L, for Liberty, and autonomy

1. Introduction

That is a concept elaborated in 1978, evoked in an article in 1979, and first published in "L'informatique libère l'humain" (L'Harmattan, 1999).

L is of material importance, since its gives a teleonomic autonomy to any digital being, but evidently in proportion to its level of being. An individual bit has no other autonomy as to stay as it is, or to beak its clock rhythm. A living being or a developed robot have intentions and sub-goals as far as their knowledge systems and behaviours allow and structure it in levels.

Everything gravitates around autonomy. For code as well as for economics. Autonomy gain through externalization: control of the environment, being given (legal) assurances. But any external extension is also source of dependency.

Autonomy increase:
- efficient: motor, automatic feeding, batteries; sensors to detect and adjust the paper feed etc.
- material: lighter processes, dematerialization; but also freedom from a definite place
- formal: from form to program, genericity. and digitization (Gutenberg)
- final : robot intentions

2. A formula for liberty !

To express the autonomy of a being, as well as its dynamic substance, state function and dynamic variety, we propose the formula :

where p_t is the probability or existence at instant t and p_i the probability of state i, among the n possible states at time t. Then L is the sum, or the integral, of the mathematical expectation of neguentropy.

As we shall see, liberty proper comes from the combination of a formula and its non total computability.

3. First comments and explanations

We have chosen L for "liberty".

Indeed, the first part of the formula (which we shall refer to as P) translates the first basis of any freedom : to be, to exist. The material freedom, so speaking.

The second member (which we shall name H) gives the entropy at each instant, and the absence of constraints to choose one or another state. To be free is to have the choice. And the wider and less constrained it is, the greater the liberty.

This formula expresses the permanent conflict opposing subsistence to free choice.

This formula expresses also the freedom of a being in respect to the other beings, and to GOS: P measures the fact it is here to stay, for some times. H expresses its unpredictability.

This formula has good sides :
- it relates to the concepts of variety, entropy and energy, and hence to information theory and to formal automata;
- H evokes at least a similitude with Heisenberg's uncertainty ;
- P may be taken as an actualization rate, if related to finance and more generally to economic calculus.

It makes a kind of synthesis of information, energy and money.

4. Causality and freedom

In the deterministic hypothesis, we can find some forms of liberty inside (to be checked). But, in general, we wont like it. Then, we have several options :
1. We assume that we still have subsets, and the problems of random and then of liberty will always be, in fine, transmitted to a large set, which we could call God, if we give to this being the character of a transcendent person ;
2. We assume that, beyond a given size, and certainly for a possible encompassing set, there are necessarily chances, indecidability, and then that some form of liberty is possible inside. (We are near the Digital Relativity). That may play on bit count of a given being, or in being count. But, here the number of dimensions of the universe is central, as it plays on distances.5. Freedom is progressive >

5. Freedom is progressive

A key point: Thesis : Liberty is not a binary value. The World must not be parted between free and unfree beings. All beings are, up to a point, free and controlled by the others.

Degrees of liberty for an industrial robot

Intuitive examples of application

1. The autonomy of a vehicle measures as well the duration of operation without refuelling as the distances accessible. Both terms are tied by speed. They are confused if speed is constant, they differ if sped is variable or controllable. In this case, there is a possibility of arbitration between a long but rather slow travel and a shorter but speedier one.

The paying load may also be considered as a form of variety, with arbitrations between load and range.

2. A control loop preserves the existence of a system and avoids its destruction. It tends to keep it back to a middle point, from which variations are possible in both ways, when dissymmetry appears when one is farther from it. Then this regulation maximizes liberty, in some manner. That is present in living beings as well as artefacts, and is the core or cybernetics.

3. Classical games like chess and checkers tend to eliminate the adversary. But they can also be seen as the conquest of an unbarred use of the whole terrain. And intermediary steps stress the importance of strategic points control for moving freely/

4. The delimitation of a proprietary space by a system is a compromise : the space is limited, but within the limits, freedom is total. And peace with the neighbours favours security.

5. The various elements of a corporation balance sheet may be considered as liberty resources as well as of survival. Income maximization, when it is not distributed to shareholders, increases the corporation autonomy (cash flow, investment capacity).

A way to elaborate is to deal separately with H or P, and even there to limit oneself to some part (short or long term for P, reduction of constraints or variety augmentation for H). Another ways:
- an organic structuration of L: liberty degrees, memory capacities, implicit parts of the hardware (to be defined)
- a functional structuration, more interesting at the end of the day, with banalization of the underlying hardware, but also a hierarchization of functions (primitives, macros, sub-programs ...).

