70 They don't fit 28 Aug 2020

The story

At University of Chicago, my physics professor (structure of matter course) tricked us with a priceless lesson. The homework solution was not an exact answer. We were to place sixteen readings into a four-by-four table so that they filled a consistent progression of energy levels. It was easy to sort the numbers into columns such that each number was a fixed step lower than the number above it—except for the last column. After I filled three columns, it was impossible to arrange the remaining four numbers to match the pattern.

In discussing the homework solution, we students complained, “but the numbers in the last column don’t fit.” He wisely called our attention to the fact that these were experimental results, not theoretical values. Real life examples are not pre-measured, neatly ordered ideals. They are elusive facts, exceedingly difficult to determine precisely. Our best experimental efforts are not assured to measure exactly as expected. In this example, he gave us a priceless life lesson.

False security

I have reassured my readers that we create our own worlds. I did not promise that they would fit. From childhood we feel secure when our results match predictably: we get the same answers as our peers; we see the same results of our efforts; we come to the same conclusions. We are easily trapped into thinking that if we arrive at a different result, we must be in error.

This false dependency on security leads to a major difficulty. Because difference threatens the security we feel in our answers, we want everything to be in agreement, to be the same as we think it should be. At times, the insecurity manifests in fierce rejection of difference.

I am old enough to realize that all our individual worlds put together will never “fit.” We might say that we differ only in terminology, in the definitions we are using. We claim the underlying reality is fixed and exact. Non-fitting numbers are always experimental errors. By now I recognize the childish oversimplification.

Broken bottlenecks

Science begins with “close-fitting” theories. Michael Fowler credited Galileo (leaning tower of Pisa experiment) with understanding that “if air resistance and buoyancy can be neglected, all bodies fall with the same acceleration …” The prize thinking was to demonstrate this experimentally, not by reading classical philosophy. However, the second article also credits Galileo with realizing incidentally that the bodies did not quite fall together. The most precise equipment of our day could shed further light on the other forces at play.

Science grows up as it finds phenomena that don’t fit established theories. Finding exceptions to supposed rules forces us to look deeper into underlying principles. Some scientists call progress “broken bottlenecks.” Much of our knowledge today grew out of investigating what did not “fit.”


Age has taught me not to force the real world into my precise categories. There may be a reality that is not subject to the measuring stick I am using, and questions that do not have exact, permanent answers. Many in the fields of religion, politics, philosophy, even “hard sciences” have attempted to quash “absurdities” that proved later to be truths.

It is typical for us to crave the security of sure answers. However, excessive dependency on the surety of what we accept insulates us against the truth we do not yet appreciate.

I remember vividly the conversation in my freshman year in which a very gentle young lady, a professor’s daughter, explained to me that what is right for me might not be right for somebody else. Today I am inviting a vast readership to join me in treasuring that realization. Let us put kindness above sureness in our incomplete beliefs.

Photo by Spencer Davis from Pexels

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