2020|5|23

From: Friend#6

Subject: Frustration

Ray G

I remember as young engineers , in med school voicing our concerns to each other,

On the lack of discipline of our new field of study Had in math processes / and application. I remember a red faced physiology professor , when I confronted him after a class where he had put an “Impressive “ integral on the chalk board , which 90% of the students had no basic knowledge of, he put up wrong , and only 2 or 3 of my class had enough math back ground to catch the mistake.

Our engineering roots are based in the hard sciences , which sought to find numerically quantifiable relationships. Every year I served on the GT/BME advisory board, we as industry members asked the question of the facility , “are the students getting enough math foundations”. Biomedical is so broad , and far reaching as a new engineering discipline, course work was crowding out math courses.

Here the world is faced with a deadly epidemic , and scientist ,those in charge ,

Are not requiring , precision in reporting of data. Precision of measurement is core to the scientific method .

You are much closer to that field than I , with your CDC connections.

1) Is it happening , and I don’t see. ?

2)Or is it the usual gov , sloppy , I’m in power you listen to me , dumb ass approach to life?

3)or the roots of medicine , as a liberal arts approach to study, with no math foundations.?

To model an epidemic one has to Make initial assumptions and guess the infectivity and lethality (and other variables)of the agent.

Once data is available , To refine the model , and redirect planning , one has to have CLEAN data. The USA death certificate process is with out any uniformality , and should not be used in any scientific paper.

I am financially conservative

, socially liberal

, libertarian against big government

But intolerant of one thing, bad science.

All of science , begins with precision of measurement .

Can you give me hope, some one near the top of the CDC has any clue how a simple circuit works and is diagramed . Or are we just “war gaming” , want-a-be generals.

(No offense to the military , this Memorial Day weekend)

Friend#6

From: Friend#6

Thought of the day.

We may not be on the same boat , but we are all in the same storm.

Friend#6

From: Ray Gangarosa

Perfect observation! I’m just writing about that in my response to your “frustration” and will incorporate it in my discussion. You’re really great at these volleyball-like setups!

From: Ray Gangarosa

What I have so far, before breaking for dinner. Comments and suggestions welcome. To be continued.

Hi Friend#6

You have raised such great questions and expressed them so well that I’m going to take a diversion from the daunting task of writing about the mathematics of life to answer your question as another blog. (Or, I have to ask myself, as a confession question, am I grabbing another delaying tactic to write a blog on an easier topic?) I have lived your questions, but not as frustration, but rather as continuous and continual revelation!

The difference between your frustration and my revelation was that I began to answer these questions in engineering graduate school by asking them in the other direction. Chaos theory hadn’t been unpacked from Henri Poincaré’s brilliant work from 1917 when I was at Georgia Tech almost 60 years later getting my master of science degree in electrical engineering in anticipation of applying to medical school, so I studied nonlinearity from the other side of the coin: how does it help living systems organize and function? I looked at generalizations of systems theory, like Volterra series (like a Taylor series expansion of Fourier pairs that considers both nonlinearity and memory) and Wiener kernel analysis (like a Gram-Schmidt orthogonalization of Volterra series so terms of different orders don’t interact), that I envisioned might allow nonlinear systems to function something like the technological devices that we build (but later discovered otherwise, as described below). When I was dating Friend#3 early in graduate school, I objected vehemently against the constraining assumptions of linear time invariant systems theory, “These damned engineers treat nonlinearity like it’s some kind of perversion! Don’t they know that all of life is nonlinear?” She didn’t miss a beat. With perfect timing, she narrowed her eyes, changed her expression to one of utter disgust, and exclaimed with dripping mock sarcasm: “You *pervert!*” That exchange has become a running joke between us ever since!

