One of the habits of human reason is to classify things, order them by means of deeper reasoning after observing them, so that a more universal significance of their relatedness can be established.
When things are observed and classified by insubstantial and incidental characteristics irrelevant to its essence, it is referred to as “paredolia.” The picture of “Jesus on Mars” is a familiar example. People can become embroiled in apparent arguments about the “significance” of this observation; arguments which really center on their own metaphysical beliefs and not the observation itself. The “devil in the World Trade Center” is another sparkling example of paredolia.
I am bothered by a “math-based puzzle” which was run in the Daily Mail today. I find it an example of paredolia, one that is meaningful to every weary physician struggling through the miasma of regulation. We await, for instance, the MACRA rule which implements what is called the Quality Payment Program, which gives doctors two options for getting reimbursed under Medicare: they can participate either in the Merit-Based Incentive Payment System (MIPS) or Advanced Alternative Payment Models (APMs).
These rules, to imply that they are something more than arbitrary and unthinking mandates, must appeal to some objective sort of logic that leads to their determination. There must be easily encoded reason – an “algorithm” – which allows an objective observer to come to the same conclusion as the thinkers who declared the algorithm to be objectively better than any other algorithm. Without such assertion, one is left with the assertion that the definers of the rules do so because they have the power to do so, and that’s the end of the discussion. “Whoever’s got the gold, makes the rules.” is the paraphrase of the cynic’s Golden Rule.
The math puzzle comes with all sorts of smug certainty to it. “Many have guessed the answer as 8 – but they’re incorrect.” The implication is that there is a right answer, rather than what is mathematically more robust – that there are a number of ways of thinking about the question that can lead to a defensible answer.
By coincidence, my first way of analyzing the question was likely the same as the “solver.” However, the “solver” asserted that he/she had the “right” answer. I do not believe there is such a thing here. If one counts the intersections of the lines, one comes up with nine on the first figure, and one of the second figure; so there are four on the third figure.
We are emotionally trained to feel good when we get approval for getting the “right” answer, and frustrated when we get the “wrong” answer. This is more social conditioning than a measurement of mathematical skill.
The node count – the number of intersections – is a good way to look at the problem. It is:
- Universal – any number of lines will give rise to a subsequent number of nodes.
- Objective – any OBSERVER will get the same result using the algorithm.
But it is not definitive. Many solutions fit the puzzle effectively; therefore, many solutions are equally correct, without further information. The number of lines, without intersections can be considered. The first figure has six lines, with 9=2×6-3 fitting the result; and the second figure, 1=2×2-3 Therefore, y=2x-3 fits just fine, and the third result would be 5 (2×4-3)
When one anoints an algorithm to be authoritative, one fixes a decision – what is the relevance of the node count? – onto the solution. Here, the decision is assumed, as it does not derive from the puzzle.
When people construct metrics for complex things, e.g. physician performance, they assume that their algorithms are, if not authoritative, at least equivalent to any others that can be generated. This is a very bad assumption, for it fixes the possible methods of quantitative, i.e. understanding, what is to be solved. The algorithm may be universal and objective; but it has no justification to exist.
This is very serious, as this is at the heart of technopathy. Just because an algorithm can be generated, does not convey any metaphysical relevance to what it implies. That much is still superstition. Scientific reasoning must test the necessity of the answer – such as Karl Popper’s falsifiability question. We are racing back into voodoo approaches to the world, guided by our faithful friends in IT.