COVID-19 – Why China Did What it Did

From the horse’s mouth. Received this morning from a Chinese  source who is a top class engineering expert.

Very revealing!

Some of the actions of the Chinese government, which seemed counter-intuitive at the time, became quite clear from this explanation.

  1. How the hell did they decide to close up Wuhan when the official death figure was only 30 something? 
    Remember that the city is a uniquely important communications hub with air, rail and river transport crossing in multiple directions (in a war they’d probably prioritize bombing the place). The time was just before the Spring Festival before the annual spring travel crush started. Closing Wuhan spoils the SF(CNY) for a huge number of people, hurts the feelings of even more and damages the economy significantly. The modelling teams were assembled much earlier than this date and this action was significantly model-driven. The models tested different actions and the actual sequence was chosen as the least bad one. Closing Wuhan on its own looked stupid to some degree, but not as the first of the sequence of actions that followed:
  2. What about the rest of the country then?
    The rest of the country was allowed to continue through the first phase of the spring travel rush, which decanted probably 1/3 of the population from large cities onto the countryside, then the entire country was closed down preventing their return. This prevented the appearance of another Wuhan, with which the government would have no way of dealing.
  3. Volunteering albeit under peer pressure is a key
    As it happened, they were able to assemble large teams of medics from elsewhere in the country (the so-called volunteers – if you were a party member not volunteering was not an option, and non-members esp. low ranking nurses had incentives such as conversion from contract worker to full-time permanent worker) to descend on Wuhan and its province Hubei en masse. This depletion of medical strengths elsewhere proved sustainable because another flareup never happened. The President did not formally thank the people of Wuhan on behalf of the nation for nothing. When the people of China hear western media portray this as an apology for government errors they find this play quite difficult to imagine/understand. The hard/cold decision was to contain the spread locally from the first and therefore those local people had to suffer more hardships without volunteering. The least the nation could do is to appreciate this.
  4. Fangcang – makeshift hospitals are effective
    The establishment of the fangcang (makeshift hospitals using stadiums and exhibition centres) seemed strange, given that you were assembling ‘suspected cases’ all in one single space. The models predicted success which was borne out by reality. This has to do with how you want to deal with suspected cases and confirmed cases with light symptoms. It was determined that these people are better assembled together under professional care and control than remain at home to self-isolate with family. Fangcang-induced infections turned out to be negligible, almost zero. With beds a few metres from each other and everyone breathing the same air how was this possible? The answers are in the obligatory wearing of masks, on-hand medical and professional help and admin and enforced discipline, and almost continuous cleaning of the environment. These put together turned out to be vastly preferable, so far as the numbers are concerned, to home isolation where people do it any amateur manner they like/can.
  5. Testing methods with replication are crucial (real engineers can appreciate the use of time redundancy and diversity)
    The testing method adopted has practically 100% accuracy in the lab, close enough to 100% to be dependable for a tested population where the infection rate is only 1%, but in the field negative results were not trust-worthy (positives are completely fine). This was also put into the models and the resulting standard changes converted a large number of suspects to confirmed in a single day (all such converted cases had negative test results, but did not pass a CT scan test). The scientists read the UK’s confident reporting of how many tested with a large proportion of negatives with fascination, and speculate that the UK may have a more reliable testing procedure. This testing situation also inspired the fangcang approach as well as the very tight lockdown measures taken across the country. You don’t get cleared just because you had a negative. You need 2-3 negatives in a row without symptoms. In other words, treat everyone as a suspect case and everyone with symptoms as a confirmed case and design your control measures based on this assumption. The CCP is able to do this, other countries maybe not.
  6. Modelling approaches, also diverse and competing, are a must.
    The modelling gravitated towards two competing camps, by design of the government organizers. One is called the maths model and the other the medicine model. The first is led by system theorists and the second, epidemiologists. The commonly seen model of first order differential equation with an R0 factor is nowhere to be seen in either groups of models actually consulted by the decision makers – they are much more sophisticated than that. The maths model consistently returned more accurate predictions with worst case on death numbers error below 7% at all stages – this is the only hard number my friend was willing to disclose. All published models, either from within or without China which have appeared have been comparatively checked with the decision models and found to be inferior, usually by a lot.
  7. Future of the models?
    There is very little chance of seeing these decision models published, not any time soon. My friend’s words: “We should not publish when there is an atmosphere in which such a publication might result in extra-science interpretations and uses” and such an atmosphere will linger for a long time, by the looks of it. I read the CCP propaganda as well as the stuff coming out of our government and can see this stuff buried deep for long. However the modellers continue to work on data from the wider world now and the government continues to listen to them. One difference between China and much of the rest of the world is that the scientists cannot just tell the government the science says this and that without providing evidence, as the members of the government can understand scientific evidence at an academic level. And they organize multiple teams to work against each other to form a peer-review like environment from the start.
  8. Protection of medics is a key factor
    The most important issue, highlighted by the models and tested in real life, is the protection of the medics. Initially the disaster was when Wuhan people crowded general-purpose hospitals where the medics were not protected. When the external teams went to Wuhan+Hubei they were well prepared and formed special-purpose facilities which had a far greater success rate with next to zero infection of medics. Although this is intuitive, the actual numerical differences made in the deaths was unintuitively large.
  9. Ventilators is a last resort when it’s 20% survival chance left.
    One of the little-publicized facts is that the starting and ending procedures of ventilator use on a patient (putting them on/off the machine) represents the standing-out worst point for medic infections. This has caused a reluctance in China of using ventilators and the threshold for their use is set quite high, leading to ventilated patients having only a 20% rate of survival – if you are not already dying you are not ventilated. So they are a bit fascinated by the current western thing about seeing ventilators as some sort of almighty saviour, esp. given the current suboptimal PPE state for medics in an environment of retired medics (presumably not young) re-joining service.
  10. Masks, hand washing – NOT to be neglected 
    On how to protect ourselves, my friend emphasizes mask wearing and hand washing – diligent mask wearing and hand washing mimics the fangcang regime to some degree. Contrary to common belief, the wearing of even three-ply surgery masks protects not only the environment from the wearer but also the wearer from the environment, and N95 masks are indeed better. He became a bit rhetorical and urged us to disregard imagined stigmatization to prioritize life, both our own and that of those who may stigmatize us.

