Entropy in Information Theory and Dreaming

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.

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

Jut kicking a few ideas around ….

Nothing may come out of it…

Solving a “Problem” or Digging a Karmic Abyss?

There is no way that you can convince the cunning and the clever of the existence of karma nor of its consequences perhaps spanning lifetimes. The cunning imagine that they can always get out of gaol free.

The only way they can learn is by experiencing the karmic consequence of karma themselves. Karma cannot be taught it must be experienced and hopefully understood.

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It is up to you if you think the above is some hippie-trippy shit or not.

At the moment deep malevolence is being visited upon two countries, Iran and Ukraine. The justification for Iran is that the Israelis in particular do not want them to have nuclear weapons. The Americans have gone along with this reasoning.

What they are in fact teaching is the need for nuclear weapons.

“If we had nuclear weapons they would not bomb the fuck out of us…”

The message is crystal clear. Negotiations with the fickle do not work. A nuclear deterrent might.

I’ll postulate that neither the Israelis nor the Americans are winning friends. They do not care overmuch, they have the big arsenals.

It is just possible that in solving the “problem” of Iranian nuclear weapons they are digging a karmic abyss. A sore which will fester for generations to come. A short term “win” may lead to a never ending grievance and problem.

The cunning may think that decapitation works but it may give rise to a hydra.

There is no way that you can ever convince the cunning and the clever of the error of their ways. It is by definition impossible.


So many people seek a reactionary short cut, an ersatz, a convenient band aid solution which buys apparent time. All they are doing is giving time for the so-called problem to evolve and  grow. To use the Boris idea of Whack-a-Mole does not eradicate the cause. It merely deals with visible “symptoms”. If you are cunning you would back yourself to be able to keep whacking moles for ever. Eventually you may have way too many plates spinning in the air. The moles may breed.

Often avoidance digs the karmic abyss ever deeper. In the profound darkness of a karmic abyss you can easily lose sight of what caused the problem in the first place. The tendency when in a hole is foolishly to keep on digging. You are committed to the hole, the “solution”.

If you are on a spiritual journey the normal faulty reasoning of society no longer works. A supposed tempting shortcut is not wise, more often than not it is a temptation. A way of looking better and coming up smelling of roses abnegates responsibility something which is karmically poor. Karma does not care about your apparent kudos, importance or reputation.

Karma is about learning the authenticity of your Soul and aiming to live life thereby.

Quite often problems are made up in the mind and can be delusional. Self-importance and arrogance are core ingredients in many so-called “problems”.


Whenever faced with a quandary or a problem a useful question  is:

Am I solving an apparent “problem” or am I digging a karmic abyss?


Vajrapāṇi Avalokiteśvara Manjushri – Power Compassion Wisdom

The three perhaps best know Bodhisattvas are Vajrapāṇi Avalokiteśvara and Manjushri. They are thought of as the embodiment, in the Buddha field, of power compassion and wisdom. They can be thought of as the three principle esoteric monadic energies, will to power, love-wisdom and active intelligence. Ray one, ray two and ray three. After all compassion is detached brotherly love advised by wisdom and “wisdom” can be thought of as the active application of intelligence and knowledge.

These three are reflected in the Buddhas of activity.

Avalokiteśvara is the second ray Bodhisattva and an archetype of love-wisdom. He emanates compassion for all sentient beings irrespective of their own personal values and actions. He is om mane padme hum or the jewel in the centre of the lotus. He emanates through the palm chakras the essence of enlightened heart. Avalokiteśvara is the Bodhisattva of the Elephant dreaming class.

These three Bodhisattvas can be seen as the benevolent aspect of what might be otherwise termed deity. These are a kind of Buddhist and energetic trinity.

As an antidote to the spread of division, xenophobia and hatred, the quality of compassion is much needed to offset the nastiness now spreading.

This second ray love-wisdom is the ray par excellence of inclusive compassion. Compassion is not to be confused with gullibility for sometimes the needed medicine lacks sugar.

Right now when the axe of cleavage and brutal coercion is being wielded humanity is in dire need of wisdom and of love. There is a bit of a drought…

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om mane padme hum

om mane padme hum

om mane padme hum

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The Nature of Consciousness – Roger Penrose Dream 24-02-2026

Here is this morning’s dream had between 4 and 7 AM.

The dream opens with me conversing mind-to-mind or telepathically with another being. We are looking down at a gathering of Tibetan Buddhists, lamas. They are dressed in robes and at the edge of the gathering, very much at arm’s length is Charlie, a nagal’s courier.

I say-think, “unfortunately Charlie is not very bright, not very intelligent. He is not intelligent enough to realise that he lacks intelligence and therefore assumes that he knows correctly a lot more than he does. It is a common problem that people are not sufficiently intelligent to understand their own lack of a well-honed intellect. As a consequence there is adamant assertion without open critical thinking.”

“Yes this is true people assume they know and understand more than they do and can be dogmatic.” Is the reply.

I then look again at the gang or committee of lamas.

