Hyper Dimensional Philosophizing

[Fredrik]

Did Oppressed ever actually acknowledge anything anyone said? I asked him questions seven or eight times, trying to illustrate where he was mixing his terms, and he never answered me.

You're right, he never directly answered any questions. That's another reason why progress has been so slow in this thread.

If anyone cares, I think this is the new thread he started.

 

[Fredrik]

Oppressed sent me a PM that I replied to a few minutes ago. My reply contained a few sentences that belong in this thread, so I'm posting them here too:

What you said about the dimension of apples was excellent. It's not like you said something I didn't already know, but you put your thoughts into words in a way that made me see things a little bit more clearly. One thing that became crystal clear is that each direction in space defines a dimension (of the kind you like to talk about). That proves that this kind of dimension is very different from the dimensions of a manifold or a vector space. If your favorite kind of dimension was somehow "the same" as the dimensions of algebra or geometry, then we wouldn't find infinitely many of them in a 3-dimensional space.

 

[PixyMisa]

Let us know how he reacts to the concept of an infinity of indeterminate dimensions.

(I'm avoiding the new thread out of respect... albeit mainly respect for my blood pressure...)

 

[GodMark2]

Let us know how he reacts to the concept of an infinity of indeterminate dimensions.

(I'm avoiding the new thread out of respect... albeit mainly respect for my blood pressure...)

I'm tempted to go over to the other board and post something like:

Here's a link to a thread where someone was asking questions very similar to yours. The questions were answered quite throughly and expertly. I'm afraid my skills at prose would not be up to the task of repeating their explanations. Perhaps their explanations would be of use to the posters on this thread.

Not for his sake, but for the sake of the people on the thread trying to show him where he's wrong.

 

[Fredrik]

Oppressed said the following in a PM to me:

This definition of dimension applies to dimensions in physics, math, engineering and so on.

Name a dimension and see if it does not apply.
...
But pick the dimension of volume or one of the length dimensions of 3D physical space. Or pick luminous intensity, mass or a 3-variable vector. Every defined dimension will conform to the definition I gave above.

I believe it's appropriate to both quote the text and answer here instead of in a PM since it's about the things we've been discussing in this thread.

I obviously can't name a dimension that isn't a dimension if the word means the same thing both times. But consider the vector space of odd periodic functions with period 2*pi. It's an infinite dimensional vector space, because the set of all functions of the form sin(kx) where k is a positive integer, is linearly independent. You asked me to name one dimension, so here we go: The dimension spanned by the function sin(5x).

It isn't related to the other kind of dimensions in any way, just like the kind of bats that live in caves isn't related to the kind you'd hit a baseball with. Someone in the other forum called it an "accident of language", and I can't think of a better thing to call it.

 

[PixyMisa]

Let us know if he responds to that with anything other than re-asserting his definition of the word "dimension". I'm not optimistic.

 

[Oppressed]

Fredrik,

I am posting again here because of the PM exchange between us and also the PM exchange with Jimbo07.

After my first post I was reading the reply posts and trying to answer accordingly to hopefully make myself better understood.

Several posters began making statements that I was wrong and that I did not understand what I was talking about. Despite the number of people on this board emphatically stating how I am wrong, this is not true. I may not have expressed my self very well or it may not have been understood, but what I said in my first post was correct.

In addition to the inability to understand each other here, post directed towards became increasingly insulting. Instead of there being an environment of people interested in any way of trying to understand what I am talking about, it came across as a very hostile environment not interested in trying to understand, insulting me and trying to insist I am wrong over something I know I am right about.

In frustration and anger, I began responding in the same insulting manner that I felt I was being barraged with.

As this proceeded to go nowhere, I question what the point is in posting on a forum where no one is interested in trying to understand what you are talking about, but rather only interested in telling you why they think you are wrong and insulting you for it. Worse, it was pulling me into insulting back at which point, I decided I should leave this forum and go to another that is not so hostile towards ideas they don’t understand.

I may not be the best at expressing myself and English is not my best subject. When I began my University studies, my English was barely good enough to allow me to get in. I have improved since, but still, my best skills are analytical and mathematical.

