Subject: Re: possible A-F...

From: [email-masked]
Date: Sat, 10 Nov 2001 14:23:26 -0000

--- In lojban@y..., thinkit8@l... wrote:
> ok, making sure not to look at historical numerals, which is 
looking 
> outward for answers instead of inward, i sketched what could by 
> symbols A-F. basically i looked at a standard 8-segment display 
and 
> saw what was easy to draw and also didn't have the rotation problem 
> of 6 and 9. here's what i came up with:
> 
> *** * * * *** ***
> * * * * * *
> * *** *** *** * ***
> * * * * * *
> * * * * *** *
> 
> that's 10-15, in order. now all i have to do is wait generations 
to 
> have hexadecimal accepted, then more generations for the numbers to 
> be standardized.

The display actually only has 7 segments. Also, the representations 
of 2 and 5 are reflections of each other.

Here are all the 128 (2^7) possibilities:

*** * * *** *** *** *** *** *** * * * *
* * * * * * * *
* * *** * * * * *** * * * * *** *
* * * * *
* * *** * * *** *

* * * * * * *** *** *** *** ***
* * * * * * * * * * * *
* * * *** * * * * *** *** *** * * * * * * *** * * * *
* * * * * * * * * * *
* *** * * *** * * *** * * *** *** * * ***

*** *** *** *** *** *** *** *** *** *** * * * * * * * * * * *
* * * * * * * * * * * * * * *
*** * * * * *** *** *** * * * * *** * * * * * * *** *** ***
* * * * * * * * * * * *
* * *** * * *** * * *** *** * * *** * * ***

* * * * * * * * * *** *** *** ***
* * * * * * * * * * * * * * * * *
* * * * * *** *** *** * * * * * *** *** *** * * *** * * * * * *
* * * * * * * * * * * * * * * * * *
* * *** *** * * *** * * *** *** * * *** *** *** * * ***

*** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** * *
* * * * * * * * * * * * * *
*** *** *** * * * * * *** *** *** * * * * * *** *** *** * * ***
* * * * * * * * * * * * * * * * * * *
* * *** * * *** *** * * *** * * *** *** * * *** *** *** *

* * * * * * * * * * * * * * * * * * *** *** ***
* * * * * * * * * * * * * * * * * * * * * * * *
*** *** * * * * * * *** *** *** * * *** *** *** * * *** *** *** ***
* * * * * * * * * * * * * * * * * * * * *
* *** * * *** *** * * *** *** *** * * *** *** *** *** * * ***

*** *** *** *** *** *** *** *** *** *** *** *** * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * *
* * * * * * *** *** *** * * *** *** *** * * *** *** *** *** * * ***
* * * * * * * * * * * * * * * * * * * * * * * * * *
* * *** *** * * *** *** *** * * *** *** *** *** * * *** *** *** ***

* *** *** *** *** *** *** * * ***
* * * * * * * * * * * * * * *
*** *** *** *** * * *** *** *** ***
* * * * * * * * * * * * * * * *
*** * * *** *** *** *** *** *** ***

Eliminating the 1 possibility with all 7 segments blank (because that 
one is actually just a space, so if this digit comprised the complete 
number then the number would probably not be recognised as being 
there, if this digit did not comprise the complete number and was at 
the beginning or end of the number then the number would probably be 
mistakenly identified as a different number, and if this digit did 
not comprise the complete number and was not at the beginning or end 
of the number then the number would probably be mistakenly identified 
as two separate numbers separated by a space) and the 47 
possibilities that aren't connected (because they could be mistakenly 
thought to be two separate numbers) leaves all the following 80 
possibilities:

*** * * *** *** * * * * 
* * * * * * * * 
* * *** * * * * *** * *** * *** *** * *
* * * * * * * *
* * *** * * * * *** ***

*** *** *** *** *** * * * * * * * * ***
* * * * * * * * * * * * * * * *
* * *** * *** * *** *** *** * *** *** * *** *** *** * * ***
* * * * * * * * * * * * * *
* * * * *** * * *** * * *** *** ***

*** *** *** *** *** *** *** *** * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * *
* * * * *** *** * *** *** * *** *** *** *** *** * * *** *** ***
* * * * * * * * * * * * * * * * * * * *
* * * * *** * * *** * * * * *** *** *** * * *** ***

