Hyper Dimensional Philosophizing

[PixyMisa]

It was confused in the first post. As others have noted, Oppressed is confusing dimensional analysis with space-time metrics, confusing co-ordinate systems with dimensions, and confusing derived and fundamental units. That's a whole lot of confusion for one post.

 

[Cuddles]

Just to add to the confusion, as people have already pointed out, there can be debate over whether charge or current should be used as the fundamental unit. However, what no-one has pointed out yet is that there is no such thing as a fundamental unit, or more correctly, the choice of fundamental units is almost entirely arbitrary.

For example, we use length and time as fundamental units, with the standard units being metres and seconds. This means that acceleration can be described as {length}{second}^-2. However, it is just as valid to use velocity and time. Acceleration would then be described as {velocity}²{length}^-1.

Not all possible choices would be valid, since it must be possible to reduce any units down to the fundamental ones, however, there are many that are valid. The fundamental set that we actually use is based on what was most relevant while the scientific method was being developed. Current is generally stated as one of the fundamental units because it was possible to measure current but charge was much harder. Now that we understand more and have better technology charge seems like a more obvious choice as a fundamental unit, but traditions tend to stick. The same is also true of time. Our current definition of time is actually a conversion from our measure of frequency, but for most people time stays as the fundamental unit because it seems more relevant from their point of view.

The point of this rambling is that, as others have said several times but in differnet ways, units and dimensional analysis have absolutely nothing to do with spacial dimensions. Actual spacial dimensions exist however we choose to describe them. Units are semi-arbitrary measures made up to suit our convenience. There is no correlation between the two.

Edit: Just in case any really odd people are actually interested, the usual notation is square brackets rather than curly ones, but the forum software treats them as code so I couldn't use them.

 

[Dilb]

For example, we use length and time as fundamental units, with the standard units being metres and seconds. This means that acceleration can be described as {length}{second}^-2. However, it is just as valid to use velocity and time. Acceleration would then be described as {velocity}²{length}^-1.

Acceleration would be {velocity}{time}^-1. Presumably you meant velocity and length, which gives {velocity}²{length}^-1. Interestingly, this makes time a derived unit {velocity}^-1{length}, or length per velocity.

 

[Oppressed]

Ziggurat,

As I said, I am perfectly capable of making mistakes, just as your are and so is everyone else.

I pulled the list of dimensions in the beginning of this post from another source listing dimensions defined in physics. I cut and pasted the list. When I first looked at the list, I briefly questioned it for completeness but was pulling it out of a reference to try and make a quick point. I found more than one reference that gave the same list.

Looking back at the list more closely, now I understand better why Luminous Intensity keeps popping up. It was in the list I found reference to as a fundamental dimension.

A fundamental dimension is one not made up of any other dimensions. When Luminous Intensity was specifically spoken about I also looked at it as a derived dimension, not a fundamental one, as the initial reference list I cut and pasted indicated. This however is really not a significant issue to become stuck upon.

If you become too stuck in the inability to view things in any other manner than the commonly accepted manner, then you blind yourself to other ways view things which might be equally valid or provide new incite.

The point of mentioning the base number system is to illustrate this. It is very normal for us to think in base 10. But, but allowing ourselves to view things in base 2, 4, 8, 16 and so on, we have made significant progress with regard to computing that otherwise would have been extremely difficult to achieve.

I can describe physical space perfectly well in spherical dimensions. The 3 dimensions of space can be the 3 dimensions used in the spherical coordinate system. Like using base 10 for our normal numerical system, using the Cartesian coordinate system is very familiar to us and thus there is great resistance to consider viewing space some other way. However, just as the base 2 system is a perfectly valid base for a numeric system, the 3 dimensions of the spherical coordinate system are perfectly valid as qualifying for the 3 dimensions of space.

If anything, since one of the major theories is that known space is like an expanding spherical bubble, perhaps the spherical coordinate system is the more appropriate coordinate system to use. Thinking of space in that manner may help to give new incite to things we are trying to describe but are as of yet having difficulty in describing.

 

[Oppressed]

Cuddles,

I like your comment about the point of arbitrary choices. That is one of the things I’ve been trying to get at.

 

[Ziggurat]

I can describe physical space perfectly well in spherical dimensions. The 3 dimensions of space can be the 3 dimensions used in the spherical coordinate system.

