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# Pattern recognition : indistinguishability of the word objects

M Michel Troublé

► To cite this version:

M Michel Troublé. Pattern recognition : indistinguishability of the word objects. 2023. hal-03973620

HAL Id: hal-03973620

https://hal.science/hal-03973620

Preprint submitted on 4 Feb 2023

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# 1 Pattern recognition : indistinguishability of the word objects

2 M. Michel Troublé :

3 * Nuclear industry : AREVA (Department of Advanced Researches : AI and Robotics)

4 * Orsay University - Institute of Nuclear Physics (PhD)

# 5 1. Summary :

6 The question is the following : can the numerical mechanisms of the ‘pattern recognition’
7 lead to the creation of sensory-motor structures that would be *self-organized* as are the
8 *living beings* that ensure in any circumstances the perenniality of their structure confronted
9 to a multiform environment that can only degrade them.

10 We demonstrate that the objects of the world that are perceived through measurements are
11 physically *indistinguishable* from the point of view of any other system that may produce actions
12 and this regardless of the properties that can be attributed to these objects. This is what we call the
13 ‘indistinguishability theorem’.

14 By virtue of the ‘indistinguishability theorem’, an *autonomous* robot that should, in our
15 image, always ensure the durability of its structure in the face of an environment that could
16 only dissociate it, given the entropic degradation of the universe that affects all inert
17 structures, is physically unfeasible.

18 2. Introduction

19 ‘Pattern recognition’ is a set of techniques that aim to identify the forms of objects from their
20 characteristic parameters in order to make decisions depending on the categories attributed to
21 these forms. ‘Pattern recognition’ is consequently a central issue in Artificial Intelligence and
22 Robotics which are essentially *sensory-motor* systems composed of *sensors* and *actuators*
23 (locomotion or gripper systems, displays) which are connected to each other in such a way that the
24 actions resulting from perception of the objects with which they interact, respond adequately to the
25 functions assigned to them.

26 In order to evaluate the relevance of the *categorizations* made by a ‘pattern recognition’
27 mechanism applied to *sensory-motor* structures provided with an Artificial Intelligence, we carry
28 out the ‘functional analysis’ of a thermometric measuring device of familiar use, a thermostat.

29 The functional analysis that allows to determine the solutions of connections between the
30 thermometric *sensor* and the *actuators* of a thermostat, is an analysis that must necessarily
31 be « out of subject ». This analysis has to determine the natural solutions of connections
32 between *sensors* and *actuators* which, « in the absence of any living being », could be
33 established spontaneously in view of the physical laws.

34 **Experimental device**

35 A thermostat (see Fig. 1) is made up of the following elements : a *sensor* (a thermometer),
36 *actuators* that turn on a ‘radiator R’ and an ‘air conditioner C’. The environment of the
37 thermostat is assumed to be only ‘hot’ or ‘cold’.
<figure><img src="image_2.png" /><figcaption>Fig. 1. Thermometric device</figcaption></figure>

Two photocells **CA** and **CB** – only sensitive to the specific shape of the mercury meniscus in the capillary tube – are positioned at two points **mnH** and **mnB** of the capillary which correspond to the two possible extreme positions reached by the meniscus depending on whether the thermostat environment is ‘hot’ or ‘cold’.

When the thermostat environment is ‘hot’ and the measurement is complete (the mercury column is stabilized) only the **CA** photocell is activated because the mercury column is in the high position **mnH**, i.e. an output signal **S1** = **1**, with **S2** = **0** (the **CB** photocell is not activated). For a ‘cold’ environment, only the **CB** cell is activated because the mercury column is in the low position **mnB**, i.e. an output signal **S2** = **1**, with **S1** = **0** (the **CA** photocell is not activated).

The states of the outputs **S1** and **S2** (**0** or **1**) of the **CA** and **CB** photocells are therefore the images of the thermal states in which the so-called ‘hot’ and ‘cold’ environments are found.

In all generality, there are logically two ways - and not only one - to take into account the totality of the information available at the two outputs **S1** and **S2** of the thermometer so that this information is transmitted for actions to the two actuators (**Radiator**, **Conditioner**):

* Consider each of the two outputs **S1** and **S2** individually.

* Take into account both outputs **S1** and **S2** simultaneously, i.e. two possibilities : - the logical combination {or} between the two outputs, i.e. $S3 = [S1 \text{ or } S2]$.

- the logical combination {and} i.e. $S3 = [S1 \text{ and } S2]$. However, since the mercury meniscus cannot objectively be simultaneously in the upper (hot object) and lower (cold object) positions, the combination $S3 = [S1 \text{ and } S2]$ is always identically null and therefore only the combination $S3 = [S1 \text{ or } S2]$ remains.

