Is there any mathematical reason why 37 is considered special or random?

Mathematically, 37 is a prime number. Uniquely, it is the median second prime factor of all integers. This means that half of all numbers have a second prime factor of 37 or less, setting it apart from other primes.

What is the 'Secretary Problem' and how does 37 relate to it?

The Secretary Problem (or marriage problem) describes the optimal strategy for choosing the best option from a sequence of unknown possibilities. The optimal strategy involves rejecting the first 37% of options to gather data, then selecting the next option that surpasses all previously seen ones. This strategy yields a success rate of approximately 37%.

Can the 37% rule be applied to real-life decisions like marriage or job offers?

Yes, the '37% rule' derived from the Secretary Problem can be applied to situations where you face sequential decisions with unknown outcomes. For example, if you aim to settle down in 10 years, you could spend the first 3.7 years exploring potential partners or job opportunities before committing to the best one encountered after that period.

Is the number 37 significant beyond its statistical or mathematical properties?

The video explores numerous anecdotes and perceived coincidences involving the number 37 appearing in various contexts, from birthdays and serial numbers to historical texts and everyday objects. A dedicated individual has spent decades collecting these instances, suggesting a widespread, perhaps subconscious, human fascination with the number.

What makes primes like 37 feel more random than other numbers?

Primes feel random because they don't appear frequently in everyday composite number contexts (like measurements or quantities). Additionally, there's no simple formula to predict the next prime number, requiring a sequential check of numbers, which aligns with the concept of randomness.

Key Moments

Why is this number everywhere?

Veritasium

Education3 min read24 min video

Mar 28, 2024|11,618,103 views|299,639|35,524

science randomness and probability 37 numbers

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Key Moments

TL;DR

The number 37 is frequently chosen as a "random" number due to psychological and mathematical factors.

Key Insights

People are poor at choosing random numbers, often gravitating towards specific digits.

The "blue seven phenomenon" suggests people favor blue and the number seven; 37 is considered its two-digit equivalent.

Mathematical properties, like being prime and its role in prime factorization, make 37 uniquely perceived.

The number 37 is crucial in decision-making strategies, like the secretary problem, maximizing success rates.

A large-scale survey revealed 37 and 73 as highly favored non-random numbers.

An extensive collection of objects and instances featuring the number 37 highlights its ubiquitous presence.

THE HUMAN BIAS FOR 'RANDOMNESS'

The video begins by demonstrating how easily people select non-random numbers when asked to pick randomly. Despite believing their choices are arbitrary, individuals consistently favor certain numbers. This tendency is exemplified by the 'blue seven phenomenon,' where people commonly choose blue as a color and seven as a number. When extended to two-digit numbers, 37 emerges as a statistically popular choice, suggesting humans have an innate, albeit subconscious, bias in their perception of randomness.

INVESTIGATING THE 37 PHENOMENON

To explore this widespread preference for 37, the Veritasium team conducted extensive surveys. Initial explorations suggested seven was a common pick for single digits, but when focusing on two-digit numbers, 37 frequently appeared. A large-scale online survey with over 200,000 responses confirmed this, showing a marked concentration of responses around 37 and its inversion, 73. Numbers like 42 and 69 were excluded as they are often chosen for reasons other than true randomness.

PSYCHOLOGICAL REASONS FOR CHOOSING 37

Several psychological factors contribute to 37's appeal. People often perceive odd numbers as more random than even ones, and avoid numbers ending in five or those perceived as 'too central' like 50. Furthermore, prime numbers, which lack simpler divisors, feel inherently more random than composite numbers. The digits three and seven themselves are frequently chosen, and 37 combines these favored digits, making it feel intuitively random and acceptable to many.

THE MATHEMATICAL APPEAL OF 37

Beyond psychology, mathematics offers compelling reasons for 37's prevalence. As a prime number, it doesn't easily factor into smaller integers, unlike numbers with common divisors. More significantly, 37 occupies a unique statistical position. It is the median second prime factor for all integers. This means that half of all numbers have a second prime factor less than or equal to 37, highlighting its central role in the structure of numbers themselves and contributing to its perceived 'randomness.'

37 IN DECISION-MAKING STRATEGIES

The number 37 is not just a statistical curiosity; it plays a critical role in optimal decision-making, particularly in situations with uncertainty, such as the 'secretary problem' or 'marriage problem.' The optimal strategy involves rejecting a certain percentage of initial options to gather information before selecting the first subsequent option that surpasses the previously observed best. This optimal rejection rate is approximately 37%, maximizing the chances of selecting the best available choice, whether for hiring, marriage, or other life decisions.

THE CULT OF THE NUMBER 37

The fascination with 37 has led to a dedicated community, with individuals like Tom Magliery actively collecting instances of the number. This collection, showcased on the website thirty-seven.org, demonstrates the number's appearance in everyday objects, serial numbers, measurements, and even political cartoons. This widespread presence, combined with its psychological and mathematical significance, suggests that 37 is more than just a random number; it's a deeply ingrained pattern in human cognition and our perception of the world around us.

Mentioned in This Episode

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●Companies

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●People Referenced

Optimal Decision-Making Strategy (Secretary Problem)

Practical takeaways from this episode

Do This

Determine the total number of options (N) or estimate if unknown.

Calculate the optimal stopping point: approximately 37% of N.

For N options, reject the first 0.37*N options to gather information.

After the stopping point, select the first option that is better than all previously seen options.

This strategy maximizes your chances of selecting the absolute best option.

Avoid This

Do not decide too early, as you'll likely miss the best option.

Do not wait too long to decide, as you may have already rejected the best option.

Do not assume a linear distribution of options; the mathematical model accounts for randomness.

Do not dismiss the strategy for smaller N or when N is unknown; the 37% rule applies to time as well.

Do not underestimate the power of intuition supported by probabilistic analysis.

Most Frequently Chosen 'Random' Numbers (1-100)

Data extracted from this episode

Question Type	Most Common Numbers	Other Notable Numbers
Pick a random number (ignores extremes, 42, 69)	73 and 37 (nearly tied)	7, 77
Pick the number fewest others would pick (ignores extremes, 50)	73 and 37 (nearly tied)
LeastPicked Number (first question)	90	30, 40, 70, 80, 60 (multiples of 10)

Common Questions

Psychologists have observed patterns in random selection, like the 'blue seven phenomenon'. For two-digit numbers, 37 is often chosen due to a subconscious perception of it being 'random enough' – not too central, not too extreme, and having digits like 3 and 7 which are prime and less common.