Harp strings and design

Having previously blogged about the mathematics of the harp, I thought I might say some more about harp design issues. It’s an interesting question that involves both physics and human factors. For simplicity, I’m going to talk about just one string, one playing the note A at 440 Hz. Of course, a real harp will have between 21 and 46 other strings.

The physics of vibrating strings gives us Mersenne’s laws, which tell us that the frequency of a string of length L is (1 / 2L) √ T / μ , where T is the tension force on the string (in newtons), and μ is the density per unit length of the string (in kg per metre).

The diagram below shows the required tension force (in newtons) for a nylon string of various lengths and diameters to play the note A at 440 Hz (click to zoom). A newton corresponds to roughly the gravitational force on 100 grams.

The first, and most obvious, design factor is that too much tension causes the string to break. Setting a design limit of 90% of the expected breaking strength means that the string must be less than 560 mm in length. Interestingly, this limit is independent of the diameter of the string.

The string must also be playable. A string that is too floppy or too tight cannot be effectively played. A rough guide is that the tension should be at least 35% of the expected breaking strength, which means that the string must be at least 350 mm long. Additional limits, which I’m ignoring here, relate to how much room the string needs to vibrate.

Thirdly, the frame can only take so much. If the frame of a 40-string harp is built to withstand 10,000 newtons (roughly the gravitational force on 1000 kg), then the average string has a limit of 250 newtons. This restricts us to the design space on the diagram outlined in red.

Finally, a harp has levers or pedals which shift the strings to be sharp or flat (the basic harp strings correspond only to the white keys on a piano). Those devices set further limits on the design space for strings.


A modern electric lever harp (photo: Athy)

It is interesting to relate this to my other interest, that of solar cars. They are vehicles, which means that they must hold a driver (and new guidelines on World Solar Challenge driver space have just been announced). They are solar, which means that their upper surface must hold a solar panel of specified size. And they race, which means that their aerodynamic drag must be as low as possible. This necessitates a variety of compromises, just as with the design of a harp. The problem is much more complex however; the space of possible solar car designs has many more dimensions than two.


Some principles of network epidemiology

Lockdowns and “flattening the curve” are very much in the news right now, so I thought it was timely to post about some principles of network epidemiology. The charts below (click to zoom) show the simulated spread of a disease (in a small “toy” population of 2000) subject to certain assumptions. The blue lines show the total number of cases over time (adding up those infected, recovered, and dead). This total number is important because some percentage of the final total will die, and we want to minimise that (if we can). The red lines show the number of current infections over time. This is important because some percentage of the red numbers are in hospital, and the red peak therefore represents peak load on the medical system.

In the top row, we have connections happening at random, with increasing social distancing happening from left to right. Moderate social distancing doesn’t change the fact that almost everybody gets the disease, but it does delay and reduce the peak, thus taking strain off the medical system. Extreme social distancing saves many lives, but only if social distancing is continued for a long time (in real terms, until a vaccine is available, which is almost certainly not sustainable).

In the middle row, we have the same number of contacts happening as in the top row, but most of the contacts are within limited social circles. Such contacts, between family members and close friends, are less serious than contacts with strangers. If Peter is your close friend, and you catch the virus, then there’s a reasonable chance that Peter caught it the same way, and so there’s a reasonable chance that your contact with Peter makes no actual difference. If Peter is a spouse, child, or flatmate, that’s quite a good chance. Contacts with strangers, however, can spread the disease from one social circle to another, and so are far more serious.

In the bottom row, we again have the same total number of contacts happening, but a few “super spreaders” have many more contacts than average (while the majority have slightly less than average, to compensate). This third scenario is significantly worse than the top row – higher, earlier, red peaks, and many deaths even when there is extreme social distancing. Unfortunately, experience has shown that medical personnel, in spite of the fantastic work that they do, have the potential to be serious “super spreaders,” because:

  • they have contact with many patients;
  • the patients are strangers; and
  • the patients are more likely than average to be elderly and/or vulnerable.

