Hyper Dimensional Philosophizing

[Cuddles]

Just poking in here ...

I believe number 4 is in error --- it should be Electric Charge (coulomb)

Not necessarily. As I said earlier, the exact choice of fundamental units is not fixes, several different systems are possilble. For the SI system either current or charge must be fundamental, and the other can be derived from a combination of the other fundamental units. The convention is to use current simply because that was discovered and measured first. Knowing what we do now, charge seems a more logical choice, but without any overriding need to change anything conventions tend to stick. It's a similar situation to that with the direction of current in electronics - the charges actually move in the opposite direction but because the convention was established before people knew that it has stuck, and there is no need to change it.

It reality there are really six fundamental units. Length, time, mass, current (or charge), colour charge and flavour. Colour and flavour have to be included because they are the equivalents of mass and charge for the other fundamental forces and cannot be derived. Temperature can be a tricky one, depending on how you define it and the system you use it can be fundamental, derived or dimensionless. In general use it is a measure of kinetic energy and so can't really be considered fundamental. Moles are often counted as a fundamental unit and it can be useful to think of them as such, but they are not actually a unit any more than the number "one" is a unit. A mole is a number, nothing more. Luminous intensity is definately not a fundamental unit because it is defined in terms of power. However, it is often mentioned as one because in the areas it is used it is often more useful to consider it as a fundamental and derive other quantities from it.

 

[PixyMisa]

Fredrik - yep. The problem is that he asked that question, and then proposed a whole bunch of impossible answers. That's how the argument arose.

 

[Just thinking]

Not necessarily. As I said earlier, the exact choice of fundamental units is not fixes, several different systems are possible. For the SI system either current or charge must be fundamental, and the other can be derived from a combination of the other fundamental units. The convention is to use current simply because that was discovered and measured first. ...

Well, I'll bet weight was discovered (realized) before mass as well.

You're right in that temperature is a tricky one -- I think it more of a measurement of convenience rather than an actual dimensional unit, like hours or days as opposed to time. (Same for moles.) A way of describing the average amount of heat energy over a system as well as determining which way heat energy will flow between systems of different temperatures.

But anyway ... we do now know that the fundamentals include charge and mass, not current and weight.

 

[Jimbo07]

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.

This isn't what I was talking about. I don't want to get into a pissing match about which units are fundamental. I'm afraid there's too much unwarranted animosity in this thread already.

I was talking about "A" space as a theoretical construct in which we solve problems. I wasn't talking about space-time. Space-time IS a vector space, but not all vector spaces are space-time... right?

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.

Yes. You're right. When we measure space-time, we use 4 dimensions. Various cosmological models (in which I'll admit, I'm not proficient) suggest more dimensions of space (or time? I don't know). I am completely unqualified to speak to the validity of String Theory, say.

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.

Not in this context of the use of the word dimension.

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.

They are not wrong... in their context. As an engineer (and if you're anything like me, you'll crave precision in terminology), you'll recognize that different disciplines will use different things according to their own conventions/traditions. It's not the same, but consider, for example, the complex coefficient. From your electrical background, you'll know it's 'j,' but from your physics background, you'll know it as 'i.' Different disciplines, same concept and context, but different terminology. Similarly, in this thread you have different disciplines, same terminology... but different context.

3 In deriving the dimension of a quantity, no account is taken of any numerical factor, nor of its
scalar, vector or tensor character.

This quote is so important, and should make it very clear that this interpretation is different than the interpretation of the word 'dimension' when used in terms of vector spaces.

I feel like I am arguing with someone over religion.

I'm very sorry for anything I've said to inflame this thread, and I'm sorry if I've been insulting in any way, but you have to admit that comments like this don't help.

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

I agreed, but thought you had it the other way around.

I quote the first sentence “By convention physical quantities are organized in a system of dimensions.”

Note the words "By convention."

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.

Again, for their context, they are not wrong. However, I'm not aware that ISO has any jurisdiction (or current interests) in regards to cosmology. I assumed that you were interested in cosmology when you started with the OP.

PixyMisa,

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

The references cited don't support the OP. Check the references I cited. I'm also willing to go offline to cite print textbooks.

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

You did. I believe you are the real deal, because by-and-large you've been civil (and besides, nobody other than a member of the ISA would admit to being a member, or even know what ISA is ).

Without getting into a credentials smackdown, I'll simply say that the program I just finished is VERY similar to what you've described yours as.

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.

