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Numbers are filled with fascinating traits and unsolved mysteries. The unpredictable distribution of prime numbers and their crystalline patterns remain unexplained, showcasing the strange and captivating nature of numerical studies.
Quantum mechanics has generated unbreakable numerical codes, extremely large numbers might theoretically form black holes in the human mind, and nearly half of Americans advocate for banning numbers. Interestingly, some cultures remain unaffected by this debate as they traditionally do not rely on numerical systems.
10. The History of Paint-By-Numbers
Leonardo da Vinci pioneered the paint-by-numbers concept as a teaching tool for his apprentices. Decades later, in the 1940s, Dan Robbins, an employee at the Palmer Paint Company in Detroit, learned about da Vinci’s innovative approach.
Motivated by this idea, Robbins developed his first paint-by-numbers design and presented it to his supervisor. Despite the initial disapproval, Robbins was urged to create designs that would appeal to the public. The kits, featuring landscapes, horses, kittens, and puppies, became a cultural phenomenon, generating $20 million in sales by 1955.
However, the market soon became flooded with imitations, leading to a decline in profits. The Palmer Paint Company was eventually sold, and now only two kits remain in production: one depicting the Last Supper and the other honoring the September 11 attacks. Robbins’s contributions were later recognized by the Smithsonian Institution, a stark contrast to the early criticism that dismissed his kits as lacking artistic value.
Robbins died in 2019 at the age of 93.
9. Bees Can Comprehend Numbers
In a 2009 study, scientists discovered a remarkable skill in bees. These insects could differentiate between groups of two, three, and four dots but struggled with larger quantities.
The experiment involved honeybees navigating Y-shaped boxes. They were trained to associate marked entrances displaying two to four dots with a reward inside.
At the fork, bees encountered two sets of dots. One set matched the number at the entrance, while the other did not. Bees that chose the path with the matching number received a sugar water reward.
The bees correctly identified two and three dots approximately 80% of the time, while sets of three and four dots achieved a 70% success rate. Researchers concluded that bees don’t count but instinctively recognize small quantities, similar to how humans instantly know there are three bottles on a shelf without counting.
8. The Fascination of Prime Numbers
A prime number is defined as a whole number greater than 1 that can only be divided by itself and 1, leaving no remainders such as 3.4. Examples of prime numbers include 2, 3, 5, and 7.
In 2017, the largest known prime number at the time, M77232917, was identified. This colossal number contained 23,249,425 digits, surpassing the previous record by nearly one million digits.
To put its enormity into perspective, writing out all 23 million digits at a rate of 1,000 digits per day would take over six decades. Fortunately, its concise form can be expressed as 2 minus 1.
This number is also a rare Mersenne prime, a type of prime number that is one less than a power of two. The discovery of M77232917 was a result of the ongoing search for Mersenne primes.
A worldwide initiative called the Great Internet Mersenne Prime Search (GIMPS) involves both scientists and volunteers. After 14 years of participation, Jonathan Pace, an electrical engineer, uncovered this prime number in 2017.
However, Pace’s achievement was short-lived. In December 2018, Patrick Laroche identified an even larger Mersenne prime: M82589933, which is expressed as 2 minus 1.
7. Understanding Dyscalculia
Dyscalculia is a lesser-known condition often referred to as “math’s dyslexia.” Those affected face challenges with basic numerical tasks, such as determining if 7 is greater than 6, calculating change for a $5.50 purchase with $10, or keeping track of a baseball score.
Individuals with dyscalculia find such tasks incredibly frustrating, but this does not reflect their intelligence. Studies confirm that people with this condition have normal cognitive abilities and are intelligent. Affecting up to 7.5% of the population, dyscalculia complicates daily life, highlighting the need for better understanding and tailored treatments.
The exact cause of dyscalculia remains unknown. However, research indicates that the brain areas responsible for mathematical processing are less active in those with the condition. Brain scans also reveal weaker connections between these regions and the rest of the brain. Despite these findings, the underlying reasons for reduced activity and connectivity remain a mystery.
6. Societies Without Numerical Systems
For most, a world without numbers is unimaginable. Phrases like “I have three children” or “This recipe requires eight eggs” are commonplace. Yet, some cultures exist without numerical vocabulary, known as anumeric or numberless societies.
Amazonian tribes are among these groups. These hunter-gatherers describe quantities using vague terms like “some” or “a few.” When researchers tested members of these tribes, adults found it challenging to track nuts being removed from a container, even when only four nuts were involved. Despite this, anumeric individuals possess the same intelligence as anyone else.
