studiot,

Since we are talking about subleties of language, writing to some is definitely a practical activity as opposed to a theoretical one.

I don't think it is an issue of subtleties (notice the correct spelling of the word). I believe it is an issue of an incorrect word being used to describe something. That's a misnomer. Sort of like NASA saying that astronauts "walk" in space when they really float. Do you think NASA is going to acknowledge their misnomer and change their description?

The word you required in your context is 'practicable'

You are correct, I stand corrected.

Ratch

 

Thank you, Ratch, for correcting my notoriously poor spelling. I'm sure others will also have noted a lot of need for this in my posts.

I'm glad we agree on the English anyway.

 

How about some other thoughts on this subject?

magnitute and direction of a quantity like force (vector)

The vectors you refer to are all examples of triples of real numbers, that is set containing 3 independent arbitrary real numbers eg {57,36,-345} is a vector from the vector space {a,b,c}.

Both the underlying space and the individual (infinite number of) vectors within it obey the axioms I set out in my originating post for this thread.

They also possess extra mathematical structure in that the Vector Space of triples is a normed vector space with a distance function. This allows the calculation of the 'magnitude' and direction.

However not all vector spaces are normed and not all poses distance or magnitude functions, which is why they are not part of the definition.

Since this is an electronics forum let us consider instead of the above triples, the vector space of all possible triples formed only from the characters 1 and 0 with the rules of addition that eg {1,0,1} ; {0,0,1} etc

1+1 = 0+0 =0
1+0 = 0+1 =1

These rules should be pretty familiar.

Also observe that the vectors satisfy all the axioms I outlined.

Now please display the 'magnitude' and direction of these vectors.

They are very important in information and coding theory so they have a practical (HA HA) significance.

And they are regular mathematical vectors although not geometric ones.

I spell checked this post and corrected three errors.

 

studiot,

Your treatise on vector space is all well and good, but it does not address my contention that a phasor is not a vector. A phasor certainly has magnitude, but what is its direction? It has a phase instead of a direction. Phasors certainly have some vector like properties, but not all, and vice versa. So I am wary of calling it a true vector.

Ratch

 

Spoken like a true gentlemen - totally ignore everything I said.

 

I think we should decide amongst ourselves if phasor and vector are the same.

I think we've already decided amongst ourselves that they are the same. We've only got one hold-out.

How about some other thoughts on this subject?

Here's one:

 

studiot,

Spoken like a true gentlemen - totally ignore everything I said.

Noted, not ignored completely. Your explanation does not leave me comfortable with considering voltage, which is the energy density of a charge, expressible as a vector quantity.

I think we've already decided amongst ourselves that they are the same. We've only got one hold-out.

thingmaker3,

A "we" of four so far. You don't count because you did not express a reasoned opinion about the veracity of the thread heading.

Ratch

 

Your explanation does not leave me comfortable

Comfortable? who said anything about comfortable?

You should have gone to my school. We had a Physics master who used to say

"A vector has magnitude and direction
A scalar has magnitude only."

He used to beat it into 12 year old boys.
We were not comfortable.

So you can imagine my dificulties when I studied maths at University to find that there was a completely new definition of vectors.

Did I think that was unwise? did I wish they had chosen another word?
Certainly.

Then I found that Physicists at University 'generalised' vectors to things called 'tensors', which had magnitude, direction and something else.
In fact the stress or strain tensors have no less than 9 components.
So vectors were special cases of tensors.


But the dear old mathematicians had further generalised vectors so that tensors were considered as special cases of vectors! In fact some objects that are not even numbers or nemeric are considered vectors by them.

Real Gilbert and Sullivan stuff.

I really am trying to help with my 'expanation', except that I asked a question you carefully dodged.

If you read any standard text on Hamming theory, boolean logic and the like you will find similar examples to mine.

Instead of 1 and 0 use black and white, or green and blue. They are still vectors and I am still asking you and my old Physics teacher to calculate their magnitude and direction.

 

studiot,

Instead of 1 and 0 use black and white, or green and blue. They are still vectors and I am still asking you and my old Physics teacher to calculate their magnitude and direction.

I wish I could have been in your classes of yesteryear, so I could absorb their reasoning and challenge it. But such cannot be. So I am clueless on how to make a scalar quantity like voltage into a vector that expresses direction.

