Friday, February 17, 2006

Sugar, Chirality, and How to Read

This post was brought on by an interesting posting over in Studeo, about an addition error.

First let me assure my readers not to get excited about my use of the word "error" here. Sometimes remarkable things come out of "errors" (look up "vulcanization" sometime for an example!) Like, perhaps, this posting.

Actually, speaking as a computer scientist, who often deals with strange requests from non-technical people, this was hardly an error at all. It might even be called a mis-stated problem. I will show you what happened.

1
2
3
+7
answer: 130

4
3
2
+8
answer: 440

As you can see, it is just a matter of how you read the question - are those supposed to be three separate digits, or was the person reading a three-digit number slowly? Ah, you see!

How do we read, anyway?

Well, we all know reading is fun, or you would not be looking at this at all. We are so used to it, unless we are rather young, and still trying to learn to read, and also trying to learn the even more useful skill of enjoying the act of reading. But since we are reading English, we must abide by the rules of English - and we start at the left and move to the right. If we were reading Hebrew, we would start at the right and move to the left. If we were reading Chinese, we would (typically) start at the top and read down. And if we were reading ancient Egyptian, we would look to see which way the birds and animals and people were facing, and start from that side (if they face left, start from the left).

Just like the reading direction matters for words, it also matters for numbers: 23 is not the same as 32. And in Roman numerals, a smaller digit to the left of a bigger digit is "subtracted" from it - but added if it is to the right of a bigger digit! Example: I = 1 and V = 5, so IV = 4 but VI = 6.

And, just to make things even more exciting, if we were reading a certain really ancient kind of Greek, we would have to do something a bit more tricky. We would read one line from left to right, and then drop down a line and read that next line from right to left! This is so strange there is a special word for that kind of writing: boustrophedon which means "turning like oxen in plowing". Maybe it's not so old - if you ever saw a "dot matrix" printer, they print that way.

Ah, yes - many interesting things in human history. But most modern languages are read from left to right.

Whew. So - I think it's time for a Chesterton quote:
I remember a man of this sort who told me he was on a spiritual plane ("we are on different planes") on which yes and no, black and white, right and wrong, right and left, were all equal. I regarded him as I should any boastful aviator who told me that from the height to which he had risen all London looked like an exact chess-board, with all the squares and streets the same size. In short, I regarded him as a liar. London streets are not equally long, seen from a flying-ship or from anywhere else. And human sins or sorrows are not equally serious, seen in a vision or anywhere else.[GKC, ILN Aug 15, 1914 CW30:145]
Well, as I am sure you know, right and left are not equal. Just put your hands out in front of you and compare! Or better: try putting your right glove on your left hand... Oh - they are different!

Now why, you ask, do I mention sugar in the title of this posting? Did you ever read the list of ingredients and see the word "dextrose"? Do you know what it means? It means "the right-hand sugar". Yes, it does. I don't have time to tell you all the chemical and optical details - as interesting as they are - but it is true. Many of the important chemicals inside living things have a special, distinct shape if you could see how the atoms are arranged. Sugar is just one of many compounds containing carbon which are "handed" (it's either right or left) just like your gloves. The technical word the chemists use is "chiral" - which comes from the Greek word for hand.

Now if you remember a little while ago I wrote something about DNA (in my posting called "Words made flesh") and said that the instructions are stuck together with sugar. (Oh ho! you laugh! Can you see what that means?) Well, it's not the kind of sugar we use on cereal. It's called "ribose". That's the sugar part of DNA. Connected to the sugar is one of the four "bases" which are written with the four letters (A, C, G, T). But the sugars are stuck together with something called "phosphate" - it ties one sugar to another. You can think of a sugar as a kind of railroad flatcar, on top of which is one of the four bases... and the phosphates are the "couplers" which hook the cars together, one to the next.

Ah ha! but the sugar is "handed!" so that means it's LIKE A LETTER - it has a "left" side and a "right" side, so that means there is a way of reading the "train" of all the bases-strung-togther! Yes, indeed. And that's how the "reading" machinery can "read" the "word" of DNA which builds your muscles and skin and the rest.

Now, to conclude, a really bad tech joke, which is actually related. First I have to explain it. (I hear the "boo hiss"... Yes, yes, yes. Just pay attention, and be ready to laugh.)

When we add, we know we can add in either order. For example: 3+4 is the same as 4+3. This is called the "commutative" property. So when we go from 3+4 to 4+3, we say that "addition of integers commutes". (That does not mean the numbers drive to work, hee, hee. No, that's NOT the joke.)

Mathematicians say that things-which-commute are "Abelian". Now you will see right away that some things are NOT Abelian - they do NOT commute - like subtraction.

But even more importantly, the hidden thing which holds our words together does not commute either! Are "evil" and "live" the same? Of course not.
Oh, you didn't know there was such a thing, a hidden thing, holding our words together? Really you didn't know??? You know what it is for DNA - it's the sugar called ribose. I can't hardly believe it - you really didn't know there was something holding the letters of these very words together? Well, I'm almost out of paper so I'll tell you about that another day.
Ahem, ahem!
OK, anyway, here's the joke:

Q: What's purple and commutes?
A: An Abelian grape.

(laugh now...)

I knew it. No one is laughing. That's OK - I said it was bad. But I'll see you later anyway. (There's more to come!)

3 Comments:

At 18 February, 2006 11:49, Blogger Rick Lugari said...

Okay, I wouldn't have gotten the joke had you not explained abelian first. With that knowledge I gave a "heh" with bit of a smile.

But then this, "I knew it. No one is laughing." made me laugh out loud. :)

 
At 18 February, 2006 12:08, Anonymous rhonda lugari said...

That was a very interesting post, Dr.Thursday.

I like this about comuters: "That does not mean the numbers drive to work" :)

And I thought the Abelian grape joke was clever, too.

 
At 18 February, 2006 12:22, Blogger Dr. Thursday said...

Now I am laughing.

And you have begun down that dark path which leads to technology!

But it's the same road some use to get to philosophy, and theology, and even more scary fields...

And next Monday morning everyone will be thinking of thousands of grapes kissing their wives and getting into their cars and driving off to work...

"Bye, honey..."
"Don't stay out in the sun at lunch, dear, or you'll get all wrinkly."

Humor - like so many good things, soundly based on 13th century metaphysics...

 

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