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The Unexpected

In critical rationalism, induction on 15/06/2011 at 3:01 pm

But in all my experience, I have never been in any accident … of any sort worth speaking about. I have seen but one vessel in distress in all my years at sea. I never saw a wreck and never have been wrecked nor was I ever in any predicament that threatened to end in disaster of any sort. (E. J. Smith, 1907, Captain, RMS Titanic)

Yesterday when I was out riding my bike, my bicycle’s front tube popped with a loud BANG! After examining it later, I realized that it was no fault of the road — no sharp rock or shard of glass — but of the tube: it was worn out so much that it split at the seam. This lead me to write once again on the topic of induction. This time, I will focus on everyday examples in order to illustrate the point that inductive inferences are as unjustified as any other conjecture about the unobserved.

I want to begin with a brief historical simplification: Francis Bacon thought that theories are (or should be) constructed only after an exhaustive observation of specific instances. We leave our biases, myths and traditions at the door, so Bacon claims, and then examine the collected data objectively. Only once the mind is a a blank slate can we put confidence in the theory that is derived from observation, for we have refrained from leaping to hasty conclusions.

Of course, this is a false story of scientific discovery. Lakatos said, “at least among philosophers of science Baconian method is now only taken seriously by the most provincial and illiterate” (Imre Lakatos, ‘Popper on demarcation and induction’, in The Philosophy of Karl Popper, 1974, p. 259). If I am to help out in insulting a dead man, nobody with the slightest familiarity with scientific practice or knowledge-acquisition in lower animals would see this as an accurate description of theory-formation.

As I’ve touched on in the past, animals are interested in problems, in cases where their inborn or conjectured expectations go awry. Humans are much the same as other animals, only that our biggest problems are now separate from maintaining equilibrium long enough to reproduce: our theories are constructed in response to our technical or intellectual problems, our violated expectations, not out of observation unclouded by any assumptions.

Furthermore, there is a logical reason for theory-formation to occur before observation: there must exist an explanatory framework in order to interpret observations and seek out patterns. All observation is theory-dependent, for no one can fully discard their prejudices without also discarding their problems.

However, let’s move this inductive inference a bit back away from theory-formation to apply it to confidence-building long after the theory has been formed. Perhaps, then, once we’ve set out to posit a particular solution to a problem, we can use these accumulated instances in order to bolster our belief in this solution.

The validity of an inductive inference after theory-formation is then inferred from a great number of singular observations. Furthermore, the very principle of induction is then inferred from a great number of singular observations of induction working successfully. This argument is, admittedly, inductive. Induction is used to justify its own use, even though numerous counterexamples exist.

Bertrand Russell gives a damning description of the inductivist turkey:

The turkey found that, on his first morning at the turkey farm, that he was fed at 9 a.m. Being a good inductivist turkey he did not jump to conclusions. He waited until he collected a large number of observations that he was fed at 9 a.m. and made these observations under a wide range of circumstances … Each day he added another observation statement to his list. Finally he was satisfied that he had collected a number of observation statements to inductively infer that “I am always fed at 9 a.m.”. However on the morning of Christmas eve he was not fed but instead had his throat cut. (The story by Russell is found in Alan Chalmers, What is this thing Called Science, Open University Press, Milton Keynes, 1982, p. 14)

Take, for instance, the millions of turkeys that die each year. Surely an inductive inference of a sort can be made: by its own lights, induction does not work. Of course, this criticism is far too weak; even though Putnam uses this ‘pessimistic meta-induction’ to argue that current scientific theories are likely to be false, my use of dead turkeys is meant only in jest, but it demonstrates that induction cannot be seriously used in order to justify induction. This argument presupposes inductive inferences are valid.

