Eclecticity's Eclectic Blog

It’s 4AM, there’s a thunderstorm, and the dogs are restless.  So, here I am on the blog trying to think of things that are entertaining.  I can’t guarantee that any of this will be entertaining, it being 4AM and all, and the dogs are no help at all in determining this one way or the other, so, if it’s boring, at least it’s something that isn’t just for math geeks.  So.  Here we go!

In the standard game of Scrabble, there is one, and only one, word in the English language which cannot be played.  It is razzmatazz.  This is because there is only one Z and two blanks.  You might think that pizzazz would also fit into this category, and you’d be right, except that there is a recognized alternative spelling, that being pizazz, which is perfectly acceptable to play in Scrabble, although I don’t think I’d waste two blanks when pizza is just as good and twice as tasty.

There are several 7 letter words which can be played if another word is on the board.  My favorite is abSQUATulate.  My grandmother’s favorite was chrysANTHEMum.

The words Kaiser, Tsar and Czar derive from the word Caesar and are attributed to Julius C.  On the other hand, the words for king in Czech (kral), Polish (krol), and Russian (korol) are all derivations of the name Charles and are attributed to Charlemagne, who is Charles I of France, Germany and the Holy Roman Empire.   

The word pococurante is defined as indifferent or nonchalant but actually means someone with a small head. 

The word cretin comes from Crete, where there were severe iodine deficiencies.  Iodine deficiency leads to many problems, including a drop in the IQ typically in the range of 10-15 points.

Also, for you geeks out there, the word awk comes from the authors of the language, Aho, Weinberger and Kernighan.  Also, yacc is an abbreviation for “yet another compiler compiler”, which, at 4AM, just seems pretty funny.

Any number which is not solely divisible by 2 and/or 5 will not be able to be expressed completely in decimal form.  I had this argument with my fifth grade math teacher, and, I maintain that I am right.  1/3 is *not* equal to .3333333333333333 no matter how many times you add an extra 3 to the end, because 1/3 times 3 is 3/3 or 1; but .33333333333333 x 3 is .99999999999999, and while that *is* “awfully close to 1, it is, in fact, *not* 1.

That is not to say, however, that decimals are worthless, or, even that they are not entertaining.  For example, if you look at elevenths and ninths, they seem to have an inverse relationship to eachother.  For example, the first four numbers after the decimal for 1/9 are .1111, whereas, the first four numbers after the decimal for 1/11 are .0909, and both patterns extend infinitely.

But my favorites are sevenths, because every decimal representation will include the repeating number “142857″, and the only difference between 1/7 and 2/7 and 3/7 and so on is where it starts in the sequence.  So, just for fun…

1/7 = .142857142857142857

2/7=2857142857142857…

3/7=.42857142857142857…

4/7=.57142857142857…

5/7=.7142857142857…

6/7=.857142857142857…

I wonder about weird things.  I wonder why there are so many lieutenant ranks among the land forces.  I wonder why the Captain rank for the Navy is so much higher than the Captain rank for the Army.  I wonder why the Major General has two stars and the Lieutenant General has three, even though the Major is a much higher rank than the Lieutenant.  And, because I wonder, I figure other people do too.  Let’s just start with the rank names.

Private – currently the lowest rank in the Army; of course, the Private was not *always* the lowest rank in the Army… at one point or another, the guys who ran headlong into the opposing army’s spears or swords were slaves or captives or prisoners.  Privates are none of these.  They got their name because they are private citizens, or citizen soldiers.

Corporals – got their name from the Latin Corps, meaning “body”.  Corporals commanded a “body of men”.

Sergeants got their name from the word “Servant”.  When a nobleman took up arms as an officer, he would take his body man with him to tend to him.  If you were a nobleman, you wouldn’t want your favorite servant reporting to some scallywag from the ranks, and so, the Sergeants were always above the Corporals, and always below the officers.  The top Sergeant in any large group was the Sergeant Major.

Captains got their name from the root word “cap” meaning Head.  The Captain would head any attack.  Often attacks utilized three prongs, so the Captain would have two men who would stand in the place of him, or “in lieu of” him: a First Lieutenant and a Second Lieutenant, the first, of course, outranking the second.  The top Captain around was the Captain Major, just like the Sergeant Major, except that the rank became truncated to simply Major.

Where a Captain would head an attack, a Colonel would head a column.  The “Col” in Colonel is the same “Col” as column.  And, while an attack would often be split into three, a column would sometimes be split into two, so a Colonel would also have a Lieutenant.

The final fighting rank was the Brigadier, who would lead a brigade.

Now, into the General ranks.  Let’s go backwards this time.  The head general, of course, was the Captain General, which got truncated to simply “General”; but as the next rank down from Captain is Lieutenant, so is the the next rank down from General the Lieutenant Generals.  And below the Lieutenant Generals would be the Sergeant Major Generals, which, like the Captain Majors, got truncated to simply Major General.

So, there we have the ranks for the land forces.  The ranks for the Naval forces, are, of course, different, and will be covered in a different post.

When I was a kid, learning my multiplication tables, 11′s were particularly appealing.  For 1-9, it was really easy to know what the number times 11 was.  8 was 88.  4 was 44.  I could do that all day.  But, for numbers over 10, it wasn’t easy at all, and I thought that was kind of a rip, because, it was *so* easy for numbers less than 10.  I figured it was still easy… it had to be… I just had to find out the trick.  So, I did. 

121, 374, 561… what did these have in common?  Well, the outside numbers added up to the inside number.  And sure enough, for all three digit numbers divisible by 11, the outside numbers either add up to the inside number, or were 11 more than the inside number (e.g., 308, 407, 616).

Great!  Now I had a way to tell, for all numbers less than 1000, if it was divisible by 11 just by looking at it.  And yet my happiness was not complete.  Because there are way more numbers bigger than 1000 than less than it.  And, how could I tell if a 17 digit number was divisible by 11? 

Well, as it happens, the same way you can tell if a three digit number is divisble by 11!

Take any number…

47138293018391038

…and highlight every other digit.

47138293018391038

Add the highlighted digits together.  In this case, they add up to 23.  Now add the non-highlighted numbers together.  In this case, they add up to 47.  Because 47 does not equal 23, and because 47-23 is not divisible by 11, 47138293018391038 is not divisible by 11.  In order to be divisible by 11, the outer numbers would need to be 2 less, the inner numbers need to be 2 more, or the outer number needs to be one less *and* the inner number needs to be one more.  So, then, 47138293018391036 should be divisible by 11.  And, indeed it is!  Also, 47138293018391058 should be divisible by 11.  And, once again, it is! 

Yay!

The word Trivia comes from the Latin tri- meaning “three” and via meaning “roads”.  In the olden days, there were very few roads.  There might be a road leading from Rome to Paris, and one from Hamburg to Sofia.  Where two roads intersected, naturally, businesses would spring up to cater to travelers: inns, smiths, et cetera.  But, in those rare places where three roads crossed, there would be large marketplaces, and, of course, you could get news from faraway places.

On a related, or perhaps wholly unrelated, note, the word Aviator comes from the Latin a- meaning “not”, plus that via again.  So, an Aviator goes where there are no roads: the sky.