You are confusing coordinate systems with dimensions, and it's complicated by the fact that you aren't even distinguishing between the different meanings of the word "dimension" either. A change in coordinate systems does nothing to change the dimensionality of a space in any way.

Like using base 10 for our normal numerical system, using the Cartesian coordinate system is very familiar to us and thus there is great resistance to consider viewing space some other way.

Resistance from whom? Not physicists. They routinely change coordinate systems in order to make calculations easier. Often the same space will be described with multiple coordinate systems depending on which aspect one wants to examine - a famous example is the standard black hole, with both Schwartzchild and Kruskal coordinates being commonly used. And both coordinate systems resemble standard spherical coordinates much more than cartesian coordinates, BTW. So you're hardly suggesting anything new here.

If anything, since one of the major theories is that known space is like an expanding spherical bubble, perhaps the spherical coordinate system is the more appropriate coordinate system to use.

I suspect you may be misunderstanding this analogy, but it doesn't matter too much for the present discussion. In any case, people who study cosmology often do use spherical coordinates, so it's not like they're missing anything because of any dogmatic adherence to a particular coordinate system.

 

[PixyMisa]

Oppressed, let's go back to luminous intensity for a moment.

I noted that this is measure of power (sort of - it's a bit of an oddball), which is measured in watts. A watt has the dimensions of {mass}x{length²}x{time^-3}. (We have -3 time dimensions there!)

What's important here, though, is not the number of time dimensions, which we can pretty much manufacture as we choose by looking at ever higher-order derivatives, or the number of length dimensions, but that we also have mass. Mass isn't space, it isn't time, it's something different, and under String Theory and similar models could be represented or otherwise generated by additional dimensions beyond the ones we're familar with.

Charge is another such property. It's not space, or time, or mass, but something different again. Electrons and protons have a mass, they exist and move in 4-dimensional space-time, but they also have a charge.

Mass is related to gravity, and charge to electromagnetism, two of the four fundamental forces. The other two forces are the weak force and the nuclear force, and their effects are known as (you'll love this) flavour and colour. (Note that I'm not a particle physicist, so any time I venture beyond the simple stuff there's a chance that I'm getting it wrong. Since we do have real live physicists on the forum, if I screw up in a major way one of them will probably come along and rescue me. )

So that's two more things that we might want to model with (or as) additional dimensions, bringing our total up to eight: Three dimensions of length, and one each of time, mass, charge, flavour and colour. Indeed, String Theory and M Theory propose a universe with 10 or 11 dimensions.

So what you are saying - that there are dimensions beyond the usual four that account for the properties of matter - is something that is taken very seriously by physicists. The problem isn't with the basic idea, just with your list of dimensions, because most of those things aren't dimensions at all.

 

[Oppressed]

PixyMisa,

The point of the thread “Hyper Dimensional Philosophizing” is not to limit ourselves to only the dimension of length, but to consider something dimension beyond length and beyond what we can prove exists. If we can prove a dimension exists, then I would no longer consider it a hyper dimension.

“Hyper dimensional” means above and beyond “Dimensional”. What is above and beyond “dimensional”? Some dimension beyond what we currently can prove exists.

The root meaning of dimensional means to measure out. The point of a dimension is to aide us in comprehending the measuring out of something. How we go about defining a dimension has many arbitrary elements to it. There are different ways you can measure out something so that the dimensions of how you are measuring that something out are very different and yet what you are measuring out is the same and the results of the measurement are the same, but in different dimensions.

I should have looked more closely at the list, I of physics dimensions I grabbed off the net. When a took a moment to more closely consider the list, I disagree with what is described as fundamental dimensions. To be a fundamental dimension, I would expect that the dimension would be one that was not a measurement of 2 or more other dimensions.

But the general idea was to expand some people’s realization that in discussing this subject a dimension might be something other than what they might have been limiting their view to. When you are going to consider new dimensions that are beyond our current ability to prove they exist, you should be prepared for the idea that the new dimension may be unlike any we know of. To prepare for what that might be, it is good to first think about all the dimensions we have defined and how we have defined them.

When we speak of space, which we have arbitrarily defined in three Cartesian coordinates, are those dimensions really fundamental or are they really a result of our attempt to measure an emergent property of other physical laws that we do not yet fully understand?

In your point of view, what are the 3 dimensions of space?

