Constraining Probability Distributions

O God Beyond All Praising (Lyric Video)

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Newtonian or Singular Events

Newtonian events are singular by definition (an action produces an equal but opposite reaction). Science that is defined this way is special; in that, we can know exactly [almost] what happened, we can exactly [almost] duplicate it, and the process is reversible. So we ultimately do the engineering and take control [almost complete] of the process. Singular problems, singular solutions.

Probability Distributions

I believe it was Jaynes that said, in one of his articles, that there was a degrees of freedom uncertainty that went up with increasing degrees of freedom; and he would prove that later. He said that about a lot of things but often forget to do those proofs.

The issue is that as uncertainty goes up we lose the possibility of following the process with Newtonian equations (we lose reversibility - and the possibility of complete control). In my view we then trade reversibility for a wave equation. If there are no particularly interesting constraints the “wave” equation is a boring distribution (and equilibration or dissipation). But with interesting constraints like eagles wings, we have interesting things happen to the wave equation. The wings, or tall buildings, or tall canyon walls becomes nodes in the system. Then the wave equation becomes a distribution of molecules that “fit” well into the combination of constraints including our nodes. Fitting well, here, makes it look a lot like the nodes are attractors.

Probability distribution problems are not singular. Multiple things are going on all at once, and they all tend to inter-react with each other. And individual activities are not predictable. We can only get a concept of a probability distribution where the outcome in the future is only understood from different "shapes" to the probability distribution.

To solve problems with probability distributions you don’t just turn a switch.

Sunset

Newtonian processes are reversible; processes of distributions (harmonics) are not reversible. Irreversibility appears to be the beginning of clocks and time (which are not reversible). Time, itself, is always the same for all distributions. Newtonian processes are reversible so the time cannot be established from these processes. Irreversible processes perform the duty of incrementing the universe so time only goes one direction. But Time is part of the uncertainty in degrees of freedom uncertainty process.

Strangler Fig

Means of Control by Constraints

Probability distributions change when they are put under constraints. There are a number of ways to respond to a constraint. The fact that distributions change under constraint is often ignored. Sometime we recognize the change from previous experience and add those possible changes into our discussion. But here it is not science, but "rule of thumb". Nothing wrong about "rule of thumb". It is at least recognizing we need to make corrections and adjustments. I am just suggesting that when we are using a "rule of thumb” it is not truly science. We should remember that there is a constraint here and the distribution is "reacting" to that constraint. So we improve our ability to define and understand the distribution (say the distribution of a pandemic) by recognizing the constraint or constraints that are affecting the distribution, and also recognizing exactly how the constraint is effecting the distribution. More things than we expect always happen when a probability distribution is constrained.

Lily Pads and Goldfish

Constraints on a distribution do not act like Newtonian processes. Distributions are not anything like several cue balls bouncing against each other. It is quite recognized, by people who regularly deal with distributions, that we cannot know what each member of a distribution is doing. Jaynes said that uncertainty (the inability to know every position and momentum of the contents) increases with the number of degrees of freedom. The uncertainty is a guarantee that we cannot know everything about a probability distribution [see: Brillouin].

Fireworks

An unconstrained distribution (It is hard to define or find an unconstrained distribution. After all we are part of everything; and much of everything causes some kind of constraint.) seems to be exponential in process.When you see the constant curling up of the graph you know there is no constraints being applied. Any constraint will bend the curve towards downward; and better constraints can make the distribution manageable. You look for an S curve (the growth curve) where there is a maximum.

Growth Curve Form

X is time or a factor in the process that is related to time - like size of an incoming constituent. Y is some measure of the size or threat of the problem at this X value. The curving over toward level is the first basis for control of a probability distribution problem.

From my perspective the present curve for the coronavirus is not quite a growth curve - it is still curling up too much. That means there is something lacking in our constraints. So we can see the constraints, or their effects, in the statistics. But that result is not a Newtonian response (i.e. every action has an equal but opposite reaction). To get more detailed on how this works - you write an equation that describes the constraints on the system; then you solve the equation [or integrate the equation] to get a set of eigenfunctions (harmonics) for what processes can happen. Probability distributions constraints can lower the degrees of freedom but never gets rid of all of them. The solution to our equation describes probability distributions that are possible from the constraints. The probability distribution does not go away. These are the things that can happen - it is still probabilistic.

Land and Sea

A little warning helps here: it is often difficult to recognize constraints or devise good constraints that constrain the distribution properly. It is even harder to represent the constraints in a mathematical formula. My experience with this is a textbook (out of the Copenhagen School) that described this process for both quantum process and for “physical” level processes. Newer wave mechanics books avoid the “physical” level because of the screams they get from Newtonian-only physicists. This process does work for tuning musical instruments, and is used that way; but they call it Newtonian - which it is not. This "tuning analysis" process is harmonics.

Jupiter Theme - God Beyond All Praising

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The simplest distributions to deal with are static; like an organ pipe. It is stationary and fixed. Then there are more complex distributions like winds or waves that are dynamic. In that case the distributions is continually changing over time (but often cyclically) so there is an extra complexity [in even recognizing what is happening]. Controlling the system is complicated by the need to know as much as we can about what is actually happening, which is not clearly obvious. We know more about that for waves than wind. Recognize that surfers are a big part of understanding wave and wave action.

