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.

Thursday, June 9, 2011

Móna Wise

My dearest internet, it has been a while. 
On deciding to view the stats on our blog earlier this evening I discovered that most of the traffic round here comes from the webspace of m'lovely Móna Wise, due to this fact she shall have a post dedicated to her. 


Now internet, Mona's more of a wordy sort as opposed to a numbers kinda gal, but with a li'l bit of messin' around I bet we can show Mona how unique she is, we'll show her special properties that she has. There aren't too many around that are quite like Mona y'know. I wont go as far as to say she's one in a million, but I will say that she is incredible, extraordinary, she makes up herself and herself cannot be divided, only by one.. (the chef I presume) What is she? 


She is Prime.


Not like Optimus Prime or anything, but a Prime number. How is that you ask? Well internet, let me show ya..
I'll list letters with their corresponding numbers
A - 1
B - 2
C - 3
D - 4
E - 5
F - 6
G - 7
H - 8
I - 9
J - 10
K - 11
L - 12
M - 13
N - 14
O - 15
P - 16
Q - 17.............. Etc, ya get the idea. 


So if we add up Mona, we get 13+15+14+1 = 43. 
And so we have it, Mona adds to 43, a prime number.


A prime number is a number that can be divided only by it's self and 1. 
2 is the only even prime number. Pick any other even number and it is clear to see that upon division by 2 it is not prime, eg, 20. 20/2 = 10. it yields another even number. 10/2 = 5  and now we see we are left with another prime. 5 can only be divided by 5 and 1. Push this a little further and you will find that every number, greater than 1, can be written as a unique product of primes. And so, you have just discovered the Fundamental theorem of Arithmetic. (It's kind of a big deal)


Why though are primes fun? 
379009 is a prime. When typed into a calculator and turned upside down, it spells Google. Perhaps we'll see it as a 'google doodle' on some calculators birthday...
77345993 is another calculator prime. It spells Eggshell.


A French composer Olivier Messiaen used primes to create ametrical music through "natural phenomena". 43, Mona, was one of his faves.


How are they useful?


For Hacking! Hackers and other computer pirates try to steal information or break into private transactions by breaking codes using incredibly large prime numbers. 


Primes are used extensively in internet security and all kinds of security really. I bet that code breaking game you had as a kid involved primes of some sort. (please don't tell me I was the only kid that had code breaking kits and games.)


How can they turn you into a MILLIONAIRE??
Find a new one and tell the US Government and they'll give ya mountains of dolla's for it. Then you must give me a cut.


So here's to Mona, 43 and Primes. Here's also to having more time to write about numbers again.


Goodnight all from Ais and Internet

Sunday, November 14, 2010

Mathemagics

Hi internet! how ya gettin on?
People give out about maths. They hate it. They can't do it. It's too hard. It's stupid. Maths sux.
Well let me tell ya. I hate it and I cant do it and its too hard, but one thing's for sure.. it doesn't suc and it's pretty cool.
Will we show 'em a few reasons why internet? gowan we will sure.

Magic
Earlier I asked for some volunteered numbers, just so you know that i'm not using 'fixed' numbers, I had some lovely audience members spew some out. One came from the wonderful Emma Wade. It was 529. Now if we reverse this, we get 925. Subtracting the smaller from the larger, we get 396. Then we reverse this to get 693. Then finally we add this to it's predecessor to receive a solution of 1089.
What's so magical about that?

Well, lets try another number, donated by the fabliss Sarah Elaine. 417. Reverse to give 714. Subtract, 714 - 417 = 297. Reverse; 792 and add 792 + 297 and what do we get...
Behold!
1089.

It's always 1089.

And this works for ANY 3 digit number, where the first and last differ by more than two.
Magnificent! Wonderous! Magical!

Well, not entirely..