As for the list, the only one I see truly questioning as a dimension is amount. I included it because I have seen it included in lists of dimensions. But, a dimension is about being able to measure out something. We have give definitions to measuring out the amount of a substance, given it the unit of mole and set this definition as common to many people in the widely accepted International System of Units. http://physics.nist.gov/cuu/Units/units.html. This just goes to further illustrate what a dimension might be arbitrarily defined as by us. We use dimensions to measure things to help us better understand what we are observing. Note that in the list of SI units at the link shows “Luminous Intensity” as a base unit. In similar lists I have seen it listed as a fundamental dimension. But as has been discussed, “Luminous Intensity” is derived from other dimensions.

How some things can be defined is very frequently very arbitrary.

 

[PixyMisa]

The point of the thread “Hyper Dimensional Philosophizing” is not to limit ourselves to only the dimension of length, but to consider something dimension beyond length and beyond what we can prove exists. If we can prove a dimension exists, then I would no longer consider it a hyper dimension.

In that case, you're talking nonsense.

There are different ways you can measure out something so that the dimensions of how you are measuring that something out are very different and yet what you are measuring out is the same and the results of the measurement are the same, but in different dimensions.

No. That is completely false. You can define different units, you can apply different co-ordinate systems, but the dimensions never change.

When we speak of space, which we have arbitrarily defined in three Cartesian coordinates, are those dimensions really fundamental or are they really a result of our attempt to measure an emergent property of other physical laws that we do not yet fully understand?

They're fundamental.

In your point of view, what are the 3 dimensions of space?

Length, length, and length.

As for the list, the only one I see truly questioning as a dimension is amount.

Amount (that is, moles) is obviously not a dimension. Neither are most of the others. It's very simple: These things are not dimensions!

I included it because I have seen it included in lists of dimensions.

No you didn't. You saw it in a list of units.

But, a dimension is about being able to measure out something. We have give definitions to measuring out the amount of a substance, given it the unit of mole and set this definition as common to many people in the widely accepted International System of Units.

As I said, units.

This just goes to further illustrate what a dimension might be arbitrarily defined as by us.

No it doesn't.

We use dimensions to measure things to help us better understand what we are observing. Note that in the list of SI units at the link shows “Luminous Intensity” as a base unit. In similar lists I have seen it listed as a fundamental dimension.

No you haven't.

But as has been discussed, “Luminous Intensity” is derived from other dimensions.

Yes. As are the great majority of units in SI.

How some things can be defined is very frequently very arbitrary.

This is particularly true when you persistently confuse the terms used in the definitions.

SI is a system of units, not of dimensions. Each of the units can be described as a set of dimensions. But they are not dimensions themselves.

 

[Ziggurat]

The point of the thread “Hyper Dimensional Philosophizing” is not to limit ourselves to only the dimension of length, but to consider something dimension beyond length and beyond what we can prove exists.

When you start talking about what you can't prove exists, you run into the problem of talking about stuff you just made up completely. There's limited usefulness in that.

As for the list, the only one I see truly questioning as a dimension is amount. I included it because I have seen it included in lists of dimensions. But, a dimension is about being able to measure out something. We have give definitions to measuring out the amount of a substance, given it the unit of mole and set this definition as common to many people in the widely accepted International System of Units.

A mole is a unit. But it is NOT a dimension. In fact, it is dimensionless. It is a pure number, and pure numbers never have dimensions. When you start talking about moles of something in particular (say, O₂), then you've got a dimension, but just moles? That's dimensionless.

This just goes to further illustrate what a dimension might be arbitrarily defined as by us.

Units are completely arbitary. But units are not the same thing as dimensions, and I'm not sure if you've gotten the distinction yet. Inches and centimeters are both units, both are completely arbitrary, they aren't equal to each other, but they have the exact same dimension: length. There is some choice in terms of what dimensions we consider fundamental. For example, between length, time, and velocity, any two can be considered fundamental. But it's not completely arbitrary: you cannot define all three as fundamental, because the relationship between them is not something we are free to choose.

 

[Oppressed]

I quote:
“In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction, based on the luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit.”

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

The root definition of dimension is “To Measure Out” meaning in the basest manner that there is some thing that we can measure. Luminous intensity is a dimension, not a spatial dimension, but still a dimension.