In my neck of the woods, this is called Engineering Physics.

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

Much like the "religion" quote, this is inflammatory, and coupled with the confusion over the use of the term "dimension" led me to question your education.

I am sorry.

Mea Culpa.

In the context of things like cosmology, I still think you might be wrong.

ETA: See Fredrik's post.

 

[Oppressed]

LOL

Well, at least I better understand why PixyMisa does not understand this. Lower level classes in science often simplify definition and then make statements about how the simple definition is a rule when if fact it is a narrowed view of a greater view, narrowed to make the subject easier to understand.

Fredrik,

Dimension is absolutely not a synonym for unit. Dimension does not equal unit.

Is about observing something and then developing a means of measuring it, for example, length. If you want to measure the distance between two points where do you begin? To measure it, you are going to count/measure the quantity of something. But what is that something? You can place your foot down in front of the first point, heading towards the second point and then place your other foot in front of the first, touching toe to heal and continue until you get to the second point. Now you have counted/measured out the distance in feet. But feet of what?

Feet is a unit of measure. Length is the dimension in which the unit feet is used to measure. A dimension has no units. In order to measure a dimension we define units of measure in that dimension that we can count.

As far as what is base, fundamental, derived and so on, I am not sure I always agree with or perfectly understand why some definitions are chosen. To be honest about it, sometimes I have worked some definitions out so I understand something and then have forgotten the proof I went through.

Why did the people putting together choose “Electric Current” as a base dimension? It is a dimension, I do not question that. But why do they define it as a base dimension which has led others to call it a fundamental dimension? I’m not sure why, I just know that they have done so.

Is not electric current the amount of charge that passes through the surface in the time T? So that I=Q/T? But, then Q=I•T. A lot of things depend upon our point of view and can result in more than one point of view being correct. This is actually one of the reasons for trying to standardize our terminology for measuring the dimensions of our physical existence that we observe, so that we can discuss something from the same point of view.

In the SI system electric charge is given the unit of coulomb “C” They define coulomb as a derived unit of measure “coulomb = ampere • second” The dimension of coulomb is derived from the dimension of “Electric Current” • “time”.

In the SI system electric flux, flux of displacement and quantity of electricity are also given the unit of measure of “coulomb = ampere • second”, but there are differences between them which result in their separate definitions.

As Cuddles points out, there are things which are defined as base or fundamental which we would probably change except that using it is so entrenched in our every day use that rather than use a less logical chose for a base dimension because it is not worth the cost and effort to change. We can and do call something a base dimension and do so successfully even though we have learned that maybe that dimension might better be defined as derived. Again, it is possible to view things from more than one point of view and have both viewpoints be correct.

As for the dimension of “Amount of Substance” and the corresponding unit of “moles”, that is definitely the one dimension I question the most as being called a dimension. And yet it has been defined and that definition has been accepted by a very large body of educated people, many of them being much smarter than I.

To understand it I had to go back to the understanding of what dimension really stands for, that is for measuring out of something.

The dimension of “Amount of Substance” has the dimension of the substance being measured out.

 

[PixyMisa]

LOL

Well, at least I better understand why PixyMisa does not understand this.

What is it that I don't understand?

You are saying that Ampere is a unit and current is what it measures? Well, fine. We know that. That was never the issue.

Meanwhile, how are you coming along with that dimensional analysis of temperature, luminous intensity, and current with respect to the Standard Model? Because once you've done that - and it's not complicated - you'll understand what the issue is.

Lower level classes in science often simplify definition and then make statements about how the simple definition is a rule when if fact it is a narrowed view of a greater view, narrowed to make the subject easier to understand.

This is true. Fortunately, I had an excellent science teacher (the same one through six years of high school, for both general science and later for physics and chemistry). He was particularly good at explaining not just the laws and equations but their historical context and how various simplified forms were derived.

Dimension is absolutely not a synonym for unit. Dimension does not equal unit.

Quite right. So will you please stop using it that way?

Why did the people putting together choose “Electric Current” as a base dimension? It is a dimension, I do not question that. But why do they define it as a base dimension which has led others to call it a fundamental dimension? I’m not sure why, I just know that they have done so.

Because it is relatively easy to measure.

Is not electric current the amount of charge that passes through the surface in the time T? So that I=Q/T? But, then Q=I•T. A lot of things depend upon our point of view and can result in more than one point of view being correct.

