physics.nist.gov/cuu/Units/bibliography.html

This site will give you links through which what I have said can be verified.

You can state I am wrong all you like, but I pull my information from 6 years of University level education, 10 years of professional engineering experience and references from the majority consensus of scientists and engineers around the World.

Oppressed, perhaps you could concede that you were using the word 'dimension' in a way that was confusing to some. It confused me--but then, I'm not that well-educated in science.

Now, can you move on? You've got these, err, parameters, aspects, qualities, factors, features, elements. How do you propose to philosophize with them?

I also note the word 'astral'. What are you going to do with that one?

 

[Molinaro]

I have checked and confirmed through multiple resources to make sure that I am right.

http://physics.nist.gov/cuu/Units/bibliography.html

This site will give you links through which what I have said can be verified.

You can state I am wrong all you like, but I pull my information from 6 years of University level education, 10 years of professional engineering experience and references from the majority consensus of scientists and engineers around the World.

From your link, I went to this page. There is a nice chart there listing the 7 base SI units.

The only mention of the word dimension on that page is the following:

The reason is that in the SI, the quantities plane angle and solid angle are defined in such a way that their dimension is 1 -- they are so-called dimensionless quantities.

So, why are you talking about dimensions, when your link says they are base units?

 

[Ziggurat]

I have checked and confirmed through multiple resources to make sure that I am right.

http://physics.nist.gov/cuu/Units/bibliography.html

This site will give you links through which what I have said can be verified.

I did. And you're wrong. Note, for example, this statement:
"The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent, as given in Table 1."
Note that it doesn't say dimensions, it says units. Units are not dimensions.

You can state I am wrong all you like, but I pull my information from 6 years of University level education, 10 years of professional engineering experience and references from the majority consensus of scientists and engineers around the World.

Your personal experience is beside the point. And your references don't say what you seem to think they say, so the fact that you use them as references is of no consequence.

 

[PixyMisa]

You can state I am wrong all you like, but I pull my information from 6 years of University level education, 10 years of professional engineering experience and references from the majority consensus of scientists and engineers around the World.

Here in Oz, dimensional analysis is a topic in highschool physics. That you apparently haven't even heard of it in six years of university and ten years of practice is something of a worry.

 

[Oppressed]

I feel like I am arguing with someone over religion.

This is first year college stuff, understanding the basic definitions of terms used in science and engineering.

The usual guide which contains the definitions used is the
"International Vocabulary of Basic and General Terms in Metrology" (VIM)
http://www.iso.ch/iso/en/prods-serv...cationList?CLASSIFICATION=MEASUREMENTS#092001

I’ve read it more than once.

Look at “Table 1. Fundamental Dimensions” from the American Meteorological Society.
http://amsglossary.allenpress.com/glossary/search?id=fundamental-dimensions1

The table lists the fundamental dimensions I have at the beginning of this thread, which you say is wrong. Are you ready to tell the American Meteorological Society they are wrong? By the way, you can get to this page through the single link I gave you in my last response.

Look at SI brochure, Section 1.3 at the following link.
http://www.bipm.org/en/si/si_brochure/chapter1/1-3.html

I quote the first sentence “By convention physical quantities are organized in a system of dimensions.” Below is then given a table which lists 7 base quantities, the symbols for those quantities and the symbols for the associated base dimension.

This is from the Bureau International des Poids et Mesures. They, like the American Meteorological Society are defining the same set of base/fundamental dimensions which you are stating is wrong. Maybe you should also contact them and tell them to correct their mistake.

From the ISO VIM (DGUIDE 99999) “International vocabulary of basic and general terms in metrology (VIM)”. Find a copy and read it.

Chapter 1: QUANTITIES AND UNITS gives a good example of some general concepts of quantities.

In section 1.7 it explains about dimensions and gives some examples.

I quote from this book:

“The conventional symbolic representation of the dimension of a base quantity is a single upper case letter in roman (upright) sans-serif type. The conventional symbolic representation of the dimension of a derived quantity is the product of powers of the dimensions of the base quantities according to the definition of the derived quantity.”

“The dimension of a base quantity is generally referred to as ‘base dimension’, and similarly for a ‘derived dimension’.”

Again, this document is stating that which you are saying is wrong. This document is from the International Organization for Standardization also known as ISO. You can contact them and explain to them how they too are wrong.

 

[PixyMisa]

This is first year college stuff, understanding the basic definitions of terms used in science and engineering.

It's really highschool stuff. So why are you getting it so badly wrong?

Can you understand that current, temperature, and luminous intensity are derived from fundamental physical properties, including charge, mass, space and time?

If you have a problem with that statement, what is the problem? Stop pointing us at other examples of people using the term "dimension" to talk about units, and address the mathematics.

Again, this document is stating that which you are saying is wrong. This document is from the International Organization for Standardization also known as ISO. You can contact them and explain to them how they too are wrong.

We're not saying that they're wrong, we're saying that you're wrong. There are two meanings of the word "dimension" at work here, and they are not referring to the same thing.

 

[Oppressed]

PixyMisa,

And I am saying you are wrong and I cite references to support that, but then you do not accept those references.

