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111
Sorry for the radio silence. Life has been busy and I haven't felt much motivating fire to post. And even when I have, I've felt it would be material that would weary you dear readers. So here is a little diversion.
I am told that people on Facebook have discovered a cosmic mystery associated with the number 111. (I don't have a Facebook account, myself). The basis for this mystery is the following:
Take your age in 2011 (e.g. say, 47).
Now add the year you were born (e.g. '64).
Low and behold, you get 111...and in the year 2011! And the crazy part is that this works for everyone born before the year 2000! (But even those born after 2000 get 11!) [Cue Twilight Zone music.]
People, this is not mysterious. Think about it this way:
2011 - 47 = 1964
1964 - 64 = 1900
2011 - 1900 = 111
A person that I explained this to was a little disappointed. They said my explanation kind of took the mystique out of it.
There are relationships among numbers that have a legitimate kind of mystique about them. This is not one of them.
Sorry if I ruined your day.
9 comments:
My day? No, this ruined my life!
Now to explain the mystery: What is being done is proving 111 years have past since the year 1900. For example, I was born in 1983, 83 years after 1900. Now, I am turning 28 later and sure enough 83+28 = 111.
This works for any other year. 2010 is 110 years after 1900. I was born 83 years after 1900 and now add 27 years since then and I arrive at 110.
In 2009 it was 109 years after 1900 and 83+26 = 109. Etc...
It is just the observation that if you were born in 19XX then you were born XX years after 1900, then add your age and you get how many total years it has been since 1900. And so we have now proved it has been 111 years since 1900!
Sorry, after rereading apparently you already resolved the mystery! I read too quickly so I apologize.
My favorite crazy pattern is any number divisible by three has it so that if you sum up the digits you get something divisible by three. For example, 81 is divisible by 3 because 8+1=9 and 9 is divisible by three. Is 16826385 divisible by three? Yes because 1+6+8+2+6+3+8+5 = 39 and 3+19 = 12 and 12 is divisible by 3.
Same thing works for 9. 117 is divisible by 9 since 1+1+7 = 9 which is divisible by 9!
Maybe not the coolest thing but I like it. :)
I almost posted about this two weeks ago. Too slow!
I slapped my forehead when I saw it on Facebook.
After I explained it to a student and her brother, they returned the next day to tell me that their dad said I was wrong. Okaaaaaaay.
I wish I could remember the author and title of a story I read long ago. Seems that humanity had become so used to letting computers do their math for them that we had completely forgotten the nature of even the most basic mathematics. In particular, we were totally dependent upon computers to conduct our missile wars (with another planet? with some enemy on the other side of the world?), who also was computer-dependent. Our side was getting badly trounced.
Then some lowly person became a phenomenally successful military adviser because he somehow discovered that 4 plus 7 equaled 11 (or whatever particular piece of basic arithmetic it was). 4 plus 7 always made 11, no matter what, no matter when, no matter who counted, no matter how many times he counted. Magically! Incredibly! Unfailingly! Because of the genius of this man and his uncanny skills, our side became able to outthink the enemy computers, to become unpredictable -- and eventually successful.
You remind me of that guy.
I suggest a more suitable problem:
1) Pick any whole number 1 or greater:
2) If it is odd, multiply it by 3 and add one to get the new result
otherwise, divide it by two and take the result.
3) repeat step 2)
Do you eventually end up in the cycle 1->4->2->1, no matter what your initial number was? The conjecture is that it is true, you always end up at 1.
This is the Collatz Conjecture, a devilish problem that we don't know the answer to. It has been successfully checked for every number up to about 10^18, but we don't know if it holds for bigger ones.
Paul—I really suck at math and at sarcasm, so I am going to ask what is probably a stupid question. Is that really a mystery to people, or are you being sarcastic? If the problem is truly a mystery, why?
It's just factoring. You'll keep going through that cycle until you finally reach the right even number that has nothing but even factors and one. It seems obvious to this math dunce.
Joseph,
Thanks for the clear explanation. I tried a couple of times to also say what you said, but it was too clumsy so I scrapped it.
Ardis,
The resemblance between me and that character is probably stronger than you realize. I am quite weak in math skills, which means that simple observations like his is about all I'm good for.
Paul2,
Similar to SilverRain, I realized that once you hit on any number 2^n, you're on the slide down to the infinite loop. Perhaps the difficult part is proving that any number put through the routine will eventually lead to that slide.
SilverRain and Jared, the density of the numbers 2^n goes to zero as n--> inf, so simple args don't work. There are some famous conjectures that hold all the way to extremely gigantic numbers, then fail. An argument plu lots of evidence is not proof to mathematicians. Check out the Riemann Hypothesis on the web to see the most famous example. When you look at number theory, it is really seductive. Something as simple as whole numbers are hiding a world of secrets and humans have such a dim light to illuminate these mysteries. Go check out Terence Tao's blog. He sometimes puts tutorial material for the public. It is amazing.
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