Maths
Consider, 529. This can be written as 500 + 20 + 9. And any 3 digit number can be written in the form 100a + 10b + c. So let's, for handiness sake rename 529 as abc for the time being. Reverse abc to give cba. Then subtract, abc - cba  = (100a + 10b + c) - (100c + 10b + a)
Ya still with me?
The bs cancel each other out and we're left with 99a - 99c.. or 99(a-c). Since the first and last digits differ by more than 2, a-c is either 2,3,4,5,6,7 or 8. So now we have that 99(a-c) is one of the following; 198, 297, 396, 495, 594, 693 or 792.
Any of these look familiar?
The final part is to add which ever one of these intermediary numbers to its reverse. So lets call our intermediary number def (which is 100d + 10e + f as before with abc) and add it to its reverse fed. Looking at the list of 7 possibilities for def we see that the middle number is always 9, and also, the first and last digits always add to give 9. i.e. d + f = 9. So, def + fed is 100d + 10e + f + 100f + 10e + d
or, 100(d+f) + 20e + d + f

which is (100 x 9) + (20 x 9) + 9

or, 900 + 180 + 9

And voila. 1089. The riddle is laid bare.

Anybody that has made it this far in the post should be commended. And well you should feel victorious in the fact that you can now see through the magic. If this is the case, you should come and do some sums with me and internet.

This post was brought to you by a quote (one i thought was quite nice. It's from a weird religious indian guy who tried to teach maths, he was a bit of a phoney but he said some nice things.)

To those who asked whether the method was maths or magic, he had a set reply: 'It is both. It is magic until you understand it; and it is mathematics thereafter.'

Goodnight internet.

Wednesday, November 10, 2010

Still getting to know each other.

Internet, I'm not so happy to inform you that when getting to know each other, we cant just talk about the good things in life, so in order to avoid completing the final 30% of my probability assignment, I' m gonna tell ya about some things I don't like.
I don't really like that it's so rainy out now.
When I was in college before i think it was TJ that made a list of things he didn't like. (Anyone remember TJ?) On the top of his list was dirty pots. I really don't like dirty pots either.
I don't like that I'm shit at exams or the fact that I've fat eye lids.
I don't like that Dee lost a pet.
I don't like the fact that I work so much while at college, I should really give myself a better chance. I do like that I have a job though.
My brother doesn't like that I didn't mention him in the things I do like. I think he thinks I'm a bit weird for writing like this. I like John and at least I'm not as weird as the midget kid that sings Katy Perry.
I don't like that I don't have parents anymore. It's weird and it saddens me.
I don't like when I cant recognize differentiation. That wrecked my head last week. Stupid. As you may have guessed from yesterday, I don't like simultaneous equations with more than 2 variables.
I don't like dogs or onions or nail biting.
I don't like that Derm's not around all the time now. But yet, at the same time I couldn't be happier that he's gone to do something good.
I guess life's not as simple as putting things into good boxes and bad boxes.
Maybe, internet, I should make the good boxes bigger and the bad boxes littler and then I could listen to Little Boxes and make my little bad boxes sound better..
What kind of boxes do you have internet?

Tuesday, November 9, 2010

Getting to know you/me/us

Hello internet.
My name is Aisling.
I feel this could be a nice little friendship so lets get to know each other a bit.
I'm currently 25 and avoiding my Probability homework. I don't really like probability as a subject, I think it's about as exciting as calculating simultaneous equations with more than 2 variables, by hand. Computers should do these things. I do like other maths though, the kind of maths that computers cant do. The thinking maths. Abstract thought...
I also like cake. I like to bake. There's this one cake that I made with sour cream and blueberries and it was kinda fantastic. Mona wants the recipe. Internet, maybe one day you will host the recipe for Mona and we can all see the joys of the sour cream and blueberries cake. Yum.
Along with maths and cake, I like cats and music and driving. These are probably my five favourite things. Although, internet, maybe I should mention that these things change on an hourly basis.
Unfortunately, I also really like cigarettes and coffee. Marlboro menthol and Lattes to be specific. I made a new friend that works in Mocha Beans. He makes really nice lattes and his name is Roland.
I love flowers. Fresh ones. Like lillies and tulips and roses and orchids.
I like sharp knives, that might sound a bit weird, but there's nothin' worse than a blunt knife when cuttin' chicken.
hmmm, what else.
I like Louise, she started a blog recently and it kinda made me want to start one. Mona's blog makes me drool. She puts pictures of many tasty things in her blog. Mona's also gonna bring me to Disney Land!
Bryan has a blog, I'll try to get interested in it but I fear his pictures wont look so tasty. But he was encouraging to me when wondering whether or not to start this. So, internet, lets be grateful to Bryan for bringing us together.
Maths, cake, cats, music, driving, cigarettes, lattes, flowers, knives, Louise, Mona and Bryan are this things I like tonight.
Internet, what do you like?