“The difficulty with the Tibetans is that they have a vested interest in being the world experts in meditation and consciousness. It is a part of their brand. They may indeed have studied Buddhist texts and the Tibetan canon and may be expert thereupon but their thinking is developed only in one area. They have not a diverse nor modern intellect. They are arrogant and not open to external thinking, they want to incorporate things into their perspective solely. It is not a two way street. They may be intelligent but they do not have a far reaching wide knowledge based intellect incorporating science. In short they are a closed shop and stuck in their ways. They are not approachable in any meaningful way because they must be, in their eyes, the experts. They do not understand that they are insular.”

I go on.

“There is a limit to so-called pure consciousness. It needs grounded and generalised via an expansive and inclusive intellect. The latter word inclusive being of great importance. There is nothing you can do when people do not have the intelligence to understand that their intelligence is limited and closed off. You cannot explain to someone something about which they lack the intelligence to understand or encompass. It is by definition almost, an impossible thing.”

“Yes. Sometimes you can only go so far.”

“There are jhanas, states of consciousness and expansive awareness, past what most of these have ever perceived. There is no way that you can convince an expert.”

The scene changes and I am in a medical / dental consultation in Edinburgh. I am with a man who is slightly older than me, his post doc researcher and a couple of younger graduate students. He is a psychologist – neuroscientist and wearing a white lab coat. He has grey wispy hair and spectacles. His postdoc is Hispanic. She has long very dark hair and is wearing blue jeans and a hoody, hood down. They are making some measurements on my brain using electrodes. I am sat in what looks like a dentist chair.

I am explaining to him that the problem with neuroscientists trying to understand consciousness is that they lack the training in meditative technique. They have no understanding personally of the states  they are trying to measure. They are measuring like blind men who have never been there. It is like making a map of a land which they have never set foot upon. The intellectual understanding of consciousness is limited therefore to rational supposition. Only a truly great intellect could “hold” and understand these states without direct personal experience of being “there”. A mind would have to be very versatile and expansive yet well controlled and quiet.

I say that maybe I should talk with Roger Penrose about the nature of consciousness.  He perhaps might understand and get the gist. If one verbalizes a state of consciousness well one can “take” another mind “there” at least partially. One can build a “picture” which might be partially shared and imagined.

The guy is initially interested.

I ask him that given he is a psych-neuro would he like to collaborate with me and Roger Penrose on a book? He no longer has to worry about his career as he is essentially emeritus.

He  thanks me for the invitation but he does not believe that I can add anything beyond what “they” the neuroscientists already know. He declines. He thinks that I am waffling.

I think that he does not know that he does not know. His intellect will not understand how limited his understanding is nor where his knowledge ends...

I awake; the dream ends.

Regional Nepotism in Buddhist Narratives ?

Although my mother, when  sun tanned could negotiate discounts from the Indian traders in the market in Gravesend, I am not of Indian nor Asian genetics. If she wore a sari and a bindi she could pass as Sikh. Yes one could say the Celtic migration had a terminus in a valley to the South East of Snowdown. I was however born a ginge…

As an outsider I note how many so-called previous lives of Buddha are in the general geo-location of Northern India – Himalayas- Afghanistan. He is often a prince and sometimes Brahmin. I note that the vast majority of Tulku rebirths are in Tibet – Nepal – North India – Bhutan area. If not there then there must be some familial nepotism.  Tulku begets tulku out of some follower or nun. I have never heard of a Viking incarnation. Once Buddhism spread East we did not get a sudden burst of Icelandic Bodhisattvas. The streets of Rio were not awash with them dancing at carnival.

My scientific mind notes this discrepancy. It seems unbalanced.

Surely a Bodhisattva reincarnating for the benefit of all sentient beings would not restrict themselves geographically or demographically?  Global impact in isolated countries high up in the mountains is not likely to be high. Skilful means suggests ploughing other wider fields.

There is a kind of perhaps spiritual snobbery. After all the Vedas and Buddhism predate Christianity and Islam. Only the pilgrim skilled in meditation, asceticism and vegetarianism can get enlightened. Beer and twice cooked chips are verboten, interdit. Turmeric is a must.

It is illogical that someone should only be born in the same geolocation if they are to garner a wider experience. If you have not tried rollmop and aquavit…you have missed something.

This for me seems slightly problematic in the around the camp fire tales of Buddha. The other problem I have is with the notion of many Buddhas stretching back millennia. The human vehicle was according to archaeology not as intellectually advanced and capable. All those millennia ago it did not look human.

How could a Buddha be Neanderthal?

There is an evidenced based narrative chronology which errs from the verbatim understanding of canon and Mahayana canon more so. If these are meant to be metaphor and parable, there is less problem.

Nevertheless is seems strange that Buddha only hung out there or thereabouts…

A Shed Load of Rinpoche(s)

Following on from my various dreams I have been looking at internet based information on Tulkus and Rinpoche types. The first comment is that there are shed loads of these. There seems to be a pecking order.

In some circles it seems that their words are hung upon and that they may be put on a pedestal. On-line there is controversy about iffy teacher-student practices. This provokes heated commentary and in some cases attack. It seems very emotive.

Looks like a minefield to me.