I learned the definition I use in my 1st year of physics. During my 6 years at Cal Poly (California Polytechnic State University) I discussed this definition in-depth with multiple professors in relation to various classes I was taking.

I do know what I am talking about.

Whether I can explain it well enough to be understood is something else.

Whether you can understand what I am talking about is beyond my control.

But no matter how much you want to tell me I am wrong or insult me is not going to change the fact that I know I am correct that the list 20 dimensions I gave at the beginning of this post are all dimensions and are but a small subset of dimensions. I am not mixing up or confusing dimensions with units. I am not mixing up or confusing dimensional analysis with space-time metrics.

I might and do make mistakes, especially when quickly writing a post.

But the basic understanding of what the definition of dimension is and how it is used to define dimensions used in science and engineering I do understand.

But there is no point in discussing this in an environment that is going to be hostile, uninterested in trying to understand and insulting to those who try to express themselves.

I am not innocent of this, because I too became insulting when pissed off at insults directed towards me.

I will try to avoid becoming upset and respond to insults with insults.

But, I will also not stay around to post if no one is going to try and understand what I am talking about while insults are repeatedly directed towards me.

 

[PixyMisa]

Oppressed, one of the reasons people have become irritated with you is that within this thread (I can't speak as to your private messages) you have never once answered a direct question. I asked you many times to answer simple questions that would help us understand what you were talking about; you never even acknowledged the questions, much less addressed them.

So, once again, please tell us whether or not you agree with this statement I made earlier:

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.

Yes? Or no? This is the key to the entire discussion.

 

[Fredrik]

I may not be the best at expressing myself and English is not my best subject. When I began my University studies, my English was barely good enough to allow me to get in. I have improved since, but still, my best skills are analytical and mathematical.

Your English is not a problem, but the fact that you consistently refuse to address anything that anyone has said to you is a huge problem. You need to stop ignoring what we say to you, and start answering questions! You also need to start telling people who have answered you, what exactly, of all the things they said, that you disagree with.

I see that you are repeating the same mistake in the other two threads you started. That's not a great idea.

But no matter how much you want to tell me I am wrong or insult me is not going to change the fact that I know I am correct that the list 20 dimensions I gave at the beginning of this post are all dimensions and are but a small subset of dimensions.

Have you even read our replies? After the initial misunderstandings on the first half of page 1, no one has claimed that you are wrong about that.

But the basic understanding of what the definition of dimension is and how it is used to define dimensions used in science and engineering I do understand.

No, you understand one of the definitions. There are lots of examples of words with multiple meanings in the English language, e.g. "bat", "pound", "tip" and "staff", so I don't understand why it's so hard for you to accept that "dimension" has multiple meanings too.

Let's get back to the things that you should answer:

1. You explained very well (using apples as an example) what you mean by "dimension". I told you several times that your definition implies that space has infinitely many dimensions (each direction being a dimension). And yet space has three dimensions. How do you explain that? (My explanation is that space has three algebraic/geometric dimensions and infinitely many of "your" dimensions).

2. You asked for an example of a dimension that isn't a dimension of the kind that you like to talk about, and I gave you one: The one-dimensional subspace of the vector space of odd periodic functions with period 2*pi, that consists of functions of the form af, where a is a real number and f is defined by f(x)=sin(5x). Why did you ignore that? Do you think that I failed to give you a correct example? If that's what you think, then what's wrong with my example?

3. In one of the other forums you got this very good (except for how he spelled "Minkowski") and very relevant question, and you ignored it:

How is the use of the word "dimensions" in the statement "velocity has dimensions of length over time" related to its use in the statement "Special Relativity can be described in terms of Minkowsky space-time with four dimensions"? I would have thought that it is an accident of language that we even use the same word for these two concepts.

If you still haven't figured out how to use quote tags in vBulletin, I suggest you figure it out before you post anything else. Reply by clicking the quote button, then edit your reply. Insert copies of the quote tags where you need them, and use the preview feature to check if you did it right.

 

[Cuddles]

I’ve taken my discussion about hyper dimensions to another forum where those posting are much more knowledgeable of the subject. Besides being a forum where what I am saying is understood, it is a better forum for such discussions anyway.