I quote:
“Physical-dimension LUMINOUS-INTENSITY-DIMENSION” and
“The fundamental dimension of luminous-intensity, as defined by the SI standard.”
http://www.ksl.stanford.edu/knowled...-dimensions/LUMINOUS-INTENSITY-DIMENSION.html

Apparently some people at Stanford University are wrong about defining Luminous Intensity as a dimension. You should contact them and explain to them their mistake.

Granted that Stephen F. Austin State University is not as well known as Stanford, but if you look through the following link, they too define Luminous Intensity as a dimension. They also define amount of substance with the SI units of mole as a dimension. Maybe you better correct them too.
http://observe.phy.sfasu.edu/courses/egr112/lectures112/ZZ-Spring2003/12

I quote:
"According to the SI, the mole is not dimensionless, but has its very own dimension, namely "amount of substance", comparable to other dimensions such as mass and luminous intensity.[2]"

http://en.wikipedia.org/wiki/Mole_(unit)

Looks like you should straighten out the International System of Units as well.

Looks like there are a whole lot of people that need correction from you over this issue.

 

[PixyMisa]

I quote:
“In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction, based on the luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit.”

Yes, it's a base unit in SI. That's an entirely arbitrary decision, and as been shown already, it isn't a dimension.

The root definition of dimension is “To Measure Out” meaning in the basest manner that there is some thing that we can measure. Luminous intensity is a dimension, not a spatial dimension, but still a dimension.

One more time: You are confusing dimensions with units.

“Physical-dimension LUMINOUS-INTENSITY-DIMENSION” and
“The fundamental dimension of luminous-intensity, as defined by the SI standard.”
http://www.ksl.stanford.edu/knowled...-dimensions/LUMINOUS-INTENSITY-DIMENSION.html

Apparently some people at Stanford University are wrong about defining Luminous Intensity as a dimension. You should contact them and explain to them their mistake.

That's the documentation for using a computer program; it is not in any way a definition of how physicists use the term.

Granted that Stephen F. Austin State University is not as well known as Stanford, but if you look through the following link, they too define Luminous Intensity as a dimension. They also define amount of substance with the SI units of mole as a dimension. Maybe you better correct them too.
http://observe.phy.sfasu.edu/courses/egr112/lectures112/ZZ-Spring2003/12

That link is broken, so I can't confirm what you say.

I quote:
"According to the SI, the mole is not dimensionless, but has its very own dimension, namely "amount of substance", comparable to other dimensions such as mass and luminous intensity.[2]"

http://en.wikipedia.org/wiki/Mole_%28unit%29

Looks like you should straighten out the International System of Units as well.

Looks like there are a whole lot of people that need correction from you over this issue.

Mostly you - you don't understand the difference between dimensional analysis and spacetime metrics. That in itself is not a problem, the problem is that this remains true after it has been explained to you repeatedly.

Yes, there is very good reason to believe there are more than four dimensions to spacetime. There are real, fundamental properties of matter that can be explained that way.

No, it has nothing to do with SI's selection of base and derived units, which are essentially arbitrary.

You can't just grab onto any use of the word "dimension" as support for your pet idea. It's been shown just how luminous intensity, power, velocity, acceleration and so on are simply combinations of dimensions already well understood. Why do you have a problem with that?

 

[Oppressed]

observe.phy.sfasu.edu/courses/egr112/lectures112/ZZ-Spring2003/04-Chapter%2014%20Unit%20Conversions.ppt

Page 12

You are confusing the dimensions used in the common view of what we call space time as not a subset of the larger set of defined dimensions. Time is one of the 4 dimensions used in this common view.

What is the dimension of time? It is not length! It is not width! It is not depth!

Time is a dimension.

You can not measure volume with time!

You can not measure area with time!

So in you limited view of what dimensions are, why is time a dimension?

The question is; why are you incapable of understanding the broader definition of what a dimension is?

If we limited our perspective so, particularly if in the process we hobble our creative imagination to only allow thinking about what we think has already been proved and thus make ourselves incapable of considering anything beyond what we already know, we would still be in the dark ages.

Scientific breakthroughs require creative thought going beyond what we already know into the area of the unproven. Then you take the unproven ideas and see if you can prove them. If an unproven idea then leads to a new proven idea, you have made scientific progress.

