### Effect of measurement:

Effect of measurement:

Taking whatever happens in nature and transducing it to the point it is accessible to human senses

[or to the “senses” of some device that’s going “take action” based on what’s happening]

[or to the “senses” of some device that’s going “take action” based on what’s happening]

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EntityList["PhysicalQuantity"]

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QuantityVariable["Pressure"]

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Pressure

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,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

#### E.g. pressure

E.g. pressure

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### What is the destination for the measurement?

What is the destination for the measurement?

#### E.g. direct human senses

E.g. direct human senses

#### Measurement: turn things into numbers?

Measurement: turn things into numbers?

### Another definition of measurement: filling in parameters from the world into a predefined model

Another definition of measurement: filling in parameters from the world into a predefined model

For “mathematical models” the parameters tend to be numbers

### Measurement is evolving to some “attractor” that represents a “thing we understand”

Measurement is evolving to some “attractor” that represents a “thing we understand”

### The world has lots of details; we want to extract a symbolic description that we “understand”

The world has lots of details; we want to extract a symbolic description that we “understand”

#### Another operational definition: it leads to nerve firings

Another operational definition: it leads to nerve firings

### “Happening” is related to building up a entailment cone of consequences

“Happening” is related to building up a entailment cone of consequences

### The measured vs unmeasured case:

The measured vs unmeasured case:

Without “measurement” you have some system and all its details matter to the future

With “measurement” the only causal consequences are ones in the “measured attractor”

With “measurement” the only causal consequences are ones in the “measured attractor”

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ArrayPlot[CellularAutomaton[184,RandomInteger[1,50],20]]

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ArrayPlot[CellularAutomaton[90,Last[CellularAutomaton[184,RandomInteger[1,50],20]],20]]

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BlockRandom[SeedRandom[24425];ArrayPlot[CellularAutomaton[{FromDigits[Tuples[{1,0},7]/.{l3_,_,l1_,c_,r1_,_,r3_}:>If[If[c==0,r1+r3,l1+l3]+c>=2,1,0],2],2,3},RandomChoice[{.5,.5}->{1,0},1000],500],ColorRules->{0->Hue[0.15,0.72,1],1->Hue[0.98,1,0.8200000000000001]},Frame->False]]

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BlockRandom[SeedRandom[24425];ArrayPlot[CellularAutomaton[{FromDigits[Tuples[{1,0},7]/.{l3_,_,l1_,c_,r1_,_,r3_}:>If[If[c==0,r1+r3,l1+l3]+c>=2,1,0],2],2,3},RandomChoice[{.6,.4}->{1,0},1000],500],ColorRules->{0->Hue[0.15,0.72,1],1->Hue[0.98,1,0.8200000000000001]},Frame->False]]

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BlockRandom[SeedRandom[24425];ArrayPlot[CellularAutomaton[{FromDigits[Tuples[{1,0},7]/.{l3_,_,l1_,c_,r1_,_,r3_}:>If[If[c==0,r1+r3,l1+l3]+c>=2,1,0],2],2,3},RandomChoice[{.4,.6}->{1,0},1000],500],ColorRules->{0->Hue[0.15,0.72,1],1->Hue[0.98,1,0.8200000000000001]},Frame->False]]

### Claim: statistical mechanical “measurements” might be of things that are basically additive

Claim: statistical mechanical “measurements” might be of things that are basically additive

The “measurement” is implementing a contractive mapping

The idea of number is a similar form of data summarization

### Contractive mapping: like identifying equivalence classes

Contractive mapping: like identifying equivalence classes

### Relation to foliations:

Relation to foliations:

A foliation is defining what events are “somehow equivalent”

#### Symbolic dynamics-like approach: take a state space, and partition it into equivalence buckets [AKA lossy compression]

Symbolic dynamics-like approach: take a state space, and partition it into equivalence buckets [AKA lossy compression]

Input: detailed raw data; output: which bucket / AKA which numerical / ....

#### Dynamics of measurement: involves time and/or involves “extent of the observer”

Dynamics of measurement: involves time and/or involves “extent of the observer”

## Purpose of observation/measurement/perception

Purpose of observation/measurement/perception

Take the details of some part of the world and equivalence/compress/attractorize them to some model which has a predefined structure “known to the observer”

## How do measurements work?

How do measurements work?

### If the state of the world is the same, the measurement will be the same [though consider QM]

If the state of the world is the same, the measurement will be the same [though consider QM]

### There is a measuring device ; and it is reused

There is a measuring device ; and it is reused

#### System is interacting somewhat weakly with the measuring device

System is interacting somewhat weakly with the measuring device

### Consider a manometer

Consider a manometer

Two fluids made of molecules; density of events is much higher in the “measuring device” fluid than the in the measured gas; viscosity of liquid higher than gas

### Human eye

Human eye

Several photons hit the photoreceptor [ultimately only one photon matters]

Some photons never make it to the photoreceptor

Measure: is it red or green?

### Imagine we wanted to make a universal measuring device ... out of certain components

Imagine we wanted to make a universal measuring device ... out of certain components

In WPP, if we could extract the causal graph we could measure everything

Given the causal graph, we know what energy is ; we know what length is

If we know MLT etc. then we can reconstruct everything.

If we know MLT etc. then we can reconstruct everything.

Imagine we have a region of causal graph .... can we evaluate its elementary physical dimensions

current ; luminosity ; amount ; temperature

[ number of electric charges ] ; [ number of photons ] ; [ number of atoms ]

[ ? temperature ]

[ number of electric charges ] ; [ number of photons ] ; [ number of atoms ]

[ ? temperature ]

### A-to-D converter

A-to-D converter

### What is measurable given a basis set of measurements?

What is measurable given a basis set of measurements?

p , p^2 [ momentum ]

{x , p } angular momentum

#### Given a certain set of measurements at a fixed time, what can we derive?

Given a certain set of measurements at a fixed time, what can we derive?

#### If we measure at multiple times, what else can we deduce?

If we measure at multiple times, what else can we deduce?

[ L^2 often associated with flow ]

#### Phase transitions as examples of continuous to discrete

Phase transitions as examples of continuous to discrete

### Measurable features of gas vs non-measurable....

Measurable features of gas vs non-measurable....

#### Software radio vs. XXXX

Software radio vs. XXXX

#### Lumped models are another example of equivalencing....

Lumped models are another example of equivalencing....

### Measurable quantities vs . all quantities [ cf computable reals ]

Measurable quantities vs . all quantities [ cf computable reals ]

### Measurability complexity....

Measurability complexity....

Locality is easier....

#### Consider molecules hitting a sensor : can one think of looking at properties of the gas as decoding a code...

Consider molecules hitting a sensor : can one think of looking at properties of the gas as decoding a code...

## Afterthoughts.....

Afterthoughts.....

#### Consider a membrane being hit by molecules...

Consider a membrane being hit by molecules...

It could be bizarrely distorted, or it could have a reasonable shape that “all moves together”