Some people notice the repeated appearance of a particular number in their daily lives, in historical records or in religious texts like the Bible. It often seems that the repetition is too frequent to be coincidental. In some cases, people have theorized that these repeating numbers have special significance or demonstrate the influence of a deity or supernatural force. Although not strictly part of numerology, this perception often assigns numerology-like attributes to the frequently appearing numbers. This has led to the 23 Enigma and other beliefs that specific numbers are at the center of a pattern or conspiracy.
Critics, on the other hand, dismiss such occurrences as coincidence for a number of reasons:
People are good at recognizing patterns. While this helps people learn to read, count and recognize faces, it can also encourage people to interpret random events as patterns. Because of the small number of numerals that exist in the world, repetitions are inevitable. Because of the small number of round, square or otherwise distinctive numbers in the world, repetitions of those are inevitable as well. These criticisms can also apply to the practice of numerology. For example, some practitioners say they see their numbers everywhere, and that this confirms that numerology is real. However, according to critics, the frequent appearance is coincidental. In addition, critics point out that people are likely to remember seeing their numbers and forget seeing other numbers. In other words, a person whose number is seven will remember seeing lots of sevens while disregarding all the sixes, eights and other numbers he encounters. People are also more likely to remember the numerical attributes that apply to them while disregarding the ones that don't. This phenomenon is known as confirmation bias.
But the biggest criticism of numerology is that it's based on an invented system of counting. This system developed to allow people to count objects in groups of ten, most likely because most people have ten fingers on which to count. Even the English words for numbers, which come from Old English, reflect these groupings of ten. "Eleven" means "one left," and "twelve" is an abbreviation of "two left."
However, this system, known as a base-10 system, isn't the only -- or even necessarily the oldest -- system of counting. Indigenous tribes in Australian, New Guinea, Africa and South America developed number systems that counted in pairs. Rather than one, two, three, four, five, six, these progressed more along the lines of one, two, two plus one, two twos, two twos plus one, three twos. Some societies also used base-12 and base-60, which we still use to tell time.
In other words, numerology, like astrology, is based on an invented system that people developed to better organize the objects around them. While people often find such systems helpful on a spiritual or emotional level, there's no scientific evidence to prove that the system really works the way practitioners say it does.