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Emergence and Evolution of Meaning

The GDI Revisiting Programme Part II: The Regressive Perspective: Bottom-Up

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“The way up and the way down is one and the same”

Heraclitus of Ephesus “Όδός άνω καί κάτο μία καί ώυτή”

Hermeneutical circle

The regressive perspective: bottom-up

• 0. The case of perception

a) limits b) Direct and inverse EM problems

• 1. Direct problem (dimensionality question)

a) Forward formulation b) Sampling theorems c) Forward problem

• 2. Inverse problem (interpretation question)

a) Forward formulation b) Sampling theorems c) The limits of observation

• 3. Interpreting reality

a) Reactive b) Reflexive c) Perspectivistic

Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

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The limits of our perception

1° We only perceive surfaces Huygens Theorem 2° Every angle around the object is necessary Uniqueness Theorem 3° The discernible details of a thing are not smaller than  Sampling Theorem 4° In case of no sensibility to phase, spatial perception is through the

• bservation at 2 surfaces feasible

Phaseless Uniqueness Theorem

Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

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The forward- and the inverse problems

The forward Problem

Maxwell laws

The inverse Problem

Huygens-Schelkunoff Theorems

S

11 qeqm J M

 

x z

?

D

y x

S D

y z

?

ET  

} , { } , {

dimesional

• 2

linear,

H E M J      ?

Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

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Unicity and Equivalence theorems

Equivalence Theorem Unicity theorem [E1,H1] [E2,H2] [E, H ] no energy crosses through D

Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

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Forward formulation

Vector potentials A and F (D’Alambert-Eq.):

                S S S S

• utside

inside ) (

• utside

inside ) (

2 2 2 2

r M F F r J A A    

) ( ) , ( ) (

2 2

r r r r          G

) ' ( 4

) ' (

r r

r r



 

R e

R j





) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( r r M r r r M r F r r J r r r J r A G v d G G v d G

V V

               

 

 

   

) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ ) ( ~ r r M r F r r J r A G G      

A F H F A E                                 1 1 1 1

2 2

j j

Convolutional solution: Fields E, H:

F

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Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

Forward Formulation

(real sources)

v d J J J z z R G R G y y z z R G x x z z R G z z y y R G y y R G R G x x y y R G z z x x R G y y x x R G x x R G R G E E E

V z y x z J y J x J

                                                                       





) ( ) ( ) ( ) )( ( ) ( ) )( )( ( ) )( )( ( ) )( )( ( ) )( ( ) ( ) )( )( ( ) )( )( ( ) )( )( ( ) )( ( ) (

2 2 1 2 2 2 2 2 1 2 2 2 2 2 1

r r r

R j

e R R R j j G



   



      

3 2 2 2 1

1 4 ) ( r r

R j

e R R βR j j G



  



     

5 2 2 2 2

3 3 4 ) ( r r

S

J

D

x y z ) ( ) ( r J r G E J  

J

) ( ~ ) ( ~ ~ r J r G E J  

J

F Only electrical currents: F=0

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Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

Forward Formulation

(equivalent magnetic sources)

) ( ) ( r M r G E  

M M

) ( ~ ) ( ~ ~ r M r G E  

M M

F

S D

x y z M

s d M M M x x y y x x z z y y z z R G s d R G E E E

S z y x S z M y M x M

                                                                      

 

 

) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ' ( ) ( ) (

3 3

r r r r M r r

R j

e R R j G



 



   

3 3

1 4 1 ) ( r r Only magnetic currents: A=0

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Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

Sampling theorems for radiating fields

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Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

Theorem 1: The minimal distance between independent

intensity values of a field generated by an arbitrary

• bject is λ/2.

Theorem 2: The maximum number of details of an object, inscribed in an sphere of radius a, which is causing an

• bserved field distribution is 16 π(a)2. This is the

essential dimension of the observation problem. Theorem 3: The minimal distance between independent values of the field corresponding to the manifestation of an object inscribed in a sphere of radius a, whose centre is at a distance d, is: d/2a.