6. Graphic representation of L

The value of one parameter at a given instant can be represented as a binary string of appropriate length (logarithm on base 2 of the number of state), padded if necessary.

Note : In fact, at a given moment, the states are fixed (but possibly unknown by an external observer). What is more interesting is the possible states at the next instant...

Note: it seems pertinent, for an intuitive appreciation of L meaning, to order the bits from left to right according to their variability.  We can then use the concept of "surface without borders" or Ruyer since, in any measure can be taken as a string of indefinite length, like a number, with the comma at the centre. Only some digits near the comma are meaningful.

This is rather evident for the right end bits. Written in the customary manner, the extension to the right relates to more precision in the measure. The more precise it is, the more fluctuating, then meaningless. For instance, the length of a metal rod, at a standard temperature, is practically constant up to the hundredth of millimetre, but after that changes with any warming and cooling. For the majority of current life rectangular beings, for example a table top, length and width cannot be precisely defined under the millimetre, since they are not machined with a better precision.

At left, after meaningful digits, a number aligns implicit zeroes. But, for a number of measures, that is a convention. For example, if we give a position in space-time, we can use few digits because we refer to a well chosen origin : sea level, Notre Dame de Paris for road distances, Jesus supposed birth for years...

To complete this view, we can present the successive states of the systems in the F function as a series of parallel lines that can be placed, for intuitive understanding, placed in a kind of perspective.

(What about a negative L...suffering ? )

7. Notes on H (neguentropy at a given moment)

For simple devices, H is practically their number of bits (or log2 of the number of their different states), weighed by an evaluation of the equiprobability of the states.

That is the neguentropy or energy in each instant
- first, intuitive notions : widen the space (materially), the range ;
- better use of space, with recognition of new differences, analysis and description, thinner resolution of the look and of the reflexion, avoiding noise (and dust..)
- number of states / equiprobability ; hence the H paradox : increase the differences... Or become indifferent ? Hence the need of a concept like "meaningful difference".

The field so drawn is suggestive enough to call for more structuration. Anyway, we have seen that any long string needs structures. We can separate
- fields with little variation, stable, constituting the being skeleton
- fields with large blank spaces, or liquid, where liberty can deploy itself, leant against the stable fields.

In the large fields, narrower ones may be defined.
L will grow mostly with field independance/orthogonality : money was first by exchange, then metallic, then paper, then purely electronic.

Too large fields are inefficient.

In some way, the centre of the line locates a good potential difference.
Safety demands large numbers. Reliability is a low failure probability, with refers (at least potentially) to a large number of tries. What the insurance companies do between the insured people, or genetics with spermatozoids, is not without relation with a large number of meaningful figures on my bank account.

These reserves are material, both for P and H. In other words, if S disposes of an indefinite width in bits, it must find a sensible distribution between wide and narrow fields. The creation of wide fields is a guarantee of survival, but is paid by a lack of meaning (meaningful differences).

At each instant (cycle ?) it is by a deployment of the strong structures of its free fields that S will adapt itself to the external world and to bloom. As the strong structure compressed in the seed, crushed by the demanding pressure of the humus gives way to the blooming of a rich plant and its golden spike, in the broad and wide Beauce fields.

But this splendour has a cost: blooming exhausts the free spaces, and rich structures wither. But not without having borne the germ for a brighter future. chanteront.

Note here that rarity is not necessarily a positive value. beings need both rare and common matter, water as well as diamonds. And a balance between them. Improbable is not always to be wished.

The being aims to regulate the right part in order to ensure the persistence on the left. From this standpoint, the centre will move, since the variability at left will decrease, expressing an elevation in L.

H is also an index of unpredictability for the outside S; The IEO formula may be taken as an external model, and L globally as a kind of resistance to the environment. H expresses E+I (+O) size, the place physically reserved by S, while P expresses time expectancy when S will keep it for itself.

Somehow, the maximum of separations is nearest to the big bang, when plasma organizes itself uniformly in elementary particles. The whole game of grouping which follows appears as a reduction of the number of "bits", let atoms drop into heavier and heavier constructions, less and less free. Anyway, from a strict physical standpoint, History seems to go slower. After the frantic activity in the fist fractions of seconds just after the bang, some billions of years see galaxy indefinitely unrolling in a universe larger and larger, but also more and emptier.

In fact, the true divisions, those who matter, are intentional. S will progressively emerge while generating life. The atomic cut is only the reverse side of the truly important one, which looks for itself through DNA as soon as Earth is borne (and perhaps even before), which makes itself more perceptible when vegetal and animal life come to activity, and which is really borne when mankind begins to mark up his space and to cut silicon zones. And it blossoms with the Greek science, get uselessly stuck in religions, and refinds itself to day out of Internet. And it will dome day go beyond Mankind itself.

