OpenEuphoria

Re: Dimension of sequences

• Posted by Jason Gade <jaygade at ??hoo.com> Sep 14, 2007
• 671 views

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.

I would say that "dimension" would refer to the minimum depth of the sequence's
elements. 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.

> 
> 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.