Consider a Flat Pond - First Parish in Needham Unitarian

Consider a Flat PondJan Galkowski

Westwood Statistical Studios

Westwood, MA

last rev May 4, 2020

Consider a Flat Pond (J. T. Galkowski) May 4, 2020 1

Thanks to Fred Kresse and the FPiN Continuing EducationCommittee for suggesting this talk.

It is dedicated to Fred.

"Think deeply of simple things."– Arnold E. Ross, paraphrasing Johann Carl Friedrich Gauss


(poll)Consider a Flat Pond (J. T. Galkowski) May 4, 2020 3

PrécisWhat this is about: How to think about complicated systems, oreven thingsI am deferring reasons why to the very end. Consider this, fornow, just fun, a game if you will.About pondsA very simple pond, and its questionBuilding a pond modelWhat can be done with the pond model?What else can be done with the pond model, or extensions?EcoMUVE

I’ll move at different speeds through material, depending upon whether I want to just showsomething, or explain it. Slides will be available after the talk so you can go through thematerial I zip past yourself.

Please enter questions into the Chat Box, but there’s a need to focus here, so I’ll answerthem, but not until the end. And if there are any left over, I’ll email you answers. Pleaseinclude your email address in the Chat Box. I’ll ask Tad to save the Chat text.


How to think about complicated things, which I will call "systems"(1 of 2)

Human mind cannot hold a lot at once.

Being able to deal with the complicated means recognizing thatup front.

Dealing with a complicated system means picking a part of itsmall enough to fit in mind and thinking deeply about it.

Then move and pick another part, and do the same.

Then consider the relationships of the parts to each other.

Then consider the relationships of each of the parts to thewhole system.


How to think about complicated things, which I will call "systems"(2 of 2)

Then add another picked part, and do the same.

Repeat until the entire system is covered.

Then figure out a diagnostic that checks (a) haven’t missedanything, and (b) the thinking done is correct.

If being scientific about it, figure out a second, and a third, anda fourth diagnostic doubting the thinking.

Eventually, this develops confidence in this abstraction, whichis sometimes called "a model".


(video of a pond)



Biotope


"quasi-biotope"


Where a scientist might end up


How in the world do you pick parts?


It depends upon the question(s)you want to answer!


So before starting, need a questions you areinterested in.If not list-able, try writing yourself a short essayabout what’s wanted.


What’s the question for this evening?

Want to understand flows through a pond.Why?Perhaps to understand pollution contaminationof ponds.Perhaps to understand basic physical featureslike water levels.


A pondBegin very simply


A pond with an inflow


A pond with an inflow and an outflow


Different numbers of outflows


Different numbers of outflows. . . and a bit about the algebra of flows


Different numbers of outflows, combined. . . and a bit about the algebra of flows


Evaporation of water is an outflow


. . . ... but it can be added in with the rest of the outflows


What about rain?


Rain is a negative outflow


But, of course, rain is a positive inflow. . . and inflows follow the same kind of rules as outflows


We can think about rates of flow


And can devise certain laws or constraints on flow


Conservation Laws


Once in hand these can be used to make predictions


What if things, like pollutants, hitch a ride on flows?Same relationship can be used!

Note wasn’t really crisp about what was flowing.Consider a Flat Pond (J. T. Galkowski) May 4, 2020 31

A nice thing about abstract models is that they sometimes generalize

The same model, more or less, is usable forother problems.For example, disposition of plastic enteringoceans . . .


All the plastic in the world, 1986-2010


All the plastic in the world, 1986-2010


Production of plastics from the United States, 1986-2010


But plastic in oceans doesn’t keep up, at least at the surfaceTrick: When a whole amount isn’t available, compare rates.


K. L. Law, et al, "Plastic accumulation in the North Atlantic Subtropical Gyre", Science, 329, 3September 2010, 1185-1188, with supplement


Study of plastic in world’s oceans


Size of plastic pieces, all the world’s oceans


Suppose there are several connected ponds . . .


What might these be used to model?


SEIR, 1


SEIR, 2


Remember that mention of the trick about rates?Comments on COVID-19 death counts and case counts

Michael Blastland

So, I mean, I’ve seen one statistician, John Ioannidis, call it a "data fiasco". Despite that, arethere things we can say with some confidence?

David Spiegelhalter

Yes, by looking at the rate of change. We can get a lot of information from rates ofchange. Rates of change, are unaffected by systematic underreporting. They’reunaffected by whether it’s done per million or just in the whole country, and so on. Soall these different ways of measuring make no difference when we monitor the rate ofchange. And that is the thing everyone is focusing on, because we’re so interested inwhether that rate is declining. In other words, what we’d love to see both in cases and indeaths is that this rapid increase smooths off into plateaus, into a constant rate, and thenfalls down as it did in China. And everyone’s trying to work out what is going to happen inthe Western countries.

– Professor David Spiegelhalter, Risky Talk podcast, "Coronavirus: Understanding the Numbers".Professor Spiegelhalter is Chair of the Winton Centre for Risk and Evidence Communication, a Bayesian, and author andco-author of many books and articles, including many in the popular press, and including a blog called UnderstandingUncertainty, The Norm Chronicles, and, with Keith Abrams and Jonathan Myles, Bayesian Approaches to Clinical Trials andHealth-Care Evaluation.


http://www.statslab.cam.ac.uk/~david/

https://riskytalk.libsyn.com/transcript-of-coronavirus-understanding-the-numbers

https://understandinguncertainty.org/

https://understandinguncertainty.org/

Can be used to think about and model possibilities . . .Imperfect immunity


Consider the following . . .


Another abstract model: Suppose . . .(Motivation only: Approximates the method being described)

There are two kinds of frogs.