This is why personal protective equipment (PPE) for medical personnel is so critically important, as are good testing protocols for medical personnel. Other kinds of “super spreaders” also occur, of course, and it is important to identify them, test them, and provide them PPE (or stop them doing what they’re doing, if it’s non-essential – some jurisdictions with supposedly strict rules are still allowing prostitutes to operate, for example).

Overall, if we look at columns in the picture (all three charts in each column have the same total number of contacts), we see that the kind of contact is just as important as the number of contacts. Isolation regulations in some jurisdictions don’t always recognise that fact, unfortunately.


Coronavirus diary #1

The SARS-CoV-2 coronavirus is changing the world. Ridiculous and selfish panic-buying is stripping supermarket shelves, in Australia as elsewhere. Everyone I know is catching up on their reading, and people are being persuaded to practice social distancing and to wash their hands.

It seems to me that if you’re under 50 and healthy, there is absolutely no need to panic. But it’s really important not to pass on the disease, if and when you catch it, to other people. Listen to your local medical advice, people!

Virus photo from NIAID Rocky Mountain Laboratories; supermarket photo by Christopher Corneschi, 9 March 2020; painting by Marguerite Gérard; hand-washing photo by Michelle Gigante/USAF.


Scientific alignment

I was thinking recently about the alignment (in the Dungeons & Dragons sense) of fictional scientists (see diagram above).

I was brought up on the Famous Five children’s stories by Enid Blyton. Perennially popular, even though flawed in certain ways, these novels star a rather grumpy scientist called Quentin (who had more than a little to do with my own desire to become a scientist). Quentin is certainly altruistic:

‘These two men were parachuted down on to the island, to try and find out my secret,’ said her father. ‘I’ll tell you what my experiments are for, George—they are to find a way of replacing all coal, coke and oil—an idea to give the world all the heat and power it wants, and to do away with mines and miners.’
‘Good gracious!’ said George. ‘It would be one of the most wonderful things the world has ever known.’
‘Yes,’ said her father. ‘And I should give it to the whole world—it shall not be in the power of any one country, or collection of men. It shall be a gift to the whole of mankind—but, George, there are men who want my secret for themselves, so that they may make colossal fortunes out of it.’
” (Enid Blyton, Five On Kirrin Island Again, 1947)

However, Quentin works for no organisation (barring some government consulting work) and draws no regular salary. He is clearly Chaotic Good.

Long before Quentin, Victor Frankenstein in Frankenstein (Mary Shelley, 1818) created his famous monster out of selfishness and hubris. However, he also desires to make things right, so Frankenstein seems to me Chaotic Neutral.

On the other hand, the experiments of Doctor Moreau in The Island of Doctor Moreau (H. G. Wells, 1896) mark him as Chaotic Evil. The same is true of the scientist Rotwang in the movie Metropolis (1927), who is the prototype of the evil “mad scientist” of many later films – in contrast to good “mad scientists” like Emmett “Doc” Brown in the Back to the Future movies (1985, 1989, 1990).

In all cases, however, there seems to be a bias towards portraying scientists as Chaotic. This is a little strange, because the organisational structures, processes, and rules governing science in the real world are better described as “ordered” or Lawful (in the Dungeons & Dragons sense). Perhaps chaotic characters are just more fun?

Not that everyone follows all the rules and procedures of course. When I take the What is your Scientific Alignment? test, my personal alignment comes out as Neutral Good.


Looking back: 1987

In 1987, my PhD work at the University of Tasmania was beginning to take shape, and I produced a technical report with some preliminary results. I also started a side-project on functional programming language implementation which was to result in the design of a novel computer (a computer, sadly, that was never actually built, although many people joined in on the hardware aspects).

Also in that year, Supernova 1987A became visible within the Large Magellanic Cloud (picture above taken by the Kuiper Airborne Observatory). The programming language Perl also appeared on the scene, and Per Bak, Chao Tang, and Kurt Wiesenfeld coined the term “self-organized criticality.” Prompted by a discovery in 1986, physicists held a conference session on high-temperature superconductivity, billed as the “Woodstock of physics.” The immediate benefits were somewhat over-hyped, however.