A 12 Day battle with COVID-19 of my colleague – in mid 40s and fit.

My close colleague Professor Patrick Degenaar

has just sent his report. With his permission I am pasting it here.

“I’ve now basically recovered from what I believe (it’s impossible to get a test) to have been a COVID19 infection.

Just so you know what you have to look forward to in the future, I kept a brief symptoms diary:

Day 1:   Very slight ache in joints

Day 2:   Asymptomatic

Day 3:   Tired, lethargic, dizzy, and out of breath

Day 4:   Reduced symptoms compared to day 3. Started to assume it was getting better.

Day 5:   Morning felt almost fine. Then afternoon: Very tired, very out of breath, heart palpitations, Mild temperature = 37.5C

Day 6:   Reduced symptoms compared to day 5, but still very tired and dizzy. New symptom: a chest pain – like a claw embedded in the chest.

Day 7:   Similar to day 6, but also developed an occasional dry cough

Day 8:   Much worse – extremely tired, very out of breath. Climbing the stairs felt like climbing Everest. Feeling like very bad high-altitude sickness. A feeling of nausea (just like bad high-altitude sickness)

Day 9:   Similar to day 8

Day 10: Starting to get better similar to day 5

Day 11: Starting to feel much better. Can ascend stairs without getting out of breath. But still tired and dizzy.

Day 12: almost OK, but still need periodic Siestas

Stay safe!”

The answer to why women are more robust to COVID-19 than men may lie in the dynamics of women’s gene pool

Today, people are asking why women are less affected by COVID-19 and have significantly lower death rate than men (in Italy, for example: more than 60% of infected are males and more than 70% of death cases are of male).

