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…

Following the footsteps of a rag doll dance…

Not all cultural references are directly transferable some are “time of life” and others are “time of man” related.  I personally view myself as being on the conservative side in that outwardly I am not outlandish. It always used to amuse me how the “goths” had less of an idea of the shadows than I did.

But Siouxsie et al. were definitely a part to the soundtrack of my life.

In the “A Discovery of Witches” TV series the notion of the main protagonist being spellbound has come to the fore. In which her parents cast a spell which both hid and prevented the usage of her powers. She was literally bound by spell or spell bound. The narrative suggests that this practice was usually reserved for insane witches and that it was a harsh thing to do, to prevent the person from living to their full potential, to inhibit and otherwise hinder them. The back story is that the “creatures” are forced to hide from the discriminatory humans and their notions of normality. Humans are depicted as prejudiced. The story also has “time-walker” as a top echelon witchcraft skill. A lot of the plot revolves around “powers” of a magical and special kind. Power ever being the motivator for political intrigue, shenanigan and skullduggery. Somehow Diana is able to summon an old text which may or may not hold the secret(s).

In physics a lot of stock is made upon observables and making an observation. If one in any way makes an observation one changes the system. For example if one “observes” a photon using a detector that photon changes the energy state of an electron. The photon ceases to be. The energy has been transformed from one thing to another. At a very local and very tiny level every act of observation changes the system.  Science rhetoric is less explicit as to the nature of interpretation and subsequent assimilation caused by the observation, the act of observation. One could say that the observation of a “handful” of particles in a science experiment can have a truly dramatic and wide ranging impact because of interpretation and assimilation to or with a previously held thought form or model. I might infer that a photon is the witness to an act of proton transfer. My observation hints at a physical process. Any observation changes the system and it cannot be undone. If I talk about it down the pub that handful of photons triggers synapses and a train of thought heads off on whichever trajectories.

I have always had a few problems with the notion of time travel because of observation. It is impossible to travel back in time without altering its forward propagation. Although pleasant as an artistic and entertaining notion it is philosophically tricky. {Ok there may be some time reversal events at sub atomic levels that I am unaware of but these may be mathematical legerdemain}. In terms of karma time travel is also problematic.

In my mind it raises an interesting thought line. “Does reminiscence alter the past or merely our recollection and narrative assimilation thereof?” We do not travel back in time to the acts of perception but how we retell what we “remember” does change our futures because our basis for world interpretation has altered if only slightly.

If for example you held a view that I was a complete bastard and you hated my guts, then any future interaction would be coloured by this framing. If on reminiscing you decided I was only a partial bastard then you have already changed the future. Your change of mind changes the future(s).

Time-walking may be seen as a reinterpretation of events previously observed. Bearing in mind that the apparatus of observation must of course be error prone and never 100% accurate. Not all instruments are sensitive nor well calibrated. We do not actually go back in “physical” time rather review our mental registers of how we have constructed the time evolving narratives. We could re-consider, re-view and possibly re-perceive. Much like an astronomer may apply correction factors to space telescope raw data. There is some “algorithm” which enables (perhaps) a more reliable assimilation. We may refuse to apply said algorithm because we are stuck in our ways and like to cling to old perceptions, prejudices and world views.

The quantum mechanics of a 75kg lump of wet proteins and fats going backwards {or forwards} in time do not seem plausible. Perception and “mind” however are clearly much less physically tangible. In a sense these may be able to travel along what might be called time-registers. In the absence of matter time has no meaning. In a sense time as it is measured is a property of matter (vibration or time to travel between spatial coordinates). How we currently measure time is by the observation of photons in a fancy physics rig.

To extrapolate wildly by measuring time we are changing our futures.

Diverse Intellectuals – Seer Time – Philosophical Dead Ends – Dream 22-10-2025

Here is last night’s dream had between 4 and 6:30 AM. I should note that I am on nocturnal low dose oral opium for the hip pain and have been for several weeks.

It starts in an urban setting on a terrace outside some kind of clubhouse or bar. I am with a man who is younger than me maybe forties. We are having a beer at a pub style table. I understand him to be an intellectual, a university professor of some sort. He is animated and has set me up with various meetings around campus. His accent has a very faint American lilt. He has crazy unkempt grey hair with partial male pattern baldness. From his random hair I guess he is Jewish of extraction. He has a satchel with papers. We are discussing models of the universe and I comment that nobody has data before the big bang and that I prefer a cyclical universe model. I am pretty sure that this is not the first universe and that this is consistent with the Vedas. He says there is no need to invoke prior universe. He says that he has lined me up with a busy day and that we should meet up later. He is a bit like the mad hatter running late. He means well and is jocular and friendly.