Considering that this thread contains at least two professional physicists it's unlikely that they are "much more knowledgeable", although it is quite possible that there are more of them. However, the very first reply on that forum says exactly what we have been saying all along. There are two entirely unrelated definitions of dimension, and you are using them as if they are both identical. Sadly, even after having that pointed out by people both here and on the much more knowlegeable forum, you still don't seem to have grasped that very basic idea.

If people disagree with you, it doesn't mean they are being rude. If people tell you you are wrong, it is entirely possible that you are. If you are unable to make a large number of people understand you, you should be aware that the only common factor is you.

As for storming off in a big huff, what is about some people that if anyone disagrees with them it's automatically because we aren't trying to understand. Oppressed, we are trying to understand. That's why there are three pages to this thread. We are trying to work out what you mean and are pointing out how what we think you mean is wrong. If we have misunderstood what you are saying, then say it again in a different way. Pretending that we are insulting you and refusing to read what you say is a great way of giving yourself an excuse to leave, but it won't help either us or yourself actually gain any understanding.

 

[PixyMisa]

I weakened and took a look at the thread at the other forum. Heh. I needn't have worried about my blood pressure; now I'm more concerned for Oppressed's.

If one person tells you you're drunk, you might ignore them. If three doctors, two biochemists and an EMT tell you you're drunk...

 

[Oppressed]

I try to avoid quoting another post as much as possible. My posts can already get long and it is a duplication of information.

I tried to answer the questions by trying to better explain myself and point to online sources people can go refer to.

If the questions and the answer to the questions all revolve around the understanding of dimension, then if I can explain well enough about the understanding of dimension then I have answered the whole group of questions.

I think I need to simplify the discussion.

I’ll answer one direct question at this time, using quotes to make you happy that I am directing my response to that specific question. Just answering one such question will make the post lengthy enough.

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.

“Luminous Intensity” is something we can measure. It is a real phenomenon which can be quantified and measured, as opposed to an imaginary or abstract concept which has no real world observable way of measuring.

As something which we can measure, luminous intensity has what is defined as a dimension and the name of that dimension is referred to as luminous intensity. When you measure luminous intensity you do so using defined units quantities of luminous intensity in the dimension of luminous intensity.

Luminous intensity was determined to be base quantity by a group of people far more knowledgeable about the subject than I. As such, the related dimension of luminous intensity is considered to be a base dimension.

“Finally, it should be recognized that although the seven base quantities – length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity – are by convention regarded as independent, their respective base units – the metre, kilogram, second, ampere, kelvin, mole, and candela – are in a number of instances interdependent. Thus the definition of the metre incorporates the second; the definition of the ampere incorporates the metre, kilogram, and second; the definition of the mole incorporates the kilogram; and the definition of the candela incorporates the metre, kilogram, and second.”

I do not understand luminous intensity well enough to explain why this body of more knowledgeable people defined luminous intensity as being a base quantity and base dimension when the definition for the unit of luminous intensity, “candela” incorporates the meter, kilogram and second. Why would they not say it is a derived quantity?

The answer to why it is considered fundamental and not derived lies in the greater knowledge of the people who made that definition. I do not know why but I do know they have defined it so and that definition has been accepted as a world wide standard.

I do know that luminous intensity is a dimension and this relates to what dimension means which is the real confusion within this thread.

 

[Oppressed]

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.

The question is do I agree with this or not.

I think it may come from a quick badly worded sentence in post 11 where I said: “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.” As sometimes happens when you are quickly responding to something, you make slips in what you are saying. I was thinking and referring to the fact that the dimension of time was referred to 3 times. It is the same dimension of time but by being referenced 3 times you get s^-3.

In my next post 16 I make a quick corrective reference to this saying “Granted the number of references I made are high, because what is required in some cases is a single dimension squared or cubed.”

When or where did I say that luminous intensity being a dimension means there is more than one dimension of time?

The definition of the unit “candela” in the dimension of luminous intensity incorporates other units of other dimensions.

