How do computers compute information?

How do computers compute information? This is a question i have been pursuing for nearly 5 years now. Now before you "computer scientists" begin to attempt to answer my question, first fully understand my question. 

Because i have asked this question to so many people, computer scientists, computer engineers, computer architects, and they have never been able to answer this question. It is somewhat frustrating that i ask this question to people who are suppose to be "experts" in their field. To people who spend most of their life working with and programming computers, yet at the same time, at the very core, have no idea how these machines actually work. The only people that have ever gotten close, or have enlightened me further in my search for the answer, are physicists. Which at first comes as a surprise, but then i think back, and realize, that the very person who invented the transistor, was a physicist. 

So what do i mean when i say, "how do computers compute information"? I literally mean, how does a group of transistors, do math, make programs, do the amazing things that i constantly see on my screen, such as play video, make games, and run simulations. ESPECIALLY, run simulations...how can a...box full of parts with electricity running through it, simulate reality, simulate physical phenomena, recreate the real world. Seriously! imagine it, a box, full of parts, is literally able to recreate, what you feel, what you see, and what you hear. Its...awe inspiring...to think that with mere material, and electricity, i can make a universe.

So i should probably discuss or clarify about this vague word called "Computation". 

When trying to understand how computers compute information, i first turned to others forms of computation i understood, such as protein synthesis. And then compare that form to the form i was trying to understand.

Just by watching the animation, you can instantly understand, I understand. how protein synthesis computes information. When I say I understand this, that means I can actually imagine building nearly any structure with this form of computation.

If I wanted to make a square, or a triangle, or a skyscraper. I know specifically how I can code this to do those things, and you do to.

I want to understand how transistor based computers compute information at this very fundamental, physical level.

I have yet to find a person who knows this, or who can explain this, to me.

Maybe you can help me?

I got this animation from a Ted talk, spoken by a professor at MIT named Neil Gershenfeld. 

http://youtu.be/5n-APFrlXDs

This ted talk really enlightened my view as to what computation really is, and problems regarding the understanding of computation.

There is one thing Neil says in this video that really interests me. 

He said, "Computer science is one of the worse things that ever happened to either computers or to science".