While there are hypotheses that this is caused by various societal and life style factors and norms, such as ‘because more men are smokers’ etc., I would like to examine potential genetic causes of that.

Men carry both X and Y chromosomes. Women carry only X chromosomes.

As I wrote a couple of years ago on my blog about the differences of dynamics between X and Y chromosomes (see links to my two articles below), I made a hypothesis that women’s chromosome pool is significantly more dynamic and mutable than men’s. The Y part of men’s genes don’t mutate. They carry Y-DNA through generations unchanged. Thus women naturally bring greater adaptability and robustness to environmental conditions than men. Contrary to that men bring certain long-term elements and inertiality, which is also important for stable societies.

Importantly, perhaps, I also showed an analogy between the combined process of gene evolution in humans and other species, thanks to the presence of both males and females) and PID (Proportional-Integral-Differential) control that is proven to be the most successful type of control in engineering systems.

So, the nature’s own PID control (where the role of P and D is greater than that of I for the purposes of quick response to effects such as viruses) makes sure that only a relatively smaller number of males compared to the number of females are needed to maintain the human kind.

So, as usual, Mother Nature and genetics are the winners in this almost game-theoretic scenario of our battle against coronavirus.

Is there any effect of weather on the spread of Covid-19?

Weather reports:

Average pressure in Wuhan in December 2019 was 1026 mbar, with some days going as high as 1040 mbar. Wind was very low too – 1-5mph. Dry.

Average pressure in Milan in January 2020 was 1027 mbar, with some days as high as 1045 mbar. Wind was very low – 1-3 mph, mostly dry

For comparison

Average pressure in Newcastle upon Tyne in February 2020 was 999 mbar, Wind was typically very strong – more than 20mph, lot of rain.

Molecular and cellular transmission:

What is the relative permittivity of air for odours and viruses? How does it depend on the weather?

Have you every walked behind a person having a lot of perfume? On a windy and rainy day, with low pressure you’d hardly feel any smell. But on a dry, sunny day, with high pressure, the scent of perfume stays so long that you can feel it even if the lady is 100-200 meters ahead of you, or even long past.

What is smell? What is its nature? In science it is explained via special types of molecules, called odorants.

With Covid-19, we have been told that we should keep the distance of 2m in social distancing. Is it enough? In what weather?

The Covid-19 cells are very small. Apparently the size of 100 nanometers. So we are talking about something like 1000 molecules. On a high pressure, dry and non-windy day, they can stay in the air probably for quite a while.

The other factor of good and dry weather is that people are much more out and about, and naturally socialise more. So, the weather and social proximity are correlated too.

Extra point. On a low pressure day our body naturally extract more fluid, mucus etc. This is actually good to help not letting virus into your body. On the contrary on a high pressure sunny day we are naturally keeping everything inside and actively breath oxygen rich air. Especially if we exercise outdoors. Perhaps, virus likes that we help it with extra oxygen and give its way into our lungs when we exercise. So is active exercising is good during those days and in a social company of potentially viral people. I am not sure.

We are often mistaken that by doing something normally good we can win. Unfortunately, there is no universal win. What’s good for your body under normal conditions may be bad under these viral conditions. Good old saying, you can’t win, man, can you!?

My hypothesis is that a good weather is really a ‘good’ promoter for viral transmission.

Electron is a two-faced Janus of Electrical and Magnetic aspects of energy current trapped in it …

Can you give me a proof that what you have inside an electron is any different from the so-called ‘empty space’. Any finite section of space has the right to say – look, I have my one epsilon and mu hence I have my own speed with which ExH travels in me. What’s wrong with this approach? The fact that electron is tiny doesn’t deprive it from the privilege of having its own ExH trapped in it. Then this electron can have both electric and magnetic Januses to turn to us in the form of its charge and spin!

My response to Akinbo’s email:



From: Akinbo Ojo <>
Sent: 14 January 2020 15:36
Subject: Re: Displacement Current in Deep Space for Starlight

Hi Alex,

When taking a medicine is worse than the disease one wants to cure I think it is wise to stick with the disease. I also ask you to take note of what Harry just posted concerning how you want to combine the equations.