Candela = lumen / steradian = the luminous intensity of a monochromatic 540 THz light source that has a radiant intensity of 1/683 watts per steradian = The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 * 1012 hertz and that has a radiant intensity in that direction of kg * m^2 * s^-3 * m^2 * m^-2 * 683^-1

How many dimensional axes does this come to? I believe it comes to 1 dimensional axis of time, 1 dimensional axis of mass and 3 dimensional axes of length such that all 5 of these dimensions are mutually perpendicular to each other.

I believe 3 dimensional axes of length are needed because of definition of steradian which requires a 3 dimensional space, though I am not 100% positive of this.

The point I was after is that luminous intensity is a dimension.

I always personally considered luminous intensity as a derived dimension, but others more educated than I have defined it as a fundamental dimension.

Luminous intensity can be described within standard 4-dimensional space-time, for example, but charge and mass are different.

When PixyMisa said this in post 9 he was wrong. Standard 4-dimensional space-time does not include the dimension of mass and the dimension of mass is required to define the unit candela of the dimension luminous intensity.

What I wrote saying in post 11 “…and 3 dimensions of time” was wrong, because I worded it wrong. I was thinking of referencing the single dimension of time 3 times resulting in a unit value of “s^-3”.

****

Now for my question.

What is space?

 

[GodMark2]

I always personally considered luminous intensity as a derived dimension, but others more educated than I have defined it as a fundamental dimension.

No, Others more educated than you defined it as a fundamental unit. A dimension (meaning a measure) consists of a quantity and a unit.

One Candela can be a dimension.

"Candela" is that dimension's unit. "One" in that dimensions quantity.

This has nothing to do with the number of "Dimensions of Space"

 

[GodMark2]

Now for my question.

What is space?

To avoid three further pages of misunderstanding:

For what definition of space are you requesting an answer.

space

–noun
1. the unlimited or incalculably great three-dimensional realm or expanse in which all material objects are located and all events occur.
2. the portion or extent of this in a given instance; extent or room in three dimensions: the space occupied by a body.
3. extent or area in two dimensions; a particular extent of surface: to fill out blank spaces in a document.
4. Fine Arts.
a. the designed and structured surface of a picture: In Mondrian's later work he organized space in highly complex rhythms.
b. the illusion of depth on a two-dimensional surface.
5. outer space.
6. deep space.
7. a seat, berth, or room on a train, airplane, etc.
8. a place available for a particular purpose: a parking space.
9. linear distance; a particular distance: trees separated by equal spaces.
10. Mathematics. a system of objects with relations between the objects defined.
11. extent, or a particular extent, of time: a space of two hours.
12. an interval of time; a while: After a space he continued his story.
13. an area or interval allowed for or taken by advertising, as in a periodical, on the radio, etc.
14. Music. the interval between two adjacent lines of the staff.
15. an interval or blank area in text: a space between the letters.
16. Printing. one of the blank pieces of metal, less than type-high, used to separate words, sentences, etc.
17. Telegraphy. an interval during the transmitting of a message when the key is not in contact.
18. radio or television broadcast time allowed or available for a program, advertisement, etc.
19. freedom or opportunity to express oneself, resolve a personal difficulty, be alone, etc.; allowance, understanding, or noninterference: Right now, you can help by giving me some space.
–verb (used with object)
20. to fix the space or spaces of; divide into spaces.
21. to set some distance apart.
22. Printing, Writing.
a. to separate (words, letters, or lines) by spaces.
b. to extend by inserting more space or spaces (usually fol. by out).
–adjective
23. of, pertaining to, or concerned with outer space or deep space: a space mission.
24. designed for or suitable to use in the exploration of outer space or deep space: space tools; specially packaged space food for astronauts.

 

[PixyMisa]

When PixyMisa said this in post 9 he was wrong. Standard 4-dimensional space-time does not include the dimension of mass and the dimension of mass is required to define the unit candela of the dimension luminous intensity.

That is technically correct. My point was that you didn't need any additional dimensions of either space or time to derive luminous intensity.

Edit: Actually, that's not quite correct. The dimension of mass is required to define luminous intensity. The candela is a unit, and is defined in terms of other units, in this case, the kilogram, the metre, and the second.

