discrete-thoughts

[discrete-thoughts]

وتلك التي أُحبها، لا اتصور معها السوء، ولا استطيعه. كأنها الذهب، وكأني الفقير الذي لا يريد أن يكون لصاً.

- المنفلوطي

[discrete-thoughts]

I hate my needs, and I hate having them.

[discrete-thoughts]

Words

It's unimaginable what different words can do; it is - often - difficult to pick the right words when speaking that - sometimes - I wish I don't speak at all ... But it gets lonely when I don't, and that hurts.

[discrete-thoughts]

When you explain a "why", you have to be in a framework that you allow something to be true

Richard Feynman

[discrete-thoughts]

أنا قوي كفاية لأقف وحدي، لكن بين فترةٍ وأخرى أحتاج لمن يمسك بيدي ويقول:

اطمئن، ستكون الأمور بخير.

شهاب الدين الهواري

[discrete-thoughts]

It’s a terrible day for rain ...

[discrete-thoughts]

Expectations

A: What ? Are you expecting something ?

B: No ... Just hoping.

[discrete-thoughts]

“‘Look at me’ is one of the most fundamental desires of the human heart.”

— Bertrand Russell, What Desires Are Politically Important?

[discrete-thoughts]

Poets ?

Poets are just people who neatly say that some things are like other things .

[discrete-thoughts]

Hearing you laugh makes me so happy

[discrete-thoughts]

I didn’t come this far, to only come this far.

Unknown (via deeplifequotes)

[discrete-thoughts]

If you can't run, jog; If you can't jog, walk; If you can't walk, crawl.

Just never stop.

[discrete-thoughts]

Too bad to be true

Do you ever feel like choking with sadness in a nightmare that you can't stand it, and you know this must be a dream because it's too bad to be true ?

I often get those, and I usually wake up just as the things are getting worse and worse, and I say "yah -with a smile- it really was a dream" and happy that every thing is ok in real life.

Actually it's so common in my dreams that I associated that bad feeling with being a sleep, and that it's just not true and can't be happening in reality.

The problem -sadly- rises when some thing in the real world happens to have such a bad impression, I can't understand right away that it is true, I think like "hmmm, it feels so bad, it must be a dream and I will wake up at some point", but I never do.

In fact, I just woke up from a dream (can't really remember it) having exactly that same bad impression about the real world; like how in the world is this real ?!

It is so bad that I can't stand the idea that it is real, too bad to be true, there must be some waking up at some point, but I find none, none at all.

[discrete-thoughts]

Divisibility by 4

It is known - and can be deduced with the help of some number theory - that for a number to be divisvle by 4, the least 2 significant digits has to be divisble by 4, and that in turn happens in 2 cases:

1. The ones digit is (0, 4, 8) and the tens is even, i.e. in the form [20n+r, n is non negative integer, r = {0, 4, 8}]

2. The ones digit is (2, 6) and the tens is odd, i.e. in the form [20n+10+r, n is non negative integer, r = {2, 6}]

Actually we can see why that happens if we consider what happens when we divide those numbers by 2 (and of course they all are divisible by 2).

Now if we have a number with the ones digit equals (0, 4, 8) and even tens digit، we will find that 2 divides both of them equally and the result will obviously still be divisible by 2 (as 0/2=9, 4/2=2, 8/2=4) at least once, thus the whole number is divisible by 4.

The other group is a little tricky though, but if we look closely, we will find that any number that starts with 2 then an odd digit when divided by 2 will give a ones digit of 6, always 6, which is still divisble by 2 at least once, and the same with the other cae, 6 then an odd tens, it will always give a number that starts with 8, again, divisble by 2 for at least one more time.

Now just for fun let's list all the numbers below 100 that are divisble by 4, sorted by the ones then by the tens, not vice versa:

00, 12, 04, 16, 08,

20, 32, 24, 36, 28,

40, 52, 44, 56, 48,

60, 72, 64, 76, 68,

80, 92, 84, 96, 88

Without even counting we can see that they form a very nice 5×5 square, so they are 25 number.

Curious enough, there are 25 numbers below 100 that are divisible by 4, that is 100 / 4 = 25.

In a sense, it is that 100 / 4 solves another elementary problem other than "if we want to divide 100 apple between 4 students, how many should we give each ?", It also is a solution for "into how many groups should we divide 100 apples so that each group will have exactly 4 apples?", i.e. 100 / x = 4 -> x = 100 / 4, of course in that sense we can see that counting 0 is some kind of a cheat and it's actually 100 that counts, but if we reformulate the question to "how many numbers below 100 that are divisible by 4 ?", Then we would logically drop the 100 and count the 0.

We can see how the last 2 question relate, if 100 can be divided into 25 groups each of size 4 (execluding 100 and including 0), so we can group each 4 continous numbers in a group then sort these groups, right then, each group will have exactly one multiple of 4, which gives 25 multiple of 4.

In fact a right formula for that last question would be ceil(100/4) = 25, it gives the same answer for this case, indeed, but it has a different meaning now and it is in a generalized form.

[discrete-thoughts]

Everything Ends

The best thing about bad things, which is also the worst thing about good things ... is that they end.

[discrete-thoughts]

I am not quiet, I am loud in my own frequency.

[discrete-thoughts]

Let us keep the future's misery for the future.