Tag Archives: dynamics

The Secret of the Universe in 6 sentences

Niall Palfreyman wrote this on the board to introduce a course in differential equations:

  1. The Secret of the Universe in 6 sentences
  2. Nature always integrates flows over time
  3. Flows always differentiate fields over space
  4. Structure determines behaviour
  5. Algebra is the study of structure
  6. Dynamics is the study of behaviour

I like it.

A little explanation is in order. I have my morning coffee in hand. It’s warmer than the room, so it’s cooling off. It’s heat winds up in the room. If I want to manage my coffee well, neither burning my tongue nor gagging down cold sludge, I need to be able to make some predictions about the future behavior of my cuppa joe. I won’t get far by postulating demons randomly stealing calorics from my cup, though that might provide a soothingly fatalistic outlook. I’m much better off if I understand how and why coffee cools.

#2, the “nature integrates flows” part of the system looks like this:


Each box represents an accumulation of heat (that’s the integral). Each pipe represents a flow of heat from one place to another. The heat currently in the house is simply the net result of all the inflows from coffee cups, and all the losses to the outside world, over all time (of course, there are other flows to consider, like my computers warming the room, and losses to the snowy outside).

In the same way, the number of people in a room is the net accumulation of all the people who ever entered, less all those who ever left. A neat thing about this is that the current heat in the cup, or count of people in a room, is a complete description of the state of the system. You don’t need to know the detailed history of inflows and outflows, because you can simply take the temperature of the cup or count the people in the room to measure the accumulated effects of all the past events.

The next question is, why does the heat flow? That’s what #3 is about. Heat follows temperature gradients, as water flows downhill. Here’s a temperature field for a coffee cup:


wikimedia commons

Heat will flow from the hot (red) cup into the cool (green) environment. The flow will be fastest where the gradient is steepest – i.e. where there’s the greatest temperature difference over a unit of space. That’s the “flows differentiate fields” part. Other properties also matter, like the thermal conductivity of the cup, air currents in the room, insulation in the wall, and heat capacity of coffee, and these can also be described as distributions over space or fields. That adds the blue to the model above:


The blue arrows describe why the flows flow. These are algebraic expressions, like Heat Transfer from Cup to Room = Cup to Room Gradient/Cup-Room Heat Transfer Coefficient. They describe the structure – the “why” – of the system (#5).

The behavior of the system, i.e. how fast my coffee cools, is determined by the structure described above (#4). If you change the structure, by using an insulated mug to change the cup-room heat transfer coefficient for example, you change the behavior – the coffee cools more slowly.* The search for understanding about coffee cups, nuclear reactors, and climate is essentially an effort to identify structures that explain the dynamics or patterns of behavior that we observe in the world.

* Update: added a sentence for clarification, and corrected numbering.

The Seven Deadly Sins of Managing Complex Systems

I was rereading the Fifth Discipline on the way to Boston the other way, and something got me started on this. Wrath, greed, sloth, pride, lust, envy, and gluttony are the downfall of individuals, but what about the downfall of systems? Here’s my list, in no particular order:

  1. Information pollution. Sometimes known as lying, but also common in milder forms, such as greenwash. Example: twenty years ago, the “recycled” symbol was redefined to mean “recyclable” – a big dilution of meaning.
  2. Elimination of diversity. Example: overconsolidation of industries (finance, telecom, …). As Jay Forrester reportedly said, “free trade is a mechanism for allowing all regions to reach all limits at once.”
  3. Changing the top-level rules in pursuit of personal gain. Example: the Starpower game. As long as we pretend to want to maximize welfare in some broad sense, the system rules need to provide an equitable framework, within which individuals can pursue self-interest.
  4. Certainty. Planning for it leads to fragile strategies. If you can’t imagine a way you could be wrong, you’re probably a fanatic.
  5. Elimination of slack. Normally this is regarded as a form of optimization, but a system without any slack can’t change (except catastrophically). How are teachers supposed to improve their teaching when every minute is filled with requirements?
  6. Superstition. Attribution of cause by correlation or coincidence, including misapplied pattern-matching.
  7. The four horsemen from classic SD work on flawed mental models: linear, static, open-loop, laundry-list thinking.

That’s seven (cheating a little). But I think there are more candidates that don’t quite make the big time:

  • Impatience. Don’t just do something, stand there. Sometimes.
  • Failure to account for delays.
  • Abstention from top-level decision making (essentially not voting).

The very idea of compiling such a list only makes sense if we’re talking about the downfall of human systems, or systems managed for the benefit of “us” in some loose sense, but perhaps anthropocentrism is a sin in itself.

I’m sure others can think of more! I’d be interested to hear about them in comments.

The Blood-Hungry Spleen

OK, I’ve stolen another title, this time from a favorite kids’ book. This post is really about the thyroid, which is a little less catchy than the spleen.

Your hormones are exciting!
They stir your body up.
They’re made by glands (called endocrine)
and give your body pluck.

Allan Wolf & Greg Clarke, The Blood-Hungry Spleen

A friend has been diagnosed with hypothyroidism, so I did some digging on the workings of the thyroid. A few hours searching citations on PubMed, Medline and google gave me enough material to create this diagram:

Thyroid function and some associated feedbacks

(This is a LARGE image, so click through and zoom in to do it justice.)