Academic practice in the UK has changed considerably in the last few decades. In the past people used to get shit-faced drunk and there was “intermingling”. This is frowned upon these days. Though no doubt some non standard interaction continues. Many academics marry students…

If people want to check my academic credentials feel free…

Based on what I am reading it looks like a barge pole jobby. That is steer well clear…

I know that I don’t know but I am now less inclined to find out. I am not glamoured thereby.

Some Rinpoche dudes get to meet presidents of countries…

If you are famous and well known you can charge a few hundred dollars for online courses…

The comment that I have in general is that a lot of the teaching material on line is of a somnambulance inducing length. It would not pass muster at a modern higher education establishment. The presentation skills need polish and focus is better than rambling…

It reaffirms for me that “guru yoga” is dangerous both for the acolyte and the guru. It also suggests that the time for gonadal basal yoga is passing. That stuff is old…wrong century…

It has been interesting having a good read around. The “discussion” on line reminded me of the Sutra below.

This idealism in which people are deified and then crucified for their failings remains a problem not just in religion. A well loved star can be cancelled and lambasted on the whim of an allegation. The worshipper takes no responsibility for the down fall of the previously worshipped.

I don’t know what those hundreds if not thousands of Tulkus and Rinpoches are doing with their lives.

They can’t all be angels…

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The Sutra Preached By The Buddha On The Total Extinction Of The Dharma

(Taisho Tripitaka 0396)

The Buddha was silent, and made no response. After Ananda had repeated the question three times, the Buddha told him, “After my nirvana, when the Dharma is about to be extinct, the Five Mortal Sins will foul the world, and the demonic-way will flourish exceedingly. The demons will become monks, to spoil and wreck my Way. They will wear lay dress [rejoicing in cassocks] and multicolored clothing. They will drink wine and eat meat, killing living things in their desire for fine flavors. They will not have compassionate minds, and will hate and envy each other.”

“At times, there will be Bodhisattvas, Pratyeka-buddhas, and Arhats, who cultivate merits diligently and treat all beings with reverence; being the objects of the people’s devotion, they will impartially preach and convert. They will pity the poor and keep the old in their thoughts, and take care of those in poverty and difficulty. They will constantly persuade the people to worship and serve Sutras and images, doing all good acts that bring merit; their wills and natures will be kind and good. They will not harass or injure people, but sacrifice themselves to save others. They will not spare themselves, but will put up with insult, being benevolent and harmonious.”

“Should there be such a being, the gang of demonic monks will unite in hating him, slandering him and blazoning forth his errors. He will be expelled and banished; they will not let him remain at that place. From then onwards, they will all fail to cultivate merit according to the Way. Temples will be empty and desolate, and will no longer be repaired, but will be allowed to fall into ruin. The monks will covet nothing but material goods, accumulating them without distribution, not doing good deeds. They will deal in male and female slaves, plow the fields and plant them, burning off the mountain forests and harming all living things; they will not have compassionate minds. Male slaves will become monks, female slaves will become nuns; they will have none of the merit that comes from practicing the Way, but rather will be filthy and depraved, foul and turbulent; men and women will not be kept separate. The reason the Way will become shallow and weak, is all because of that type of person.”

Impermanence – Cop Out or Motivation?

The trouble is you think you have time...

Siddhartha Gautama

I have paraphrased here something I read in the Dhammapada. In this the notion that there is always tomorrow or mañana and demain is hinted at. People can put things off over and over. This especially  true of anything which is inconvenient. Even though they know that they need to address something they put it off. People can justify inaction to themselves rather than put themselves out or do something positive perhaps transformative. The safety of the unpleasant status quo of life is so tempting; the inertia of sameness is like a duvet. The fear of risk forbids any reward for courage.

It is evident that life is impermanent. Everyone without exception dies. Which means that allotted time is finite.

It is easy to fall into the trap of “hey man all is impermanent” and use that as a cop out for not doing anything. If nothing lasts, nothing matters, so why bother? If  all of life is an illusion then why interact, why take part?

It is easy to take an overly passive view on karma. If everything is pre-ordained and fated because of past actions why try to ameliorate? That is a gist of karma. At some stage you have to interact in a meaningful way to work with your karma and acquire karmic merit. You have to learn the lessons that karma has in store and which you have selected for yourself by your actions. Karma is there to teach. You need to learn your lessons otherwise you repeat your folly ad infinitum.

Impermanence teaches that you have little or no time in which to act and yet you must not be obsessed about result or outcome because these are not permanent or real.

It is easy to get the balance wrong and be overly dismissive and fatalistic or to try to force things to fit how you want them to be and thereby create more karma. If you put things off you are deciding so to do. Procrastination cannot work on karma.

You have no time, much less leisure than you imagine, so get busy but do so without obsession or desire for guarantee. Impermanence teaches that all forms of obsession are folly. It also teaches that you have little time to figure out what it is you need to learn and then to seek out those lessons.

In any given life, time is not a luxury which one in reality has.

Copping out because things are impermanent is copping out, it is a form or “reasoned” and “excused” inertia and avoidance.

Whereas impermanence might encourage you not to waste a single second of your allotted time.

Working with impermanence as a fact to acquire skill and discernment is a very profound and meaningful practice.

Impermanece teaches balance and the middle way.