You are wearing blinders so tight you can even get past the basic realization dimensions are a measurement of something. You want to separate the analysis of “All Dimensions” from the analysis of “Space-Time Dimensions” but the analysis of “Space-Time Dimensions” is a subset of the analysis of “All Dimensions”.

If we are going to consider the possibility of additional dimensions we do not yet know of and therefore we can not prove they exist because you can not prove something you do not know, then you have to be prepared to consider something NEW.

The result might be “Space-Time-Quantumshift”.

We already use expanded dimensional models of space-time to create what appear to be more accurate models. Such models which began as new unproven ideas have since had supportive observations and testing done which give them greater credibility as being true.

 

[PixyMisa]

You are confusing the dimensions used in the common view of what we call space time as not a subset of the larger set of defined dimensions.

Baloney. I have explained that many physicists believe that this is exactly the case, and shown you some of the properties that might well be explained by those extra dimensions.

Time is one of the 4 dimensions used in this common view.

What is the dimension of time? It is not length! It is not width! It is not depth!

Time is a dimension.

Yes, it is. Where have I said anything else?

You can not measure volume with time!

You can not measure area with time!

So in you limited view of what dimensions are, why is time a dimension?

Because there is no more fundamental property or set of properties that can be used to describe time. This is not true for any of the units on your list with the single exception of mass.

The question is; why are you incapable of understanding the broader definition of what a dimension is?

I understand it pretty well. You are simply choosing nonsensical examples.

If we limited our perspective so, particularly if in the process we hobble our creative imagination to only allow thinking about what we think has already been proved and thus make ourselves incapable of considering anything beyond what we already know, we would still be in the dark ages.

Maybe so, but if we listened to everyone who spouted random nonsense, we'd still be in the paleolithic.

Scientific breakthroughs require creative thought going beyond what we already know into the area of the unproven. Then you take the unproven ideas and see if you can prove them. If an unproven idea then leads to a new proven idea, you have made scientific progress.

What scientific breakthroughs require most is a deep understanding of the existing theory. Also - this is a little beside the point, but still worth saying - scientific theories are never proved, only disproved.

You are wearing blinders so tight you can even get past the basic realization dimensions are a measurement of something.

No, you're thinking of units.

You want to separate the analysis of “All Dimensions” from the analysis of “Space-Time Dimensions” but the analysis of “Space-Time Dimensions” is a subset of the analysis of “All Dimensions”.

That doesn't mean anything.

If we are going to consider the possibility of additional dimensions we do not yet know of and therefore we can not prove they exist because you can not prove something you do not know, then you have to be prepared to consider something NEW.

Maybe, but talking nonsense gets you nowhere.

Area is not fundamental, it's just {length²}
Volume is not fundamental, it's just {length³}
Velocity is not fundamental, it's just {length}{time^-1}
Acceleration is not fundamental, it's just {length}{time^-2}

And so on. This is all perfectly well understood, and nothing more is needed. In fact, if you try to shove new dimensions in to explain these things, the maths stops working.

The result might be “Space-Time-Quantumshift”.

Again, that doesn't mean anything.

Again, mass, charge, "flavour" and "colour" are real properties that are not described by four-dimensional spacetime, and may indeed constitute additional dimensions. The same cannot be said for your list of units.

We already use expanded dimensional models of space-time to create what appear to be more accurate models. Such models which began as new unproven ideas have since had supportive observations and testing done which give them greater credibility as being true.

That's half true. There are such models, as I've said a number of times, and they are taken seriously. But none of the models of space-time with more than 4 dimensions have been experimentally confirmed.

 

[GodMark2]

The root meaning of dimensional means to measure out.

Incorrect. You should have said "The layman's definition of 'dimension', when used a a verb is 'To measure out'"

Unfortunately, layman's definitions aren't precise enough to get anything meaningful done. So, most words have slightly different definitions in science. Most often, the layman's version is similar to the Scientific version, but the differences are quite important.

The scientific definition of the dimension of a space is "The minimum number of coordinates required to locate a point in that space", which an be shown mathematically to be identical to "The Maximum number of coordinates for a given space, such that changing any one coordinate has no effect on the any remaining coordinate." or, to use your layman's terminology "The number of basic ways the space itself may be measured"

So far, we have found three length dimensions, one time dimension (which can also be described as a length dimension, and indeed must be so described when talking about relativistic events) and one dimension each for mas, charge, flavor, and color.