– Provided with an « out of subject » thermostat which is thus made up of the 3 outputs **S1**, **S2**, **S3** of its *sensor*, a technician then carries out the experiment described below which consists in connecting the 3 outputs **S1**, **S2**, **S3** of the *sensor* to the two *actuators* (**Radiator** and **Conditioner**).

The ‘rule of thumb’ followed by the technician is then the following : the **Radiator** and the **Conditioner** must be switched on when the room temperature is low (object ‘cold’) or high (object ‘hot’) respectively, in order to meet the functioning that is expected from a thermostat.

To carry out this operation in an exhaustive way - as Nature would spontaneously do in the absence of any human being - the technician, following a probabilistic approach, then constructs the Universe of all possible events (as in ‘game theory’), i.e. the implementation of 4 ‘natural’ thermostats which are equally probable, by connecting the outputs **S1**, **S2**, **S3** to the actuators.

**thermostat n°1** consisting of the following two connections :

- connection between the **S1** output and the ‘Conditioner’.

- connection between the **S2** output and the 'Radiator'.

**thermostat n°2** consisting of the following connections :

- connection between the **S1** output and the ‘Conditioner’.

- connection between the **S3** output and the 'Radiator'.
77

78

thermostat n°3 consisting of the following two connections :

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- connection between the S3 output and the 'Conditioner'.

80

- connection between the S2 output and the 'Radiator'.

81

thermostat n°4 consisting of the following two connections :

82

- connection between the S3 output and the 'Conditioner'.

83

- connection between the S3 output and the 'Radiator'.

84

The technician then checks whether the experiment he has implemented from the four equally probable 'natural' thermostats, in order to eliminate any arbitrary choice of connections, meets the objective that has been set : (1) the 'Radiator' should be switched on when the thermostat environment is 'cold', (2) the 'Conditioner' should be switched on when the environment is 'hot'. To this end, the technician successively presents a 'hot' object and then a 'cold' object to these 4 different thermostats and notes their different responses :

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■ 'hot' object, hence the activation (e.g. at 1) of outputs **S1** and **S3** (I. 56) :

91

thermostat n°1 → <u>Conditioner on</u>

92

(due to the **S1-Conditioner link** - I. 72)

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thermostat n°2 → <u>Radiator and Conditioner simultaneously in operation</u>

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(due to the **S1-Conditioner and S3 Radiator link** - I. 75 and 76)

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thermostat n°3 → <u>Conditioner on</u>

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(dû au lien **S3-Climatiseur** - I. 79)

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thermostat n°4 → <u>Radiator and Conditioner simultaneously in operation</u>

98

(due to the **S3-Conditioner and S3 Radiator link** - I. 82 and 83)

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■ 'cold' object, hence the activation (e.g. at 1) of outputs **S2** and **S3** (I. 56)

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thermostat n°1 → <u>Radiator on</u>

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(due to the **S2-Radiator link** - I. 73)

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thermostat n°2 → <u>Radiator on</u>

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(due to the **S3 Radiator link** - I. 76)

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thermostat n°3 → <u>Radiator and Conditioner simultaneously in operation</u>

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(due to the **S3-Conditioner and S2 Radiator link** - I. 79 and 80)

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thermostat n°4 → <u>Radiator and Conditioner simultaneously in operation</u>

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(due to the **S3-Conditioner and S3 Radiator link** - I. 82 and 83)

108

## Summary of responses from the 4 thermostats :

109

■ With the presentation of the 'hot' object :

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thermostats 1 et 3 : <u>Conditioner on 2 times</u> (I. 91 and 95)

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thermostats 2 et 4 : <u>Radiator and Conditioner on 2 times</u> (I. 93 and 97)

112

■ With the presentation of the 'cold' object :

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thermostats 1 et 2 : <u>Radiator on 2 times</u> (I. 100 and 102)

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thermostats 3 et 4 : <u>Radiator and Conditioner on 2 times</u> (I. 104 and 106)

115

Objects which are qualified as 'hot' and 'cold' by the technician, are therefore both *different* by the fact that the 'Air conditioner' as well as the 'Radiator' are **switched on separately twice** on the 4 thermostats, but also *identical* because the 'Air conditioner' and the 'Radiator' are **switched on simultaneously also twice** on the 4 thermostats.

116

117

118
Consequently, the ‘hot’ and ‘cold’ objects that interact with the thermostat are therefore statistically *indistinguishable* as regards the actions they can entail on the two *actuators* whatever the properties attributed to these deux objects, since the thermometric *sensor* of the thermostat is physically *unrelated* of any other possible *sensor* (the gravitational attraction between the elements being totally negligible at our scale).

What is noteworthy, the fundamental *indistinguishability* of the macroscopic objects of the world
revealed by an experimental demonstration performed on a thermostatic device, is the logical
extension of the *indistinguishability* of particles in ‘quantum mechanics’, which microscopic
particles are at the origin of the existence of all macroscopic objects whose properties we measure.