The usual list of new species described in 1987 includes Fleay’s barred frog from northern New South Wales and south-eastern Queensland (picture below taken by “Froggydarb”).

In the world of books, James Gleick popularised chaos theory with his Chaos: Making a New Science, Allan Bloom wrote The Closing of the American Mind (which Camille Paglia called “the first shot in the culture wars”), and Donald Trump co-wrote Trump: The Art of the Deal (nobody imagined that he would be President one day).

Horror writer Stephen King had a good year, with The Tommyknockers and several other novels being published. The term “steampunk” was coined in 1987, and Orson Scott Card’s Speaker for the Dead, the sequel to Ender’s Game, won the Hugo Award for best science fiction or fantasy novel (it also won the Nebula Award in 1986, the year it was published).

In music, The Alan Parsons Project released their album Gaudi (which included the single below), U2 released The Joshua Tree, and Linda Ronstadt, Emmylou Harris, and Dolly Parton released Trio. The Billboard top song for 1987 was the rather silly 1986 single “Walk Like an Egyptian.”

Films of 1987 included 84 Charing Cross Road (based on the wonderful 1970 book by Helene Hanff), Bernardo Bertolucci’s The Last Emperor, Japanese hit A Taxing Woman (マルサの女), sci-fi action film Predator, Australian film The Year My Voice Broke and, of course, the cult classic The Princess Bride (based on the 1973 novel by William Goldman).

In this series: 1978, 1980, 1982, 1984, 1987, 1989, 1991, 1994, 2000, 2004, 2006, 2009.


The worms crawl in, the worms crawl out

Underneath (or, perhaps, to the side of) adult culture sits an often poorly documented culture for children alone. There are, of course, many songs and stories directed by adults to children, but true child culture consists of games, riddles, songs, stories, and rules directed from children to other children.

A rather dark example, largely specific to North America, is the Hearse Song below (the video gives a more complete version, but I must warn my readers – it’s really very gross, and not at all suitable for adults):

Don’t ever laugh as a hearse goes by
For you may be the next to die
They wrap you up in a big white sheet
From your head down to your feet
They put you in a big black box
And cover you up with dirt and rocks …
And the worms crawl in, the worms crawl out
The worms play pinochle on your snout …

The song is essentially a form of gallows humour picked up by children at around age 10 – about the age that children first come to grips with the inevitably of death (although it is rather surprising, given that the US is a majority-Christian society, that Christian views of death barely appear in the song at all). The excellent article on the song by Charles Doyle also reports military versions of the song from World War I recorded by Carl Sandburg and John J. Niles, but those appear to draw on earlier childhood versions.

I’ve been experimenting with a textual analysis focussing on song snippets containing lines devoted to interment (2 to 6 lines, depending on the version). I compared versions with a variation of the Levenshtein distance at the word level, using a table of related words, and allowing for permuted lines. The multi-dimensional scaling diagram below collapses the calculated distances into two dimensions. The phrase “Doyle var” refers to variants listed by Doyle (e.g. “They put you in a big white shirt / And cover you up with rocks and dirt”), whereas “Alternate” refers to versions I have collected myself on the Internet (e.g. “They wrap you up in a bloody black sheet / And throw you down a thousand feet”). A large amount of mishearing and misremembering seems to be going on.

The numbers in brackets on the chart indicate the number of lines in each snippet. The 2-line child versions form a visible cluster in the diagram, with 4-line versions by modern bands (Harp Twins and Rusty Cage) a little more distant, and the World War I versions on the periphery all quite different:

Distances can also be visualised as an UPGMA tree. However, this cannot really be interpreted as an evolutionary tree, in that the 4-line band versions seem to be combining lines from multiple 2-line versions. Indeed, there seems to be a large pool of rhyming pairs within the culture that is assembled and reassembled in various ways, rather than any canonical song. Perhaps this reflects the character of the verbally innovative child culture in which the song (or, rather, song family) dwells.