Pandemics [forest fires and riots] add the problem of multiple dynamic distributions being part of the problem. You not only don't know exactly what is going on in each distribution - but you also don't know how exactly the many different distributions affect each other and then the total distribution. In this case a Lotka-Volterra analysis can be a choice for clarifying how the system operates [See: https://web.ma.utexas.edu/users/davis/375/popecol/lec10/lotka.html]. These equation develop a predator-prey process, I think that can be adjusted to use for any competing distribution systems.

https://web.ma.utexas.edu/users/davis/375/popecol/lec10/lotka.html

The result of our analysis gives us two lines (the inner one for predator and the outer one for prey) that is roughly two circles. This is about the best we can do in the case of a open system and using Newtonian expressions that designates the most likely result at each stage. Each line represents a donut that is not shown because we ultimately are solving for the most likely path of each effect. The line does show the "life" of the predator-prey cycle.

The Processing Problem

With a system that has more than one content there are issues that canot be ignored. I will examine these processing issues.

In a chemical plant you have tanks and pipes and processing steps (some of those done in tanks - others done a special processor) and mixers and mixing methods and transfer methodologies. Chemicals come in from different places for a reason. They are mixed and stored and piped to different places in a certain order. The issue that is most prominent in any process is that unmixed chemicals must be mixed with the proper other chemicals in a controlled way. For most formulas the mixing needs to be rapid and complete. If we don’t have good control over the mixing we can’t guarantee the outcome. The outcome could be hit or miss depending on the actual (if it is not another specified standard) mixing.

This is where the pandemic folks particularly in much of Europe and the blue states had difficulties. The lock down process used guaranteed there would be uneven mixing of existing virus stages. This seems to be less true in the red states and Sweden. Their statistics were not perfect but much smoother than the other two groups. The statistics show the problem as the attempted return to “normal” was fraught with jumps and skips (large jumps and skips) where the virus jumped out at us in surprises and spurts. Perhaps if we followed a better, more locally controlled close-down methodology ( or used a controlled partial close down) we could solve the problem better.

The blue states controlled the lockdown from central headquarters. The red states allowed more flexibility so there was more local control of processes. Locals can control their environment locally better than a central control headquarters.

Enough said. Viruses don’t just go away. Once China dumped it on us we are stuck. But we can manage the virus carefully in the future to reduce the risk of lives. And I don't mean permanent lockdowns - just for the fun of it. You cannot end all loss of lives. We live in a dynamic universe. Just blaming all the lives on Trump is silly and stupid, and just causes more loss of life. The important thing is to find out the specific processes that worked in the past and do more of that; and also find out the specific processes that did not work and do less of that.

https://web.ma.utexas.edu/users/davis/375/popecol/lec10/lotka.html

Additional information on the Lotka-Volterra model can be found at other WWW sites:

Model Description and Realization on "STELLA"

Lotka, A. J. 1925. Elements of physical biology. Baltimore: Williams & Wilkins Co.

Volterra, V. 1926. Variazioni e fluttuazioni del numero d'individui in specie animali conviventi. Mem. R. Accad. Naz. dei Lincei. Ser. VI, vol. 2.

Competing distributions show the characteristic of cycles and cycling. These, in a sense, reveal the process of time in a complex manner. Competing distributions are the ultimate of natural time processing. The Drum of Life is the Lotka-Volterra cycle. Yes, we eat cows, but we also constrain the whole process so we are in control. We don't run out of cows - usually. Supply chain management is ultimately Lotka-Volterra; and some people do that in their head, with a few scribbles on paper. And an adaptation of supply chain management needs to be a part of pandemic control and constraint.

https://www.investopedia.com/terms/s/scm.asp

Bree Sunset

Pasteur and Epidemic Harmonics 

Pasteur gave a series of warnings about epidemics. One thing Pasteur said about epidemics - because he saw this happening - is that they kill more people when they spread faster. There is no reason in Newtonian science for this claim so scientists often just don’t mention it.

But this problem is not a problem caused by Newtonian issues. This is a problem related to distributions and harmonics. It is like a fire or a flood. When the fire or flood gets out of control, then there is much more damage. The problem is caused in a dimension of a distribution being uncontrolled.

In a normal “room” the forces of entropy are constrained by the equilibrium in the room. In a flood or forest fire (or an epidemic) the equilibrium forces are overwhelmed. The destruction is far worse because it is out of control. This is harmonics.

So when the president is talking about the epidemic and about ways to slow the spread the virus, that saves lives. One of the ways he tries to slow the growth is by calming people. But the media wants excitement. But excitement literally means more death. So to me these media people are murdering people with their efforts to stop Trump from slowing the epidemic and thus saving lives.

Dr. Jerome Heath

#coronavirus #epidemics #Trump

Controlling Probability Distributions

Tchaikovsky-Hymn of the Cherubim - Liturgy of St John Chrysostom

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Harmonics of Nature

Hermeneutics in Agile Systems Development

Dr. Jerome Heath

#coronavirus #pandemic #epidemic #time #statistics #physics #newton #harmonics #distributions #probability #constraints #copenhagen #degreesOfFreedom