DYK?: DID YOU KNOW

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Here are a couple that I found interesting.....I am a big FAN of  HBO's ROME, and I was wondering this exact question--IF there are any descendants of Julius Caesar?----while watching this engaging series-- 

I have been watching the Discovery Channel's "Roman Week." It got me to wondering. Do any ancestors of people like Julius Caesar, Nero, Cleopatra, etc., live today??

- Allan H.

ANSWER:

That seems exceedingly unlikely, as "ancestors" means the people who came before them (e.g., Nero's great-grandfather, not his great-grandson.) Maybe some of the ancient Romans discovered the secret of immortality, but I never heard about it.

But certainly there are some people around today who are distantly related to those famous old Romans. Unfortunately, genealogical records from the first millennium A.D. are essentially nonexistent, so connecting the work of modern genealogists to the royal genealogies of the Roman Empire is virtually impossible.

However, based on probability theory, if anyone from 2,000 years ago has any descendants living today, they probably have millions of direct descendants living today.

Think about it this way:

Every person has, on average, two children.
Your children are, on average, about 25 years younger than you. So a "generation" lasts about 25 years.
(Obviously you can quibble with these assumptions; I'm only using them for illustrative purposes.)

After 25 years, a man will have two descendants: his children. After 50 years, his two children will each have two children of their own, so he will have four living descendants. (For our purposes we'll only consider the latest generation to be "living descendants," even though previous generations may still be living.)

In other words, the number of living descendants (latest generation only) doubles every 25 years. Over 2,000 years, the number would double 80 times, and as we saw in the previous answer, doubling is mighty powerful stuff. After 2000 years, the total number of living descendants in the present day would be 280. That's a lot:

1,208,925,819,614,630,000,000,000
Now you're probably thinking, waitaminnit, there aren't even 7 billion people alive today — it would be impossible to have 1.2 septillion living descendants! That's true. At some point, your descendants would inevitably have to mate with each other. (It's not that gross — we're talking about 28th cousins here.) So instead of each descendant generating two new descendants in the next generation, each pair of descendants (husband and wife) will generate two new descendants. This will slow the growth.

There are smarter ways to calculate it, but the conclusion is inevitable: If the descendants of Julius Caesar, Cleopatra and — if you view The Da Vinci Code as history and not fiction — Jesus Christ didn't die out after a few generations, then there are almost certainly millions of them alive today.

Going back 1,000 more years to 1,000 B.C., if anyone alive at the time has surviving descendants (clearly some of them do — we didn't come out of thin air), probability theory says that everyone alive today — Europeans, Africans, Asians — is that person's direct descendant!

QUESTION:


Would you take a job making $375,000/year or work for a penny a day, in which it doubles each day, for a year? (For example, the first day, 1 cent, the second day, 2 cents, the third day, 4 cents, fourth day, 8 cents, etc.)

I know the answer... but I would like to know the easy way of figuring it out, besides working it on a calendar for each day... have any easier solutions?


ANSWER:

you start with a penny on your first day, and double your daily salary each subsequent day, a little observation tells you that your total holdings each day will be equal to twice that day's salary, minus one penny. (There's a more complicated derivation for this, but it's easy enough to eyeball.) Your daily salary doubles every day, so that's easy to figure out. It's just Daily Salary = 2(n-1), where n = the number of the day (first day = 1, second day = 2, ...)

So the formula for how much money you will have in total is:

Total Salary = (2 x Daily Salary) - 1
Total Salary = (2 x 2(n-1)) - 1

This simplifies to: Total Salary = 2n - 1

If you work every day of the year, you would make a total of:

2365 -1 = $7.52 x 10107

This is basically an uncountable amount of money (and twice as much in a leap year!).

Under the every-day-doubled payment system, after working 25 days, you would already have $335,544.31 in your pocket. Obviously, if you worked the 26th day, you would come out ahead of $375,000 per year. (You'd have $671,088.63, to be precise.) You'd be a millionaire by your 27th day, a billionaire by your 37th day.

The lesson to be learned here: doubling is a very powerful operation. When things grow geometrically, they grow very quickly.

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