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.


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Complexity vs Randomness

I’ve posted before about randomness and complexity. The montage above illustrates the distinction sometimes made between regular, complex, and random patterns. The text examples below provide another illustration:

Regular Complex Random
aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa … 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, … BdhBt BMgkn YCbfR enFwJ DlMyq KFNoi rRdlu JwdTc IPoim oeFnQ gnhqq pqXon cIVVn rAOrx XtbcQ rZTBF sxeTi hLmBt gREOe Udrwt QHEMW OCBeV gQrHb gKbWa lklBL ivZMg JJrGa xVOZj QQBpb rfZWQ qRKTa ZEktK ofhTD UOXrm ZJAJs LPloV NhFjy …

But how does one measure complexity? Grassberger notes that the widely-used Kolmogorov complexity is simply a measure of randomness. In other words, the use of Kolmogorov complexity implicitly assumes that complexity is just “randomness lite.”

There are three significant groups of people who doubt this. First, those complexity scientists who speak about the “edge of chaos” see the borderlands between regularity and randomness as being critically important, and in need of formal characterisation. However, rather than attempting to measure “complexity” in a way which would give both regular and random patterns low scores, this behavioural zone is now typically studied in terms of correlation length and other critical phenomena.

The second group are those critics of evolution who, believing ex nihilo nihil fit, assert that complexity has to come “from somewhere.” If complexity is just “randomness lite,” then random variation plus natural selection are sufficient to produce complex structures (indeed, in silico, the successes of genetic algorithms and genetic programming support that idea). Doubting this, these critics of evolution (such as Michael Behe) have suggested alternate definitions of complexity (irreducible complexity and specified complexity). However, since these alternate concepts have not been rigorously defined, they are not generally accepted outside the “intelligent design” community.

The third group, which includes figures such as Stuart Kauffman, also claim that random variation plus natural selection is inadequate to explain the evolution of biological complexity. However, they believe that the processes of self-organisation studied by the first group provide the missing explanation. This group does not use an agreed-upon formal definition of complexity, focussing primarily on simulation models in which non-trivial structures emerge. Their approach is interesting, but (as far as I can see) still vigorously debated.

Thinking about complexity

I was recently involved in a discussion on complexity. Complexity seems like a natural idea – “abababababababababababababababababababababababababababababab” is a simple sequence of letters, while “Whether ‘tis nobler in the mind to suffer the slings and arrows of outrageous fortune” is a complex one. Actually formalising this idea is a little tricky, however. As with some other concepts (time, for example), we recognise complexity when we see it, but actually defining complexity is difficult. One of the leading approaches is Kolmogorov complexity.

Roughly, Kolmogorov complexity measures the complexity of a sequence by the simplest program that can generate that sequence, which is a formal way of finding the simplest description of the sequence. For example, that first sequence is simple because it can be described as “ab”×30.

The simplest programming language I know is combinatory logic (much simpler even than Turing machines). Combinatory logic has all the theoretical power of any other language, but programs are composed only of brackets and the constants S and K (which I will treat as equivalent to 0 and 1). The brackets satisfy (x y) z = x y z. Execution proceeds by term rewriting, and there are just two execution rules:

S x y zx z (y z)K x yx

We can set up a version of Kolmogorov complexity based on combinatory logic. Through Gödel numbering, each program in combinatory logic is associated with a natural number. Execution of the programs gives finite or infinite sequences of S, K, and brackets. I will treat S as 0 and K as 1, ignoring the brackets. I will treat finite sequences as repeating.

Program #0 in the Gödel numbering is just the constant S, which terminates immediately and is equivalent to producing the sequence “0,0,0,…” Program #1 is just the constant K, equivalent to “1…” A slightly more complex program is #96, which is S S K K S, and executes as follows:

1. S S K K SS K (K K) S

2. S K (K K) SK S ((K K) S) = K S (K K S)

3. K S (K K S)S

Execution stops with S in this case, which is equivalent to producing the sequence “0…”

I will take the simplest program producing a sequence to be the first program in the Gödel numbering, with the complexity of the sequence being the number of bits in the Gödel number. The two sequences “0…” and “1…” therefore both have complexities of one bit. Repeating pairs have complexities of 2 or 3 bits, while repeating triples have complexity 4 to 6 (see below). Because programs may produce unproductive infinite loops, actual calculation of the complexity of a sequence is not always possible.

Sequence Program Complexity
010101010101010101010101010101 = 01… #3 2
101010101010101010101010101010 = 10… #4 3
010010010010010010010010010010 = 010… #8 4
001001001001001001001001001001 = 001… #9 4
100100100100100100100100100100 = 100… #13 4
011011011011011011011011011011 = 011… #15 4
101101101101101101101101101101 = 101… #25 5
110110110110110110110110110110 = 110… #49 6

Some more complex sequences (having non-trivial descriptions) are listed below. The highest complexity will be associated with random sequences – which implies that random-number generators are machines for creating complexity. In the images at the top of the page, the random pattern of mineral flecks in granite therefore form the most complex pattern. That may or may not be what we intended the word “complexity” to mean.

Sequence Program Complexity
010000100001000010000100001000 = 01000… #141 8
001010010100101001010010100101 = 00101… #153 8
010110101101011010110101101011 = 01011… #167 8
000110010001100100011001000110 = 00011001… #183 8
010000100010000100010000100010 = 010000100… #189 8
001000001000001000001000001000 = 001000… #198 8
000101001000101001000101001000 = 000101001… #201 8
001000010010000100100001001000 = 00100001… #216 8
001000100100010010001001000100 = 0010001… #233 8
010100101010010101001010100101 = 0101001… #251 8
010101101010101101010101101010 = 010101101… #275 9
001100011000110001100011000110 = 00110… #305 9
000010000001000000100000010000 = 0000100… #333 9
001110110011101100111011001110 = 00111011… #359 9
010110010110010110010110010110 = 010110… #369 9
001010001010001010001010001010 = 001010… #392 9
010100011010001010100011010001 = 010100011010001… #407 9
000001010000100000101000010000 = 0000010100001… #425 9
001000010001000010001000010001 = 001000010… #434 9
010001001000100100010010001001 = 0100010… #465 9
001001101001001001101001001001 = 001001101001… #471 9