We can create many different measures of these dimensions, but a measure is distinctly NOT a dimension. We can combine various basic measures to create composite measures, but those composite measures are not dimensions.

When we speak of space, which we have arbitrarily defined in three Cartesian coordinates, are those dimensions really fundamental or are they really a result of our attempt to measure an emergent property of other physical laws that we do not yet fully understand?

In your point of view, what are the 3 dimensions of space?

You have several choices. The common one is Length, length, and length. But you could also use Angle, Length and Length, or even Angle, Angle, and Length. In each case, you need three coordinates, you can't get by with fewer, so space has a maximum dimension "3". In each case, you can change one of the coordinates without affecting the pother two, so space has a minimum dimension "3". Minimum = Maximum -> only one possible answer = "3".

How some things can be defined is very frequently very arbitrary.

Yes, that's why we have the scientific definitions, so when we use a term, we know exactly what each the other is talking about. When you try to use layman's definitions in a scientific discussion, you will often come to completely wrong conclusions.

 

[Oppressed]

GodMark2:

It is the scientific definition of “Dimension” of which the scientific definition of the “Dimensions of Space” is a subset.

You do mention something which agrees with something I have said, but I am sure others will disagree with you for that. Space can be defined in terms of the dimensions length, angle, angle. But, to be fair, the dimensions of angle are in my opinion derived. I have also heard them referred to as supplemental dimensions but I do not know what difference was intended by that. Angle is generally considered dimensionless but not quite, because is a length divided by a length, which is not truly dimensionless but requires the ratio of two lengths.

I can and have described 3 dimensional space using the dimensions of one length and two angles. But this does not remove the fact that the dimensions of the two angles are derived from two dimensions of length.

But there is another confusion being made here and that is the difference between a dimension and a physical reality. Dimensions are an arbitrary creation of ours. We make up a definition for dimension.

Space simply is. Space exists in its physical reality regardless of how we try to define and measure it with dimensions.

What is not arbitrary about dimensions is how accurately it models the physical reality we are trying to define and measure.

So someone can arbitrarily come up with a definition of physical space, like defining it in three dimensions of length and that model may work pretty darn well. That is, until some people come along, thinking outside the box, using their imagination combined with experimentation, and they find that the 3 dimensions used to define space don’t actually quite work 100%. Those 3 accepted dimensions do not precisely define and measure space.

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.

Why exactly they chose these quantities and dimensions as base I do not know, but they did. 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.

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.

Some dimensions which we are trying to prove really exist relate to the leading edge of physics and the fact that space can NOT be perfectly described in 4 dimensions. We know that our 4 dimensional model of space is flawed and imperfect.

But then there is also the fun of considering dimensions which can not be proven and for that matter are likely to never be proven. These are the dimensions needed for science-fiction. When a spaceship leaps from normal space into hyperspace and then back to normal space while having traveled a normal space distance at a speed many times greater than the speed of light, how might that dimensional space be described? What extra dimensions would be needed?

Both of these topics are fun to me.

But to become bogged down by people who have such blinders on that they can not even realize that we have a plethora of known dimensions besides that of length and time to ponder about when trying to consider a new dimension we have yet to prove exists is like trying to discuss evolution with a highly religious individual where you can not get past the argument that God created everything.

 

[Ben Tilly]

Whatever physical dimensions we agree on, there is no question that there are plenty of reasons to think in larger numbers of dimensions than that. Let me give a ridiculously simple example - look at the space of possible configurations of the human body. Even if you grotesquely simplify the human body, you get a lot of parameters. Here are a few:

2 knees, each of which may be bent over some range of angles.
2 elbows, each of which may be bent over some range of angles.
2 shoulders, each of which has 3 dimensions of motion. (up/down, forward/back, rotate your arm bone)
2 hips, each of which has 3 dimensions of motion.

I'm up to 8 dimensions, and I haven't even started in on what your neck, spine, wrists, ankles, fingers, etc can do. Let alone the fact that our various bones do not all have the same length. Clearly, describing the configuration of a given human body requires a lot more than 3 dimensions! (And it isn't just a straightforward n-dimensional region, there are design limits because, for instance, your elbow will only bend so far, and your hand can't go into your body.)

This example may seem contrived, but it is not at all contrived if you're trying to model a human being in a computer. Or if you're trying to build a robot.