Over the years, I’ve come to realize that nonlinearity actually is some kind of perversion. The gradually-bending nonlinearities that I was studying lead to sensitivity to initial conditions — i.e., chaos! — because a system’s operating mode depends on when and where it intersects a specific part of the curve. The now-famous logistic map is a perfect example of how a common, garden variety nonlinearity (literally) can generate all kinds of chaos. Throw in any kind of interaction and the system can get thrown into entirely different operating regions at the drop of a hat. No critical process could tolerate that kind of unpredictability. It has taken me the better part of 45 years to reconcile these contradictions — not least because nature doesn’t want to reveal her secrets, and getting past its high-energy barriers demands making commitments to the highest of principles. That’s how I’ve gotten to theology, not through any of the usual ways that people come to religion.

Besides modulating the running joke between Friend#6 and me, that realization has been the source of great revelation, which I have alternately resisted and embraced many, many times over and over again. Nonlinearity seriously gets in the way of designing the way engineers always want to do, yet it is essential to life, most notably in contact inhibition. It has taken me 45 years to approach and avoid this conflict so I could fathom the mathematics of life.

You have seen enough in my abstract and introduction to the mathematics of life to appreciate the source of this universal frustration, which manifests in many different ways, e.g., the schisms between progressives and conservatives, the fragmentation you describe within conservatism as your own brand of it, my utter contempt for Donald Trump, and our frustration in medical school with the state of biological knowledge about engineering principles. You wanted the mathematics, so I will express my explanation in mathematical terms.

Schrödinger’s equation for quantum physics is the basis for all chemical reactions, here expressed for a single nonrelativistic particle to represent the wave function Y of an organism or a planet’s civilization:

where **r** is space and *t* is time, *h*-bar = *h*/2p is Planck’s constant, m is the square of the speed of wave transmission, V is the quantum potential, and Y is the quantum wave function — which, in this case, represents how an organism or civilization holds together and steers its way through structural space and time.

Although there are only three terms in this equation, another term is implicit: any kind of phase change that might arise when this system interacts with any others within its event horizon. Since we’re talking about organisms and civilizations, such “phase changes” are laden with value, meaning, and purpose, and can span the spectrum from spectacularly great (“transformation”) to spectacularly catastrophic (“collapse”) events.

There are (at least) three huge bottlenecks for applying this equation to life and civilization: (1) it has little explicit memory for the system’s past, (2) it lacks the capacity to anticipate the generally predictable course of likely events in life and civilization (e.g., through the preprogrammed sequence of embryogenesis; the predictable metabolic paths of homeostasis, homeodynamics, and pathogenesis; the mental models of creative thought, and the anticipatory capabilities of artificial intelligence), and (3) it is so dependent on system configuration and timing as to be impossible to solve (specifically, Schrödinger’s equation is inhomogeneous, with one operation, the Ñ^{2} term, in the realm of space (i.e., system structure) another operation, the ∂/∂*t* term, in the realm of time (typically system timing of events), and the third term, V, in either or both). Over the course of evolution, and then again, every time an embryo recapitulates that same sort of development process, an organism adapts to a changing environment, a child is educated, an adult responds to changing circumstances, or an engineer designs a computer controller, life itself has modified its own design to get around these major bottlenecks.

It’s easier to see how life got around the first bottleneck, the absence of memory in the chemistry of life. First DNA in prokaryotes and then eukaryotic organelles, life incorporated into the equation a handle into its past. Life developed the potential term V as an integral over time,

where the system could also access the instantaneous signal v as well. Prokaryotes can develop memory a little, eukaryotes a lot better, civilizational “sleepwalking through history” yet considerably better, and full-fledged civilizational design at least has the possibility of getting it almost perfectly.

Civilization does far better job of incorporating memory by setting up society as cumulative culture, beyond the confines of lifetimes, as people leave their legacies behind for later generations. We can look back through history at the culture at any time, going back hundreds of generations. Ideally, human civilization might become a permanent, stable, and benevolent fixture in the biosphere by letting this memory extend, at least in principle, for an infinite number of human lifetimes who “pass the baton” from the distant past into the indefinite future, in making each successive cultural era a better planetary citizen.