Fascinatingly, all humans are born without numerical understanding. It requires a collective effort—family, education, and social interaction—to teach someone the complexities of numbers. Research suggests that numerical cultures are a relatively recent development in humanity’s 200,000-year history.
5. The Concept of Unbreakable Randomness
Generating random numbers is crucial, especially for encrypting sensitive data on computers. However, hackers often exploit vulnerabilities to predict or manipulate these algorithms. Surprisingly, creating truly random numbers is a complex challenge, often requiring unconventional solutions.
In 2018, a groundbreaking experiment achieved the first “unhackable” method by leveraging quantum mechanics. Researchers used two photons (light particles) to produce genuinely random numerical sequences.
Photons inherently exist in a state where they can point either up or down. Before measurement, their positions are equally probable, making them inherently unpredictable.
Scientists paired photons to ensure they began in a neutral state, confirming they were neither up nor down initially. This approach proved successful.
The interaction between paired photons provided a neutral reading before they flipped, enabling researchers to develop an algorithm capable of generating truly random numbers.
4. Prime Numbers Mimic Crystal Structures
Prime numbers are often regarded as the fundamental elements of mathematics. Yet, their unpredictable nature has puzzled scholars for centuries. This randomness has fueled the ongoing search for larger primes. It wasn’t until theoretical chemists approached primes from a fresh perspective that a semblance of order was discovered.
In 2018, a study treated primes as if they were physical entities, akin to atoms in a crystal. To analyze atomic patterns in crystals, scientists observe how X-rays scatter. Unlike liquids, which produce chaotic scatter patterns, crystals yield consistent, orderly results due to their rigid atomic structures.
Using software, researchers simulated X-rays scattering off a million prime numbers. While they anticipated a liquid-like pattern due to the primes’ randomness, the results revealed a unique crystal-like arrangement unlike any known crystal.
3. The Concept of Black Holes in the Human Brain
Extremely large numbers are often given unique names, such as googol, TREE(3), and Graham’s number. Graham’s number, for instance, is the result of a 64-step calculation that becomes unmanageable after just a few steps, producing trillions of digits.
Graham’s number pales in comparison to TREE(3), which is considered impossible to fully comprehend or represent. While humans possess remarkable mathematical abilities, understanding such colossal numbers isn’t innate. This raises the question: what would happen if a number like TREE(3) were stored in the brain in decimal form?
The theory takes a dark turn. The brain has a finite capacity for information. Mathematicians suggest that overloading it with excessive data could theoretically create a black hole within the brain. Alarmingly, numbers smaller than Graham’s number could potentially trigger this phenomenon.
2. The Push to Ban Numerals
In 2019, CivicScience, a research firm, conducted a poll asking participants whether Hindu-Arabic numerals should be eliminated from the U.S. education system.
Over 3,600 individuals participated. When the results were projected, they indicated that roughly half of Americans supported banning these numerals. This was surprising, as Hindu-Arabic numerals consist of the digits 0 through 9. It’s likely that many voters misunderstood the term. The name originates from their development in India around AD 400 and their adoption by Arabic cultures, which added their own modifications.
The Western world has used 0 to 9 for so long that their origins are rarely considered, and many assume they are inherently Western. The strong support for the ban may stem from tribalistic tendencies.
Researchers suggest that when people adopt “facts” to align with their group identity—a hallmark of tribalism—it can lead to prejudice. This isn’t just directed at the Middle East but also fuels divisions within the U.S. between those advocating for the ban and those who see it as misinformation.
1. AI’s Emergent Numerical Understanding
Computers can perform calculations at astonishing speeds, far surpassing human capabilities. However, humans maintain an advantage in one key area: the ability to intuitively recognize quantities, such as identifying three apples or three cats without explicit counting. In contrast, computers require specific instructions to identify and count objects.
This innate ability to perceive quantities, recognize symbols like the number 3, and understand abstract numerical concepts without counting is known as “number sense.” Since computers lack this capability, artificial intelligence (AI) still falls short of matching the broad cognitive abilities of humans.
In 2019, it was reported that an AI system unexpectedly developed a form of number sense. The AI was initially trained for basic object recognition. Unlike humans, computers typically analyze pixels, lines, and shapes to identify objects. Once the AI learned to recognize objects like apples, it could then count them.
Surprisingly, the AI developed a human-like number sense, distinguishing that three apples and three cats are different yet share the commonality of the number 3. Researchers observed that specific parts of the AI’s network spontaneously adapted to recognize abstract numbers, mirroring the behavior of actual brain neurons.