The only place I see usefulness for the ExH concept is in transmission lines (co-axial cables) where E can travel in the core wire and H can travel alongside in the space between. But there are no such transmission lines or co-axial cables in space so this type of energy current cannot work in empty space.



The cacophony of particularities in Maxwell’s equations … at the end of the day, it’s only Catt’s Heaviside signal that puts things right!

Over the last couple of week I have been witnessing an interesting email discussion about Maxwell’s equations between 2-3 people trying to come to terms with the difficulty of accommodating the notion of displacement current in free space and ‘sorting out’ the Ampere’s law. The latter combines, for whatever reason, both the elements of propagating field (not requiring charged particles as this field can propagate without involving massed matter) and current density (implying the existence of massed particles).

I have drawn my own conclusions out of this discussion, which ended up with conclusions that the above mentioned difficulty cannot be easily resolved with the bounds the temple of the classical electromagnetics with its holy book of Maxwell’s laws.

Here are my comments on this:

To Ivor Catt:

Following your theory where the Heaviside signal travels (and can only do so) with the speed of light in the medium, such a speed is entirely determined by epsilon and mu. Thus, where we have an interface between very low epsilon dielectric and very high epsilon metal, from the point of view of energy current, we have the effect similar to friction (against the metal surface – like a rotating wheel goes forward on the ground thanks to experiencing friction against the ground). And thanks to this “friction” it prefers to trolley along the metal wire, or between the metal plates of the capacitor.

To David Tombe:

Catt’s theory works at a different level of abstraction. This is the level of fundamental energy current. This level underpins “charged particles”. The latter are the result of the ExH energy current trapped in corresponding sections of space. What’s important is that that trapped energy never stops inside those particles as it can only exist in the form of ExH slabs moving with speed of light in the epsilon-mu medium. So then, when you apply energy current travelling outside those particles, there is an interesting interaction with the energy current inside those particles.

The entire world is filled with energy current fractally sectioned into fragments determined by space sections. 

All I can say is that in my opinion you misunderstand the domain of action of Catt’s theory. It does not consider static electric field. That’s it. There’s no such a thing as static EM energy. It can only move at speed c=dx/dt, in all directions. 

And this energy fills up space according to its epsilon/mu properties.

There’s no need for Maxwells equations to be involved in Catt’s theory. All these equations are partial, like Greek gods.

To Ivor Catt:

I, perhaps surreptitiously,  was awaiting for your email, either in public or in private.

Coincidentally, about an hour ago, I typed a message intended to be sent to the whole list from that discussion (adding Malcolm, who I think is on the same wavelength with us), saying:

“Ivor, please, say something, because these people are facing an impossible task of ‘squaring the circle’ of a set of Maxwell’s laws into something coherent – but the reason why it is impossible is that no one actually knows exactly what Maxwell meant by that list of laws dressed into fairly sophisticated mathematics. So, Ivor, the same fate may be with you, unless you say something, in some 20 years from now {well, it looks like I miscalculated by 5 years from your estimate of 2045!} no one will know exactly what Catt meant by his energy current”.

Then some invisible force pushed me to discard that email! And now, I had an evening walk to my office to freshen up my mind, and here I see your email.

Sadly, people, don’t listen and can’t liberate themselves from the heavy chains of those (partial) laws – which are like, indeed, those separate gods of Greeks or Romans being responsible for one aspect of life or another or one phenomenon in nature or another. They can’t understand that the Occam’s Razor of nature wouldn’t tolerate having so many (purportedly, fundamental) relationships, with lots of tautology in them. All those relationships, taken individually, are contrapuntal and superposing.

People can’t understand that there is no need for stationary fields, no need for separate treatment of charged particles etc. Everything comes naturally as a result of energy current trapped in sections of space, where it continues to move.