So the memory-generalized Schrödinger equation becomes

Here’s where life addressed — and always has to keep addressing — the second bottleneck, the unsolvable inhomogeneous partial differential equation in both space and time. Life replaced the Ñ^{2} term (which is an integral with respect to structural space) with a related term, a time-limited function that is linear in time, by setting up a clock that maps structural body segments laid down during embryogenesis. The system then uses the elapsed time as a cue for each segment as to when it should start and stop developing. To the system as a whole, the term Ñ^{2} term is replaced by a set of spikes in time *t* that are synchronized to a specific set of events in structural space **r**, which mathematically still is, overall, a constant in time.

I should also note that, since the modified Schrödinger equation has a kind of symmetry in space and time, civilization provides the option of solving in terms of either space (“hardware”) or time (“software”). Hardware derives from the stationary moieties, charges (which correspond to the integral of v with respect to *t*) and masses (which, within molecules, hold charges in place and thereby correspond to the system configuration, i.e., the Ñ^{2}term). Software corresponds to the two (near-) relativistic moieties, photons (the ∂/∂*t* term) and spins (the phase change term). For software to function reliably, the hardware must first be solidly in place and itself function reliably. Thus, the order of the unfolding of life and civilization was established at the beginning of the universe, when the five moieties first appeared after the big bang!

The trouble is that this complicated change in variable involves setting up different regimes for all three terms, which then have to start from scratch, “boot up”, and develop into a functional system. Babies can’t just pop out of the womb and function as mature adults. But at least life can solve the modified Schrödinger equation, so the person can stay alive as he/she learns how to function in the world.

To see how this works, let’s consider the developmental terms, denoted by primes, that are new functions of time. Ignoring the imaginary term (as if to consider mass reactions, like reaction-diffusion processes), substituting a single Dirac delta function d to represent the set of spikes in *t* for the Ñ^{2}term, and rearranging slightly, we see that life has managed to simplify the modified Schrödinger equation into a form like

If the integral referred to Y*‘* instead of v*‘*, we could take a Laplace transform of this equation to get, respectively, 1/s, constant, and s terms; then multiplying by –s/k_{2}, we would have

— which is solvable by simply using the quadratic formula!

We can imagine how this might happen by shifting our attention to civilization, noting that mathematical induction proofs assure that the same physics holds in both cases. We also note that, knowing these relationships, we have the option of *designing* the system so that its wave function equation is solvable. Over the course of evolution, life would have had the same option, but with civilization, we have the advantage of applying analytical tools instead of just tinkering at the margins by trial and error.

Identify the wave function Y*‘* as the waveform of human civilization and v*‘* as instantaneous culture at any time *t* in any region **r**. Recall that we substituted the temporal integral of culture v*‘* for society V*‘*, which represents cumulative culture. All these terms depend on geographic region **r**.

Each Dirac delta function d selects one moment out of continuous time and pulls it out of obscurity to have special significance. The historical moments I have selected for their mathematical significance correspond to central Christian doctrines: the kingdom of God, the body of Christ, the Holy Spirit, God’s creation. In this case, I didn’t set up a clock to pick them out, as embryogenesis does, but instead used powers of abstraction that are unique to civilizational design. Then the time integral of instantaneous culture introduced a cumulative selection process, effectively looking at how these processes contribute to the sum of a whole. All this was done under assumptions of linearity (which is remarkable in itself), although the theological doctrines I’ve chosen each contain notions of self-sacrifice that extract the essence of contact inhibition — that is, preparing to sacrifice one’s own interests and life itself to advance the state of the universe (God’s kingdom), human civilization (the body of Christ), earth’s life support system (the Holy Spirit), and the future of life on earth (God’s creation). I didn’t choose the moments when those concepts were derived because I was a Christian (because at the time, I was only attending Christian services for informational purposes), but rather because I was (and am) a scientist. I chose those principles because they are the most important ones in all of life and all of its continuation as a civilizational process. That is the mathematical process by which I selected from the integral that represents cumulative culture V*‘* the most important concepts for humanity’s becoming a good planetary citizen | a responsible partner with God | a species capable of co-creative construction of God’s kingdom | and the steward of a civilization that can exist, in stable equilibrium and/or in transformative, beneficial dynamics, with the rest of life on earth indefinitely over evolutionary and geological timescales for as long as God wants our civilization to last.