Ratch

 

studiot,
I wish I could have been in your classes of yesteryear, so I could absorb their reasoning and challenge it. But such cannot be. So I am clueless on how to make a scalar quantity like voltage into a vector that expresses direction.
Ratch

I'm in complete agreement with Studiot's remarks about vectors. Ratch, you are thinking geometrically about a specific kind of vector (one in R^3), with a particular multiplication operation (the cross product--vectors in general don't have this operation), and attempting to fit these ideas onto vectors generally. They don't necessarily fit.

A vector is simply an element of a vector space, and vector spaces are defined as Studiot showed early in this thread. The ordered tuple (1, 0, 1, 1) is a member of the vector space R^4, for which there is no cross product and no box product. In order for a vector to have a direction, the vector space must have a distance function (or metric) defined for it. There are many choices for distance functions. For example, I could define the distance between the origin and (1, 0, 1, 1) as 1 + 0 + 1 + 1 = 3, and that would be perfectly legitimate. I could also define it in the more usual way of sqrt(1^2 + 0^2 + 1^2 + 1^2) = sqrt(3), and that too would be perfectly legitimate. My point is that to be able to determine the direction of a given vector, you need to find a vector whose magnitude is 1, that is a scalar multiple of the original vector. If the vector space is not associated with a distance function, it makes no sense to talk about a vector's direction.

 

Mark44,

I'm in complete agreement with Studiot's remarks about vectors. Ratch, you are thinking geometrically about a specific kind of vector (one in R^3), with a particular multiplication operation (the cross product--vectors in general don't have this operation), and attempting to fit these ideas onto vectors generally. They don't necessarily fit.

OK, then explain how phasors are vectors. Stick to 2 dimensions, which phasors are. And tell me why they are called phasors instead of vectors. Why was a different word coined? Phasors used to be called "sinors". How is a sinor different from a vector?

Ratch

 

Ratch, you have every reason to be confused.

The use of the word 'vector' by mathematicians to describe an enormously wide ranging concept is, in my opinion, very very bad.

This is because of the development of more limited usage in other disciplines.

However it is not within my gift (or yours) to change matters, so we must learn to live with it until the combined wieght of opinion moves towards a new word.

So let me summarise

Physics has established the heirarchy scalar, vector, tensor to refer to classes of entities which have individual identity but require one, two or more than two pieces of information to completely specify them.

Exmples are Energy, Force, Stress respectively.

Each of these posess the property that we can always add a finite number of like entities together to get another entity of the same type.

So 20 joules plus 30 joules makes 50 joules etc.

This makes good physical sense at elementary level and also has the advantage of corresponding to the idea of a single number(scalar), a row or column of numbers (vector) and a matrix of numbers (tensor). These matrices must be square.

Under this scheme a simple number can also be regrded ast a zero order tensor, a vector as a first order tensor and a matrix as a second order tensor........

Mathematicians have looked at this scheme and extracted what they see as the key property of this heirarchy - that we can add like entities and always end up with another one of the same type.

They have then, in their usual way, generalised this and dubbed the branch of mathematics 'Linear Analysis' and called the principal actors on their stage 'vectors'.
This generalisation leads to most of the useful and solvable applied mathematics today.

However I only wish they had chosen a new and better name.

 

I did give an algbraic/trigonometric description of phasors as vectors in my post #2 in this thread.

However if you prefer a geometric view and in two dimensions, try this.

All two dimensional geometric vectors can be considered as pairs of numbers {x, y} that cover the entire plane.

Phasors are a specific subset of this plane lying on the unit circle about the origin.

They inherit the properties of all vectors {x,y} in the plane.
That they form a proper subset (vector subspace) of the plane so that adding any two phasors will always produce another point on the circle, not anywhere else in the plane I will leave as an exercise for the reader to demonstrate.

 

And tell me why they are called phasors instead of vectors.

The relation of "phasor" to "vector" is akin to the relationship of "Roquefort" to "Bleu." http://en.wikipedia.org/wiki/Phasor_(electronics) A phasor is a two dimensional vector.

Why was a different word coined?

It's that evolution of language thing again. This is akin to using "fax" as a verb instead of "send a facsimile."

