OpenEuphoria

Re: Dimension of sequences

• Posted by Fernando Bauer <fmbauer at hot?ail.c?m> Sep 25, 2007
• 625 views

Hello Igor!

Igor Kachan wrote:
> 
> Hello Fernando!
> 
> Fernando Bauer wrote:
> > 
> > Hello Igor!
> > 
> > Igor Kachan wrote:
> > >
> 
> [snip]
>  
> > > 
> > > See please:
> > > }}}
<eucode>
> > > global function MaxDepth(object o)
> > >     integer n, x
> > >     if atom(o) then
> > >        return 0
> > >     else
> > >        n = 0
> > > 	for i = 1 to length(o) do
> > > 	    x = MaxDepth(o[i])
> > > 	    if x > n then
> > > 		n = x
> > > 	    end if
> > > 	end for
> > > 	return n + 1
> > >     end if
> > > end function -- it is function by Ricardo Forno, genfunc.e lib 
> > > 
> > > ? MaxDepth({{{{}}},{},{{},{{{{{{{{{{{{}}}}}}}}}}}}},{{{{{{{{}}}}}}}}})
> > > ?
> > > MaxDepth({{{{1}}},{1},{{1},{{{{{{{{{{{{1}}}}}}}}}}}}},{{{{{{{{1}}}}}}}}})
> > > </eucode>
{{{
 
> > > The maximum depth is 14, all right.
> > > Count please the '{' signs, opening the deepest sequence,
> > > to be sure.
> > > It seems to be a good parameter for description of a sequence.
> > > Now a sequence has its own second dimension, and may be
> > > considered as some 2-dimensional object, which can contain
> > > description of any-dimentional real and unreal objects -
> > > vectors, matrixes, tensors, lists, arrays, trees, books,
> > > images ... etc, etc.
> > > Sequence itself really has two own dimensions - length and depth,
> > > I think now. So attempts to give it some *single* dimension
> > > may be not very productive.
Ok. Thanks to your fantastic picture below, now I understand your concept!

> > 
> > Just to make clear, this concept of 2-dimensional object, or dimensionality
> > 2 as you define, is a higher abstract concept, and is not my original
> > definition
> > of "dimension" which is your Depth.
> 
> I do not think that it is more abstract, it is very clear, if
> you'll just draw a sequence as the pretti_print() draws or as
> it is drawn below? for example:
> }}}
<eucode>
> ?
> MaxDepth({{{{1}}},{1},{{1},{{{{{{{{{{{1,{1},1}}}}}}}}}}}},1,{{{{{{{{1}}}}}}}}})
> -- --{                                                                   }
> --    {     },{1},{                                 },1,{               }
> --     {   }       {1},{                           }     {             }
> --      {1}             {                         }       {           }
> --                       {                       }         {         }
> --                        {                     }           {       }
> --                         {                   }             {     }
> --                          {                 }               {   }
> --                           {               }                 {1}
> --                            {             }
> --                             {           }
> --                              {         }
> --                               {1,   ,1}
> --                                  {1}
> 
> or:
> 
> -- --{                         }
> --   { },{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!

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!!

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.

> It is something like to just icicles or stalactites.
> Did you see the icicles in Brasilia?   
So far, I didn't. :)

> 
> And these dimensions are very demonstative, not abstract at all.
> They are just dimensions of some sheet of paper, needed to draw
> this graphical representation of some sequence.
Ok. Your picture shows this very well!

[snipped]

>  
> Regards,
> Igor Kachan
> kinz at peterlink.ru

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.

Thanks,
  Fernando