Measuring Vectors: Defining Direction and Magnitude

[RaduAndrei]

On wiki measurement is defined as: Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events.

So a number.

For scalars, I agree because they are described by a single number.

But what about vectors? They have magnitude, but also direction. You must measure that direction too. Vectors are described using multiple numbers.

 

[anorlunda]

On wiki measurement is defined as: Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events.

So a number.

For scalars, I agree because they are described by a single number.

But what about vectors? They have magnitude, but also direction. You must measure that direction too. Vectors are described using multiple numbers.

That's correct, you need more than one measurement to fully define a vector. A compass gives direction, and a ruler measures distance. That does not invalidate the meaning of measurement. The direction can be compared with other directions and the distance with other distances.

Consider a gas in a container. It would take many measurements of different properties to fully describe it. Nothing wrong with that.

 

[Dale]

Usually a vector is measured by projecting onto several basis vectors, each such projection being a scalar. So I think it still applies, but it would be nice if it specifically addressed that case.

 

[ZapperZ]

On wiki measurement is defined as: Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events.

So a number.

For scalars, I agree because they are described by a single number.

But what about vectors? They have magnitude, but also direction. You must measure that direction too. Vectors are described using multiple numbers.

A number assigned to A characteristic! A vector has TWO characteristics, magnitude and direction.

Zz.

 

[RaduAndrei]

A number assigned to A characteristic! A vector has TWO characteristics, magnitude and direction.

Zz.

So for you a vector is an object. For example, velocity is an object.

I would have seen the object as a physical system. And this physical system has properties. And those properties that are measurable are called physical quantities.
And measurement would be the assignment of a number to a physical quantity of a physical system.

What is your definition for an object?

Also according to wiki: In physics, a physical body or physical object (sometimes simply called a body or object; also: concrete object) is an identifiable collection of matter,

So an object is a collection of matter. A vector is not a collection of matter.

So you must have another definition for what an object is. What is it?

I think it is important that we speak the same language.

 

[RaduAndrei]

That's correct, you need more than one measurement to fully define a vector. A compass gives direction, and a ruler measures distance. That does not invalidate the meaning of measurement. The direction can be compared with other directions and the distance with other distances.

Consider a gas in a container. It would take many measurements of different properties to fully describe it. Nothing wrong with that.

It may or may not invalidate it based on what your definitions are for an object, a characteristic, an event. Please tell me your definitions first.

 

[ZapperZ]

So for you a vector is an object. For example, velocity is an object.

I would have seen the object as a physical system. And this physical system has properties. And those properties that are measurable are called physical quantities.
And measurement would be the assignment of a number to a physical quantity of a physical system.

What is your definition for an object?

Also according to wiki: In physics, a physical body or physical object (sometimes simply called a body or object; also: concrete object) is an identifiable collection of matter,

So an object is a collection of matter. A vector is not a collection of matter.

So you must have another definition for what an object is. What is it?

I think it is important that we speak the same language.

A "velocity" doesn't exist out of nothing. You don't look at nothing and associate it with a "velocity". It is associated with an object! A object may have a property called "velocity". This velocity has two numbers associated with it.

Why is this so difficult?

You first asked about a vector, and now you're asking about the definition of an "object". Where exactly are you going with this? On second thought, don't answer that.

Zz.

 

[RaduAndrei]

A "velocity" doesn't exist out of nothing. You don't look at nothing and associate it with a "velocity". It is associated with an object! A object may have a property called "velocity". This velocity has two numbers associated with it.

Why is this so difficult?

Zz.

Because "Measurement is the assignment of a number to a characteristic of an object or event,"

You said that a vector has two characteristics when you read that definition. So you saw the vector as an object.

If the definition was "Measurement is the assignment of a number to a characteristic of a property of an object or event," then I would have realized my mistake. In fact, i would have not even made this topic. I would have figured it out on my own that a property like the velocity has two characteristics.

 

[ZapperZ]

Because "Measurement is the assignment of a number to a characteristic of an object or event,"

You said that a vector has two characteristics when you read that definition. So you saw the vector an object.

No I don't. You are using my answer, and associating it with what you read in Wikipedia as if what is written in Wikipedia is the word of God when you are dissecting every word and nuances out of it.

If you know what a vector is, and realize that it has two numbers associated with it, then we're done. Otherwise, I see this discussion as chasing its own tail.

Zz.

 

[RaduAndrei]

No I don't. You are using my answer, and associating it with what you read in Wikipedia as if what is written in Wikipedia is the word of God when you are dissecting every word and nuances out of it.

