Galois Theory, AGI, etc

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TITL:
   *Galois Theory as Applied to the Hypothesis*
   *of AGI Terminal Extinction Risk Mitigation*
   *By Engineering Methods*.
   *By Forrest Landry,*
   *September 9th, 2022*.

ABST:

A summary of the method by which one can know
   that AGI Convergent Extinction cannot be prevented
   by any 'error correction' or 'safety protocol' or
   'design practice' of/for/on any future AGI.

TEXT:

We claim that it is 100% possible to know, now, today,
   that it is 100% impossible to 'align' AGI,
   and/or to establish/create any viable notion of 'safe' AGI,
   to within any reasonable limits
   and over any ethical timescale,
   using any present or even any future possible
   technology, means, or method.

We are using the term "impossible" in two ways:.

- 1; That the change and risk of a failure
      of AGI alignment/safety
      that has human-species-wide-lethal outcomes
      is strictly and asymptotically convergent toward *certain*
      over sufficient time
      (hundreds of years, as an outside limit,
      and potentially much much faster/sooner),
      and that it is strictly impossible,
      given any reasonable definitions of AGI, etc,
      for the nature of this trend to be otherwise.

- 2; That we fundamentally cannot
      obtain, have, or establish by any means,
      (ie, that it is impossible to obtain, etc),
      any sound and valid statistical guarantee
      that the probability of the failure of AGI alignment/safety
      over any reasonable ethical long term
      (ie, for example; a few hundreds of years)
      is guaranteed to be constrained at or below
      some reasonable percentage X,
      as an upper maximum allowable bound
      on the chance/risk
      of human-species-wide-lethal outcomes.

That a good way to express the overall result is:.

- 1; where given AGI (as defined/characterized by @B);
      that there is,
      unavoidably,
      an overall inexorable convergence
      towards total human/economic/ecosystem extinction
      over the moderate long term
      (one or two centuries); and;.

- 2; it is fully knowable (today)
      that this total future extinction convergence
      cannot be shifted
      by (on the basis of)
      *any* combination of
      *any* current or future engineering methods --
      ie, that AGI simply cannot be made "safe"
      for any real meaning of that term.

A characterization of how it is possible to know
   and be formally assured of
   the logical entailment and necessity of statement @1 above
   has been at least partially documented elsewhere,
   and is therefore beyond the scope of these summary notes.
   Herein we are concerned with a brief description
   and explanation of the means by which
   we might also formally and fully know @2 above.

The technique of our proof is akin to Galois Theory --
   ie, that the span of the kinds of problems
   that specific sets of operation types can solve is limited.
   Galois theory provides a means by which
   a formal proof can be obtained
   that not all types of tools
   can solve all (types of) problems.
   That when given a definite known tool-set,
   or any possible extensions of just that tool-set,
   that there will always be some (important) problems
   that are fundamentally inherently unsolvable
   with any combination of the techniques/methods given.

There are aspects of the Godel Theorem in this also:
   While *some* tools can solve *some* problems,
   that this does *not* imply that there is,
   or can be, *any* hypothesized 'total set of tools/techniques'
   that can 'solve all problems' --
   ie, that there is not any finite set of tools ("Axioms")
   that can solve all possible problems (ie; "identify all truths").
   Partly, our result is also based on Shannon Entropy and
   on at least two distinct varieties of complexity theory.
   There is even an indirect connection with Bell's Theorem,
   which on the basis of a strict necessary inequality,
   can show that certain features of reality
   are either accounted for in any theory of physics,
   or are not, (to the failure of physics).

Galois Theory goes somewhat farther in providing a "meta-technique"
   (or in our case, an exemplar meta-meta-technique)
   by which, given a definite finite set of tools,
   we can absolutely characterize,
   in the hyperspace of all possible problems,
   the exact boundary between
   which problems are solvable with that specific toolkit,
   and which are not.
   Similarly, this implies that,
   when given a specific definite problem,
   that we can know in advance
   whether or not a given set of specific tools/techniques
   will *ever* be able to solve that specific problem --
   or whether any such effort is an exercise in futility.
     - for example, see (@ Galois Theory https://en.wikipedia.org/wiki/Galois_theory) for more information.

Here are some summary notes based on the above Wikipedia article:.