I think the next big leap where Catt’s vision will show its power will happen in high-speed computing and a massively parallel scale – truly high-speed! Until then we will probably fight against the Windmills of stale minds and deaf ears …

This confused discussion between David Tombe and Akinbo (not sure if Malcolm has seen that) is an illustration of the fact that behind the mathematically elegant façade of Maxwell’s laws there is a massive mess of physical concepts, a cacophony of man-made and contrived ‘pagan-like’ beliefs and disbeliefs (e.g., did Maxwell mean that or not?), which may work in special cases. The fact that these beliefs can work in special cases of success in growing crops or hunting/herding animals in some regions of the world, or in a more modern terms, wiring up a Victorian mansion and sending data to Mars rovers. But how they are going to succeed in the future when needs Terabit/s  data rates or picosecond latency in accessing storage, nobody knows. I am less inclined in dividing people into true scientists, careerists or other categories. Historical materialism (which we had to study back in the USSR) gave pretty good explanation of all kinds of folk under the sun. Nobody is saint here. It’s just a personal comfort matter …

To Akinbo Ojo (in reply to his email attached below):

Just combine ∇2E = µε(∂2E/∂t2) or ∇2H = µε(∂2H/∂t2)  into one eqn, replacing E and H with ExH, and you’ll have the Heaviside signal (aka energy current) propagating in space with speed of light in the epsilon/mu medium, and that’s all what is needed by Catt’s theory, and that what fills up fragments of space, in order to form transmission lines of particular Z0, capacitors, inductors, elementary particles, etc.

Everything in the world is filled up with this energy current, and any such an entrapment of energy current turns sections of space into elements of matter (or mass)!

From: Akinbo Ojo <>
Sent: 14 January 2020 14:20
Subject: Re: Displacement Current in Deep Space for Starlight

Hi David,

I didn’t say there was an error. I said given the Ampere and Faraday equations when you follow the curls and substitutions you will confront something that would be unpalatable to you and which you must swallow before you can get ∇2E = µε(∂2E/∂t2) or ∇2H = µε(∂2H/∂t2).



Static vs Dynamic when referring to the electric field in capacitor

I wrote in my paper “Energy current and computing” ( ):

“there is no such a thing as a static electric field in a capacitor. In other words, a capacitor is a form of TL in which a TEM wave moves with a single fixed velocity, which is the speed of light in the medium”.

This statement causes some controversy – Ivor Catt refers to it as “heresy”.

Here I would like to explain what is meant here by static/dynamic:

One of the important aspects of considering the distinction between ‘static’ and ‘dynamic’ is that of what we mean by dynamic/static in the first place.

I think that the notion of dynamic/static, first of all, concerns as to whether a particular value (say, electric field intensity E) changes in time or not, i.e. whether dE/dt is non-zero or not. Another notion of dynamic/static is about the movement of the value in space (and, necessarily in time because movement in space cannot be instantaneous!), so if we talk about the electric field E, we can be talking about dE/dx being non-zero, and here is the critical notion of the link between dE/dt and dE/dx, which MUST be mediated by dx/dt (speed of light in the medium!). The latter MUST BE ALREADY SET UP, ab initio, and that’s what Ivor Catt’s Heaviside signal is about. So, even if we have an impression that something is static – like electric field in a fully charged or fully discharged capacitor, this impression will be viewed in the form of contrapuntal dE/dt=0, we somehow need to retain the notion of c=dx/dt being constant and non-zero. But then the immediate question arises of: what is there that is moving in a longitudal direction at speed c? And the answer is the Heaviside signal! What else? So, my understanding is that THIS MOVING THING is what makes me state that that there is no such a thing as a static electric field in a capacitor!