If you know what a vector is, and realize that it has two numbers associated with it. Then we're done. Otherwise, I see this discussion as chasing its own tail.

Zz.

Of course I associate it with what I read on wikipedia. I made this topic with that definition in mind. I read that definition and it did not conform with what I already knew. How can you assign a single number to a characteristic of an object? Thus i made this topic so someone can shed light on this definition. Maybe someone would say"no, that definition is wrong, here is how I would define measurement"

I am not saying it is the word of God. In fact I've just questioned that definition by making this topic. If it was the word of God, I would have just believed that definition without questioning it.

Of course when you read something you must dissect every word and filter it through your own mind. I don't just believe what is written on wikipedia.

I know that a vector has associated two numbers to it (a 2D vector at least). I have a masters degree in electronical engineering. I am not asking about vectors here. I am asking about that definition.

 

[ZapperZ]

Of course when you read something you must dissect every word and filter it through your own mind. I don't just believe what is written on wikipedia.

Then you've just wasted time on something you don't believe in. I can point to you many MORE dubious issues with Wikipedia (do a search on here).

I can understand wanting to understand something that was written in a reputable text. What you did here, I do not understand. Have you ran out of things to do?

Zz.

 

[RaduAndrei]

Then you've just wasted time on something you don't believe in. I can point to you many MORE dubious issues with Wikipedia (do a search on here).

I can understand wanting to understand something that was written in a reputable text. What you did here, I do not understand. Have you ran out of things to do?

Zz.

Then lead me to a reputable text about measurement. Maybe I will find a good definition there.

 

[RaduAndrei]

What I did not understand is that I put up a definition about measurement here, questioned it. And then came 3 answers that appeared to try to defend that definition.

 

[ZapperZ]

What I did not understand is that I put up a definition about measurement here, questioned it. And then came 3 answers that appeared to try to defend that definition.

You like to make huge jumps to conclusion that are unjustified.

I did not defend the definition. What I saw was someone who made a mistake in thinking that a concept can ONLY have ONE property or characteristics. You started by saying that a vector is a "measurement" and erroneously think that it should spit out only ONE number based on that definition. This is what I pointed out to be wrong.

You don't measure a "vector". You measure field strength and then you measure the direction of that field strength! In other words, you make TWO measurements, and these measurements define the vector at that point.

I have better things to do with my time. I'm done here.

Zz.

 

[RaduAndrei]

You like to make huge jumps to conclusion that are unjustified.

I did not defend the definition. What I saw was someone who made a mistake in thinking that a concept can ONLY have ONE property or characteristics. You started by saying that a vector is a "measurement" and erroneously think that it should spit out only ONE number based on that definition. This is what I pointed out to be wrong.

You don't measure a "vector". You measure field strength and then you measure the direction of that field strength! In other words, you make TWO measurements, and these measurements define the vector at that point.

I have better things to do with my time. I'm done here.

Zz.

I do not think we are going anywhere with this haha

I do not think I said anywhere here that vector is a "measurement".

Anyway.

 

[sophiecentaur]

I agree with Zapperz. Wiki is a fantastic initial resource for all sorts of things but all its contents needs to be treated with caution and is often from unverified sources. This thread is basically about Classification, which can amount to little more than Trainspotting. There are more fruitful topics . . . . . . .

 

[anorlunda]

I hate threads that debate the meaning of natural language words. It is a big waste of time.

Mathematics is precise. language is not. You can not compose a sentence without natural language.

 

[RaduAndrei]

I agree with Zapperz. Wiki is a fantastic initial resource for all sorts of things but all its contents needs to be treated with caution and is often from unverified sources. This thread is basically about Classification, which can amount to little more than Trainspotting. There are more fruitful topics . . . . . . .

Classification is very important and not only in physics.

I agree about wiki. That's why I made this topic. I did not agree with that definition. But maybe you have a more suitable definition.

 

[RaduAndrei]

I hate threads that debate the meaning of natural language words. It is a big waste of time.

Mathematics is precise. language is not. You can not compose a sentence without natural language.

I do not think is a big waste of time. Mathematics may be precise, but physics is not mathematics, physics only uses mathematics. Physics describes the world. We can't escape the natural language words.

Great physicists in the past were also great philosophers of science.

 

[jbriggs444]

Classification is very important and not only in physics.

If you can measure the velocity of something, it does not matter whether you know what the word "measure" means.

 

[Drakkith]

Arguing about the precise definition of something which doesn't have a precise definition isn't going to get anyone anywhere. The flexibility of natural language is both a strength and a weakness.

Thread locked.