PROLÓG 1 2 3 4 5 6 7 8 9 10 11 12 EPILÓG

How to build your own copy of the tautomat

We work with databases. The explanations are optimized for someone who uses data records (as opposed to subscripts of a vector).

Steps to follow:

1. define aspects of (a,b)
2. define collection used in tautomat
3. sort on a,b and then on b,a: observe differences
4. sort on 72 possible combinations of αβ
5. eliminate doubles from among the 72 sorts, catalogise clans
6. observe properties of chains, find your first chains
7. find standard chains
8. build two Euclid spaces from stzandard chains
9. merge/fuse the 2 Euclid spaces into 1 Newton space
10. do QED, get your Aha-experience
11. discuss Natural Order (play with a. generate random permutation, b. find most close among 72 sorting orders, c. find most distant to result of b., d. is result of a more distant to b than c?) [that is: is there a natural order?]
12. create plane x: (b-2a,a-2b), y: (a-2b, b-2a); find 10 chains; find such chains that include standard chains; establish properties of distinct logical archetypes.

For each of these steps, there is illustrative material and some explanations (speculations) under (www) plus ‘tautomat’ (dot) ‘com’. You can also write me a note: umok,vedesin-at-gmail.com

Good luck and drop me a line if you like the concept.

Step 1&2: build table A, define columns and rows

For i= 1 to 16; For j = i to 16

Write a=i, b=j, c=a+b, k=b-2a,u=b-a,t=2b-3a,q=a-2b,s=17-(a+b),w=2a-3b

Next; Next

Step 3&4 generate SQalfabeta

Sort the data set on 72 combinations starting with ab,ac,…,aw,ba,bc,…, ending ws

For i=1 to9, for j=1 to 9, if i=j next

Alfa=substr(i,‘abckutqsw’)

Beta=substr(j,’abckutqsw’)

Sort table a on alfa,beta

Col_name=’SQ’+alfa+beta

Fill up column named &col_name with 1..136

Next, next

Step 5: mark identicals

Generate table V [veritas] with 72 rows SQalfabeta 72 columns SQgammadelta containing .t. for SQalfabeta[i]=SQgammadelta[j] I,j 1..136, clan no, clan name for groups of identicals. Members of the clan share the name of that member whom we have encountered first.

Mark present permutation of primary arguments which is in starting case ‘abckutqsw’ which orders positions in all subsequent tables. Mark no of .t. and clan strengths.

Step 6: introduce chains

Generate table T [transit] with columns

1. present permutation primary arguments
2. alfabeta (column of sort SQ ‘from’)
3. gammadelta (column of sort SQ ‘into’)
4. values of (a,b) (and any additional you wish to see)
5. chain no
6. step no
7. place from
8. place to

add link to a,b, sum up a,b per chain into carry_a, carry_b

Step 7: standard chains

Make statistics of chains. Find those 10 reorders which have 45*3+1 chains. (Carry_a=18, carry_b=33) Call the 3 that move together in a chain of a standard reorder triplets.

Step 8: Euclid spaces

Find such reorders which can be assembled into a 3-dim space having 3 common axes. Build two 3-dimensional spaces with axes made up of standard reorders (ca,ka,qk; ck,kq,qa). Use triplets’ “to” values in table v as x,y,z coordinates. Generate a point in a 3-dimensional space by non-axiomatic means.

Step 9: Newton space

Merge the contents of the two Euclid spaces into one with axes C,K,Q. Picture points in unified space as 4 variants of points in Euclid space.

Establish properties of points existing with coordinates and carry_ properties

Step 10: Sequence

Change permutation of primary arguments. Redo the complete exercise. Find that in table V the no of .t. has changed.

Therefore the properties of the points of step 9 have changed, as somewhere a chain does not exist which would exist if SQalfabeta was not in every 136 steps identical with SQgammadelta. Therefore, at least one carry_ value is different.

This is the QED for genetic information transfer, as the sequence change of linear arguments influences the properties of matter/space complexes.

Find history of reorders being mirrored in ties among values’ order determining table clan.

Step 11: Natural order

Look closer into kq_qk. See it as a plane thru which chains cross. Order table v such that the steps in the chains are referenced by being in one of kq_qk eccentricity classes (chain of kq_qk)

Step 12: Logical archetypes

Starting the model with all possible primary sequences, there is no rule restricting the form of what is the case. All chains are possible, the minimal concept is of a plane and a chain. The chain can be anywhere on the plane and have any properties. As soon as it is anywhere determined, its properties are restricted. The eccentricity measure of kq_qk (which chain of kq_qk they belong to) classifies the objects.

The chains going thru kq_qk have a synchronicity. Their spatial references are given by their properties as members of standard chains. The more consistent spatial references are included in the chain the more “determination” they possess. (Find triplets from Step 8 being included in chains that cross in temporal congruence with one of kq_qk eccentricity class /chain/). Make overview of points based on chains’ no of triplets included, eccentricity class stability.

The proposition is that the form of members within a group of logical archetypes comes from the offset differences within the chains that cross kq_qk, and the differences among groups come from differences within kq_qk, that is crossing from an eccentricity class into a different one.