* *** *** *** *** *** *** *** *** *** *** *** *** *** * * * *
* * * * * * * * * * * * * * * * * * * * * * *
* * *** *** *** * * * * * * *** *** *** * * *** *** *** * * *** ***
* * * * * * * * * * * * * * * * * * * * * * * * * 
*** *** * * * * *** *** * * *** *** *** * * *** *** *** * * ***

* * * * * * *** *** *** *** *** *** * * ***
* * * * * * * * * * * * * * * * * * * *
*** * * *** *** *** *** *** * * *** *** *** ***
* * * * * * * * * * * * * * * * * * * * *
*** *** *** *** * * *** *** *** *** *** *** ***

Organising all these 80 possibilities into rows so that each row 
contains only reflections and rotations of the other possibilities in 
that row gives all the following 29 rows:

***

***

* *
* *
* * * *
* *
* *

***

*** ***
* *
* * * *
* *
*** ***

* *
* *
*** *** *** ***
* *
* *

* *
* *
* *
* *
* *

***
* *
* * * *
* *
***

*** ***
* *
*** *** *** ***
* *
*** ***

*** *** * *
* * * *
* * * *
* * * *
* * *** ***

* *
* *
*** ***
* *
* *

* *
* *
*** ***
* *
* *

* *
* *
*** ***
* *
* *

***
* *
*** ***
* *
***

*** *** * *
* * * * * *
* * * * * * * *
* * * * * *
* * *** ***

*** *** * *
* * * *
*** *** *** ***
* * * *
* * *** ***

*** *** * *
* * * *
*** *** *** ***
* * * *
* * *** ***

*** ***
* *
* *
* *
*** ***

* * * * * *
* * * * * *
*** *** *** ***
* * * * * *
* * * * * *

*** *** * *
* * * * * *
*** *** *** ***
* * * * * *
* * *** ***

*** * *
* * * *
* * * *
* * * *
* * ***

*** *** *** ***
* * * * * *
* * * * * * * *
* * * * * *
*** *** *** ***

*** *** * * * *
* * * * * *
*** *** *** ***
* * * * * *
* * * * *** ***

*** ***
* *
*** ***
* *
*** ***

*** ***
* *
*** ***
* *
*** ***

* *
* *
***
* *
* *

*** * *
* * * *
*** ***
* * * *
* * ***

*** *** *** ***
* * * * * *
*** *** *** ***
* * * * * *
*** *** *** ***

***
* *
* *
* *
***

***
* *
***
* *
***

10 possibilities are already used for the digits 0 to 9. Here are all 
10:

*** * *** *** * * *** *** *** *** ***
* * * * * * * * * * * * * *
* * * *** *** *** *** *** * *** ***
* * * * * * * * * * * * *
*** * *** *** * *** *** * *** ***

Eliminating these 10 and all 10 reflections and rotations of them (20 
possibilities altogether) leaves all the following 60 possibilities 
organised into all the following 21 rows:

***

***

* *
* *
* * * *
* *
* *

***

*** ***
* *
* * * *
* *
*** ***

* *
* *
*** *** *** ***
* *
* *

***
* *
* * * *
* *
***

*** ***
* *
*** *** *** ***
* *
*** ***

* *
* *
*** ***
* *
* *

* *
* *
*** ***
* *
* *

* *
* *
*** ***
* *
* *

***
* *
*** ***
* *
***

*** *** * *
* * * * * *
* * * * * * * *
* * * * * *
* * *** ***

*** *** * *
* * * *
*** *** *** ***
* * * *
* * *** ***

*** *** * *
* * * *
*** *** *** ***
* * * *
* * *** ***

*** ***
* *
* *
* *
*** ***

*** *** * *
* * * * * *
*** *** *** ***
* * * * * *
* * *** ***

*** * *
* * * *
* * * *
* * * *
* * ***

*** *** *** ***
* * * * * *
* * * * * * * *
* * * * * *
*** *** *** ***

*** *** * * * *
* * * * * *
*** *** *** ***
* * * * * *
* * * * *** ***

* *
* *
***
* *
* *

*** * *
* * * *
*** ***
* * * *
* * ***

So you could choose any 6 of the above 60 possibilities as long as 
each one was from a different one of the 21 rows, one for each of the 
6 hexadecimal digits A to F, which are used to represent numbers 10 
to 15.

Incidentally, why do you want hexadecimal to become accepted anyway? 
What's wrong with binary? ;)

Sincerely,
Robert