| A birthday is a date on which a person breathes | | | | to play. The birthday paradox states that given a |
| his first outside his mother's womb and prepares | | | | group of 23 randomly chosen people, the |
| himself for a new life. It is the beginning, a window | | | | probability is more than 50% that at least two of |
| to the chance of a lifetime. It is an occasion to be | | | | them will have the same birthday. If the number |
| commemorated just as a nation commemorates | | | | of people increases to 60 or more, the probability |
| its birth or as an organization celebrates its | | | | is greater than 99%. However it cannot actually |
| founding. However the underlying question still | | | | be 100% unless there are at least 366 people. |
| remains as to why one celebrates his birthday. Is | | | | One should not take it to be a paradox in the |
| it the fact that they have survived another year | | | | true sense of the word , as in the sense of |
| against many odds that life gave them the | | | | leading to a logical contradiction. In fact it is |
| opportunity to chance upon or is this day the | | | | described as a paradox because mathematical |
| expression of a hope to live another year? None | | | | truth contradicts candid or gullible intuition. |
| of the above, it would seem. If it is the past year | | | | One can try it himself. If one is at a gathering of |
| that one is commemorating, would he still raise a | | | | 20 or 30 people, and each individual's date of birth |
| toast to it if he were to receive some bad news? | | | | is asked, it is likely that two people in the group |
| Not likely. But why? What is the relevance of | | | | will have the same date of birth. It always |
| information about the future when one is | | | | surprises people! The reason this is so surprising is |
| celebrating the past? This is perhaps because of | | | | because an individual is used to comparing his |
| an astrological lore. The wise men noticed that | | | | particular birthdays with others. For example, if a |
| when the sun hit the same spot in the heavens | | | | person meets someone randomly and asks him |
| that it held on a person's date of birth, that day | | | | his date of birth, the chance of the two of them |
| turned out to be extremely fortunate. This lucky | | | | having the same birthday is only 1/365 (0.27%) |
| pattern brought joy, and thus the birthday person | | | | which is extremely low. Even if he asks 20 |
| wanted to celebrate. | | | | people, the probability is still low -- less than 5%. |
| This substantiates the fact that it is not the past | | | | So one feels that it is very rare to meet anyone |
| that is foremost on one's minds but the the | | | | with the same date of birth as his. |
| future. One celebrates the success at having | | | | When 20 people are put in a room, however, the |
| arrived so far because such successful resilience | | | | thing that changes is the fact that each of the 20 |
| allows him to continue forward. This day is the | | | | people is now asking each of the other 19 people |
| expressions of unrestrained, unbridled, blind faith in | | | | about their date of birth. Each individual person |
| one's own suspended mortality. But as one | | | | only has a small, less than 5%, chance of success, |
| moves up the ladder of age, he gets closer to | | | | but each person is trying it 19 times. So that |
| the inevitable death. So we can conclude that | | | | increases the probability dramatically. If one wants |
| birthdays are about self-delusions defying death. | | | | to calculate the exact probability, one way to look |
| They are about preserving the sweet memories | | | | at it is like this. He should mark his birthday on the |
| of immortality. They are forms of acting out | | | | calendar. The next person who walks in has only |
| one's magical thinking. By celebrating our existence | | | | a 364 possible open days available, so the |
| on this day, we bestow on ourselves protective | | | | probability of the two dates not colliding is 364 |
| charms against the meaninglessness and | | | | 365. The next person has only 363 open days, so |
| arbitrariness of a cold, impersonal, and often | | | | the probability of not colliding is 363/365. If one |
| hostile universe. It is customary in many cultures | | | | multiplies the probabilities for all 20 people not |
| to celebrate this day, for example by having a | | | | colliding, then one gets: 364/365 * 363/365 * ... |
| party with family and/or friends. | | | | 365-20+1/365 = Chances of no collisions. That is |
| The excitement of this occasion doubles when | | | | the probability of no collisions, so the probability of |
| one shares his birthday with another person. In | | | | collisions is 1 minus that number. The next time |
| this regard the Birthday paradox has a major role | | | | you are with a group of 30 people, try it! |