Same Day Birthday- A Paradox?

A birthday is a date on which a person breathes his first outside his mother’s womb and prepares himself for a new life. It is the beginning, a window to the chance of a lifetime. It is an occasion to be commemorated just as a nation commemorates its birth or as an organization celebrates its founding. However the underlying question still remains as to why one celebrates his birthday. Is it the fact that they have survived another year against many odds that life gave them the opportunity to chance upon or is this day the expression of a hope to live another year? None of the above, it would seem. If it is the past year that one is commemorating, would he still raise a toast to it if he were to receive some bad news ? Not likely. But why? What is the relevance of information about the future when one is celebrating the past? This is perhaps because of an astrological lore. The wise men noticed that when the sun hit the same spot in the heavens that it held on a person’s date of birth, that day turned out to be extremely fortunate. This lucky pattern brought joy, and thus the birthday person wanted to celebrate.

This substantiates the fact that it is not the past that is foremost on one’s minds but the the future. One celebrates the success at having arrived so far because such successful resilience allows him to continue forward. This day is the expressions of unrestrained, unbridled, blind faith in one’s own suspended mortality. But as one moves up the ladder of age, he gets closer to the inevitable death. So we can conclude that birthdays are about self-delusionally defying death. They are about preserving the sweet memories of immortality. They are forms of acting out one’s magical thinking. By celebrating our existence on this day, we bestow on ourselves protective charms against the meaninglessness and arbitrariness of a cold, impersonal, and often hostile universe. It is customary in many cultures to celebrate this day, for example by having a party with family and/or friends.

The excitement of this occasion doubles when one shares his birthday with another person. In this regard the Birthday paradox has a major role to play. The birthday paradox states that given a group of 23 randomly chosen people, the probability is more than 50% that at least two of them will have the same birthday. If the number of people increases to 60 or more , the probability is greater than 99%. However it cannot actually be 100% unless there are at least 366 people. One should not take it to be a paradox in the true sense of the word , as in the sense of leading to a logical contradiction. In fact it is described as a paradox because mathematical truth contradicts candid or gullible intuition.

One can try it himself . If one is at a gathering of 20 or 30 people, and each individual’s date of birth is asked, it is likely that two people in the group will have the same date of birth. It always surprises people!The reason this is so surprising is because an individual is used to comparing his particular birthdays with others. For example, if a person meets someone randomly and asks him his date of birth, the chance of the two of them having the same birthday is only 1/365 (0.27%) which is extremely low. Even if he asks 20 people, the probability is still low — less than 5%. So one feels that it is very rare to meet anyone with the same date of birth as his.

When 20 people are put in a room, however, the thing that changes is the fact that each of the 20 people is now asking each of the other 19 people about their date of birth. Each individual person only has a small,less than 5%, chance of success, but each person is trying it 19 times. So that increases the probability dramatically. If one wants to calculate the exact probability, one way to look at it is like this. He should mark his birthday on the calendar. The next person who walks in has only a 364 possible open days available, so the probability of the two dates not colliding is 364/365. The next person has only 363 open days, so the probability of not colliding is 363/365. If one multiplies the probabilities for all 20 people not colliding, then one gets: 364/365 * 363/365 * … 365-20+1/365 = Chances of no collisions. That’s the probability of no collisions, so the probability of collisions is 1 minus that number. The next time you are with a group of 30 people, try it!