Believability of Evidence
A conclusion can be difficult to picture without being poorly supported. When evidence conflicts with intuition, examine the data, assumptions, and reasoning; the feeling that a result is unbelievable does not settle whether it is useful or true.
THE IDEA
Believability of Evidence
Paper folding makes exponential growth hard to picture. A reported practical limit of 12 folds[16] is not a mathematical ceiling on repeated doubling: physical folding depends on the sheet’s size, thickness, and material. The thought experiment sets those practical obstacles aside and asks how thick the stack would become if each fold doubled it.
Start with ordinary notebook paper, roughly one-tenth of a millimetre thick. Seven folds produce a stack about as thick as a notebook. Three more bring it to about the width of a hand. At 14 folds, it is roughly a person’s height. At 17, it is taller than a typical two-story house; three more, for a total of 20, bring it to about a quarter of the height of Chicago’s Willis Tower, formerly the Sears Tower.
At more than 30 folds, the stack would extend beyond the conventional boundary of space, though the atmosphere has no sharp outer edge. At more than 50, it could exceed the distance to the Sun, roughly 94 million miles. At 103 folds, it would exceed the observable universe’s stated diameter of 93 billion light-years. Using approximately 186,000 miles per second for the speed of light gives an illustrative diameter of about 5.4671216 × 10^23 miles.
The arithmetic follows a simple rule: multiply the starting thickness by two raised to the number of folds. The physical task becomes impossible long before the largest comparisons, but the idealized calculation remains intelligible and testable. Difficulty imagining its result is different from finding a flaw in the calculation.
That distinction matters when interpreting evidence. Findings that agree with familiar beliefs are easy to accept. Surprising findings prompt questions: Was the data corrupted? Does the method fit the question? Was there a computational error? These are useful checks. If they do not reveal a problem, the remaining feeling that the result cannot be right may reflect the limits of intuition.
Surprise alone is not cognitive dissonance, and it does not prove a finding correct. Dissonance can arise when new evidence conflicts with beliefs to which we are committed. The response should be to examine the conflict and the strength of the evidence, rather than automatically defend the old belief or embrace the new result.
Quantum mechanics offers another example of a theory whose successful predictions can be easier to verify than to visualize. It helps explain the behavior of semiconductors used in modern computing. Superposition describes a quantum state as a combination of possible states. Entanglement describes correlations between systems. Neither means that objects are consciously aware of distant objects.
Quantum teleportation transfers a quantum state using entanglement together with a classical communication channel. It does not allow instantaneous communication or establish that human consciousness creates physical reality. Nor is quantum mechanics restricted in principle to subatomic particles. Familiar images of a person being simultaneously alive and dead are poor substitutes for specifying a physical system, its state, and how it is measured.
Einstein challenged whether the quantum description was complete. Calling its implications ‘spooky interactions’ conveys their unfamiliarity, but the useful question is what the theory predicts and how well those predictions survive testing. Semiconductor devices provide practical evidence for relevant quantum principles; they do not validate every dramatic analogy made about the theory.
The lesson for decisions is to distinguish intuitive plausibility from evidential support. An analytically derived result can be valuable even when it is hard to picture, but a model’s output still depends on its assumptions and validation. There is no need for a leap of faith where the evidence can be examined.
Arthur Conan Doyle’s phrase captures the appeal of following a conclusion beyond intuition: ‘Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth’. In practice, an analysis may not have eliminated every alternative. Even deeply held beliefs should be open to revision when stronger evidence becomes available.
When to use it
A corporate analyst presents a model showing that a small change in pricing leads to massive revenue growth, but the pattern seems too good to be true. Use the believability of evidence principle to evaluate the model's robustness before discarding it.
A medical study reveals that a common treatment is ineffective, contradicting decades of practice. Despite cognitive dissonance, the evidence should guide new protocols.
Evaluating a counterintuitive marketing result against the experiment’s design and later evidence before deciding whether to continue the strategy.
Assessing the predictions and evidence for an unfamiliar theory instead of accepting or rejecting it because of how strange it sounds.
FROM THEORY TO EVERYDAY LIFE
In practice
Paper Folding and Exponential Growth
With ordinary notebook paper, 50 idealized doublings would create a stack of astronomical height but still short of the Sun, roughly 94 million miles away. At 103 doublings, the stack would exceed the stated observable-universe diameter. These are thickness calculations, not physically achievable folding demonstrations.
Quantum Mechanics and Technology
Quantum mechanics helps explain semiconductor behavior in microchips despite being difficult to visualize. Superposition and entanglement do not imply conscious awareness, and teleportation does not permit instantaneous communication. The theory’s value rests on tested predictions.
A MOMENT TO REFLECT
Put it to work.
Think of a time when data contradicted your strong intuition. How did you reconcile the evidence with your initial belief?
In your field, what widely accepted but counterintuitive finding do you find hardest to believe? What would it take for you to fully embrace it?
What checks would help your organization distinguish a well-supported surprising result from a model error?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- Evidence-Based Decision-Making How to Leverage Available Data and Avoid Cognitive Biases (Andrew D. Banasiewicz)