“Contrapuntal superposition” of Heaviside signals unravelled as a lookalike state coding problem in asynchronous circuit design

This article by Ivor Catt – published (now more than) 40 years ago – proposed looking at transverse electromagnetic (TEM) wave by means of the so-called Heaviside signal. Heaviside signal is basically EM “energy current”, described by Poynting vector ExH (E and H are electric and magnetic field intensities, respectively), that travels and can only travel in space with a speed of light in the medium, fully determined by its fundamental parameters permittivity (epsilon) and permeability (mu) – i.e., c=1/sqrt(mu*epsilon). The key point here, I should again stress, is that ExH cannot stand still – it can only travel with speed of light. One might ask, where does it travel? It travels where the environment – i.e the combination of materials – leads it to, and in practice it predominantly goes where the effective impedance of the medium is smaller. The effective or characteristic impedance of the medium, Z0, is also fully determined by the permittivity (epsilon) and permeability (mu), i.e. Z0=sqrt(mu/epsilon). Moreover, Z0=E/H – this is sometimes called the constant of proportionality of the medium.

Why is this look at the TEM wave more advantageous than some other looks, such as for example, the so called “rolling wave” of the alternating concentrations of magnetic energy 1/2*mu*H^2 and electric energy 1/2*epsilon*E^2 in the direction of propagation? As Catt shows in the above article, this more conventional way is actually meta-physical, because it is based on the assumption of causality between the electric field and magnetic field and vice versa. The latter is a form of tautology because it creates a non-physical, but rather, mathematical or equation-based “feedback mechanism”, which does not make sense in physics.

Another important issue that calls for the use of Heaviside signal is that it retains the notion of the travelling EM “ExH slab” in each direction where it can travel, and hence its change-inducing geometric causality between points in space. As exemplified by the effects of travelling TEM waves in transmission lines (TLs), this look, for example, naturally separates the incident wave from the reflected (of the interface with another medium) wave, or from another wave that may travel in the opposite direction. As a result, the analysis of the behaviour of the TL becomes fuller and can explain the phenomena such as superposition of independent waves in cases such as cross-talk between TLs. Here is another paper by Ivor Catt – published more than 50 years ago – and subsequent clarifications – of the superposition of the even and odd modes (modes of TEM travelling with different speeds of light in the medium due to different epsilon and mu conditions arising between adjacent pairs of metal lines).

As shown in these papers, the view provided by the conventional theory is necessarily contrapuntal – it looks at the combined EM field in every point in space and in time. As a result it simply overlays the travelling ExH signals. And that’s what one can see by measuring voltage and current in points of interest on the TL. Or, equally, what one could see on the oscilloscope’s waveforms at points in space. Interestingly that looking at the same time at a number of points, in a spatially orderly way, leads to a conjecture that there is an interplay of several travelling TEM waves, but the conventional rolling wave approach would not explain the physics behind them properly!

What is remarkable in this for me is that this reminds me the difference between two types of models in asynchronous control circuits and how one of them obscures the information revealed by the other. One type of model that is based on recording purely binary encoded states of the circuit (akin to the contrapuntal notion). The other is based on a truly causal model (say Signal Transition Graph – or STG – called Signal Graph or Signal Petri Net in my early publications: or, where we have the explicit control flow of signal transitions or events running in the circuit. The difference between these two looks is often manifested in the so-called Complete State Coding problem (cf ). If we only look at the contrapuntal notion of the state without knowing the pre-history of the event order we cannot distinguish the semantically different states that map onto the same binary code provided by the signals. To distinguish between such states one needs additional information or memory that should be either provided in the underlying event-based model (the marking of the STG) or by introducing additional (aka internal or invisible) signals (in the process of solving the CSC problem).

I am not claiming that the above-noted analogy leads to a fundamental phenomenon, but it reflects the important epistemic aspect of modelling physical world so that important relationships and knowledge are retained, yet in a minimalist (cf. Occam’s razor) way. Some more investigation into this analogy is needed.

Clearing my way through quantum entanglement – things are actually rather trivial …

The end of year 2019 was marked for me by a sudden revelation about the entanglement (aka EPR) “paradox”. Here is my confession, first. For a long time I had been thinking that the “superposition or entanglement paradox” consisted in the following:

Two particles (possessing a certain probabilistic characteristic such as a spin) originating from the same source were entangled, i.e. connected by, say, one being in phase alpha, while the other one in opposite phase (180-alpha). Then the particles were be sent into different directions of travel and remained entangled and what’s important their alpha parameter would still be unknown. Then at some point in time and space one of the particles would have been measured, and say found to be equal to 1 (I suppose we can use binary encoding without loss of generality). Now, here comes my misinterpretation: Then at the very same moment in time the other particle would be disentangled and its value would be exactly opposite, i.e. equal to 0. Therefore the paradox (in my interpretation) was as follows: (1) the state resolution in time is simultaneous for both particles, i.e. while forcing the measurement of the first particle we immediately have the measurement of the second particle; and (2) the state resolution on terms of value of one particle would completely determine that of the value of the second particle.