The bottom half is the thyroid control system, as it is typically described. The top half strays into the insulin regulation system (borrowed from a classic SD model), body fat regulation, and other areas that seem related. A lot of the causal links above are speculative, and I have little hope of turning the diagram into a running model. Unfortunately, I can’t find anything in the literature that really digs into the dynamics of the system. In fact, I can’t even find the basics – how much stuff is in each stock, and how long does it stay there? There is a core of the system that I hope to get running at some point though:

Thyroid - core regulation and dose titration

(another largish image)

This is the part of the system that’s typically involved in the treatment of hypothyroidism with synthetic hormone replacements. Normally, the body runs a negative feedback loop in which thyroid hormone levels (T3/T4) govern production of TSH, which in turn controls the production of T3 and T4. The problem begins when something (perhaps an autoimmune disease, i.e. Hashimoto’s) diminishes the thyroid’s ability to produce T3 and T4 (reducing the two inflows in the big yellow box at center). Then therapy seeks to replace the natural control loop, by adjusting a dose of synthetic T4 (levothyroxine) until the measured level of TSH (left stock structure) reaches a desired target.

This is a negative feedback loop with fairly long delays, so dosage adjustments are made only at infrequent intervals, in order to allow the system to settle between changes. Otherwise, you’d have the aggressive shower taker problem: water’s to cold, crank up the hot water … ouch, too hot, turn it way down … eek, too cold …. Measurements of T3 and T4 are made, but seldom paid much heed – the TSH level is regarded as the “gold standard.”

This black box approach to control is probably effective for many patients, but it leaves me feeling uneasy about several things. The “normal” range for TSH varies by an order of magnitude; what basis is there for choosing one or the other end of the range as a target? Wouldn’t we expect variation among patients in the appropriate target level? How do we know that TSH levels are a reliable indicator, if they don’t correlate well with T3/T4 levels or symptoms? Are extremely sparse measurements of TSH really robust to variability on various time scales, or is dose titration vulnerable to noise?

One could imagine alternative approaches to control, using direct measurements of T3 and T4, or indirect measurements (symptoms). Those might have the advantage of less delay (fewer confounding states between the goal state and the measured state). But T3/T4 measurements seem to be regarded as unreliable, which might have something to do with the fact that it’s hard to find any information on the scale or dynamics of their reservoirs. Symptoms also take a back seat; one paper even demonstrates fairly convincingly that dosage changes +/- 25% have no effect on symptoms (so why are we doing this again?).

I’d like to have a more systemic understanding of both the internal dynamics of the thyroid regulation system, and its interaction with symptoms, behaviors, and other regulatory systems. Here’s hoping that one of you lurkers (I know you’re out there) can comment with some thoughts or references.

So the spleen doesn’t feel shortchanged, I’ll leave you with another favorite:

I think that I ain’t never seen
A poem ugly as a spleen.
A poem that could make you shiver
Like 3.5 … pounds of liver.
A poem to make you lose your lunch,
Tie your intestines in a bunch.
A poem all gray, wet, and swollen,
Like a stomach or a colon.
Something like your kidney, lung,
Pancreas, bladder, even tongue.
Why you turning green, good buddy?
It’s just human body study.

John Scieszka & Lane Smith, Science Verse

Climate, the Bailout, and the Blame Game

I’ve been watching a variety of explanations of the financial crisis. As a wise friend noticed, the only thing in short supply is acceptance of responsibility. I’ve seen theories that place the seminal event as far back as the Carter administration. Does that make sense, causally?

In a formal sense, it might in some cases. I could have inhaled a carcinogen a decade ago that only leads to cancer a decade from now, without any outside triggers. But I think that sort of system is a rarity. As a practical matter, we have to look elsewhere.

Socioeconomic systems are at a constant slow boil, with many potential threats existing below the threshold of imminent danger at any given time. Occasionally, one grows exponentially and emerges as a real catastrophe. It seems like a surprise, because of the hockey stick behavior of growth (the French riddle of the lily pond again). However, most apparent low-level threats never emerge from the noise. They don’t have enough gain to grow fast, or they get shut down by some unsuspected negative feedback.

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Climate War Game – Is 2050 Temperature Locked In?

This slide became known as “the Angry Red Future” at the war game:
The Angry Red Future

Source: ORNL & Pew via Nature In the Field

After seeing the presentation around it, Eli Kintisch of Science asked me whether it was realistic to assume that 2050 climate is already locked in. (Keep in mind that we were living in 2015.) I guessed yes, then quickly ran a few simulations to verify. Then I lost my train of thought and lost track of Eli. So, for what it’s still worth, here’s the answer.

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The Switch to Small Cars – Not So Fast

The NYT reports that a switch to efficient cars is underway, as evidenced by, among other things, an increase in market share for small cars from an eighth of the market at the height of SUV-mania to a fifth today, together with a sharp drop in large truck and SUV sales.

If sustained, such a shift would signal a very significant sensitivity of vehicle efficiency purchasing habits to fuel prices – perhaps much larger than the low short run price elasticity of gasoline demand. However, I think there is reason to interpret these recent events cautiously, lest they prove a little less astonishing in the long run. Continue reading

Life Expectancy and Equity

Today ScienceDaily brought the troubling news that, “There was a steady increase in mortality inequality across the US counties between 1983 and 1999, resulting from stagnation or increase in mortality among the worst-off segment of the population.” The full article is PLoS Medicine Vol. 5, No. 4, e66 doi:10.1371/journal.pmed.0050066. ScienceDaily quotes the authors,

Ezzati said, “The finding that 4% of the male population and 19% of the female population experienced either decline or stagnation in mortality is a major public health concern.” Christopher Murray, Director of the Institute for Health Metrics and Evaluation at the University of Washington and co-author of the study, added that “life expectancy decline is something that has traditionally been considered a sign that the health and social systems have failed, as has been the case in parts of Africa and Eastern Europe. The fact that is happening to a large number of Americans should be a sign that the U.S. health system needs serious rethinking.”

I question whether it’s just the health system that requires rethinking. Health is part of a complex system of income and wealth, education, and lifestyle choices:

Health in context

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