Statistical divergences signal real structure and must not be truncated away.

Evidence

No one would have reacted badly to a distribution with an infinite fifth moment; nevertheless its exponential would also have an infinite expectation. Altogether, it used to be safe for scientists to believe that the universe is organized for simplicity and the conveniences of the mathematicians. But my fifty-year long study of complexity suggests otherwise. … For example, what can you deduce from knowing the average sales of a US software firm in 2003? It is the ratio with a numerator somewhat higher than the sales of Microsoft and a denominator that is meaningless because it is overly dependent on the smallest sales used in taking the average. What about the expectation of a `nearly’ log-normal variable? It is so extremely sensitive to inevitable deviations from lognormality that it hardly matters. … The lesson for finance: divergences may or may not be significant, but must not be papered over in advance. — Donald MacKenzie, An Engine, Not a Camera, 1525

Categorization

• DEFINE: Clarifies why infinite moments matter: truncating tails yields finite but meaningless values.
• DEEPTHINKING: The Mandelbrot argument that cutoffs producing finite moments can be mathematically sterile while confronting divergences yields progress — inverting the usual statistical intuition — is genuinely dense and paradigm-shifting.
• QUESTION: The analogy between the ultraviolet catastrophe (cutoff = quantum, physical reality) and finance divergences — does the author ever identify an analogous genuinely physical cutoff for finance?
• XREF: connects to: Response acquiescence can forge fake statistical links between unrelated measures; Practical statistical convenience, not empirical fit, drove finance’s retention of the normal distribution — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 510; Independent partitions sum dB attenuations but real ones underperform this

Broader Connections

• Response acquiescence can forge fake statistical links between unrelated measures #qualifies (0.75)
• Independent partitions sum dB attenuations but real ones underperform this #exemplifies (0.75)
• Practical statistical convenience, not empirical fit, drove finance’s retention of the normal distribution #expands (0.70) — Donald MacKenzie, An Engine, Not a Camera, 510