Thursday, July 21, 2011

Turning Order into Chaos

(it wont be the first time I do it!)

Let's play some games. Word games. Yes, you heard me. Words.
You may be wondering why I want to play with words when I usually play with numbers, but through these games I would like to show you that even behind word games lie some serious mathematics. And hopefully through this you will also see that maths is not just arithmetic. Mathematics does not always have to contain numbers. I truly believe this is where maths starts to go wrong for people. In particular with fractions. If I had a penny for every time that someone said... aw I just got lost when they started bringin' in xs and ys and as and bs...
Anyway, Let's play : )

I dunno what the game is called, I'm not even sure it has a name but y'know the game where you start with one word and you change one letter at a time and try to get to another word.
here's an example. Turn zany into daft.
zany-many-mane-mine-mint-lint-lent-dent-deft-daft
This is a pretty easy one. Something more challenging would be to turn Order into Chaos.
I'll leave this up to you. First one with a good response gets a free bun.

So for those of you waiting with bated breath, here's the maths. Within this game lies a theorem. Loosely named the Ship-Dock theorem it gives a little insight into why some of these puzzles are more difficult than others. Turn Ship into Dock.
Try it first!

(I bet you didn't try it)

Ship-Dock Theorem.
If you notice the positioning of the vowels in the start word and the end word. In ship the vowel is in the third position and in dock it is in the second position. The theorem basically says that for a vowel to 'jump', one of the intermediary words must contain two vowels.
Here's an example of one route you could take
Ship-slip-slop-slot-soot-loot-look-lock-dock
There are plenty of alternative routes you can take to get your ship into your dock but no matter what way you go, you will always find that at least one word will have at least 2 vowels.

Now, the beauty in mathematics, let's prove it.
First, let's presume it's true. I mean, it seems pretty reasonable.
So how do we figure this out? How does the vowel move? Does it jump? Does it run away and come back later? Is a new vowel space created and then old one deleted?
At some stage the word must change from having one vowel to having two. The vowel in ship cannot disappear because you can only change one letter at a time. All 4 letter words in the english dictionary must have at least one vowel, the only way a vowel can jump position is to change from a vowel at position 3 and a consonant at position 2 to a consonant at position 3 and a vowel at position 2. This implies that two letters must change at the same time and that certainly cant be done! That's the whole point of the game! and so, in one move, change the consonant in position 2 to a vowel and then you'll have a vowel in position 2 and 3, then change the vowel in position 3 to a consonant. It's the only way.
Q.E.D as they say.

What's the point in all this?
Well, now when you're turning Order into Chaos, at least you know a trick and can form a strategy!

Fair play if you made it this far, it was a little drawn out I know, but at least now I hope you feel like you can tackle the trickier word games and understand them a little better. And let you be glad that I didn't go into the fact that all these games are are networks of nodes and connectors and shortest routes and ....

I could go on all night. But even for me, there's more to life.

Goodnight Internet, have fun with your words.

3 comments:

  1. you know, i kinda loved that! i got lost with the ship dock thing though... i tried and failed and then got jealous when i saw you made it! x

    ReplyDelete
  2. I have no idea what this all means and was hoping there would be a blueberry and lemon cake at the end instead of a ship or a dock. Well?
    I need to see you - come out this week. The Chef is off work and we are doing foodie photos for the book.....t'will be fun!

    ReplyDelete
  3. It's taken me over a year but I think I have a solution:

    order - orier - frier - flier - flies - flees - fleas - pleas - pleat - cleat - cheat - chert - chart - chars - chaos

    Now admittedly some of those words seem a bit unusual, namely: orier, frier, and chert. But 'chert' is a kind of rock, 'frier' a variant spelling of 'fryer' (and also the flesh of a medium-sized young chicken), and 'orier' is in the English version of wkitionary, so I think I win.

    Do I get a bun now?

    ReplyDelete