He leads me off to a mid-multi rise building which is an office block he wants me to meet someone there. She is a psychology-philosophy cross over academic. We get to her office which is clean and immaculate. More top end business than nutty professor. He leaves me with her. She is tall of Germanic demeanour with mustard brown immaculately pressed slacks and an expensive green silk shirt. She is interested in evidence for the psychology of the soul. It is a non-publishable sideline interest of hers. I explain some of my views. She says that she would like to have more discussions with me later that evening. She takes my left hand and places it between her legs on her pubis. I can feel her genitalia. I withdraw my hand. I ask if that is on offer later and she says that maybe it is. She does not understand that I am no longer fussed about sex. She is completely relaxed and unfazed, sex to her is no big deal, a kind of work out. She is pretty formidable and focussed clearly on what she wants.

The scene changes and I am introduced to a small more geeky-nerd come woman with dark hair. She is a professor in game theory and logistics. She and I start to talk about games of logistical journeys. On top of an empty upturned beer barrel she has a simulation of a game for a delivery. She shows me. I explain to her that I have not the faintest idea what game theory is. She moves onto to poker. She says that she can mentally calculate the odds of each hand from current position of play. I say that such a thing would bore me and take away the fun. I say that were I to play I would do so intuitively. Her eyes light up. She is fascinated by the statistics of intuition and is convinced that it is a real phenomenon. She suggests that we have a few hands of draw poker later.

She leads me off to a laboratory building in which I meet a tallish man dressed in a M&S style navy jumper and blue chinos. He is clearly some kind of physicist. We start talking a bit about ultrafast and he maintains that time is a very important thing. I say that time is subjective and nowhere near as objective as he imagines it to be. From the point of view of a seer, time can be expanded or compressed. Perception and time are a part of the same phenomenon. I explain that highly skilled martial artists and sports people can slow the time so that it is perceived differently from others. That is why a 100 mph tennis ball is easier for them to hit. From a seer’s perspective time is like a tram line along which one can place perception at will and this includes far into the past. The physics of time around the putative big bang was very much more nonlinear than it is imagined today.

The physicist takes me to a different part of the building. We are in an atrium outside a lift when the doors open and out flounces a tall man with and expensive long leather jacket and longish hair. With him is a younger acolyte whom I know to be his student and homosexual lover. The man in leather is a well-known published  philosopher. I think to myself that he is a right knob, a bell-end and pretentious. The physicist is also not a fan. I am led off into an office with sofa and armchairs. Alone with philosopher and acolyte we start to discuss. He drops names like a machine gun. I say that in my opinion philosophy as a discipline is at a dead end, stuck. This is because one has always to compare back to previous lines of thought and endlessly refence the development of thought over millennia. Who cares what people thought before modern science? Philosophy is therefore stuck in a bad time warp. He thinks me an uneducated uncivilised heathen and I think him a bell end.

The dream ends.

Alice & Bob – Quantum Jobs

Prompted by the answer to a question on University Challenge, I typed Alice and Bob into the font of paid for promotion previously known as a search engine. The Mecca of product placed wisdom came up with a French quantum start up called Alice and Bob. They have received 100 million series B funding. They also have a fairly extensive job vacancy list. It was a tad French and probably not overly attractive internationally except for those fond of Alice in Paris Francophiles. French job descriptions can be as rigid as a rigid thing. They do not travel well.

Maybe there is a general shortage of quantum savvy job applicants….

It occurred to me that the Quantum hype has been drowned out by the deafening AI roar. Maybe it has gone submarine like AUKUS.

That Luddite Herr Trump has been threatening the Harvard intellectual property (IP) portfolio. What a great way to ensure the death of US inventiveness and technological superiority, discourage invention and application for patents unless they are handled by MAGA lawyers, toadies and sycophants!! Already the incentive to NOT have an idea whilst at a university is high, because contractually the university owns your IP. Best stifle ideas until you are a free thinker…

Sometimes holes can be difficult to get out of. That can include ways of thinking and playbooks.

It looks like Herr Trump is going to try again to leverage Ukraine into accepting a fait accompli agreed with Vlad the Impaler in Alaska. This forceful manipulation is an old Trump play. If he keeps alienating people, he may find himself in a hole like increasingly Billy-no-mates Israel. Trump does not understand that “friend” has a different meaning in KGB speak.

Oh look another groundhog…where did that come from….

What is the first rule when you find yourself in a hole?

Human beings can be pig-headed and stubborn. Inventive people do not share the same deal or no deal mentality as realtors. They are easily discouraged and disincentivised. One day the straw goes on the camel’s back, one too many.