Any entity enhances its autonomy, is structural richness as well as its lifespan on both ways :
- by taking if out of other entities, which are captured, absorbed, merged, assimilated, or simply destroyed to save material space;
- by cooperation, win-win, and for that building more and more sophisticated relations, at the bases with a trimming of entity to entity distance.

That happens as well in the mineral life (inter atoms distance in the molecules), vegetal and animal (population density in a biotope), psychological (animal security distance, human distance between families), or properly digital with its specific distances, especially in digital relativist models.

Indeed, to live its independence, any entity demands, around its borders, a sufficient amount of not structured space, so that environmental moves do not perturb too much. That has to be compounded with the price to pay for the synchronization organs in autonomous units.

One difficult issue remains to be settled: compounding the L of different entities when they cooperate. Some ideas have been given for instance by Condorcet (when he shows that insurance is profitable both to the insured and to the insurer) or by Titli (distributed control theory).

France ages pyramid in 2016.

8. Notes on P (life expectation)

P is the life expectancy of the being. Energy consumption may be considered as a shortening of P, for instance.

Our beings cannot be immortal, at least have an infinite number of cycles. If so, their L would be infinite or their H rapidly nearly vanishing.

The formula depends strongly on the time slicing. The slicing could be :
- internal (clock cycle)
- external (another beeing clock, or the global clock, if that is meaningful)

Can S change the rate of its clock, for instance ? Here we should study conversions between cycle length and variability. Probably, when I increase the clock rate (supposing that we have a reference to a deeper one...), variability will decrease, or become meaningless after some limit. That may be compared with the right part in the H line.

Any computation of P implies hypotheses
- on the nature of perturbations brought by the environment
- on the P of S parts.

According to the results, strategies will be widely different. A closed system, strongly protected, does not need to invest in Defense. It can concentrate on H to reduce its constraints (for humans, democracy, games, learning). But it cannot increase its vital space (a notion to define...). Example: gas in a closed room. Pushed to the limit : death.

Nevertheless, even closed, the system may have quasi-indefinite aptitudes to develop its information system, and tends to increase H by reinforcing the meaning of small differences (sophistication) or by opening itself to rather useless processes (discussion about angels sex...).

On the other hand, if H changes little, and the S cannot change it, it will concentrate on its P horizon.

9. H-P arbitration and compositing

S has to arbitrate between H and P. More freedom today reduces the life expectancy, but also the freedom expectancy for tomorrow. However, there are also positive feed-backs. Examples:
- buy P against H: insurance policy,
- buy H against P: chance games,
- identity/safety dialectics, (Cyrano de Bergerac),
- association and cooperation with other systems.

The maxima in L are probably far from extreme choices in favour of H or P.

Another paradox : S cannot chose to die, even to suicide, that is a major limit on its H. Could we find a computation to show when suicide is finally an augmented L for the S ? With for instance a strongly widened H during the period between now and the planned suicide/death time ? Can we build suicidal beings ?

For biological type beings, P and H are framed by the development stages, from conception to old age through education and maturity.

 

Note scolastique. Du libre arbitre chez Thomas d'Aquin

Summa Theologica. Question LXXXIII . De libero arbitrio. Articulus primus.

Utrum homo sit liberi arbitrii.

Respondeo dicendum quod homo est liberi arbitrii: alioquin frustra essent consilia, exhortationes, praecepta, prohibitiones, praemia et poenae.

Ad cuius evidentiam, considerandum est quod quaedam agunt absque iudicio: sicut lapis movetur deorsum; et similiter omnia cognitione carentia. Quaedam autem agunt iudicio, sed non libero; sicut animalia bruta. Iudicat enim ovis videns lupum, eum esse fugiendum, naturali iudicio, et non libero: quia non ex collatione, sed ex naturali instinctu hoc iudicat. Et simile est de quolibet iudicio brutorum animalium.

Sed homo agit iudicio; quia per vim cognoscitivam iudicat aliquid esse fugiendum vel prosequendum. Sed quia iudicium istud non est ex naturali instinctu in particulari operabili, sed ex collatione quadam rationis; ideo agit libero iudicio, potens in diversa ferri. Ratio enim circa contingentia habet viam ad opposita; ut patet in dialecticis syllogismis, et rhetoricis persuasionibus. Particularia autem operabilia sunt quaedam contingentia: et ideo circa ea iudicium rationis ad diversa se habet, et non est determinatum ad unum. Et pro tanto necesse est quod homo sit liberi arbitrii, ex hoc ipso quod rationalis est.