Seven varieties of metaphysics

I was having a discussion with someone recently on metaphysics, so I thought I would blog about it. Here are seven varieties of metaphysics, describing three “layers” of reality (and yes, I am oversimplifying for brevity).

The first is Platonism. Plato believed that there was a hierarchy of Forms (Ideals), of which the highest was The One (Plato’s version of God). These Forms or Ideals were the true reality, and the physical objects we touched, saw, and tasted were only shadows of that true reality (that is the point of the allegory of the cave). The physical orange which we see and eat reflects Ideals such as “Fruit,” “Sphere,” and “Orange.” Neoplatonism continues and extends this point of view.

Saint Augustine and many later Christians held to a Christianised Platonism, in which the Ideals were thoughts in the mind of God (the Christian God, naturally). The physical objects we touched, saw, and tasted had a greater importance in Christian Platonism than they did for Plato – after all, when God created those objects, “God saw that it was good.” Much as with Platonism, the regularities that people see in the physical universe are explained by the fact that God created the universe in accordance with regularities in the Divine thoughts. However, Christian Platonism does not have the metaphysical hierarchy that Platonism or Neoplatonism have – in Christian Platonism, God makes direct contact with the physical universe.

Aristotle also reacted to Plato by increasing the importance of the bottom layer, and Aristotle’s thought was Christianised by Thomas Aquinas as Thomism. However, in Thomism the all-important bottom layer does very little except to exist, to have identity, and to have properties assigned to it. It is also not observable in any way. This can be seen in the Catholic doctrine of transubstantiation. According to the Tridentine Catechism of 1566, the bread and the wine of the Eucharist lose their bottom (“substance”) layer (“All the accidents of bread and wine we can see, but they inhere in no substance, and exist independently of any; for the substance of the bread and wine is so changed into the body and blood of our Lord that they altogether cease to be the substance of bread and wine”), while the bottom (“substance”) layer of the body and blood of Christ becomes metaphysically present instead.

Idealism denies that the physical universe exists at all. The followers of Mary Baker Eddy take this view, for example, as did George Berkeley. Only thought exists. To quote a famous movie line, “there is no spoon.” These thoughts may be independent of whatever God people believe in or, as in monistic Hinduism, they may be actually be the thoughts of God (in which case, only God exists).

The last three kinds of metaphysics deny the existence of any kind of God. In Platonist Materialism, this denial is combined with a Platonist approach to mathematics, about which I have written before. Mathematics exists independently of the physical universe, and controls the physical universe, in the sense that the physical universe follows mathematical laws. Roger Penrose is one of many scientists holding this view.

In what I am calling Extreme Materialism, the existence of an independent mathematical world is also denied, i.e. there is an empiricist approach to mathematics (mathematics simply describes observed regularities in nature). This view seems to be increasing in popularity among non-religious people, although it causes philosophical problems for mathematics.

Finally, the concept of the Mathematical Universe holds that the so-called “physical universe” is itself composed only of mathematical objects – only mathematics exists (which makes this, in fact, a kind of Idealism).


In praise of the humble flagellum

The bacterial flagellum (above) is a fascinating device. It contains a molecular motor which rapidly rotates the filament. Whipping around, the filament drives the bacterium forward. In some bacteria, running the motor in reverse causes a random tumble. Amazingly, the combination of forward motion, random tumbling, and a simple sensor allows a bacterium to “home in” on a target (see four simulated example runs below). The idea is to do a random tumble whenever the sensor shows the bacterium heading in the wrong direction. An actual steering mechanism is not necessary – the bacterium gets to the target in the end.

William Dembski and Michael Behe famously argued (via the somewhat informally articulated concepts of specified complexity and irreducible complexity) that the flagellum was too complex to have evolved. Their argument fell apart with the discovery that the flagellum shares components with other bacterial gadgets, such as the injectisome, and thus could potentially have evolved in stages (although in fact the injectisome seems to have evolved as a simplification of the flagellum, and the evolutionary history of the flagellum remains a mystery).