Sometimes that tired old play book simply does not work. Thinking the same way that gets you into a problem cannot help to get you out of it.

There is no point in trying to explain this to someone who is vehemently adamant that they know best. Advice is as unwelcome as a dose of antibiotic resistant syphilis.

Some people are obsessed at the notion of a “corporate” solution when none exists. They may get all their ducks in line to present someone with a fait accompli sure that such a thing is irresistible. Even so-called intelligent people like professors can think like this. They can seek within group consensus oblivious that people outside the Olympian Ivory Towers do not think like them. This may not occur.

It is quackers.

People often talk with the monkey and ignore the organ grinder completely…

Anyway…

Has AI killed off the notion of quantum computation?

Where will they put all the server farms?

Is this what our future looks like?

Gedankenexperiment – Quantum Telepathy or Quantum Telekinesis

In the background I have been mulling over whether to attempt to draft a patent application concerning quantum telepathy as it might be applied to the current groovy quantum area. This morning between a sleep and waking a question appeared to mind, “Quantum Telepathy or Quantum Telekinesis?”

I’ll make an initial comment.

It is safe for me to publicly publish my speculations on-line because in no way can they detrimentally harm any career of mine at some august institution into which I might have been sectioned under the mental health act. I am free to make a fool or an arse of myself because it cannot negatively impact on tenure or promotion.

There has been a lot of interest in things called parapsychology among the public if not academia. Taboos remain. The notions of telepathy and telekinesis have not yet been proven extant, though they are found throughout culture and in some cases religion. We have Professor Charles Xavier and the X-men, we have spoon benders. In Buddhism we have Abhijñā or higher powers.

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Abhijñā

In the Pali Canon, the higher knowledges are often enumerated in a group of six or of three types of knowledge.

The six types of higher knowledges (chalabhiññā) are:

  • “Higher powers” (iddhi-vidhā), such as walking on water and through walls;
  • “Divine ear” (dibba-sota), that is, clairaudience;
  • “Mind-penetrating knowledge” (ceto-pariya-ñāṇa), that is, telepathy;
  • “Remember one’s former abodes” (pubbe-nivāsanussati), causal memory, that is, recalling one’s own past lives;
  • “Divine eye” (dibba-cakkhu), that is, knowing others’ karmic destinations; and,
  • “Extinction of mental intoxicants” (āsavakkhaya), upon which arahantship follows.

From Wikipedia

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Your common or garden scientist is unlikely to have much credulity for these, though the script writer might. There have been experiments to test extra sensory perception using inter alia Zener cards.

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I don’t know about you, but these images a very boring, I could have used the F word in participle here. Who in their right mind would be excited to transmit or receive these? Not me, YAWN.

If you were to construct an experiment on telekinesis without Magneto you might want to start with the tiniest measurable change, something with a vanishing mass something like 1×10−18 eV/c2. In other words photons. If the mind can move anything or change anything then photons are a good starter for ten. They move quick but don’t weigh much.

In the field of quantum technology one branch pertains to spontaneous parametric down conversion. In this a single photon is “destroyed” “annihilated” and two daughter photons are “created”. Momentum of all types ought to be conserved. Under low light level conditions these daughter photons can be created in a quantum superposition state. Where their polarisation is a mix of horizontal and vertical polarisation, that is until said state in measured. If you measure one photon to have vertical polarisation then the other must have horizontal polarisation. The quantum superposition state collapses. The two photons somehow have information about the state of each other. This transfer of information is a faster than  speed of light thing. One photon says on measurement, “hey, I am vertical” and telepathically the other photon knows “I am horizontal.” The photons have a mind of their own and unless they are really clever, they do not know how we label them or describe them.  They do not care what we think or how we describe.

The photons could, to stretch things, be said to be in telepathic rapport with each other.

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At the single photon level the notion of polarisation is a bit tricky. Polarisation is a wave-like, multiphoton, phenomenon.  It describes how a bunch of photons pass through a selective physical device. There is a bit of magic between the descriptions of single photons and the more bulk properties, perhaps a grey area of science in the statistics of low particle count number. A single photon may fail to pass through a polarisation gate which means that its twin photon is allowed to go through, to get past the bouncers and into the night club. If the first photon is not on the guest list, its twin must be.

The physics when carried out over many events predicts well the number of horizontal and vertical photons. The detection of a horizontally polarised photon accurately predicts the arrival in time, and hence path length, of its erstwhile conjoined twin. The first observation operation separates the conjoined twins. One can accurately time bin polarisation heralded photons.

We now have a candidate scenario for a parapsychology experiment which has a miniscule change in terms of mass {momentum} and a binary change in terms of information.

