## What does one measure?

What does one measure?

#### Turn an aggregate effect into a number

Turn an aggregate effect into a number

E.g. pressure , temperature

#### Did something happen or not?

Did something happen or not?

E.g. Geiger counter

### Measuring e.g. mass or amount of substance

Measuring e.g. mass or amount of substance

E.g. balance measuring mass

cf A to D converter

#### Measurement by comparison

Measurement by comparison

Length, mass, time, ....

[ Is this rod longer than that rod? ]

#### Measurement by counting

Measurement by counting

[ How many rods does it take to cover this? ]

## In WPP everything is graph theoretic

In WPP everything is graph theoretic

#### E.g. time is a counting of events for an observer in the causal graph

E.g. time is a counting of events for an observer in the causal graph

#### E.g. energy is flux of causal edges

E.g. energy is flux of causal edges

## When can one measure?

When can one measure?

How much fluid is in the Great Red Spot?

We’ve got to identify an object about which we make a measurement

E.g. liquid has a definite volume; gas does not

E.g. solid has a definite length (as well as volume); liquid does not have a definite length

E.g. an electron has a definite mass, but it can have any momentum

E.g. what things have nontrivial expectation values in QM (e.g. distance from nucleus to an electron has meaningful value; orientation of a S electron does not)

#### What is the length of water flowing through a river?

What is the length of water flowing through a river?

Pressure is meaningful for a gas, not a solid

Length is meaningful for a solid, not a gas

For a liquid, there is potentially a meaningful distance between eddies....

E.g.

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RandomEntity["PhysicalQuantity",10]

Out[]=

,,,,,,,,,

Measured quantities need systems in which they are occuring

## Function of measurement: “standardize” some actual phenomenon

Function of measurement: “standardize” some actual phenomenon

#### Transform the phenomenon to something that we humans intrinsically sense

Transform the phenomenon to something that we humans intrinsically sense

### Pressure measurement

Pressure measurement

Transducing from properties of a gas to properties of a solid/liquid

Each individual molecule from a gas hitting a solid surface just has a small effect on the solid overall, as opposed to making a tiny pit in the surface

In a manometer ... one could have every gas molecule collision produce a local deformation in the liquid surface

For what coordinate system is the fluid surface in a manometer “easy to describe”

What about a manometer that is made of another gas?

As the “measurement gas” gets more and more nonideal, it becomes a more convincing measuring device

#### The fact that liquids and solids are useful for measurement is a consequence of our features as observers

The fact that liquids and solids are useful for measurement is a consequence of our features as observers

#### The position of the liquid surface is somehow robust

The position of the liquid surface is somehow robust

#### Set up a coordinate system to measure the position of the liquid surface

Set up a coordinate system to measure the position of the liquid surface

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ListLinePlot[Evaluate[Table[i,{i,0,1,.05},50]]]

Out[]=

In[]:=

ListLinePlot[Evaluate[Table[i+.1Sin[100t]+.1Sin[100Sqrt[2]t],{i,0,1,.05},{t,0,50}]]]

Out[]=

### Vision

Vision

Only works because there are blobs of light from things we consider to be objects

A random photon field would be incomprehensible to our brain

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RandomImage[]

Out[]=

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ImageIdentify

,All,10,"Probability"

Out[]=

0.352341,0.356241,0.356241,0.356253,0.356253,0.0121276,0.00436992,0.00391394,0.00386537,0.00386537

### States of matter

States of matter

Infinite number of dof all coherently work together to make something that can be classified as a state of matter....

In a definite phase, the system is characterized by a small number of e.g. order parameters

### Measurement is about taking a large number of dof and filtering to a small number of dof

Measurement is about taking a large number of dof and filtering to a small number of dof

E.g. for vision, we go from a photon field to object recognition

#### Fundamentally an observer wants to “make a decision”

Fundamentally an observer wants to “make a decision”

The observer has a bounded brain, so it’s got to reduce out most of the detail of the actual system

### Liquid is also basically “going to an attractor”

Liquid is also basically “going to an attractor”

## Metamodel:

1. system goes to an attractor

2. the observer can tell “which attractor” it went to

Metamodel:

1. system goes to an attractor

2. the observer can tell “which attractor” it went to

1. system goes to an attractor

2. the observer can tell “which attractor” it went to

#### Consider the case of all being cycles:

Consider the case of all being cycles:

#### This effectively has an invariant that characterizes the different “attractors”

This effectively has an invariant that characterizes the different “attractors”

Compare:

[[ need to find the attractor states here ]]

cf https://www.wolframscience.com/nks/p597--statistical-analysis/

## Measurement in the hypergraph

Measurement in the hypergraph

#### Use black hole formation to do your measurement

Use black hole formation to do your measurement

Above the Schwarzschild mass you’ll make a black hole; otherwise you won’t

#### Can we turn a state of the system into an “observer identifiable” “attractor feature”

Can we turn a state of the system into an “observer identifiable” “attractor feature”

#### E.g. from bubbling atoms of space, particles can emerge;

or from emes, identifiable axiomatic structures

E.g. from bubbling atoms of space, particles can emerge;

or from emes, identifiable axiomatic structures

or from emes, identifiable axiomatic structures

## Examples

Examples

#### E.g. scintillation counter

E.g. scintillation counter

lots of details of the ionizing particle and the crystal etc. end up just producing “the same photon”

#### E.g. semiconductor thermometer

E.g. semiconductor thermometer

Lots of detailed heat ... promotes electrons to the conduction band ... where they are easy to identify

#### E.g. rain gage

E.g. rain gage

The drop fall in many positions and patterns; but when they fill up the rain gage, it’s an attractor because the only thing that matters is the total volume of fluid

## Measurement: turning things into a recognizable “standard form”

Measurement: turning things into a recognizable “standard form”