(via foresity)

(via foresity)

My dream wedding reception.

(Source: ya7oby, via byzeldiven)

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**Dünyanın en güzel sözlerine, en tatlı klibine sahip şarkısı :)**

İsveçli** I’m From Barcelona**'nın “**We’re From Barcelona**" şarkısı:

I’m gonna sing this song with all of my friends

And we’re I’m from Barcelona

Love is a feeling that we don’t understand

But we’re gonna give it to ya

We’ll aim for the stars

We’ll aim for your heart when the night comes

And we’ll bring you love

You’ll be one of us when the night comes

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From James Liu's answer to What has Quora taught you?

Quora has taught me:

- … to better appreciate life: Leonard Kim Murat Morrison Rory Young
- … to better appreciate my freedom: Jon Davis
- … to look for life lessons everywhere: Cyndi Perlman Fink Lou Davis
- … to be more observant: Oliver Emberton
- … to be interested in history: Andy Lee Chaisiri
- … to enjoy the important things: Julie Prentice Mark Savchuk Margaret Weiss
- … to better appreciate creativity: Ariel Williams Faye Wang
- … to think more on philiosophy: Joshua Engel Marcus Geduld
- … to explore spirituality & atheism together, not separately: Barry Hampe
- … to be more verbal on equality: Erica Friedman Dan Holliday
- … to be vocal but grounded: Jan Leadbetter Charles Faraone Claire J. Vannette
- … to dabble in everything: Sanjay Sabnani Garrick Saito James Demetrios
- … to view the world: Varsha Iyer Caroline Zelonka Simon Brown
- … to love spaaaaaaaaaaaaaaaaaaaaaaaaaaaace more: Robert Frost
- … to dig deeper in my passion of computer science: Miguel Paraz Jessica Su
- … to further explore the unknown: Jesse Lashley
- … to have more rational and result driven decisions: David S. Rose Mark HarrisonMichael Wolfe Ian McCullough
- … to exhibit personal passion while exhibiting social leadership: Marc Bodnick
- … to explore my favorite industry (games): Jeff Kesselman Daniel Super
- … to be more-informed (opposing his tag-line): Marq Hwang
- … to think about what’s beyond my own scope of existence: Hunter McCord
- … to question my ‘current’ ever changing bias: Brian Browne Walker
- … to think about the biological scope of my existence: Ian York
- … to possibly grow a kick-ass beard, and enjoy photography: Tom Byron
- … to enjoy life my own way, following a lead by example: Danita Crouse
- … to laugh and enjoy all the little things, regardless of complexity: Xu Beixi
- … to stay thoughtful and ever-chase the monument of knowledge: Alex K. Chen
- … to ask again, even if I think I know the answer: Joel V Benjamin

I’ve learned a lot from these wonderful people. They are leaders in my quest for knowledge. Knowledge is limitless and timeless.

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I have a theory about the human mind. A brain is a lot like a computer. It will only take so many facts, and then it will go on overload and blow up.

- Erma Bombeck

From Michal Forisek’s answer to Can the Halting Problem be avoided by checking every possible input?

**Emphasis Added.**

*

People who learn about the halting problem

often get to the stage where they already(on an intuitive level)accept that it holds— given an arbitrary algorithm and an arbitrary input for that algorithm, we cannot decide whether the algorithm will terminate.

However, peopleoften get the incorrect impressionthat the hardness of the problem lies in the infinity of possible inputs.

This seems quite plausible: who knows what the algorithm does for all of those nasty huge inputs, right?Now,

armed with this “understanding”,we move from theory to practice.

In practice, we usually have an upper bound on the size of the input to our program.

Suddenly, there are only finitely many possible inputs.

And this is where people tend to ask the question: “Cannot we circumvent the halting problem in this case? Isn’t it possible to check whether this algorithm terminates for each of these finitely many inputs?” (And also: “Even though it can be impractically slow, cannot we, in theory, verify the correctness of a program simply by checking that it works for all allowed inputs?”)Now,

in order to understand why we cannot do that, you need to understand where the true hardness of the halting problem lies. It has nothing to do with the size of input. In particular:

Deciding whether a program that takes no input terminates is as hard as solving the halting problem in general — that is, as answering the general question “does program P terminate on input I?”.

This is actually a very easy reduction.If you knew how to solve the “simpler” version for programs that take no input, you could solve the “general” version as follows:

take the program P, and modify it to obtain a program Q that never reads the input.

Instead, you hard-wire the input I into Q, and whenever P would read input, Q just reads the next part of the hard-wired input I. Obviously, deciding whether Q terminates (without any input) = deciding whether P terminates on input I.Here’s another example that very nicely illustrates where the real difficulty of deciding the halting problem lies.

It’s not the size of the input. It’s the potential infiniteness of memory used during the computation,and the fact that already very simple rules can create very complex program behavior.

*

Consider the

following simple string-rewriting algorithm:

rules = { ‘a’:’bc’, ‘b’:’a’, ‘c’:’aaa’ } n = int(input()) S = ‘a’*n # a string of n ‘a’s while len(S) > 1: S = S[2:] + rules[S[0]]

*

It doesn’t get much simpler than this: in each step, remove two letters from the beginning, and append a few new letters at the end. Here’s what the program does for n=10 if we print S after each iteration of the while-cycle:

aaaaaaaabc

aaaaaabcbc

aaaabcbcbc

aabcbcbcbc

bcbcbcbcbc

bcbcbcbca

bcbcbcaa

bcbcaaa

bcaaaa

aaaaa

aaabc

abcbc

cbcbc

cbcaaa

caaaaaa

aaaaaaaa

aaaaaabc

aaaabcbc

aabcbcbc

bcbcbcbc

bcbcbca

bcbcaa

bcaaa

aaaa

aabc

bcbc

bca

aa

bc

a

and it terminates. It also terminates for n=47 — but the process takes 40492 steps, and the longest S during the computation has 242 characters.

Now comes the question:

does this particular algorithm terminate for every possible positive integer n? The answer is: we don’t know yet.Read that again. A program with four simple lines of code.A program that just repeats a single deterministic step. What do you mean, “we don’t know yet”? Well, we don’t. The question whether this particular tiny program always terminates is equivalent to the Collatz conjecture — which is a famous open problem in mathematics.