I have found that modern scientists have a certain arrogance that was not as evident in the past–a sense that “science has arrived,” and “we didn’t know better back then, but we got it right, now.” And it is this feeling that science cannot do wrong now, I believe, more than anything else, that is dangerous. The other day, I heard on CBC radio (Canadian Broadcasting Corporation is Canada’s public broadcaster, and might be compared to NPR, but it also comprises three radio streams and does broadcast content from alternative, contemporary, and classical music to talk radio) the other day that some scientists had begun to think that the greenhouse gases were out of control and that a viable solution would be to build an orbiting solar shield to counter global warming. That is precisely the kind of thinking that I find is absolutely irresponsible that happens across the pure, applied, and social sciences. We see it in medicine when a researcher makes the leap from “low blood levels of X result in Y,” to a drug that raises X and causes all sorts of complications with Z, W, and the other due to complex interactions that were difficult to anticipate given the rigid framework of quantitative methods. We see it in economics when we build increasingly accurate econometric models that are great for explaining what is causing economic crises and then try to operate these models in reverse to fix economies.
Some of the most famous and pivotal scientific developments of our time were once developed by Catholic priests and monks. Some of the most compelling mathematical and engineering developments have been made by devout Muslims in the earlier years of Islam. Yet now, the divide between science and religion has never been greater; indeed, the father of modern genetics can be considered a Catholic priest, Gregor Mendel, who studied heritability in pea plants. Having completed my own degree largely in molecular genetics (although I also extensively studied evolutionary and population genetics) before I had converted to Catholicism, people look at me in amazement and wonder how I can responsibly call myself a Catholic, knowing what I do as a scientist. Still more are shocked that I converted from no religion to Catholicism after completing my degree.
Before beginning my MBA in 2000, I was faced during my GMAT exam with a question pertaining to government funding of the arts, as part of my Analytical Writing Assessment. I cannot, of course, go further into detail about the question since I signed an agreement not to disclose test questions, but at the time I still held the belief that arts, such as literature and visual arts, should be maintained as hobbies, while artists supports their own–and society’s–needs through being a regular employed contriburing member of society. I now see the value of government funding of the arts. I now see the value of what could not be achieved without this freedom. I extend the same belief to science. With increasing funding coming from industry–with its associated expectations to do science that satisfies an intermediate- to short-term business goal–it is vital that the government maintain adequate funding–especially to the pure sciences–such that research without directly obvious commercial application or that runs afoul of current industry wisdom will still be carried out. University research must not be allowed to become an extension of a pharmaceutical R&D lab.
It is interesting how I arrived at that belief through inductive reasoning. I have recently become a huge fan of the Rubiks Cube, and subsequently, all of its larger cousins available commercially, ranging from the 2×2x2 Rubiks Cube to the 7×7x7 V-Cube 7. I have made many discoveries in pure inductive reasoning through it. I often found that traditional logic puzzles have a weakness where any critical thinker can “outsmart” the questions by thinking of exceptions and “what ifs.” Indeed, that might be the *responsibility* of a critical thinker. But reduced to coloured cubelets moving around, the Rubiks-type cube puzzles present to me a pure opportunity to study reasoning, much like Chess is to strategy.
I realize that there exist many algorithms to solve the cube, some of which involve no problem-solving or strategic skills whatsoever, and while I do not find much value in using these mindlessly following steps to solve the cubes, I do now encourage all beginning cubers to learn the simplest beginner methods–which reduce solving the basic 3×3x3 cube to six basic steps, recognizing a simple situation, and repeating a series of repeated moves–in order to be able to solve the cube well enough without thinking that the cuber can begin to focus on watching the behaviours of the cubelets. When I begin teaching someone to DJ or play the piano, for example, it is impossible to learn things like phrasing or articulating motifs while still trying to learn the technical skills; thus, beginners to musical instruments must focus on technique before interpretation. Likewise with cubing, a beginner set of algorithsms helps be able to solve the cube and focus entirely on studying the cubelet movements without being distracted by also thinking how to solve the cube.
But once someone is able to solve the cube in under roughly two minutes, I advise abandoning the beginner method for more intuitive ones. My favourite of these, the Jessica Fridrich method, eschews the initial first- and second-layer algorithms for a set of intiutive steps that complete the first two layers simultaneously.
When one progresses to the 4×4x4 cube (and higher order cubes), they will recognize immediately that the most common general solutions for them are to reduce the cube into a 3×3x3 and solve as usual–all centre cubelets are filled in and move as a single centre, and all edge cubelets between corners are paired and move as a single edge piece. There are issues that can arise in a 5×5 that could not exist in a 4×4 (a 5×5 has a 3×3 centre, whereas a 4×4 has only a 2×2 centre–in order to fill in 5×5 centres, it is necessary to fill in a 2×3 on one face, and a 1×3 on a separate face; then displace a 1×3 line of the 2×3, rotate the face, and return the displaced 1×3 in the empty 1×3 slot). This strategy had to be deveoped because the 4×4 only had two 1×2 slots for centres, whereas the 5×5 has three 1×3 slots.
When generalizing, therefore, is the pattern to fill in centres layer-by-layer, or to fill in two separate halves of a centre and join them? That is also not evident yet because the 5×5 does not have enough layers to abstract that information.
Moving onto the 6×6x6 cube (which has a 4×4 centre), it is readily apparent that the way to fill in centres is buiding two separate 2×4 segments and merging them because once a 3×4 block is created, attempts to displace and replace a
1×4 block will disrupt the portion of the block between the middle of the cube and the second layer. Moving onto the 7×7, new challenges to the approach that worked so well for the 4×4, 5×5, and 6×6 come into view that could not exist because of the fewer layers in previous cubes.
But all other strategies and algorithms remain the same as lower-order cubes.
It is that elegance, beauty, and simplicity, the complexity, that I have come to appreciate from cubing. And the process of abstracting generalizations that apply to all (n-layer) cubes that I learned by developing strategies for solving (n-1)-, (n-2)-, and (n-3)-layer cubes, for example.
The same inductive reasoning do we strive for in qualitative research designs.