Forward (discretized) problem

• Phenomena observed at D (u,v)

corresponding to a set of sources

                                                    ) , , ( ) , , ( ) , , , , ( ) , , , , ( ) , , , , ( ) , , , , ( ) , ( ) , (

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 N N N N N N M M M M N N N M M

z y x z y x z y x v u G z y x v u G z y x v u G z y x v u G v u v u f f       

Green equation x’, y’, z’  u, v

Source (object) Observation domain

Phenomena Source

                                             

 

 

) , , , , ( ) , , , , ( where

1 1 1 1 1 1 n n n M M n n n n N n n N n M M

z y x v u G z y x v u G ψ ψ    ψ ψ Ψ f T

n n

f f

Wave function

Direct problem (manifestation of reality)

f T     

 n

f

N n n 1

ψ Ψ

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Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

• A good way to suit our problem (to be

invertible) is locating N punctual sources over S regularly spaced at a distance λ/2χ

          

projection

f T

OBSERVED

Ψ Ψ

   

. projection . 1 projection

, min ] [

OBS OBS

d Ψ Ψ f T T T T f

f

    

  

• Which can have a unique solution.

Inverse problem

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Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

1. A Finite Number of Details related to the object can be found. 2. Such number depends on the surface bounding the object. 3. The volumetric distribution of an object cannot be known only based on its manifestations on the environment. 4. The description of the object that can be achieved corresponds to a projection of the inner inhomogeneities over S.

• Fundamental limits to the observation problem, not related to

sense structure, but to the differences that can be found

• Related to the maximal a posteriori knowledge
• ComplexityObject can be > Complexityits Manifestation

The limits of observation

Given Unknown

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Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

The meaning-offer of observation vs perception

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Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

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On the search of the electromagnetic reality

“Faraday, in his mind's eye, saw lines

• f force traversing

all space where the mathematicians saw centres of force attracting at a distance...” J.C. Maxwell

• The more complex the sensitive structure, the greater

the ambiguity of its perception and the more accurate the determination of the object.

• The cell has several means to sense the environment and

to adapt to those variations which are relevant for its survival

Interpreting reality (reactiv)

flagellum nucleolus nucleus

photoreceptor

chloroplast contractile vacuole

eyespot

paramylon pellicle

flagellar swelling

• Protovision of the Euglena

viridis:

brightness (high/low), direction

• Animal vision:

accuracy and ambiguity

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Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

Interpreting reality (reflexive)

a) regular hole or irregular coloured protuberance b) irregular protuberance or regular coloured hole

• The preferred perceptions tend to be those corresponding

to the simplest configurations (Ockam’s razor)

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Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

• nto-epistemic information

Reality itself Complex Structure of perception and intellection

+

unitary act: sensing reality

 transcendence (openness)

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Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

Generalized method of successive projections

Perspectivistic approach to reality

Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

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Perspectivistic approach to reality

• Is False Information no information?

Contradictions(within epistemological level), p = 0

• (Floridi-GDI) I = 0? ∊ Epistemological closure
• We need new models, thus I↑ ↑ ∊ Epistemological openness

Oppositions (between significance and reference), p > 0

• (Floridi-GDI) I < 0? ∊ Pragmatic closure
• They might give information about the kind of pragmatic

situation in which the opposition appear (e.g. there is no communication cooperation) ∊ Pragmatical openness

Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

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• Maxwell counted with following partial relations:

– Coulomb  E = Q/r  div E =  – Ampere & Bio-Sabat  ∮H = I/r  rot H = J – Faraday  ∮E = dФ/dt rot E=dB/dt – He founds out 

Id = dE/dt  rot H=dE/dt

• Einstein saw the need to reconcile Newton mechanics

and Maxwell relations

Reconstruction of EM reality

rot H = dE/dt + J rot E = dH/dt div E =  div H = 0

Emergence and Evolution of Meaning: GDI revisiting programme - Part 2: regressive perspective – Bottom-Up

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Is information a sufficient basis for cognition?

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This work is subject to a Creative Commons Attribution- Noncommercial-NoDerivativeWorks 3.0 Spain licence. This work is free to copy, distribute, display, and perform under the following conditions: Original author credit must be provided: Díaz Nafría, J.M. and Zimermann, R. (2011). Emergency and evolution of Meaning. (Presentation). Milton Keynes: DMD2010; Commercial use, altering, transforming, or building upon this work is not allowed. The full licence can be consulted on: http://creativecommons.org/licenses/by-nc- nd/3.0/es/deed.es