Kind 1 always Blue, moves about ponds, but only toleratesitself in these ponds; no other Blue frogs.

Kind 2 can be in Red, Green, and Pink varieties, but thesealways remain in their own pond.

Frog counts by Kind are known in two of three ponds.

And suppose we know that Blue frogs on average hang outwith M frogs of Kind 2, and avoids ponds where it can’t.

Observing Blue frogs in two ponds, estimate M̊ = 2+42 = 3.


The actual Network Scale-Up Method ("NSUM") : Exploiting small worlds(Inspired to include this by Dr David Berman’s great talk a few weeks back)

Frog’s (people’s, ISP’s, fish-in-school’s, etc) social networks are onaverage representative of the population.

j ∈ {Green,Pink,Red}.

Mi,j : So, "ask" each i of a set of n Blue frogs "How many Red frogs doyou know?", "How many Green frogs do you know?", etc.

Ci = ∑j∈{Green,Pink,Red} Mi,j.

T : Get an estimate of the total number of frogs in all the ponds youcare about.

Estimate of number of Red frogs as T ∑ni=1 Mi,j∈{Red}

∑ni=1 Ci

.

In the case below T = ∑i Ci so simplifies to ∑ni=1 Mi,j∈{Red}, a census.


NSUM case : unrestricted


NSUM case : unrestrictedThis ends up being a census


NSUM estimate of overall population


Ecosystem models for education andremote learning


EcoMUVE, 1


EcoMUVE, 2


EcoMUVE, 3


EcoMUVE, 4


EcoMUVE, 5


EcoMUVE, 6


EcoMUVE, 7


Book Recommendationsand References







References on NSUM, plastic waste in oceans, and how to use SEIR and flows

Bernard HR, Hallett T, Iovita A, et al, "Counting hard-to-count populations: thenetwork scale-up method for public health", Sexually Transmitted Infections, 2010,86:ii11-ii15.

Solé R, Fontich E, Vidiella B, Duran-Nebreda S, "The paradox of constant oceanicplastic debris: evidence for efficient microbial biodegradation",bioarxiv.org:10.1101/135582v.

Jambeck JR, Geyer R, Wilcox C, Siegler TR, Perryman M, Andrady A, Narayan R, LawKL, "Plastic waste inputs from land into the ocean", Science, 13 Feb 2015, 347(6223),768-771, with supplement.

Law KL, Morét-Ferguson S, Maximenko NA, Proskurowski G, Peacock EE, Hafner J,Reddy CM, "Plastic Accumulation in the North Atlantic Subtropical Gyre", Science, 3Sept 2010, 329.

Cózara A, Echevarrıa F, González-Gordillo JI, Irigoien X, Úbeda B, Hernández-León S,Palma A T, Navarro S, Garcıa-de-Lomas J, Ruiz A, Fernández-de-Puelles ML, DuarteCM, "Plastic debris in the open ocean", Proceedings of the National Academy of Sciences,15 July 2014, 111(28), 10239-10244.

P. Dawkins, "Section 2-7: Modeling With First Order Differential Equations", Paul’sOnline Notes, Lamar University.


https://doi.org/10.1101/135582

https://science.sciencemag.org/content/347/6223/768

https://science.sciencemag.org/content/329/5996/1185

http://tutorial.math.lamar.edu/Classes/DE/Modeling.aspx

http://tutorial.math.lamar.edu/Classes/DE/Modeling.aspx

. . . And Mathematics, if interpreted properly, has something to say aboutpolitics and activism (As does "right-brained thinking", in my opinion)

The moral is clear: in the absence ofcomprehensive knowledge, a deliberate changein the ecology, even an apparently minor one, isa very risky proposition.

From Morris W Hirsch, Stephen Smale, Differential Equations, Dynamical Systems, and LinearAlgebra, Academic Press, 1974, from Chapter 12, "Ecology", page 273.



Thank you!


Q & A


Why(From my personal perspective)

A. Druyan, C. Sagan, The Demon-Haunted World: Science as a candle in the dark, 1997.There is a diminuation, for whatever reason, in skill with this kind of thinking.This is unfortunate, for we have serious problems with which to contend.Climate disruption, continuing social injustice, income and racial prejudice andinequality, distorted policy.There is a sense among some, unfortunately, that logic, mathematics, reason, are’European colonial skills and means of apprehension’. They are judged somehowtainted as a result.I cannot personally accept this. Indeed, despite my deep respect for mystical andwholistic means of apprehending the world, those are not the only vehicles.Such is a postmodern notion of Catholic sin, that thought is sin. That makes no sensefrom either a UU or from the perspective of psychology.Thoughts are morally inert.From a practical perspective, if someone is to have a meaningful engagement withpolicy or science, these attitudes and this lack of skill is an impediment.And, practically speaking, an opponent well-armed with these skills using them forimmoral purposes will beat any number of well-intentioned people, however they aremotivated: Dominic Cummings.So, this talk is a kind of a prayer that this delusion will dissipate, and some of thethings we know and do which make us capable, which make us individually powerful,won’t be lost.


Abstract: Consider a Flat Pond (Jan Galkowski)

We often need to consider or think deeply about complicated things. No onecan do that, at least not directly. This is a talk addressing thinking aboutthinking, how to approach complicated things, processes, and phenomenain parts, but not in pieces. It’s about simplifying so something can be deeplyunderstood, then re-introducing complexity but in a controlled way. Theapproach is widely used in the sciences and engineering and mathematicsbut in this Lyceum, delivered over Zoom, I will argue that it can be appliedto ponds, to other ecological problems, social systems, and forecasting theSARS-CoV-2 outbreak.

Most time will be spent considering a pond. Quick illustrations will be givenin an relating to plastic waste in the oceans.


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Consider a Flat Pond - First Parish in Needham Unitarian