Let’s just use the same trick for the Y*‘* ∫_{-¥}^{t} v*‘* dt term that life did for the Ñ^{2} term, by considering civilization to be an embryonic process, imagining that instantaneous culture mapped to structural development of human civilization, and assigning Dirac delta functions d to the correspondences between structural space and civilizational time. However, this time, there are a couple differences: (1) the Dirac delta functions for the most significant events in history (the emergence of Christian doctrines that have physical significance) are embedded in the integral over time and (2) instantaneous culture v*‘* is part of cumulative civilization Y*‘*. Thus, there are both spikes at specific events and continuous, cumulative effects of civilizational development over time. The spikes are going to set up multiple echoes and the cumulative effects will cause smearing, but since we have the luxury of using analytical tools to design the system structure, we could get rid of them and set up the desired integral in time. This admittedly incomplete analysis shows more about how difficult it is to tune up an organism’s metabolism to solve the mathematics of life — or to convey a realistic impression of life in a civilization — as to carry the process to a good design without the distortions of a metabolic (or civilizational) echo chamber. We will discuss the implications of such reverberating echo chambers below in the context of developmental islands.

I am convinced, with a little more mathematical sophistication and a careful choice of civilizational design, this general approach could set up the solvable quadratic equation above. From the civilizational application of the mathematical trick that life developed, we get some intuitive insight into how it works (especially because the notation and analysis I used was very sloppy and not very revealing!).

It’s important and instructive to note how many developmental systems life creates under two different circumstances: without and with interactions. See my (finished) discussion of the mathematics of life for a more complete account. For these purposes, just recall that there are 4 terms to the equation if we include phase change.

- Without interaction, there are 4 stages for life + (4 – 1) stages at the level of {hardware + software} = 7 stages, with nature deciding the final phase change at the higher level. Hardware has to set a developmental regime for past and present, software for future, and nature decides whether irreversibility is acceptable. Each developmental regime arises from a stimulus-response process at the level of life, which translates to an equivalent input-output representation at the level of hardware and software technologies. This looks like a pyramid of triangles.

This set of 7 triangles looks like patterns postulated by the fundamentalist sect of dispensationalists as the way history will play out over time. They think the end is near, but I think their assumption of no interaction basically postulates that human civilization is a unicellular process that will come to an extinction event in the end times. That is a mistake an embryo would make, forgetting its multicellular origins and only remembering its unicellular-like development until it had to burst into a multicellular design. What we are fighting about is that we all got stuck in our own developmental islands and can’t communicate until we realize we’re all part of a larger multicellular process and structure, at which time we will all be destined to pull together again. By contrast, dispensationalists are hellbent on inducing a miscarriage just at this critical unicellular-to-multicellular transition, which is so prone to spontaneous abortion. (Isn’t it ironic that such fundamentalist sects are so determined to preventing elective abortions but so intent on causing our civilization to undergo spontaneous abortion before it even starts developing multicellular structure!)

Let’s look at how this unicellular-like superorganism would play out, even though it doesn’t fit with the natural pattern of a multicellular existence that human civilization should follow. Each such developmental module forms a unit that can get recursively embedded in the same pattern of triangles-within-triangles anywhere else in the diagram. So, for example, like a fractal, we can think of this pattern of 7 triangles as the lower right triangle in another pattern of 7 that builds on it, and that pattern of 7 as the lower right on another pattern of 7, etc., and so on “*TO INFINITY AND BEYOND!*” (as Buzz Lightyear would say, in mathematical nonsense language).

The whole pattern might look something like a Serpinsky triangle, which is a kind of fractal. I don’t think these are fractals, however, because the operation is really the opposite or inverse. A fractal is composed by a recursive mathematical operation that generates a spatial pattern. This thing is composed by a recursive mathematical (developmental) process that generates a multilevel spatial and temporal process (like life and civilization). I have been calling it a “carftal”, but if that name doesn’t fit, I’m open to better suggestions.