This is not true when you come to describe the fundamental properties of the physical universe. Current is not a fundamental property; charge is. Though this is actually a much lesser issue than temperature and luminous intensity. Current is not explained by the other units you have already listed, and is reasonable to make it a base unit in a system of measures. But temperature and luminous intensity are clearly derived from the units already listed.

 

[PixyMisa]

Oppressed, let's go back for a moment to something you said earlier:

By the way, luminous intensity can not be described only within the standard 4 dimensions of “Space-Time”. I believe that to describe luminous intensity you need 1 dimension of mass, 1 dimension of solid angle, 2 dimensions of length and 3 dimensions of time.

This is what I have a problem with.

By dimensional analysis, this is correct. (As I've mentioned, luminous intensity actually has some fudging applied to it, but that's not relevant to the point.)

But you're talking about the number of dimensions the Universe has.

The fact that we can measure something we call "luminous intensity" absolutely in no way means that the Universe has more than one time dimension. All it means is that we're taking the third derivative of something with respect to time.

Do you agree with this? If so, then we are just arguing about terminology (and your original list of "dimensions"). If not, then there's no hope for the thread.

 

[Cuddles]

But anyway ... we do now know that the fundamentals include charge and mass, not current and weight.

But that's the whole point, we don't "know" this because it is not something that can be found out, it is something we define ourselves. Current is the fundamental unit because we define current as the fundamental unit. The whole point of my post was that such definitions are largely arbitrary, although within certain bounds. Charge and mass are no more fundamental than current and weight, the definitions fundamental units are purely for our convenience and nothing else, they are not defined by the universe.

It is a similar situation to that with coordinate systems. We can define space as either x,y,z or r,theta,phi. Neither one is more correct than the other, they are both arbitrary definitions that are convenient to use in different situations. All the universe tells us is that we need three dimensions and places certain limits on how we can define them. The same is true for units. We need at least 6 fundamental units in order to measure everything, but exactly what we choose as fundamental and how we derive other units is entirely up to us. Saying that current is wrong as a fundamental unit is exactcly the same as saying that spherical coordinates are wrong.

Incidentally, the difference between mass and weight was known well before SI, and pretty much before any decent attempt at standardising units, so that was never a problem.

 

[HghrSymmetry]

It's a lot easier to generalize physical laws when adding more space-like dimensions to our theories than time-like ones, but there's nothing that absolutely precludes doing the latter.

Agreed. 12 dimensional F-theory doesn't seem to garner as much attention. Perhaps because the two dimensions of time results in making the prediction of future states impossible as well as making matter unstable.

Compactifying the extra time dimension does theoretically solve the problem though.

 

[PixyMisa]

Agreed. 12 dimensional F-theory doesn't seem to garner as much attention. Perhaps because the two dimensions of time results in making the prediction of future states impossible as well as making matter unstable.

Compactifying the extra time dimension does theoretically solve the problem though.

Cool. I was wondering if there were models with multiple dimensions of time.

The new vacua described as F-theory were discovered by Vafa, and it also allowed string theorists to construct new realistic vacua — in the form of F-theory compactified on elliptically fibered Calabi-Yau four-folds.

Ow, my brain!

 

[Fredrik]

Oppressed, let's go back for a moment to something you said earlier:

(Quote)

This is what I have a problem with.

By dimensional analysis, this is correct. (As I've mentioned, luminous intensity actually has some fudging applied to it, but that's not relevant to the point.)

But you're talking about the number of dimensions the Universe has.

I agree with what you're saying here. I also found an example that's much worse than the one you quoted:

In our measuring of space time we typically use 4 dimensions [1], but the number and types of dimensions [2] greatly exceed that of the 4 [1] in the typical definition of space-time. Just as this simple definition of space time requires 4 dimensions [1]to describe it, luminous intensity measured in candela requires multiple dimensional [2] references to describe it. Granted the number of references I made are high, because what is required in some cases is a single dimension [2]squared or cubed.

A red "1" means that he used "dimension" meaning the dimension of a manifold. A red "2" means that he used it meaning a class of units.

The part of the first sentence that begins after the comma is one of the worst abuses of language I've seen. He feels that he doesn't need to mention the word "dimensions" after the 4, because the structure of the sentence implies that it's 4 of whatever was mentioned earlier. The word that was used earlier was "dimensions", but then it meant something completely different.

"Steve's wiener grew larger as his girlfriend started to touch it, and at dinner she sliced it, fried it, and ate it with french fries".

