Comments on tumbler ordering

[Berend van Berkum <berend@xxxxxxxxxx>]

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