- With interaction, there are 4 developmental stages ´ 3 levels = 12 developmental modules or islands, with the final module just being a placeholder for all future transformations of the system. The first level is that of life, the second that of hardware, and the third that of software. This proliferation of developmental systems establishes the “intellectual islands” that have so frustrated you and fascinated me. Here is the simplest table showing how these processes play out:

level | stage 1 | stage 2 | stage 3 | stage 4 | |

life: | 1 | physics | chemistry | unicellular life | multicellularity |

“hardware”: | 2 | anticipation | contact inhibition | universality | toolboxes |

“software”: | 3 | optimization | applications | fluency | partnership |

As shown in my (final) blog on the mathematics of life, the developmental islands that have frustrated you as a physician-engineer are between levels 1 and 2, specifically those between the two adjacent islands “multicellularity” (your clinical practice as a family physician) and “anticipation” (which is where analog linear circuits reside). My path has taken me from “physics” through “optimization” and slightly into “applications”, a span of 10 developmental islands. Nobody can get to “fluency” alone, and “partnership” is a placeholder for partnership with God!

But since these are just names without further elaboration (and I haven’t yet finished my blog on the mathematics of life), let’s expand this table to show some granular detail. Note: It’s misleading to portray academic disciplines as a progression of frontiers, especially since the biomedical engineering interface between life and hardware constrains boundary conditions to analog technologies, which obviously can also use software in its downstream circuits. The frontiers represent how life must unfold, not any kind of grading system.

Note that the origins of biomedical engineering straddle the particularly awkward, 2-level span between medicine/physiology and analog linear circuits and ultimately range over the 5 developmental islands of medicine, analog linear circuits, bilateral interactions, multilevel interactions, and toolboxes. Epidemiology and biostatistics follow a parallel track along 4 of the same developmental islands but don’t (yet!) intersect much with biomedical engineering because their medical origins have concentrated more on the contact inhibition of bilateral interactions than on the linear analog realm of circuits. However, the mathematics of life provides a gateway for unifying academic disciplines but puts great pressure on humanity to use those insights wisely, because the ultimate arbiter is nature’s judgment whether we’ve become good enough planetary citizens — and it can vote to cause our civilization to collapse!

level | stage 1 | stage 2 | stage 3 | stage 4 | |

life: | 1 | physics5 moieties in the universelife’s 4 interacting moietiespast | present | future | irreversibility | chemistrySchrödinger’s equationreaction-diffusion processes | unicellular lifeevolution → embryogenesisunicellular-to-multicellular transition | multicellularitymedicinephysiologyBME, part 1 of origins |

viruses: “hijack, jump ship, and destroy” paradigm | solving life’s equations: developmental processes | prokaryotes: greedy downhill search | eukaryotes: parallel competitive search | ||

“hardware”: | 2 | development | downhill search | parallel competitive search | parallel cooperative search |

anticipationanalog linear circuitsPID control with feedforward modelBME, part 2 of originsprerequisite: realistic worldview | contact inhibitionbilateral interactiontradeoffs and compromiserealm of epidemiology and biostatisticscharacteristic: saturating (sigmoidal) curvespitfall: timing errors | universalitymultilateral interactionsdigital circuitslinear and switching abilitycharacteristic: sharp transitions, no timing errors | toolboxescomputers and networksreliable hardware substrate for potentiating softwarecivilizational design: cooperative construction, building from both sides | ||

“software”: | 3 | optimizationtypes: selfish, developmental, competitive, and cooperative searchescorresponding realms for life: viral, developmental, multicellular, civilizational | applicationsbiomimicrysystematic civilizational designothers?? | fluencyobservations of how life works, beyond current abilities of human engineering | partnership with Godgateway to fluent civilizational transformationprerequisite: good planetary citizenship (since nature dictates transitions and can rule with collapse) |

BME = biomedical engineering

I still haven’t figured out how best to bring tables like this to life. Each topic one discusses has a table like this, so it’s always different depending on what aspects of reality are under discussion. In fact, I think such tables will be seen as a universal language for theological discourse. On other occasions, I’ll go through tables like this systematically one cell at a time, but for purposes here, I’ll just point out features I haven’t discussed yet.