My problem was not in understanding why (2) was true. That was quite clear to me for a long time, especially after my discussions with experts like Professor Werner Hofer, who explained to me, a non-expert on quantum theory, that both particles, once entangled, would retain their phases and in that respect would remain information-wise connected. My problem was in accepting and understanding (1), which I my view violated temporal causality and no action at distance. I could not accept the fact that there would be no delay between the initiated measurement of the first particle and simultaneous resolution of the second particle. The reason for my conundrum was that I am a firm believer in causality of related events in time, and I could not accept (1).

But, thanks again to good old Werner (!), with whom we talked a few days before Christmas 2019, I realised that there is actually no paradox at all here. What actually happens is that – there is no issue (1) involved! The resolution of the second particle in fact can happen concurrently or independently of that of particle one! And the whole pathos of the EPR was only in part (2). This gave me an enormous relief and peace of mind needed for the coming festive season. The expected asynchrony and delay-insensitivity of the physical world had been restored! And, as far as part (2) is concerned, that was a trivial thing to me – this is purely a combinatorial (non-sequential in terms of automata) issue of one value being statically opposite to the other value – what’s the big deal !?

Now, what annoyed me in all this conundrum, well, obviously my own naivety and my inaccurate reading about the EPR paradox. On the other hand, I think that the lack of clarity in separating the issues of timing from value, i.e. when and what, that is quite symptomatic of the 20th century mathematical physics, involving complex quantum mechanical constructions, is what makes engineering-minded people like me – who expect both these issues to be properly addressed – confused and misled!

Happy days!

Correction on my previous blog and some interesting implications …

Andrey Mokhov spotted that to satisfy the actual inverse Pythagorean we need to have alpha=1/2 rather than 2. That’s right. Indeed, what happens is that if we have alpha = 1/2 we would have (1/a)^2=(1/a1)^2+(1/a2)^2. This is what the inverse Pythagorean requires. In that case, for instance if a1=a2=2, then a must be sqrt(2). So the ratio between the individual decay a1=a2 and the collective decay is sqrt(2). For our stack decay under alpha = 2, we would have for a1=a2=2, a=1/2, so the ratio between individual decay and collective decay is 4.

It’s actually quite interesting to look at these relations a bit deeper, and see how the “Pythagorean” (geometric) relationship evolves as we change alpha from something like alpha<=1/2 to alpha>=2.

If we take alpha going to 2 and above, we have the effect of much slower collective decay than 4x compared to the individual decay. Physically this corresponds to the situation when the delay of an inverter in the ring becomes strongly inversely proportional to voltage. Geometrically, this is like contracting the height of the triangle in which sides go further apart than 90 degrees – say the triangle is isosceles for simplicity, and say its angle is say 100 degrees.

The case of alpha = 1/2 corresponds to the case where delay is proportional to the square root of Voltage, and here the stack makes the decay rate to follow the inverse Pythagorean! So this is the case of a triangle with sides being at 90 degrees.

But if alpha goes below 1/2, we have the  effect of the collective decay being closer to individual decays, and geometrically the height of the triangle where sides close up to less than 90 degrees!

Incidentally, Andrey Mokhov suggested we may consider a different physical interpretation for inverse Pythagorean. Instead of looking at lengths a, b and h, one can consider volumes Va, Vb and Vh of 4-D cubes with such side lengths. Then these volumes would relate exactly as in our case of alpha=2, i.e. 1/sqrt (Vh)=1/sqrt(Va)+1/sqrt(Vb).