Model – Dreamyoga

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This from Wikipedia

Entropy { Information Theory}

In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable’s potential states or possible outcomes. This measures the expected amount of information needed to describe the state of the variable, considering the distribution of probabilities across all potential states.

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Entropy in information theory is directly analogous to the entropy in statistical thermodynamics. The analogy results when the values of the random variable designate energies of microstates, so Gibbs’s formula for the entropy is formally identical to Shannon’s formula. Entropy has relevance to other areas of mathematics such as combinatorics and machine learning. The definition can be derived from a set of axioms establishing that entropy should be a measure of how informative the average outcome of a variable is. For a continuous random variable, differential entropy is analogous to entropy.

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Introduction

The core idea of information theory is that the “informational value” of a communicated message depends on the degree to which the content of the message is surprising. If a highly likely event occurs, the message carries very little information. On the other hand, if a highly unlikely event occurs, the message is much more informative. For instance, the knowledge that some particular number will not be the winning number of a lottery provides very little information, because any particular chosen number will almost certainly not win. However, knowledge that a particular number will win a lottery has high informational value because it communicates the occurrence of a very low probability event.

The information content, also called the surprisal or self-information, of an event E is a function that increases as the probability of an event p(E) decreases. When p(E) is close to one the surprisal of an event is low, if p(E) is close to zero then the surprisal of an event if it occurs is high.

There is zero surprise when the probability is one.

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Are dreams high entropy?

What happens when p(E) is close to zero?

And do dreams contain information of high informational value?

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On and off over the years I have had “intuitional discomfort” about the notion of quantum superposition states. Is it physics or our description of physics? Are we making an ersatz by making a quantum supposition, a sticking plaster for some deeper physics we do not yet understand. It does look a bit of a hotch-potch.

Quantum physics has a God-like quality which dare not be questioned…

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From Microsoft Quantum

Superposition is a fundamental concept in quantum mechanics, describing the condition in which a quantum system can exist in multiple states or configurations simultaneously. Classical bits can exist in two possible states, typically labeled as “0” and “1”. In contrast, because a qubit is a quantum mechanical system, it can exist in the “0” state, the “1” state, or any state that is a linear combination of 0 and 1.

Mathematically, superposition is a linear combination of “0” and “1” and can be written as:

|ψ⟩ = α|0⟩ + β|1⟩

where |ψ⟩ is the state of the qubit, |0⟩ and |1⟩ are the basis states (or the computational basis states), and α and β are complex numbers called probability amplitudes. The probability amplitudes determine the probability of measuring the qubit in either state when a measurement is made.

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Is the prepared qubit then “natural” or have we imbued it with information which we have decided for it in our labelling. This labelling presupposes no extra physics. A photon might have vertical polarisation, horizontal polarisation or if paired a superposition of both; horizontal and vertical as opposed to horizontal or vertical.

Unless the superposition is somehow aware of our labelling how does it know how we expect it to behave?

If one of a photon pair is measured as horizontal it must communicate that information instantaneously to its erstwhile twin.

Is it physics or information?

A good question.

How much entropy is associated with that information?

If the superposition collapses on measurement then in an idealised physics the probability of the other pair member “knowing” its state is one. It has little informational value as it comes as no surprise.

If eigenfunctions are used to prepare a description of a quantum supposition then they must have a difference in the set of quantum number qualities to be eigenfunctions. They may be energy eigenvalue degenerate in isolation but because of the difference in quantum number that degeneracy must be split, if only slightly under some condition or other, which means that they do not share entirely equal probability on being prepared into a superposition.

The qubit will have a tiny inherent bias.

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I keep getting this sense of discomfort that there is something we are not getting and that we are happy sitting with an intuitionally uncomfortable quantum superposition description…it just seems cobbled together.

It is a bit of a mind fuck…

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Do dreams bring real world information?

If so is it surprising and of high informational value?

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I have just re-read a dream of mine from 2008 in which I see a Breton landscape and am chatting with an extroverted French man who is the spitting image physically and in behaviour of my recent physiotherapist.

Was this information, coincidence or my confirmation bias retro-fitting a dream to a current observable?

If dreams do indeed carry information then the implications of this are high.