How is a sinor different from a vector?

They are NOT different. Synonomous with "phasor," "sinor" is a sub-category of "vector."

 

Extract from Chambers Dictionary of Science & Technology

"Complexor (Elec Eng)

A representation of a single frequency, sinusoidally alternating voltage or current, which with similar complexors in a plane, can be manipulated as though they were complex numbers on an Argand Diagram.

Also called phasor and sinor."

There are you happy now ?

 

which with similar complexors in a plane,

Oh, no... you typed "complexors." He's going to go ape. You know that, don't you?

 

studiot,

They have then, in their usual way, generalised this and dubbed the branch of mathematics 'Linear Analysis' and called the principal actors on their stage 'vectors'.
This generalisation leads to most of the useful and solvable applied mathematics today

I looked in a good book on linear analysis and could not find any reference to "phasors". The book was Linear Algebra by G. Hadley.

However I only wish they had chosen a new and better name.

The name is OK. You have still articulated what the big difference between vectors and phasors are. See further below

Phasors are a specific subset of this plane lying on the unit circle about the origin.

They inherit the properties of all vectors {x,y} in the plane.
That they form a proper subset (vector subspace) of the plane so that adding any two phasors will always produce another point on the circle, not anywhere else in the plane I will leave as an exercise for the reader to demonstrate.

There is more to phasors than that. From Circuit Analysis, by Irving L Kosow, 1988, p. 446, "… Phasors may represent periodic sinusoidal and nonsinusoidal waveforms, as long as they are time varying. Since phasors are expressed in the two-dimensional complex plane, they are not space coordinates like vectors. …". So you cannot have a phasor unless you are representing a time-varying quantity. The time varyiing aspect is what was missing from your explanation.

thingmaker3,

The relation of "phasor" to "vector" is akin to the relationship of "Roquefort" to "Bleu." http://en.wikipedia.org/wiki/Phasor_(electronics) A phasor is a two dimensional vector.

Nope, here's why. No one has ever come across a problem that goes somelike like this: "Find the phasor of the force pulling 3 newtons north and 4 newtons east." They always say vector, not phasor. Why is that? Because vectors and phasors do not mean the same or almost the same thing. There is a time-varying periodic aspect to phasors.

It's that evolution of language thing again. This is akin to using "fax" as a verb instead of "send a facsimile."

No, it's not. It is a misnomer, not an evolution.

They are NOT different. Synonomous with "phasor," "sinor" is a sub-category of "vector."

As explained above, the time-varying periodicity of phasors puts them out of the subcategory definition. Phasors support division, but vectors do not.

Oh, no... you typed "complexors." He's going to go ape. You know that, don't you?

Not unless you aver that complexors are the same as vectors.

To summarize, phasors can be thought of as rotating vectors, provided you define those particular vectors as a complex quantity that can be drawn on a Argand diagram. The vectors also have to rotate in a periodic manner or the resultant phasor does not exist. I am going to close with one more quote, this time from Circuit Analysis, by Allan D. Kraus, 1991, p 351, "Some authors use the words phasor and vector interchangeably, but here this practice will be resisted. Although phasors behave like vectors, which are directed quantities in space, they will not be referred to as vectors."

Furthermore, I remember my physics teacher referring to "vector space" and "phasor space"

Ratch

 

To summarize, phasors can be thought of as rotating vectors, provided you define those particular vectors as a complex quantity that can be drawn on a Argand diagram.

By all the gods of all the pantheons! Ratch has finally agreed with me! I think I may die of shock now.

po-TAAAAAAAAYYYY-to

po-TAAAAAAAAHHHH-to

 

thingmaker3,

By all the gods of all the pantheons! Ratch has finally agreed with me! I think I may die of shock now.

You should read the post more carefully. I did not agree with you. In fact, I gave an example problem where "phasor" is not simply a substitution for "vector."

Ratch

 

You should read the post more carefully. I did not agree with you. In fact, I gave an example problem where "phasor" is not simply a substitution for "vector."

Your logical fallicy is called "the straw man argument." Nobody here claimed "phasor" was a substitution for "vector." The term "sub category" does not mean the same thing as "substitute."

I'm curios: what is your native language?

And you DO agree with me. You just call it something else.