The fundamental point that Dembski and Behe were attempting to make can be illustrated by the simple experiment summarised in the chart above. This experiment presupposes three genes (A, B, and C) all created by single point mutations on copies of existing genes, such that the combination of all three genes creates a useful widget. In the “flat landscape” case, this combination must arise entirely by chance. This takes a very long time (on the experimental assumptions used, an average of almost 14,000 generations). Dembski and Behe were probably right to suggest that, if the bacterial flagellum had to arise that way, it could not have evolved in the time available since the earth was formed.

In the “parallel evolution” case, however, each of the genes A, B, and C are assumed to be independently beneficial. The A-B-C combination then evolves very quickly. Evolution of the bacterial flagellum may have included aspects of parallel evolution, if components of multiple older widgets were “co-opted” for the flagellum.

The evolution of the bacterial flagellum is generally assumed to have instead been a case of “sequential evolution” (gene A is beneficial on its own, gene B is beneficial in the presence of gene A, gene C is beneficial in the presence of genes A and B, etc.). However, it is not at all clear what the sequence of genes producing the bacterial flagellum might have been (suggestions on this topic by Liu and Ochman have been criticised), nor is it clear what the sequence of intermediate benefits might have been (given that the injectisome was not an intermediate stage). Further research on the humble, but amazing, bacterial flagellum is clearly still required.


Complexity and Randomness revisited

I have posted before (post 1 and post 2) about order, complexity, and randomness. The image above shows the spectrum from organised order to random disorder, with structured complexity somewhere in between. The three textual examples below illustrate the same idea.

Regular Complex Random
AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA … It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, … ShrfT e6IJ5 eRU5s nNcat qnI8N m-cm5 seZ6v 5GeYc w2jpg Vp5Lx V4fR7 hhoc- 81ZHi 5qntn ErQ2- uv3UE MnFpy rLD0Y DI3GW p23UF FQwl1 BgP36 RK6Gb 6lpzR nV03H W5X3z 2f1u8 OgpXy tY-6H HkwEU s0xLN 9W8H …

These three examples, and many intermediate cases, can be distinguished by the amount of information they contain. The leading way of measuring that information is with Kolmogorov complexity. The Kolmogorov complexity of a block of text is the length of the shortest program producing that text. Kolmogorov complexity is difficult to calculate in practice, but an approximation is the size of the compressed file produced by good compression software, such as 7-Zip. The chart below shows the number of bytes (a byte is 8 bits) for a compressed version of A Tale of Two Cities, a block of the letter ‘A’ repeated to the same length, and a block of random characters of the same length:

The random characters are chosen to have 64 possible options, which need 6 bits to describe, so a compression to about 75% of the original size is as expected. The novel by Dickens compresses to 31% of its original size.

But does this chart show information? Grassberger notes that Kolmogorov complexity is essentially just a measure of randomness. On this definition, random-number generators would be the best source of new information – but that’s not what most people mean by “information.”

An improvement is to introduce an equivalence relation “means the same.” We write X ≈ Y if X and Y have the same meaning. In particular, versions of A Tale of Two Cities with different capitalisation have the same meaning. Likewise, all meaningless random sequences have the same meaning. The complexity of a block of text is then the length of the shortest program producing something with the same meaning as that text (i.e. the complexity of X is the length of the shortest program producing some Y with X ≈ Y).

In particular, the complexity of a specific block of random text is the length of the shortest program producing random text (my R program for random text is 263 bytes), and we can approximate the complexity of A Tale of Two Cities by compressing an uppercase version of the novel. This definition of complexity starts to look a lot more like what we normally mean by “information.” The novel contains a large amount of information, while random sequences or “AAAAA…” contain almost none:

Those who hold that information satisfies the rule ex nihilo nihil fit can thus be reassured that random-number generators cannot create new information out of nothing. However, if we combine random-number generators with a selection procedure which filters out anything that “means the same” as meaningless sequences, we can indeed create new information, as genetic algorithms and genetic programming have demonstrated – although Stuart Kauffman and others believe that the evolution of biological complexity also requires additional principles, like self-organisation.


