Re: Dimension of sequences
Jason Gade wrote:
Hi Jason! Thanks for your reply. Interesting concepts.
>
> Fernando Bauer wrote:
> >
> > Hello All,
> >
> > A basic question about sequences.
> >
> > Suppose that a "retangular sequence" is a sequence generated by using
> > iteratively
> > the function repeat() beginning with an atom. Then, I think we can say that
> > the dimension of a retangular sequence is the number of calls to repeat()
> > function.
> > (atom=dimension 0, vector=dimension 1, matrix=dimension 2, ...).
> >
> > Now, let's say we have a sequence like { 1, {1,1} } which is not retangular.
> > Then, a question arise:
> >
> > What is the dimension of a non-retangular sequence ?
> >
> > a) the maximum depth of the sequence.
> > b) an integer number.
> > c) a fractal number.
> > d) a sequence which depends on the structure.
> > e) the dimension concept does not apply.
> > f) I don't know.
> > g) other.
>
> Interesting question. I think that (d) is probably the most correct answer.
>
> The sequence is a one-dimensional sequence with a maximum depth of two. So it
> depends on the structure.
Could you explain better with an example or show the algorithm to generate that
sequence?
>
> I would say that "dimension" would refer to the minimum depth of the
> sequence's
> elements.
Isn't the minimum depth of a sequence always equal to 1? Could you explain
better how you obtain this minimum depth?
I'm using the concept of depth used by Forno's genfunc.e library.
> Someone who is more mathematically inclined will probably tell me
> how wrong I am though.
>
> > Trying to answer that question, others more basics and related to that arise
> > to me (sorry if they are stupid!):
> >
> > What is the dimension of the circumference ?
> > a) 1 , because the area of the circumference is zero. It is a curved 1D
> > object.
> > b) 2 , because the circumference exists in a bidimensional space.
> > c) Both. It has 2 types of dimensions!
> >
> > Same question for a line not closed as, for example, the form of letter "U".
>
> (c) as I answered above. A circumference in one dimension would consist of
> just
> it's length, and would therefore be just a line. But the coordinates around
> the circumference definitely have two dimensions.
Do you know the names of these 2 types of dimensions?
>
> >
> > Thanks for your reply,
> >
> > Regards,
> > Fernando Bauer
>
>
> --
> A complex system that works is invariably found to have evolved from a simple
> system that works.
> --John Gall's 15th law of Systemantics.
>
> "Premature optimization is the root of all evil in programming."
> --C.A.R. Hoare
>
> j.
Regards,
Fernando Bauer
Porto Alegre - Brazil
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