[Fis] Can We Go Beyond the Limits of Formal Systems?

[Karl Javorszky]

Dear Lou,

(count = and ≠ differently, 2024 01 06)



Thank you for the serious and elaborate restatement of principles we agree
on. Your politely implied question was: What use tabulating numbers, we
only see that as a result what we have set as rules?

The sceptics is well-reasoned. It is on me to show that this time it is
different, that my shuffling of numbers is really, really something new and
produces spectacles like Nature does.



I specifically enjoyed your sentence:

*it helps to look at the simpler examples where one does not have the ideal
that the formal system might be rich enough to express everything including
the logical structure of proofs and demonstrations.*

because your ideas: a: start from simple, from bottom up, b. how rich
(flexible) is the logical language to express complicated interdependencies
(eg in AI or genetic) deal with central points of what we discuss here.



Ad 1. Start from scratch

We address the conflict that *(1,3) *is on *3rd *rank in the sequence
*(1,1),(1,2),(1,3),…
**but **4th *rank in sequence *(1,1),(1,2),(2,2),(1,3),…*(which are sorts
of *a,b). Eq. 1*

Like Pythagoras, we draw two axes in the sand and point out place *x: 3, y:
4 *as a logical dissolution of the conflict by giving it a solution in the
next higher dimension.

Change in attitude required. So far, we use the Sumerian concept of Unit,
comparable to a playing card one side saying “1” and the other side
uniform. Up to today, we count the height of the stack of elementary units
as the content of the message. The invention turns over the Sumerian
playing cards and finds *136 *different symbols etched on the reverse side.
We play a completely different game, within the general game, based on
secret signs that signify belonging to cooperators, if circumstances arise.

Do it your own way, don’t depend on others. Use only deictic definitions.
Create a cohort of pairs of *(a,b); a **≤ b;  a,b **≤ 16. *We listen to
chamber music performed by *136 *individuals.

Ad 2. Flexibility of the language

We live in the correct impression that the world can be described by a
language that uses unform units. The language itself does not hinder us to
express differences and contradictions. The inner controversy demonstrated
by *Eq. 1. *can easily be thematized and narrated.

Seen as a planar coordinate, the contradiction of *Eq. 1 *dissolves. The
language is flexible enough to express the observed facts, if only we would
observe the facts.

My point in answering you:

This is no joke. Neurology makes use of a numeric fact, which lies in fine
details of how we count (perceive) ≠ before a background of =, and = before
a background of ≠. If Nature uses *two *basic descriptive properties of a
heap of input, we should try to do likewise. The argument that *0,1 *are
also *two *reference systems, is void, because *0,1 *are symbols of an
abstract nature, while ≠, = describe material differences that are gradated
and within limits and thresholds.

It is nebbich a fact that one has more variants of space available to
accommodate that many material variants that *n *objects can be
incorporating, *if and only if the objects number < 32 or > 97. *We may
like or not like the fact, but it remains true that the possibly existing
variants of material properties of the objects will not fit in the number
of available spatial segments which the objects can produce, *if and only
if the objects number 32 < n < 97. *

We do not invent anything Nature would not have discovered. The syntax of
the DNA is the best argument. Let your logical primitives exercise and the
first thing they do is building sequenced threesomes of one of among four
(restricted to one of two of two pairs),



Dear Lou, thank you for your efforts to build bridges for me. The relative
isolation of this new family of algorithms lies in the requirements you
pointed out at the beginning. If something is that new, that an update on
a+b=c is necessary, it is necessarily self-contained and uses deictic
definitions. It is pure chance that the Eddington constants and the DNA
support the hair-raising ideas transmitted here.



We have a complicated rhetorical situation here. Let us grow to the
challenge while we discuss that the central idea of information is that
something is *otherwise, *that in the Sumerian system nothing ever can
be *otherwise,
*therefore the rational language appears to be inadequate to describe,
discuss or express something that can not exist by its nature.

No reason to be overly pessimistic, Some nephews of Pythagoras have surely
played with diverse toy soldiers, exercising them, and some say to have
heard Pythagoras curse under his beard: what a horrible spell dampens my
ability to tabulate and memorize! Elementary logical symbols allow
recognizing elementary logical patterns if we perform elementary logical
operations on them! I wish I could live in some 2600 years hence. I’d have
computers and I’d show them what is a pattern.



Friendly greetings:

Karl
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