Dreams

Phew... Back home after an excrutiating 5 days in the hospital. Got an infection from dunno-where, and they needed to pump in super solid antibiotics into my veins to keep the bacteria from killing me.

Anyway, i realized that i've been dreaming a lot recently.. And a lot means like on average once everyday. Which i would think is justifiable to be called a lot. I also discovered that dreams are easily forgotten. For eg i dun remember any dreams that i had last year.. Although the probability shows it highly likely that i must have had at least one last year.. Thus i've decided to record my dreams in this blog:D

I would think my dreams to be more interesting than my life. So it should be alright.

Okay i had two dreams this morning.

-I dreamt that i had a big house party. Everyone i knew was there.. Even Mr Boo lol.. And he was betting on some F1 stuff with my smallest uncle.. And there was this Huge fridge in the middle of my living room that had lots of vegetables.. (Yuck!) And then i woke up..

-I dreamt that i was on the bus with darren. Then my second aunt boarded the bus. I was lazy to acknowledge her and so pretended not to see her.. With some success.. After a short while, my first aunt boarded the bus.. I also tried to pretend i din see her. Unfortunately, my converstaion with darren got so loud that my second aunt noticed and turned back. "Aye Ah boy!" To which i pretended an enthusiastic reply. "Aye er gu!" Sadly, my first aunt heard this and called me.. And after that they were like telling me what to do.. Eg.. Eat more vegetables.. And i got so pissed off and stressed out that i fainted. When i woke up, i was in my room and my first aunt was talking to me. Though i cannot remember what she said. I woke up and looked around. There was a cabinet with a hell lot of pokemon cards.. Anyway i then asked my aunt,"wheres my friend?" and she told me that he had left.

Haha even in my dreams, Darren has no brotherhood.

Now that i think of it though, it is certainly strange that in our dreams, the places we know will always look a bit different from the actual places. But we will never fail to recognize it. Its like, in reality my room has no glass cabinet. But when i was in that room in my dream, i knew it was My room. Strange isn't it?

Anyway i woke up after that, went down, switched on the tv and began browse thru the channels. And i was reaching chnnel 5 when i saw kids central. And then i realized. SHIT! Just missed Pokemon!! ARGHHHH NOOOO...

I Totally forgot!!! Its a bit mysterious to find the relation between pokemon on kids central and pokemon in my dream, When my conscious mind has totally forgot about it... Somemore todays episode is the beginning of the fourth generation series leh. and for a few months now on kids central there has been NO pokemon. Its almost as though my subconscious mind told me, " Wake up you sleepyhead, theres pokemon now!!!"

Damn this is certainly scary. What if my subconscious mind had already formulated a Hell-Breaking maths theorem and my conscious mind just didn't knew about it!?!?!

Oh well.. I said in the last post that i'll begin modular arithmetic today, i'm too lazy to go thru all of it, so i'll start with something light.

In fact we use modular arithmetic in everyday lives.

For eg on the clock, 14 o'clock is almost always referred to as 2 o'clock. Extending this concept, 25 o'clock would be 1 o'clock and 120 o'clock would be 0 o'clock.

And thus we write 120 is congruent to 0 (mod 12), where 12 means the number in which the following numbers tend to "reset". And mod just means well, modular.

This is in fact equal to saying that when you divide 120 by 12 and 0 by 12, theire remainders are the same.

So using this we can can come up with whole systems of numbers. For eg.

13=3 (mod 5)
17=1 (mod 4)
100=1 (mod 9)

As my previous reader meticulously pointed out, the actual notation is not an equals sign. Rather it is something like that but with three strokes. To which mathematicians read "is congruent to" I can't find it in my computer. And even if i can i'm too lazy to use it. And besides if we consider (mod n) to be a function of x, then it would certainly be legitimate to write something like 5=14 (mod 9) , with he equal sign REALLY meaning equals..

I was really quite surprised that she knew because modular arithmetic is not taught in Singapore at either secondary or jc levels...At least not in the formal curriculum.. I was pretty sure few people would know it haha..

Anyway to show how this might be useful, know that substitution and adding and multiplying to both sides an equal integer is a legitimate operation. While dividing by a common integer isn't.

for eg 10=1(mod3)----------------------(1)
we want to find out that if k is an integer,
whats 10^k under mod 3.

The answer is just one cause we can substitute the 10 in 10^k with 1( as shown in the first equation.) and 1^k is certainly equals to one. so we have 10^k=1(mop 3)

This in fact proves that when you divide any power of 10 by 3, you will always have a remainder of one.

for eg 100=1(mod3)
1000=1(mod 3)
10'000=1(mod 3)
And so on ...

I'll show how this can be immensely powerful in mathematics.

For now see if you can solve the following congruences


y=30 (mod 8)
x=51 (mod 5)
z= 288(mod 4)

-A few extra facts for the inclined.

-notice that if p is a prime number, p will never be zero under (mod n), where n can be from 2 to (p-1)

-Also any number equals to 0 under mod 1.

- And mod 0 just doesn't exist..

Oh well i'll stop here for now.. Wow doing this certainly is not effortless..