Are we then as blind as the turkey about the future status of sufficient clean water and food production, stable climate, peak oil, and so on? And if these environmental and social problems do exist, why think we can arrive at a solution in time? All we have at hand is the fact that up until this moment, we have always come up with a solution to our problems. But this is an inductive observation! I do hope we are smarter than Russell’s turkey and realize that this answer is fallacious. As I’ve said before, success does not guarantee, or make more probable, future success. That dog won’t hunt.

I take Popper’s solution to the problem of induction to be the only option left: scrap the assumption that theories are created through a procedure of inductive inferences and replace it with the assumption that theories are conjectures, myths, that need no justification. While conjectures often correspond with the traditional inductive inference, they are not inferences; one does not seek instances in support for prejudicial conjectures. Since confirmation teaches nothing and provides only psychological comfort, one seeks instances that refute. A falsification (reductio ad absurdum), if it is true, is decisive. A confirmation, if it is true, is often question-begging (a petitio principii).

In this way, the philosophy of conjectures and refutations renders redundant the entire theory of induction, along with all its contradictions. It does not matter where an idea comes from; what matters is how we deal with it by attempting to expose its shortcomings.

This brings me back to my bicycle. Each day I ride that bicycle to work; each past event of my bicycle successfully getting me from point A to point B does not mean that I should be any more confident of its future success: natural wear and tear on the tube will soon let all the air out in one large BANG!, leading me, Pangloss, to become Cassandra, harping on and on about bicycle tires. The lesson I am trying to get across is that things break, or to speak far broader, things change. The world is not static.

When I say that things change, I mean both in that our understanding of things change over time, and that the physical world around us is always in flux. Both engineering and the theoretical sciences then suffer under their own problems of induction (Nassim Taleb’s The Black Swan is an enjoyable journey through this problem).

One historical illustration of the failure of induction in engineering is the unfortunate case of the Challenger disaster. I recommend that you read Richard Feynman’s appendix to the report in full, for the paper reads as a thorough condemnation of inductive inferences in engineering:

The argument that the same risk was flown before without failure is often accepted as an argument for the safety of accepting it again. … The phenomenon of accepting for flight, seals that had shown erosion and blow-by in previous flights, is very clear. … There are several references to flights that had gone before. The acceptance and success of these flights is taken as evidence of safety. … The fact that this danger did not lead to a catastrophe before is no guarantee that it will not the next time, unless it is completely understood. When playing Russian roulette the fact that the first shot got off safely is little comfort for the next.

Lastly, I turn to a squash court beneath Alonzo Stagg Field at the University of Chicago on December 2nd, 1942: a group of physicists began to experiment on the Chicago Pile-1: a pile of alternating layers of uranium and graphite blocks. When a uranium atom splits, it releases neutrons. Some neutrons escape the pile, some neutrons strike another uranium atom and cause an additional fission. The average number of neutrons escaping from a single uranium atom undergoing fission that cause another fission will be denoted as k. When k < 1, the pile is “subcritical”. When k > 1, the pile is “critical”. Fermi calculated that the pile will reach k=1 between layers 56 and 57 of the Chicago Pile-1.

On that day, all but one of the control rods were withdrawn, allowing for an increase of neutron activity in the pile. Fermi ordered the final control rod withdrawn about half-way out. The geiger counters clicked faster. Several minutes later, Fermi ordered the rod pulled out another foot. Again the radiation rises, then levels off. The rod is pulled out another six inches, then another, then another.

Finally, 3:25pm, Fermi orders the rod withdrawn another twelve inches. That first critical reaction had k of 1.0006. If Fermi had piled on one more uranium brick or pulled out the control rod any further, that would have been a very big difference. If Fermi, rather than thinking that between 56 and 57 layers the pile would go critical, had reasoned that 57 layers ought not to behave all that differently from 56 layers, Fermi’s inductive inference while conducting the experiment would have brought about a horrible catastrophe.

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  1. The actual original analogy by Bertrand Russell (1912) was less colorful and involved a chicken, rather than a turkey. https://books.google.com/books?id=U03TCgAAQBAJ&pg=PT31

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