Expand Your Small Infinities

How knowing your limits can help you overcome them

ESA/Hipparcos/J. de Bruijne, CC BY 4.0

Imagine for a moment that you are right about everything.

Suppose you did the research, thought carefully, and arrived at a model of the world around you which precisely matched reality in every way. How would that change the way you lived?

You would certainly not spend much time pondering questions about why something happened; every event would make sense. If people tried to argue against your explanations, you would always have an answer, since in the end, you would always be right.

But that also describes someone who is not always right: a dedicated conspiracy theorist.

Was Pepe Silvia an alien walrus?

I am not talking about your everyday, “the media is biased” sort of conspiracy. Think more your hardcore, “walrus-like aliens have taken over the Illuminati” conspiracies. People who believe these ideas also have an answer for everything. Even though many of us can see the flaws in their perspective, no argument seems to persuade them. In fact, they see supposed weaknesses as reinforcing their conclusions: “Of course he denied being an alien walrus in disguise, that’s exactly what an alien walrus would say!”

Author G.K. Chesterton remarked that the mind of such a conspiracist “moves in a perfect but narrow circle. A small circle is quite as infinite as a large circle; but, though it is quite as infinite, it is not so large. In the same way the insane explanation is quite as complete as the sane one, but it is not so large… The lunatic’s theory explains a large number of things, but it does not explain them in a large way.”

To be sure, most of us do not believe in tusked yet intelligent extraterrestrials. But given our capacity for self-deception, we accept other small infinities. Research on the “left-brain interpreter” shows how we routinely (albeit unconsciously) tell ourselves tales of our own personal conspiracies.

In one experiment, a “split-brain” subject (an epilepsy patient who had most of the connections between each side of their brain removed to prevent seizures) was shown two words: “music” and “bells.” However, each was only shown to one eye, causing their left brain to see “music” and their right brain to see “bells.” They verbally (left brain) attested to seeing “music,” but when asked to point (right brain) to a picture representing the word, they chose an image of bells from among other musical options. When asked why, they claimed to have heard bells outside shortly before the experiment. Absent knowledge of the right brain seeing “bells,” the left brain essentially made up an explanation.

Clip from a documentary on split-brain research.

While these processes are not quite as obvious in a normal brain, they still happen. Every day, we face a flood of information we have to synthesize and process while navigating the world. For better or worse, our minds continually take shortcuts to handle that deluge, no matter how careful and rational we might think we are in making decisions. Many times, these shortcuts actually serve us quite well. But as storytellers at heart, we make sense of events through narratives we construct, and we underestimate how much those narratives influence our reasoning. Consequently, we underestimate how much we’re wrong about.

In fact, the more our outlook seems complete, the more reason we have to be skeptical of its veracity. Occam’s Razor only works well for very fine cuts: when solving very large problems, a simple explanation has a greater chance of being a small infinity rather than a comprehensive solution. If you feel as though you have an answer for everything, it is theoretically possible you have figured out more of reality than all the billions who came before you, but it is far more likely you have compressed reality into a narrow circle that makes sense to you.

Should we just give up, then? The closer we think we are to truths about the universe, the greater the chance we’re actually tricking ourselves. Does our narrative nature stymie success in any pursuit of proficiency? Are we forever doomed to ignorance and uncertainty? Are we just wrong about everything?

In a word, no. And history provides an illustration as to why. In the 17th century, scientists such as Isaac Newton developed ways of measuring how objects move and interact, such as their energy or gravity. For over 200 years, people used these equations to understand the world and develop new ideas.

Yet the whole time, those equations were wrong.

OpenLearn chart showing how far off one Newtonian formula becomes as you approach the speed of light (c).

How was that possible? Well, the equations were mostly right; they work quite well in a wide variety of contexts. When objects get extremely large or extremely fast, though, you have to apply some changes discovered by Einstein. Those changes become so insignificant in everyday situations that no one realized they were necessary for a few centuries. Even after Einstein’s updates, physicists realized other adjustments would be needed for extremely small objects, such as subatomic particles. All of these newer expressions look very different from the formulas they replace, but still produce the same results most of the time.

Essentially, the old methods were right enough. They were wrong in the larger, grander sense of describing all possible situations, but they encompassed the parts of reality that were necessary for those past calculations. They enabled many people to succeed along the way, but they could only carry science so far.

A tale of two bicycles.

You can think of an idea being “mostly right” in another sense: accuracy vs. precision. Consider the two images above; is it right to say the set of lines and circles on the left is a bicycle? Yes, but in a particular sense that would not hold in every context. The icon on the left captures the basic concept of “bicycle,” yet it lacks nearly all of the detail in the photo on the right. Both are accurate representations, but only one is very precise.

Both of these examples illustrate how a framework can produce good answers in a range of situations while breaking down in others. Similarly, we can rely on stories that seem quite justified but remain incomplete; with some of life’s messier questions, the limits to such stories may be difficult to discern. Still, certain explanations may come close enough to reality that any remaining inconsistencies fail to matter most of the time.

As Newton and Einstein before us, we have tools available to test and trim our model of the world, bringing it closer to the truths we seek. While the odds of embracing incomplete explanations increase the more we are able to incorporate in that model, we can simultaneously decrease the odds of being drastically, dangerously wrong through research, discourse, and reflection.

We should never forget, though, that our model is never truly finished. As we agreed at the start, none of us is right about everything. Knowing the hurdles we face in trying to identify when we are wrong and understand what’s actually right, we can each practice three habits to counter their impact:

  • Retain a margin of humility in your conclusions. I feel quite confident about some of my convictions, and I am not afraid to defend them with passion. But even those cases do not exclude the possibility I remain mistaken. I may be convinced that I have applied enough available resources in assessing an idea to avoid getting it completely wrong, but I always want to remember that I am probably more wrong than I realize. How I express my thoughts should allow for the possibility of future amendments and avoid mocking or condescension.
  • Recognize when your opponent has a point. When we do feel confident, we may wait in vain for a perfect enemy. If someone presents a critique or a counterargument, we have a natural tendency to look for holes. But if we dismiss their case on a technicality or focus only on its flaws, we may overlook observations (whether subtle or prevalent) that our model does not currently account for well. Even if our viewpoint is still 99% correct, we may eventually face a context where the remaining defects lead us badly astray.
  • Refine your perspective with time. Life can be truly overwhelming. As we try to cope, the extremes of feeling nothing can be meaningfully known or clinging dogmatically to narrow explanations may tempt us with their simplicity. But as we take time to study, listen, and care, we discover the nuances around us that give reality its texture. Set aside the goal of a mythic destination where you are right about everything. Instead, picture your understanding of the world as a garden for you to cultivate. Engage with this process of continuing to learn and grow as the horizons of your understanding expand.

An analytical romantic. I help people understand how they fit into the world.

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