 

[Oppressed]

PixyMisa,

The Known Universe is exactly what I am talking about, but what you don’t seem to realize is that the Known Universe consists of everything we can detect.

The Known Universe does not care one bit about what we call a dimension, a unit or how we go about measuring aspects of the Known Universe. If the definitions and methods used are valid enough then we result in a valid abstract model for helping us to understand the Known Universe.

Space and Time is just a small fraction of what we can detect and measure in the Known Universe.

The whole point of dimensions is related to measuring something. If you can observe something and can measure it by breaking it into some quantity of units, the dimension of what you are measuring is the unitless common underlying basis of what you are making units out of to count.

Anything you can measure and count has a related dimension, which is something a lot of people don’t quite grasp.

Luminous Intensity is something we can observe and measure. We have chosen arbitrary units for the dimension of Luminous Intensity to measure it with.

There are some things we can measure in more than one way, yet each way can be valid.

When it comes to space, we do pretty well defining space with 3 dimensions, but this has been found to have flaws and is not perfect. Being driven to understand such things as we are, we don’t settle for the flawed yet very useful 3 dimensional model of space. So we come up with more complex models to better fit what we can observe, but to the best of my knowledge, we have not yet found a model that explains everything we can observe about space.

Beyond that, we dream, we imagine, dimensions beyond space which would allow for fantastic things to occur, such as faster than light travel, Astral space where spirits might dwell or alternative universes. There is no evidence to support these wild dreams, but it becomes an interesting mathematical exercise to see if models can be thought of which might allow for such to exist.

If we are going to think about dimensions beyond what we know of, then understanding what a dimension can be is pretty important if you are going to consider what a undiscovered dimensions might be.

 

[Fredrik]

Oppressed, I've been reading more of your posts, and now I'm less convinced than I was before that you understand the two different meanings of the word "dimension". If you want this discussion to move forward, you should probably say something that proves that you do.

 

[Oppressed]

Fredrik,

If I were an English major and/or if I were writing this as a paper checked for grammatical errors of slips in stating something I might be bothered. But really, you want to spend all that effort trying to figure out something to nitpick on rather than understand the concepts?

I’m writing quickly composed posts in my space time for the fun of it. You are not my English teacher.

If you are interested in the topic of hyper dimensions using the meaning “Dimensions Beyond Those Known” then you should be trying to understand what I am talking about, not trying to tear apart the English used in quickly written posts.

 

[Jimbo07]

If I were an English major and/or if I were writing this as a paper checked for grammatical errors of slips in stating something I might be bothered. But really, you want to spend all that effort trying to figure out something to nitpick on rather than understand the concepts?

Then use math. It's succinct!

 

[Fredrik]

I really don't care if your posts contain grammatical errors as long as I understand what you're saying. The problem is that I don't, and others seem to understand even less of what you're saying. Since I don't understand what you're saying, I can't tell what you understand and what you don't, so I don't know what I should tell you.

I also think that you would save time by expressing yourself more carefully. Most of your discussion with PixyMisa, Ziggurat and others (which I assume took many hours) could have been avoided if you had spent 30 minutes making sure that anyone who tries will understand you.

I'm going to bed now, so I won't be reading any more replies today, but maybe I'll write something tomorrow. In the meantime, I think it would be a good idea if you could at least tell us that you know that the word "dimension" can mean two completely different things. The impression I'm getting when I'm reading your posts is that you understand that there are two definitions, but don't think there's a significant difference between the two.

 

[Oppressed]

I’ve defined what dimension is multiple times. I know what and how the definition of dimension is and it’s use in math, physics and engineering.

I’ve pointed you to links on the web that can further explain this.

I feel like I am arguing with a bunch of high school kids that can not grasp the meaning of dimension. At this point I am coming to the conclusion that further argument over it is fruitless and that you are not able to grasp the concept of the meaning of dimension.

Contact people associated with the defining of the SI standards of measurement and ask them directly. I know the answer, because I have been given that answer before, many times.

If the definition of dimension is beyond your grasp to understand then there is little point to arguing about it further.

I guess if I want some interesting discussions over hyper dimensions I will have to contact some of my old friends who I studied with and discuss it with them, as they will be able to grasp the concept.

 

[GodMark2]

I’ve defined what dimension is multiple times.

Yes, you have. unfortunately for you, you can't just make up definitions and use them as the basis for an argument. You need to use the same definitions that others in the argument are using.

I know what and how the definition of dimension is and it’s use in math, physics and engineering.