This way of thinking (about the limits of the extent of
      the use of the common algebraic mathematical operators)
      began with some very old classical geometry problems,
      which were attempting to be solved with just the tools of
      a compass and a straightedge: 'squaring the circle',
      'doubling the cube' and 'trisecting the angle'.
      These sorts of puzzles were explored and attempted
      by thousands of thinkers over more than a thousand years,
      all without success (@D).
      A later exploration of the means by which
      these sorts of problems
      might potentially be better understood and solved,
      using the more powerful mathematical tools
      of algebraic and analytic geometry, etc,
      eventually became more fully generalized
      in the question:.

> Does there exist a formula
         > for the roots of a fifth (or higher) degree polynomial equation
         > in terms of the coefficients of the polynomial,
         > using only the usual algebraic operations
         > (addition, subtraction, multiplication, division)
         > and application of radicals (square roots, cube roots, etc)?.

It turns out, via the Abel-Ruffini theorem,
      that there are equations (examples were given)
      for which such a solution (a formula) cannot exist.
      Galois Theory goes further by describing exactly the boundary
      between what sort of equations are possible to be solved
      with just these operations,
      and why it why it is just not possible
      (ie; is strictly/logically impossible)
      to use just these operators
      for most (the vast majority) equations of degree five or higher --
      ie, equations which are generally describing
      of anything with even moderate complexity.

Our interest is:.

- 1st to notice that *all* of the effects/methods of engineering
      are based on *only* the application of the principle of causation,
      as modelable by *only* some combination
      of mathematics and/or computer science (@A),
      and that;.

- 2nd, it is fundamentally inherent
      in the nature of the modeling process itself
      (ie, as a/any combination of a definite set
      of logical/physical operators/operations),
      on both a real physical and on a mathematical level,
      that there are hard inherent limits
      on what can and cannot be modeled/predicted,
      and that therefore;.

- 3rd; that there are definite and inherent limits
      on what sorts of outcomes (or characterizations of outcomes)
      can be achieved
      using *any* combination of engineering,
      causative modeling, mathematical, or algorithmic process (@C),
      and finally;.

- 4th; that the problem of "ensuring that AGI is safe/aligned
      to within some low/reasonable X% of risk of total extinction"
      is strictly within the set of unsolvable/impossible problems
      given any possible combination of any extension
      of the named operators and problem solving techniques.

:Notes:

- $A; where observing; that the following is a formal IM triple
   necessary and sufficient to the practice of 'engineering':.
     - physics (as pure immanent, when in 1st person).
     - mathematics (pure omniscient; always is 3rd person).
     - computer science (applied transcendent; 2nd person).

- $B; that the notion of 'General Artificial Intelligence/agency'
   specifically implies:.

- 1; multiple diverse domains of sense and action
     (as an inherent requirement of the notion of 'generality').

- 2; intrinsic non-reducible possibility for self modification
     (as due to the multiplicity of domains of sense/action,
     and of the inherent inter-relationships of these domains).

- $C; where from the above, that therefore:.

- 3; that the meta-algorithm
     (the learning/adapting/changing process)
     is effectively arbitrary (and thus subject to
     Halting Problem and Rice Theorem type limits);
     (where based on unknowable complexity dynamics
     of those domains, via micro-state amplification, etc);
     hence;.

- 4; that it is _inherently_undecidable_ as to whether
     *all* aspects of its own self agency/intention
     are fully defined by *only* its builders/developers/creators.

- $D; never under-estimate the degree to which
   some population of male engineering type persons,
   due to unconscious evolutionary drives and biases,
   inherently wants to have something to prove,
   and that when/upon hearing that something "is impossible",
   will strive unceasingly to "be the one" who does the impossible --
   and is "right" when "everyone else is wrong".
   Hence we end up with any number of people
   attempting to do 'over unity' perpetual motion machines
   and/or to demonstrate and actually make
   various mathematical (or engineering) impossibilities.
   Unfortunately, such actions in this case --
   attempting to make a long term "Safe" AGI --
   must be treated as as criminal act,
   equivalent to global genocide
   and so must be maximally socially circumcised/taboo/shunned,
   whether explicitly by national/international law,
   and/or by some sort of strong popular prohibition.

:menu

If you want/need to send us an email,
   with questions, comments, etc, on the above,
   and/or on related matters, use this address:

ai@mflb.com

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