Are functionals united with the vector space which they operate on?

[jaketodd]

Are functionals united with the vector space which they operate on? For example, Physics is a functional of Behavioral Psychology. However, Behavioral Psychology does not include Physics. Am I correct?

Thank you,

Jake

 

[Landau]

Is this a joke?

 

[HallsofIvy]

Are functionals united with the vector space which they operate on? For example, Physics is a functional of Behavioral Psychology. However, Behavioral Psychology does not include Physics. Am I correct?

Thank you,

Jake

What does this have to do with "vector spaces"? For that matter what does it have to do with mathematics?

Perhaps it would help if you gave a precise definion for your use of "functional" here.

 

[jaketodd]

I assumed (apparently incorrectly) that functionals could be applied to the abstraction levels of concepts.

Sorry about the confusion; I'm new to these concepts.

What got me asking this question is from Wikipedia: "A spin network, immersed into a manifold, can be used to define a functional on the space of connections on this manifold."
http://en.wikipedia.org/wiki/Spin_network

So I guess what I'm really asking is: Is the map the functional provides, on the space of connections on a manifold, united with the spin network that is immersed into the manifold in order to obtain the functional?

Thanks,

Jake

 

[zhentil]

Also, could you give us a mathematical meaning to "united"?

 

[jaketodd]

Also, could you give us a mathematical meaning to "united"?

The best I can do is try conceptually: In the concept of spacetime, space is united with time. Does that bring to mind a mathematical representation?

Thank you for bearing with me,

Jake

 

[mordechai9]

Lol, this is really funny actually. No offense, but you're not making any sense. :) . These math concepts have very precise meanings... if you want a philosophical discussion, you should ask in the philosophy forum. :)

 

[jaketodd]

But isn't everything representable with math?

 

[HallsofIvy]

No, why in the world would you think so?

 

[jaketodd]

What can't be defined with math? That's kind of a philosophy question, and I can already hear objections to this thread turning into that. So if you don't want to, don't worry about not responding.