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Heuristics and Axioms

Heuristics and Axioms - pattern recognition


Heuristic (/hjʉˈrɪstɨk/; Greek: "Εὑρίσκω", "find" or "discover") refers to experience-based techniques for problem solving, learning, and discovery that finds a solution which is not guaranteed to be optimal, but good enough for a given set of goals.

Derived from a Greek word that means "to discover," heuristic describes a rule or a method that comes from experience and helps you think through things, like the process of elimination, or the process of trial and error.


a self-evident truth that requires no proof. 2. a universally accepted principle or rule. 3. Logic, Mathematics. a proposition that is assumed without proof

An axiom or postulate is a premise or starting point of reasoning. As classically conceived, an axiom is a premise so evident as to be accepted as true without controversy.

Heuristics are devices for reducing the complexity of problem solving to experience based techniques such as rule of thumb, common sense, intuition, “logic” etc.. Using lateral elbow pain as an example based on common sense it would be reasonable to assume that the pain is from the elbow rather than referred from elsewhere given that then the most likely condition based on prevalencies is tennis elbow. The exhausting effort of a full examination is avoided by this heuristic but you can immediately see the problem of completely trusting in it. But this is generally how humans work with everyday problem solving and unfortunately many clinicians with diagnosis. Heuristics can be extremely useful but effort must be made to confirm their conclusions and avoid the cognitive bias’.

Axioms, are statements that are self evident truths that do not need proving and maxims are generally seen to be more like ethical or moral guidelines. An axiom currently in vogue in physical therapy at the moment is that criterion validated tests are better than those that have not been subjected to comparison with a gold standard or that research evidence is better than other forms of evidence. On a different level there is if a muscle is weak it needs strengthening and if tight stretching. As with all axioms there are exceptions and all four of these statements are not necessarily true and may in fact need proving, in which case they are really opinions rather than axioms. However, so widespread the belief in them they take on the role of axioms.

Probably the best known maxim in medicine comes from the Hippocratic oath saying that whatever else you do don’t make things worse, a translation from the more formal, “first do no harm”. More useful because it is less obvious are the old saw “if you hear hoof-beats think horses not zebras”, “if it looks like a duck, waddles like a duck and quacks like a duck, it is a duck”. Both are reminders of ways of thinking about a thing, keep it simple, the common or obvious is probably correct, or more formally the “common disease, common variant” hypothesis.

It is worth remembering though that zebras do beat their hooves and if you were in Africa the saying would be reversed.

Occam’s (Ockham) Razor is an example of an axiom and is probably the most useful of all in problem solving. The loose translation is that all things being equal the simplest solution is probably the true one. While this is not an accurate translation of the axiom (Latin being the language in which it was originally written and actually stated that make as few assumptions as possible when choosing between alternative hypotheses) it works very well for our purposes. It is not a scientific truth but it is a reminder that unless there is a good reason chose the hypothesis that makes least assumptions. Using the lateral elbow pain example again, there might be two things causing the pain, a tendonopathy and referral from the neck, possibly three things the previous two and a biomechanical dysfunction of the radiohumeral joint and so on. Now it is possible that two or more distinct pathologies may be causing the same pain but the probability is extremely small that this is so and you should not go there until you are forced to by more information. For example the patient may tell you that gripping is painful but so is sitting quietly watching TV (assuming that the patient is not an addicted channel hopper). This and the duck and zebra axioms we love to challenge wanting the solution to be the rarest and most complex diagnosis that is possible, we hate the common place and simple.

Hickum’s dictum (don’t you love the way that sounds) states that “a patient can have as many diseases as he damn well pleases”, I’m assuming this is a direct quote from Hickum who must have been fed up with the requirement that the diagnosis should be one pathology that explains all of the patient’s symptoms. In physics there is a principle (their axiom) that states that solutions should be economical and where possible elegant and this has either been ripped of from there or this is a an inborn requirement for humans. In general it is better to explain everything by one condition, if nothing else it simplifies treatment planning and implementation but if there is more chance of three common causing three different symptoms rather than one rare condition causing them all then all things being equal go with the three common conditions.

Treat the patient not the numbers; the uncertainty principle. Statistics are about averages and means and the way numbers cluster around them, they do not deal in individuals, we do! In physics and chemistry statistics are used all the time, in fact quantum mechanics depends on it but the physicist and chemist are dealing with particles that are essentially the same as all the other particles or similar molecules. Bodies falling in a gravitational field are completely predictable and so statistics work for the individual. The reason why it works this way is because chemists and physicists deal with extremely simple systems and even then they tend to have to reduce them still further to get their models to work, but our patients are dissimilar from each other and most diseases and condition present differently, sometimes extremely different from person to person. Because something only occurs to 1:1,000,000 adults it doesn’t mean that it doesn’t occur it means that it does occur but the chances are that you are not going to see it. But somebody has to and it might be you so keep it in mind but don’t see zebras.

Sutton’s law basically states that you should do only the tests that are appropriate for you hypothesis. In case you are interested Sutton was a bank robber who when caught was asked why he kept robbing banks. His answer was “because that’s where the money is”. We have a tendency to do tests because first they are available and cost nothing but time (seemingly), and second because we have been told that’s what we should do in the name of not missing anything. If we had to pay for each test then we might be a little more frugal with them. It really isn’t any different in principle to getting X-rays on everybody who has sprained their ankle or hurt their neck and there are algorithms to avoid exactly this. Not only is it a waste of time and money it is often counterproductive. Take, as an example, magnetic resonance imaging every patient complaining of low back pain, how many would demonstrate disc bulging, degeneration and other odds and ends that are completely irrelevant to their back pain. If you know what the problem probably is at any given time only use the tests that move you onto the next level, this includes questions.

As becomes apparent most of them contradict one or more others so these are really not axioms in the strictest sense of the word if two or more of them can be correct yet they are opposite in intent from another they cannot both be true all of the time and this is exactly how you should use them. More than anything they are guidelines on how you approach a problem and can be combined into two statements.

First everything must be based on probability not possibility so choose the solution that best fits the facts and if two are more solutions are possible first choose the most probable but remember that uncommon conditions and variants do occur but they are probably not occurring now (Occam’s razor, ducks and zebras, Hickum’s dictum and statistical failure).

Second, ask only those questions and do only those tests that are immediately pertinent to the immediate problem. If you are looking to make a diagnosis do so, if etiology do that but do not ask questions concerning etiology if you are solving a diagnostic problem (Sutton’s law).

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