Complexity in medicine: some thoughts

I have been thinking recently about medicine and complexity, as a result of several conversations over many years. In particular, the Cynefin framework developed by Dave Snowden (see diagram below) seems a useful lens to use (this thought is not original to me – see among others, the articles “The Cynefin framework: applying an understanding of complexity to medicine” by Ben Gray and “Cynefin as reference framework to facilitate insight and decision-making in complex contexts of biomedical research” by Gerd Kemperman). I will also refer to two case studies from the book Five Patients by Michael Crichton, which is still quite relevant, in spite of being written in 1969.


The Cynefin framework developed by Dave Snowden. The central dark area is that of Disorder/Confusion, where it is not clear which of the four quadrants apply (image: Dave Snowden).

The Cynefin framework divides problems into four quadrants: Obvious, Complicated, Complex, and Chaotic. In addition, the domain of Disorder/Confusion reflects problems where there is no clarity about which of the other domains apply. In medicine, this reflects cases where multiple factors are at work – potentially, multiple chronic conditions as well as one or more acute ones. These conditions can exist in all four quadrants. Ben Gray gives the example of a child with a broken arm linked to both a vitamin deficiency and an abusive home environment. Several quite different interventions may be required.

The Obvious Quadrant

The quadrant of the Obvious applies to conditions with clear cause and effect, where there is a single right answer. According to Dave Snowden, the appropriate response is to sense what is going on, categorise the situation as one on a standard list, and then to respond in the way that people have been trained to do. This response may be trivial (a band-aid, say), or it may involve enormous professional skill. In medicine, much of nursing falls in this quadrant, as does much of surgery.

Michael Crichton’s Five Patients discuses the case of Peter Luchesi, a man admitted to Massachusetts General Hospital during 1969 with a crushed arm and nearly severed hand, as the result of an industrial accident:

Three inches above the left wrist the forearm had been mashed. Bones stuck out at all angles; reddish areas of muscle with silver fascial coats were exposed in many places. The entire arm about the injury was badly swollen, but the hand was still normal size, although it looked shrunken and atrophic in comparison. The color of the hand was deep blue-gray.

Carefully, Appel picked up the hand, which flopped loosely at the wrist. He checked pulses and found none below the elbow. He touched the fingers of the hand with a pin and asked if Luchesi could feel it; results were confusing, but there appeared to be some loss of sensation. He asked if the patient could move any of his fingers; he could not.

Meanwhile, the orthopedic resident, Dr. Robert Hussey, arrived and examined the hand. He concluded that both bones in the forearm, the radius and ulna, were broken and suggested the hand be elevated; he proceeded to do this.

Outside the door to the room, one of the admitting men stopped Appel. ‘Are you going to take it, or try to keep it?’

‘Hell, we’re going to keep it,’ Appel said. ‘That’s a good hand.’

Once the surgeons had sensed the problem and categorised it as an arm reconstruction, a team of three surgeons, two nurses, and an anaesthetist (all highly trained in their respective fields) then spent more than 6 hours in the operating theatre, repairing bone, tendons, and blood vessels. Certainly not trivial, but a case of professionals doing what they were trained to do.

The Complicated Quadrant


Public Domain image

The Complicated quadrant is the realm of diagnosis. Information is collected – in medicine, that generally means patient history, blood tests, scans, etc. – and is then subjected to analysis. This identifies the nature of the problem (in an ideal world, at least), which in turn indicates the appropriate response.

Diagnosis by physicians typically searches for the cause of an illness, while diagnosis by nurses typically focuses on severity. This reflects differences in the responses that physicians and nurses have been trained to provide (the triage officer in a modern hospital is typically a nurse).

Decades of work have gone into automating the diagnosis process – initially using statistical analysis, later using expert systems, and most recently using machine learning. At present, the tool of choice is still the human brain.

In general, modern medicine excels when it operates in the Obvious and Complicated quadrants.

