Fwd: [berend@xxxxxxxxxx: Re: Comments on tumbler ordering]

[Berend van Berkum <berend@xxxxxxxxxx>]

----- Forwarded message from Berend van Berkum <berend@xxxxxxxxxx> -----

From: Berend van Berkum <berend@xxxxxxxxxx>
Date: Sat, 30 Jan 2010 21:16:04 +0100
To: roger gregory <roger@xxxxxxxxxx>
Message-ID: <20100130201604.GA28439@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>

On Sat, Jan 30, 2010 at 11:56:55AM -0800, roger gregory wrote:
> > 
> > Xu88.1's demo frontend orders these tumblers as follows:
> > 
> > 1.1.1 < 1.1.2 < 1.1.3 < 1.1 < 1.2.1 < 1.2.2 < 1.2 < 1.3.1 < 1.3 < 1.4 < 1 < 2
> If so I consider this a bug.  I've always considered tumblers in the mathematical infinitesimal sense, tis is well defined in results in the other ordering.  

Ah, so the idea to use tumblers as 'insert anywhere' is more a of a kludge or syntactic sugar than anything to do with Xanadu i guess.

> How did you determine this ordering from the code?
> 

By using the compare implementation in Xu88.1's demo FE (green/pyxi/x88.py)

    line = [
        Address(1),
        Address(1,1),
        Address(1,1,1),
        Address(1,1,2),
        Address(1,1,3),
        Address(1,2),
        Address(1,2,1),
        Address(1,2,2),
        Address(1,3),
        Address(1,4),
        Address(1,4,1),
        Address(2)
            ]
    line.sort()
    line = ' < '.join(map(str,line))
    print line
    assert line ==  '1.1.1 < 1.1.2 < 1.1.3 < 1.1 < 1.2.1 < 1.2.2 < 1.2 < 1.3 < 1.4.1 < 1.4 < 1 < 2'

vs. the one in minxu/tumbler.py:

if __name__ == '__main__':
    line = [
        tumbler(1),
        tumbler(1,1),
        tumbler(1,1,1),
        tumbler(1,1,2),
        tumbler(1,1,3),
        tumbler(1,2),
        tumbler(1,2,1),
        tumbler(1,2,2),
        tumbler(1,3),
        tumbler(1,4),
        tumbler(1,4,1),
        tumbler(2)
            ]
    line.sort()
    line = ' < '.join(map(str,line))
    print line
    assert line == '1 < 1.1 < 1.1.1 < 1.1.2 < 1.1.3 < 1.2 < 1.2.1 < 1.2.2 < 1.3 < 1.4 < 1.4.1 < 2'


> On Jan 30, 2010, at 11:30 AM, Berend van Berkum wrote:
> 
> > 
> > Hi list,
> > 
> > 
> > been thinking about a use of tumblers and now bumped into a curiosity.
> > 
> > I know tumblerlines from online comments, from Jeff Rush's minxu and an LM87.1
> > blurb in my revised Dream Machines. But now i see the latter two order 
> > tumblers differently from that proposed in e.g. Tumbler Arithmetic [1]. 
> > Instead they compare as follows:
> > 
> > 1 < 1.1 < 1.1.1 < 1.1.2 < 1.1.3 < 1.2 < 1.2.1 < 1.2.2 < 1.3 < 1.3.1 < 1.4 < 2
> > 
> > And this makes it impossible to insert anything before 1, 1.1, etc.
> > (Nevertheless, this is how Nelson illustrates a tumblerline of Xu88 addresses 
> > in LM87. Perhaps the ordering was confused with the hierarchical addresses of 
> > Udanax Green? It just dawns on me how little the (number of) digits in the 
> > components mean.)
> > 
> > Xu88.1's demo frontend orders these tumblers as follows:
> > 
> > 1.1.1 < 1.1.2 < 1.1.3 < 1.1 < 1.2.1 < 1.2.2 < 1.2 < 1.3.1 < 1.3 < 1.4 < 1 < 2
> > 
> > So the infinite set of addresses in space 1 are ordered before address 1. 
> > To insert between 1.1 and 1.2.1 you a). append after 1.2 or b). insert before 
> > 1.2.1. At new addresses 1.3 or 1.2.1.1. 
> > 
> > I think this is how tumblers should be ordered, but I find the difference 
> > between the addresses curious, and myself thinking how the front-end would 
> > interpret the number of digits. 
> > One could look at the structure as a list of embedded dynamic arrays, which on
> > the other hand is why I think of tumblers often.
> > 
> > 
> > regards,
> > 
> > Berend
> > 
> > 
> > --
> > [1] http://www.udanax.com/green/febe/tumblers.html
> > 
> > 
> 

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 E: berend@xxxxxxxxxx
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