If one was to try to influence the weighting of the quantum superposition state, the entangled state, in the equation above one could perturb the normal statistically verifiable distribution. In the equation above the horizontal and vertical are given equal weighting, 50:50 not ‘phone a friend.

By telepathy one might read and perhaps alter the information, by telekinesis one might rotate the polarisation sate weighting in the entangled pair. Conferring a more horizontal bias to one of the conjoined pair. It would be semantic if it is information or property which is altered.

To meditate  in a dark room with lasers is not to everyone’s taste. It was once to mine, the so-called Zen of laser alignment. It is a good, isolated environment for experimentation.

I think I might have the bones of an experiment which offers more likelihood of success than trying to mind-to-mind boring cards.

It is not Possible – Fish ‘n Chips

I am quite fond of a challenge from time to time. Especially when those challenges seem nearly impossible. A part of the motivation behind doing a start-up company was to find out, by way of experimentation, if it was actually possible. I was serious about the idea of the company as well. But the difficulty seemed like icing on the cake. We raised £5 million start-up funds {year 2000} based on one day of concentrated pitches. People were very surprised at the time. My personal pitch to fund hit rate remains very high at 100% with one outfit saying to come back later if/when we wanted a bigger funding tranche.

The more I think about it the idea of trying to get a potentially ground breaking {premature} patent in Quantum Telepathy granted under my new alias is attractive. We already have Quantum Heralding and Quantum Teleportation, so why not? Given that quantum remains a “hot topic” there will be tech companies and patent watchers doing key word monitoring. There may be governmental interest globally. When shit loads of money is involved people monitor intellectual property (IP). Portfolios are important and valuable. There is intelligence gathering.

It might be a flash in the pan tomorrows chip wrapper kind of story.

Such a patent application would appear on the radar, so to speak. Nobody would take me seriously because Man-in-his-shed Ltd is not a renown company or institution. Someone would scan read the application because it would be their job so to do. In all likelihood it would stop there. Unless someone wanted a light interest kind of quasi-joke story to go with the cute fluffy animals at the end of the news. I am no industrial or corporate threat. My shed contains no lasers simply a sit-on mower and a hedge trimmer. I have not worn a suit in over a decade.

Already I am the only quantum optics patent holder in the rural farming commune where I live. At a guess the local newspapers might find this quirk worth a few column millimetres.

The weirdest outcome would be predictivity.

In a film script a number of possible yet unlikely plot lines could ensue…

You never know what might happen. It is sufficiently off-the-wall to have highly unpredictable results. Once the radar blips anything might happen…

hmmnnnnn…

Qubit Coherence Time Dream 20-03-2023

This dream came after watching Roger Penrose discus “before the big bang” on YouTube. He suggested that in a thermalized black body compliant universe evidenced by the cosmic microwave background energy spectrum where E=hν = mc2, time or inverse time, frequency, does not exist in the absence of matter. “Time” can be curved to “before” the big bang of our current universe. Similarly at an infinitely expanded universe full only of radiation, photons, time again has no meaning without mass.

The dream starts in the refreshment area or bar off a hall full of poster presentations at a “perimeter” conference on quantum and quantum computing. I am talking with a “famous” prof in his early forties and he is holding court to some post docs and post grads. He is skinny with a beard and unruly hair. He is white. As far as he is concerned, I am a nobody.

I say to him that if I have understood it correctly the biggest drawback for quantum computing is qubit coherence time and thereby quantum fidelity. He says yes.

I say that a qubit is a counter-entropic state artificially manufactured in matter in many systems. In these matter based systems tremendous cooling is required to prevent coupling to the nearby thermal bath states which tend to bring about dephasing and lack of fidelity for the prepared qubit. He agrees.

I say that is why they need fuck off big fridges to get close to absolute zero, which is again a counter entropic state when viewed more than locally. He agrees.

That dephasing happens on a temperature and proximity dependent time scale.

I say that thermodynamics is a property of matter and hence time, without matter entropy as no meaning, nor does thermodynamics.

I ask him why nobody is pursuing fast or ultrafast time domain quantum computing? He does not reply.

I say to him if the prepared qubit state is addressed before dephasing occurs, we can use time to outwit or outpace thermalization to bath. Time domain quantum computing could be the answer.

He nods.

I say that the other problem stems from the cycle time of write to zero of the matter involved in the prepared qubits. It should be possible to use a second pulse similar to the state preparation one to reset the qubit clock on a hundreds of megahertz laser repetition rate. We then have a prepare and subsequent write to zero even if the qubit state has been used or partially used in computation. The matter is then ready for us to contravene entropy by writing a qubit.

As the dream ends, I think that it is a fair way from Guru Rinpoche.