The Complex Quadrant

The Complex quadrant is the realm of interactions. It is inherently very difficult to deal with, and cause and effect are difficult to disentangle. The paradigm of information collection and analysis fails, because each probe of the system changes it in some way. The best approach is a sequence of experiments, following each probe with a response that seems reasonable, and hoping to find an underlying pattern or a treatment that works. Michael Crichton provides this example:

Until his admission, John O’Connor, a fifty-year-old railroad dispatcher from Charlestown, was in perfect health. He had never been sick a day in his life.

On the morning of his admission, he awoke early, complaining of vague abdominal pain. He vomited once, bringing up clear material, and had some diarrhea. He went to see his family doctor, who said that he had no fever and his white cell count was normal. He told Mr. O’Connor that it was probably gastroenteritis, and advised him to rest and take paregoric to settle his stomach.

In the afternoon, Mr. O’Connor began to feel warm. He then had two shaking chills. His wife suggested he call his doctor once again, but when Mr. O’Connor went to the phone, he collapsed. At 5 p.m. his wife brought him to the MGH emergency ward, where he was noted to have a temperature of 108 °F [42 °C] and a white count of 37,000 (normal count: 5,000–10,000).

The patient was wildly delirious; it required ten people to hold him down as he thrashed about. He spoke only nonsense words and groans, and did not respond to his name. …

One difficulty here was that John O’Connor could not speak, and so could not provide information about where he felt pain. He appeared to suffer from septicaemia (blood poisoning) due to a bacterial infection in his gall bladder, urinary tract, GI tract, pericardium, lungs, or some other organ. Antibiotics were given almost immediately, to save his life. These eliminated the bacteria from his blood, but did not tackle the root infection. They also made it difficult to identify the bacteria involved, or to locate the root infection, thus hampering any kind of targeted response. In the end (after 30 days in hospital!) John O’Connor was cured, but the hospital never did locate the original root infection.

Similar problems occur with infants (Michael Crichton notes that “Classically, the fever of unknown origin is a pediatric problem, and classically it is a problem for the same reasons it was a problem with Mr. O’Connor—the patient cannot tell you how he feels or what hurts”). As Kemperman notes, medical treatment of the elderly often also falls in the Complex domain, with multiple interacting chronic conditions, and multiple interacting drug treatments. Medical treatment of mental illness is also Complex, as the brain adapts to one treatment regimen, and the doctor must experiment to find another that stabilises the patient.

Similarly Complex is the day-to-day maintenance of wellness (see the Food and Wellness section below) which often falls outside of mainstream medicine.

The Chaotic Quadrant

The Chaotic quadrant is even more difficult than the Complex one. Things are changing so rapidly that information collection and experimentation are impossible. The only possible response is a dance of acting and reacting, attempting to stabilise the situation enough that it moves from Chaotic to Complex. Emergency medicine generally falls in this quadrant – immediate responses are necessary to stop the patient dying. In the airline industry, the ultimate (and extremely rare) nightmare of total engine failure shortly after takeoff (as in US Airways Flight 1549) sits here too – each second of delay sees gravity take its toll.

Success in the Chaotic domain requires considerable experience. In cases where the problem is a rare one, this experience must be created synthetically using simulation-based training.

Food and Wellness

Michael Crichton notes that “The hospital is oriented toward curative treatment of established disease at an advanced or critical stage. Increasingly, the hospital population tends to consist of patients with more and more acute illnesses, until even cancer must accept a somewhat secondary position.” There is, however, a need for managing the Complex space of minor variations from wellness, using low-impact forms of treatment, such as variations in diet. Some sections of this field are reasonably well understood, including:

Traditional culture often addresses this space as well. For example, Chinese culture classifies foods as Yin (cooling) or Yang (heaty) – although there is little formal evidence on the validity of this classification.

There remain many unknowns, however, and responses to food are highly individual anyway. There may be a place here for electronic apps that record daily food intake, medicine doses, activities, etc., along with a subjective wellness rating. Time series analysis may be able to find patterns in such data – for example, I might have an increased chance of a migraine two days after eating fish. Once identified, such patterns suggest obvious changes in one’s diet or daily schedule. Other techniques for managing this Complex healthcare space are also urgently needed.