Just what is your educational background? Mine has been questioned and I am responding.

The core of my studies was all about science and the use of science in engineering. I excelled in all elements of science. The only thing which ever pulled my grades down was classes like history or English composition.

I minored in physics I taking General Physics I, II and III, Modern Physics I and II, Electromagnetic Fields and Waves I and II, Special Theory of Relativity and Solid State Physics. With rare exceptions I earned As in all science and math related classes, the exceptions being when I only earned Bs.

I was a member of the honor society Eta Kappa Nu. I was and am a member of ISA and IEEE.

Particularly in classes relating to spatial understanding I did particularly well in. Vector Dynamics for example. Another example was Electromagnetic Waves where I had to learn how to model dynamic fields of energy in 3 spatial dimensions and show how a charged mass would be effected traveling though the fields, taking into account field gradients and curl, and being able to translate the model between Cartesian, Cylindrical and Spherical coordinates systems.

I’ve done a whole heck of a lot of study and work with dimensions, graduated with honors and am currently a Senior Systems Engineer. Four of my professional years of experience were in research, the last six being in industry which pays better.

I know what a dimension is, but apparently you do not.

 

[PixyMisa]

And I am saying you are wrong and I cite references to support that, but then you do not accept those references.

Those references do not address the point. Instead of Googling the word "dimension", perform a dimensional analysis on temperature, luminous intensity and current, with reference to the Standard Model of physics.

Just what is your educational background? Mine has been questioned and I am responding.

I'm a Computer Science dropout. But I was awake during highschool physics class.

The core of my studies was all about science and the use of science in engineering. I excelled in all elements of science. The only thing which ever pulled my grades down was classes like history or English composition.

Good for you. In that case, you'll have no trouble with the little task I set you above.

I minored in physics I taking General Physics I, II and III, Modern Physics I and II, Electromagnetic Fields and Waves I and II, Special Theory of Relativity and Solid State Physics. With rare exceptions I earned As in all science and math related classes, the exceptions being when I only earned Bs.

I was a member of the honor society Eta Kappa Nu. I was and am a member of ISA and IEEE.

Particularly in classes relating to spatial understanding I did particularly well in. Vector Dynamics for example. Another example was Electromagnetic Waves where I had to learn how to model dynamic fields of energy in 3 spatial dimensions and show how a charged mass would be effected traveling though the fields, taking into account field gradients and curl, and being able to translate the model between Cartesian, Cylindrical and Spherical coordinates systems.

I’ve done a whole heck of a lot of study and work with dimensions, graduated with honors and am currently a Senior Systems Engineer. Four of my professional years of experience were in research, the last six being in industry which pays better.

That's all very nice. Unfortunately the facts don't agree with you.

As I said, analyze how current, temperature, and luminous intensity relate back to the standard model. You'll quickly find that they are not in any way fundamental. They are defined as fundamental units under SI for convenience, not because they are intrinsic properties of matter. Particularly luminosity, which has some significant fudge factors in it.

 

[Fredrik]

Oppressed, you have convinced me that you're not the only one using the word "dimension" as a synonym for "unit", but it's still not a good idea to do so. The reason the sources you cite can get away with it and you can't is that they're not doing it in a text about dimensions of space-time. The word "dimension" means something else entirely in that context, and you seem to know that, so you should have been able to anticipate that you would cause a lot of confusion.

These are examples of what I consider appropriate uses of the word "dimension" in the context of units:

1. Grams and ounces are two different units of mass. The quantity x = 100 grams = 3.527 ounces has dimensions of mass. (I think most physicists use the plural form here, I don't really know why). Note that in this context a dimension is a class of units.

2. If we didn't know that the volume of a sphere is 4*pi*r³/3, where r is the radius, we could still estimate its order of magnitude using dimensional analysis: A volume has dimensions of length³, and the only length needed to specify the size of a sphere is its radius, so we estimate the volume as r³. (This estimate is wrong by a factor of about 4 and probably isn't very useful, but that's beside the point).

In the context of manifolds (like space-time) the definition is quite different. A manifold is equipped with a set of functions (called charts by mathematicians and coordinate systems by physicists) that map open subsets of the manifold into the set Rⁿ (i.e. the set of ordered n-tuples of real numbers). The number n is called the dimension of the manifold.

By the way, the prefix "hyper" often means something else too. For example, a "hypersurface" in an n-dimensional manifold is an (n-1) dimensional submanifold. You can think of space as a hypersurface in space-time.

The question you've been asking in this thread (if I understand you correctly) is this: If we take a space-time manifold with more than four dimensions as a model of our own universe, and imagine an experiment that measures the magnitude of a displacement into one of the "extra" dimensions, would the result be in meters, seconds or some other unit?

(You're asking about the dimensions of dimensions, with the first "dimensions" not meaning the same thing as the second. No wonder people get confused, or think that you have confused two very different meanings of the word).

 

[Molinaro]

Well said Fredrik.

If we take a space-time manifold with more than four dimensions as a model of our own universe, and imagine an experiment that measures the magnitude of a displacement into one of the "extra" dimensions, would the result be in meters, seconds or some other unit?

That is exactly what Oppressed has been trying to ask.