The most important point for this discussion is that all the developmental stages are separate islands of thought and action, each one building on its predecessors that were prerequisites for its advancement, but ultimately and foundationally disconnected. The price we pay for solving the equations of chemical and civilizational metabolism is this fragmentation. This is our Tower of Babel, the high-energy barrier that life extracts that forces us to work to stay connected. In one Star Trek episode, Spock does a Vulcan mind-meld with a being that notes how lonely we humans are. And, Friend#6, you said it perfectly yesterday, “We may not be on the same boat, but we’re all in the same storm.”

Here is the ultimate significance of that fragmentation: it can be deadly in itself! Medical science uses that fragmentation explicitly in antibiotics and chemotherapy to disrupt and kill pathogens and cancer cells, respectively. And right now, as we approach a pivotal inflection point in human civilization, we are compelled to overcome that fragmentation, begin to coalesce as a multicellular-like structure, and ultimately act in fluid, fluent fashion, like a thinking organism, or else our civilization will die or suffer birth defects.

The frustration we felt as medical students who had been exposed to a different discipline in engineering, which continues in you but morphed in me, is just exasperation at fragmentation. It is closely related to what our civilization is experiencing under lockdown to contain COVID-19, unable to advance our simultaneous expectations for health and wealth. Nature has given us a reprieve for meditating on our values, but we cannot linger in this dead zone forever, any more than a bacterium with a ruptured cell wall or a cancer cell with disrupted replication due to therapeutic drugs intended to kill it.

I’ve expressed my opinion before that clearly COVID-19 wasn’t intended to kill or damage human civilization, but just to fire a warning shot over our bow. Its targeted high-risk populations — the elderly, the immunocompromised, those with chronic health conditions, etc. — are a reminder that nature can and will subject the human population to natural selection pressures if we continue to misbehave, present an existential threat to the earth’s life support system, and threaten the future course of life on earth.

I believe the coronavirus is not as damaging to us as what we have been, and still are, doing to ourselves. The (finished) blog on the mathematics of life presents an experiment illustrating how our reverberating echo chamber and Tower of Babel fragmentation. Find a 4-column article online (representing the four interlinked narratives of 1. past: minorities | 2. present: progressives | 3. future: conservatives | 4. irreversibility: irreversibility). Let’s consider that article to be a gold standard for truth, e.g., a scientific paper. Select All, Copy the article, and Paste it into a one-column document in a word processor application. Unless you have a very intrepid word processor specialized to deal with multi-column selections, the new document with the pasted article will have multiple broken threads, reflecting column boundaries, page headers and footers, and likely even the order in which edits were made as the 4-column article was composed.

Now imagine the implications of this fragmentation under different circumstances:

- A microbial infection or neoplastic tumor undergoing pharmacological therapy would not be able to reconstruct the threads of its metabolism, and so those cells would die in large numbers.
- A society experiencing such fragmentation, buffeted by reverberating echoes, and confronted by significant smearing would not only lose the thread that describes reality, it would also get very confused. Each faction would try to finish its own version of the uncompleted narratives, changing the tone to suit its own preconceptions — which generally would be very different from that in the original document. Some people with very different biases would regard the original tone of the article with suspicion and fill the new voids with conspiracy theories. The fragmented society might experience violence, hate crimes, and even civil war.
- Imagine (as I do) that civilization is at an inflection point when it has to get in synchrony with the earth’s dynamics or suffer irreversible harm, yet some of the factions are hostile to what needs to be done. Their resistance amounts to an existential threat to the future of human civilization and life on earth. The frustration, fragmentation, and polarization intensify. Civil war is a possibility.
- Consider the further possibility that ideologically fragmented and oppositional parties conduct a dialog, based on what they agree is important in life. Suppose they agree on foundational scientific and theological principles that can lead them logically to consensus.

I’ll send this as a blog to the whole group when I finish it.

Best wishes,

Ray G

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