I personally will trust what my dreams say about a situation over and above what a human being may or may not assert. If there is good physical evidence I will trust that over dream…

This notion of surprise as being a component of information {new} is interesting. The concept of information entropy in a world of fake news and a verbose Trumpian professor, is appealing.

Information and opinion are not the same. It is possible to speak for a long time without giving any reliable information which comes as no surprise. Were there to be anything new {and reliable} that would be very surprising and information rich.

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Any description or model must occlude at least partially an occult reality of some kind. Because we do not know the true and extensive nature of that reality we can at best describe it. Such a description must be informative and allow a measure of prediction as to the measurable evolution of events in space-time. We should be honest that our description is not ultimate truth. Behind all known physics there is always something occult, unseen and as yet unknown. History teaches us this

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Jut kicking a few ideas around ….

Nothing may come out of it…

I speculate that many like to “win” an argument and be “right”. Some dread being demonstrably wrong. But the diamond sutra advises against seeking the absolute…

Our schooling demands answers which correspond in alignment to the quasi-consensual mark scheme. I have seen “A” level students marked wrong because, even though their answer was correct and accurate {according to my expert opinion}, it did not comply with the dogmatic mark scheme prepared by the thought police. Straying from the agreed dogma yields a poor grade and can prohibit further education.

There is an ethos to conclude, to be right, and to want to know where one stands. People can seek certitude when in fact there is none. They may misconstrue adamant assertion with accuracy and broad applicability. In fact, over simplification can be very attractive. There is a bit of laziness. Many rely on the imagined omniscience of “they”. If the herd deems it so, then it must be. Individual thinking and the expression thereof can lead to prompt and irrevocable social isolation.

One of things, I like to do is to take some kind of conceptual framework and then apply it to my life, to see if there is any fit. I don’t do this in a quantitative way rather I try it on like a moccasin. If it appears to fit as a thought experiment, I note the fit and then like a child with a sandcastle rub it out. I am really not fussed if I am right or wrong, nor with the quality of fit. I am fluid and don’t need fixed descriptors nor to be corralled by a conceptual framework. I am mindful that were the outcomes of these experiments accurate and those within the framework aware of this, implications might follow. Some of these within the model could be wide ranging.

Some might find this annoying.

“Tell me the answer!!!”

I also like the idea of all or nothing situations in which there is no negotiable middle ground. Herein lies a problem. Whenever I mention that I do not negotiate people immediately see it as a negotiation strategy which it is not. I am not responsible for the perceptions and conclusions of others. If they like to interact transactionally via negotiation, they may transfer their preference onto their interpretation of me. They may see me through their lens, which may have aberration and distortion.

Which model, which thought experiment applies? The answer is quite a few.

It would be very easy to characterise me as a spendthrift quasi-functional alcoholic who threw it all away, and as a result is a socially isolated loser eking out his end of days in self-induced poor health.

This model has only a very local implication and using Occam’s razor, paraphrased:

Entia non sunt multiplicanda praeter necessitatem.

As a model which fits it is the simplest and the best.

Therefore all other models are speculations and by way of embellishment.

People like complexity and may not be satisfied, though it is possible to leave things here with this characterisation. My (our) physical plane life does not impinge beyond a small geographical radius and a set of healthcare professionals. I very rarely travel more than 35km in radius. I have only travelled more than 150km once in six years.

There is no need to invoke any other explanation. I have played with various alternatives.

This then is a nothing situation, a null, a default

There are various other interpretations which may be a tad more grandiose, but although there is a hint of applicability, they are inconsistent with observable circumstance. These interpretations may further be inconvenient. Any model must have use or else it cannot be tested thus a theoretical possibility remains speculation and likely to fade into the mist. There is no point developing a use-less model, when viewed from one angle. Inconvenience is also not a desired property of a model. This can lead to jettison.

Reductionist thinking can limit but it also simplifies.

The thought experiment in the absence of tangible and measurable data often leads back to the null or near null hypothesis, which is the safe conclusion.

We all often unconsciously apply the model or bias which suits us best, which is easiest for us to assimilate and has little inconvenient implication for us.

Tag: Model

Entropy in Information Theory and Dreaming

A Fondness for Thought Experiments