OpenEuphoria

Re: Dimension of sequences

• Posted by Igor Kachan <kinz at p?terlink.ru> Sep 25, 2007
• 660 views

Hello Fernando!

 Fernando Bauer wrote:
    Igor Kachan wrote:
[snip]
> > }}}
<eucode> 
> > -- --{                         }
> > --   { },{1},{           },1,{ }
> > --   { }     {1},{       }   { }
> > --   {1}         {       }   { }
> > --               {       }   { }
> > --               {       }   { }
> > --               {       }   { }
> > --               {       }   { }
> > --               {       }   {1}
> > --               {       }
> > --               {       }
> > --               {       }
> > --               {1,   ,1}
> > --                  {1}
> > </eucode>
{{{

> > 
> Very elucidative pictures! Now, I understand your concept of dimensionality
> 2.
> Maybe we could call it Igor's plane? Kachan's plane?
> And, as you said, it can represent all the sequences!

Let's call it Length-Depth Diagram, LDD.     

> Now, following your reasoning:
> 1) a sequence can contain description of any-dimensional real and unreal
> objects
> - vectors, matrixes, tensors, lists, arrays, trees, books,images ... etc, etc.
> 2) all sequences can be represented in the Kachan's plane.
> 3) Kachan's plane can be represented in a sheet of paper.
> Then:
>   - Any-dimensional real and unreal objects can be represented in a sheet of
> paper! 
> or maybe:
>   - Universe can be represented in a sheet of paper!!

It is not that big news, all our old good books consist
just of sheets of paper, and they represent not only
Universe, but much more, sometimes.    
Same about sequences.

> Now, I can't even imagine something as abstract as this!! 
> (abstract= "the concentrated essence of a larger whole")
> This concept is so wide-ranging that I don't know if it has some use,
> since all the sequences have the same dimension 2.

Good, the question about the dimensionality of sequences themselves
seems to be answered, it is just 2, and these two dimensions can be
considered as maximum length, Length, and maximum depth, Depth.

But Length of Euphoria sequence is limited by the current Euphoria
integer.
For Depth, seems to be same limit, machine memory at least.

[snip] 
 
> I appreciated very much your view about this.
> I still have another approach about the "dimension of sequences", but before
> I post it, I want to implement it in Euphoria.
> The line of reasoning is: a NRS is a set of RS where each one has a known
> integer
> dimension. Then, the dimension of a NRS is a sequence formed by that
> dimensions.

OK, interesting, the specific structure of a sequence is involved.
Let's wait.

Good Luck!

Regards,
Igor Kachan
kinz at peterlink.ru