Re: Comments on tumbler ordering

[roger gregory <roger@xxxxxxxxxx>]

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

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
> 
>