And yet, you don't seem to realize that Physics and engineering use completely different meanings for 'dimension'.

I feel like I am arguing with a bunch of high school kids that can not grasp the meaning of dimension.

Actually, you're arguing with at least one professional engineer, who majored in Physics and Mathematics in college with extensive postgraduate work. Unlike some people, whenever possible, I prefer to allow the argument to speak for itself, instead of dragging unnecessary qualifications of the proponent of it.

At this point I am coming to the conclusion that further argument over it is fruitless and that you are not able to grasp the concept of the meaning of dimension.

I was thinking the same thing several posts ago.

Contact people associated with the defining of the SI standards of measurement and ask them directly. I know the answer, because I have been given that answer before, many times.

Well, I just asked my boss, who was on the committee in 1971, he said you were so wrong there wasn't a word to describe it.

If the definition of dimension is beyond your grasp to understand then there is little point to arguing about it further.

I guess if I want some interesting discussions over hyper dimensions I will have to contact some of my old friends who I studied with and discuss it with them, as they will be able to grasp the concept.

Feel free to come back when you wish to discuss reality.

 

[Oppressed]

Okay, I will try one last time.

Dimension is commonly used to refer to spatial dimensions and time, but the term dimension is all about measuring quantities of something. When you measure the quantity of something of the same nature and characteristics, there is a dimension to that measurement, be it length or be it apples.

If you go to measure something and measure out any arbitrary unit of that something, and then measure out another arbitrary unit of the same something, the units can be added together, even if you have to do some conversion, but both arbitrary units will have the same dimension.

For example, to use that which people are very familiar with, take the distance between two points. We can measure that distance. We can select an arbitrary unit smaller than the distance we want to measure and then count out the quantity of the units that fit along the length. The dimension is what the units consist of. You can arbitrarily define all manner of different units, but if you are measuring the distance between two points all these units consist of the same dimension.

In a similar manner, let’s say you have 1,000 apples. You want to measure how many apples you have. You define a unit of measure for the apples as 12 apples = a dozen apples. You can then count out how many apples you have in that unit of measure and say 83 and 1/3 dozen apples. You can also define as a unit of measure of 120 apples = a small gross of apples and count the apples by those units. But the real dimension of what you are counting in is not based on the units and thus the dimension in this case is apples.

I already know this is difficult for some if not all of the people here to understand and we do not normally think in terms of what dimension are we counting apples in. We do however think of this in fields like chemistry where large quantities of a substance are measured out. This is how and why the SI Dimension of “Amount of Substance” was defined and the unit of mole defined. The actual dimension of “Amount of Substance” is whatever the substance is that you are measuring.

Here are a series of links to a common source following the issue of dimensions, measurements, quantities and units of measure.

There is enough information through these links you should be able to figure out the meaning of dimension with relation to its use in science and engineering.

If not one of you can read through this and come to understand the meaning of dimension, I am not going to continue trying to explain it.

http://en.wikipedia.org/wiki/Dimension
http://en.wikipedia.org/wiki/Measurement
http://en.wikipedia.org/wiki/SI_base_unit
http://en.wikipedia.org/wiki/Fundamental_units
http://en.wikipedia.org/wiki/Physical_unit
http://en.wikipedia.org/wiki/Physical_quantity
http://en.wikipedia.org/wiki/Quantifiable
http://en.wikipedia.org/wiki/Dimensional_analysis
http://en.wikipedia.org/wiki/Metrology
http://en.wikipedia.org/wiki/Systems_of_measurement
http://en.wikipedia.org/wiki/International_System_of_Units
http://en.wikipedia.org/wiki/National_Institute_of_Standards_and_Technology
http://en.wikipedia.org/wiki/International_Bureau_of_Weights_and_Measures

http://en.wikipedia.org/wiki/Natural_units

A quote from this last link as an example:
“
Some physicists have not recognized temperature as a fundamental dimension of physical quantity since it simply expresses the energy per degree of freedom of a particle which can be expressed in terms of energy (or mass, length, and time)
“

Note that the some physicists who do not recognize temperature as a fundamental dimension do not question temperature being a dimension, just that they believe it should be a derived dimension.

 

[Molinaro]

What your lastest attempt shows is that you still don't see the 2 different definitions of dimension. You are taking the unit of measurement aspect of the word and equating it with a degree of freedom within a spatial manifold.

That was wrong the first time you did it, and it's still wrong now.