Similarly in many other modelling situations, by the time you've finished describing your design parameters, you're in a high dimensional system. And it isn't just abstract theory - I know of real optimization problems in economics and engineering which involved several thousand dimensions. An excellent example which I saw an article on over a decade ago is the design of soft drink cans. The goal: design a can which uses as little metal as possible but holds a fixed amount of fluid under pressure and will survive normal drops, contact with sharp objects, etc. Coca-Cola spent several million dollars on this optimization problem, and the number of dimensions in their highly non-linear mathematical models was huge. However their savings completely paid for the program.

So there are some good reasons to think about lots and lots of dimensions in the mathematical sense.

 

[PixyMisa]

You do mention something which agrees with something I have said, but I am sure others will disagree with you for that. Space can be defined in terms of the dimensions length, angle, angle.

That's a valid and frequently used co-ordinate system; yes. And it means that there are three dimensions of space.

But there is another confusion being made here and that is the difference between a dimension and a physical reality. Dimensions are an arbitrary creation of ours. We make up a definition for dimension.

No.

So someone can arbitrarily come up with a definition of physical space, like defining it in three dimensions of length and that model may work pretty darn well. That is, until some people come along, thinking outside the box, using their imagination combined with experimentation, and they find that the 3 dimensions used to define space don’t actually quite work 100%. Those 3 accepted dimensions do not precisely define and measure space.

No.

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.

No. Look at the name you just wrote. International System of Units.

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

Units. Not dimensions.

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

And then you decided that they were dimensions rather than what they really are - units.

Why exactly they chose these quantities and dimensions as base I do not know, but they did.

The history of each of the units in SI is documented, and in many cases, interesting. That doesn't make them dimensions.

Seems to me Luminous Intensity is a derived dimension

Unit.

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

Units.

as the base upon which the built the SI system of units and measurement.

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.

Then why are you so insistent that your mistaken interpretation of the word "dimension" is correct and that the work of leading physicists into multi-dimensional explanations of observed reality is wrong?

Some dimensions which we are trying to prove really exist relate to the leading edge of physics and the fact that space can NOT be perfectly described in 4 dimensions. We know that our 4 dimensional model of space is flawed and imperfect.

No. It's incomplete. As far as it goes, it is extremely accurate.

But then there is also the fun of considering dimensions which can not be proven and for that matter are likely to never be proven. These are the dimensions needed for science-fiction. When a spaceship leaps from normal space into hyperspace and then back to normal space while having traveled a normal space distance at a speed many times greater than the speed of light, how might that dimensional space be described? What extra dimensions would be needed?

One would suffice.

Both of these topics are fun to me.

That's fine.

But to become bogged down by people who have such blinders on that they can not even realize that we have a plethora of known dimensions besides that of length and time to ponder about when trying to consider a new dimension we have yet to prove exists is like trying to discuss evolution with a highly religious individual where you can not get past the argument that God created everything.

I don't believe that you've actually read anything anyone else has written.

There are real properties of matter that physicists are working to model as additional dimensions. These properties are mass - which is on your list, charge - which is related to current, "flavour", and "colour".

Temperature is a measure of energy, derived from mass, length, and time.
Current is a derived unit from charge and time.
Luminous intensity is a derived unit from mass, length, and time.
Amount of substance is just a number. A mole is simply 6.02x10²³ of whatever you're counting.

The idea that there may be additional dimensions is a great insight, and physicists have been studying this since early in the 20th century. The only problem with your idea is that you are choosing things as your extra dimensions that just don't work.

Take a look at the Wikipedia article on the Standard Model. The Standard Model describes all the different types of matter and the forces that unite them. This is the fundamental nature of the Universe; this is what you need to explain with your extra dimensions.

 

[Just thinking]

Just poking in here ...

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

 

[Oppressed]

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. While there are a great many things one can do in life while wearing so many blinders, if you participate in the effort to better our existing knowledge of physical reality or expand our knowledge of physical reality into new unknown areas, your blinders would be a grave hindrance.

Dimension is all about measuring something. 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.

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

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.

But, in general, all the other dimensions they define units of measurement for are derived from the product of these 7 dimensions, each with an associated power.

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

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.

By realizing this, we can discover that sometimes there are different ways of looking at something which are both found to be equally valid and equally provable.

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.

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.