What I wrote saying in post 11 “…and 3 dimensions of time” was wrong, because I worded it wrong. I was thinking of referencing the single dimension of time 3 times resulting in a unit value of “s^-3”.

Right.

So you agree that one actual dimension of time (plus three of space and one of mass) suffices to produce what we refer to as luminous intensity?

By the way, you took 24 paragraphs to answer a yes-or-no question, and I'm still not sure what your answer is.

What is space?

In what context? I'm not brushing you off; context really matters.

Luminous intensity was determined to be base quantity by a group of people far more knowledgeable about the subject than I. As such, the related dimension of luminous intensity is considered to be a base dimension.

No. This claim is immediately refuted by your next paragraph.

“Finally, it should be recognized that although the seven base quantities – length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity – are by convention regarded as independent, their respective base units – the metre, kilogram, second, ampere, kelvin, mole, and candela – are in a number of instances interdependent. Thus the definition of the metre incorporates the second; the definition of the ampere incorporates the metre, kilogram, and second; the definition of the mole incorporates the kilogram; and the definition of the candela incorporates the metre, kilogram, and second.”

Yes!

Mind you, this is exactly what everyone here has been telling you since you created this thread.

I do not understand luminous intensity well enough to explain why this body of more knowledgeable people defined luminous intensity as being a base quantity and base dimension when the definition for the unit of luminous intensity, “candela” incorporates the meter, kilogram and second. Why would they not say it is a derived quantity?

Probably historical reasons. Here's a history of how the definition of the candela changed over the years.

The answer to why it is considered fundamental and not derived lies in the greater knowledge of the people who made that definition. I do not know why but I do know they have defined it so and that definition has been accepted as a world wide standard.

No. You're ascribing magical wisdom to a fairly ordinary standards committee. The unit is obviously derived, so it's a derived unit. What they call it is secondary.

Don't get so hung up on names! It's the mathematics that actually tells you something useful. The moment you do the dimensional analysis on luminous intensity you know it's derived, and not fundamental. It doesn't matter if a thousand dictionaries say a thing is so if the mathematics of it proves that it's not.

 

[Oppressed]

GodMark2 and PixyMisa,

Luminous intensity is a dimension. Your stating otherwise is wrong. I have previously pointed you to proof of this. You can choose to ignore that.

We should be able to agree to disagree over this at this time.

I state it is a dimension and you state it is not. Neither of us is budging over our position.

So lets move on to arguing over space.

 

[Oppressed]

The space I am asking about is space as defined in physics which is three ordinary dimensions. Not the more advanced concepts, but simple flat space, Euclidean space.

The purpose is to try and keep this simple.

If I say:

“Three-dimensional space is the physical universe we live in. The three dimensions are commonly called length, width, and breadth; although any three mutually perpendicular directions can serve as the three dimensions. Space is a fundamental quantity.”

Is this a basic definition you can agree with?

 

[PixyMisa]

GodMark2 and PixyMisa,

Luminous intensity is a dimension. Your stating otherwise is wrong. I have previously pointed you to proof of this. You can choose to ignore that.

You can call it a dimension if you wish; that's fine, you're just using different terminology.

But you must understand that this meaning of dimension is different to the meaning you used in your question. You asked, in relation to the concept of hyperspace, what additional dimensions the universe might have beyond the four of space-time. Luminous intensity is not a meaningful answer.

The space I am asking about is space as defined in physics which is three ordinary dimensions. Not the more advanced concepts, but simple flat space, Euclidean space.

Space as defined in physics (since early last century, anyway) is non-Euclidean, but we'll skip over that for now.

If I say:

“Three-dimensional space is the physical universe we live in. The three dimensions are commonly called length, width, and breadth; although any three mutually perpendicular directions can serve as the three dimensions.”

Is this a basic definition you can agree with?

Yes.

Space is a fundamental quantity.

The word quantity seems slight odd here; not sure if that's important.

 

[PixyMisa]

Just looking back at the thread, we were already at this point in post 11. Everything said since then still stands.

Unless you have accepted what has been explained to you - that, for example, no matter what the SI committee claims, luminous intensity is a derived quantity - you are not going to make any progress.