For my own records.
1. Math, Calculus and counting
I never quite understood calculus until I heard someone put it this way, not the original words but the basic ideas: before calculus, we are doing measuring shapes of very conventional shapes, like squares, rectangles, triangles, we got all the simple formulas, mutilple by each sides etc. then how about irregular shapes, how do we calculate the areas? yes we do it by couting tiny unit squares inside whatever shapes, then sum the whole thing we got the area! does it sound familiar, yes its almost the idea of Riemann sum, which is the very foundation of calculus. of course things get messier and messier after introducing more shapes functions and extended everything into higher dimensions, like not only do we want to calculate area which is summation of 2D space, we also want to know the volume aka 3D space summation.
So, all i want to say is, calculus is mathmatical counting at a more general/complicated level, with calulus we count every fucking thing. This is in fact in line with the basic idea of math(or my personal very shallow idea of what math actually is), math is counting, of couse people will argue its more than that! but I insist, the very core idea of math is counting, and only after that do we have all the general summaries of truth or patterns discovered by counting numbers. then why do we count? because we need to measure. how do we measure? we measure by addition. we mearue length by counting all the unit dots in a line; we measure areas by adding unit lines together, imagine adding all unit dots in one line, then do it repeatly, which is how multiplying works; we measure volumes by adding areas together, which feels like an iteration of areas addition on top of an iteration of lines addition on top of an iteration of unit dots addition. how about 4th dimention then? another iteration on top of 3d measures.
Back to the idea, why do I talk about elementary computations that every kid knows? Because I want to conclude(feel free to disagree) that math is about counting, and finding patterns through counting. We use counting to measure/symbolize/understand world. I guess thats why peopel always say math is the closest to truth/nature/god etc.
2.logic and programming
Lets start with a basic question. What is computer? Its a machine which do computing just like its name! how does it do it? it does computations by fliping bits which is the basic unit of chips, by fliping massive amount of tiny bits in very short period of time, computers counting/computing/recording numbers. So again, what exactly does computer do? put it in a more abstract way, it does simulations of complicated computing procejures.
One word, simulations, it is what I want to describe the essence of computers in relation with the major topics I want to talk about here.These multi-stage simulations are carried out by a combination of computing numbers and logics simulations. Here I first mentioned logic. In mathmatics, logic has more rigorious definition, but I want to think it in a simple way, it is the glue to gluing numbers counting and stages of counting together.
So what is programming according to all my previous definitions of logic and computers? I think, programming is to create simulations of combinations of different countings and logics, though this whole process takes so many stages from a bit flip on the chips to high level programming abstractions like declare a variable.
3.to put it simple
To summarize, math is counting, programming is to create simulations of countings glued by logics. computer gives us tremendous amount of power to do all kinds of simulations, and by doing all these simulations we can find answers to specific questions, we can optimize answers, we can basically simulate/abstract/recreate the real world since we already tried to simulate everything.
4.why are we talking about all these abstract concepts?
The point is simulation.
We want to simulate everything in real world. and math, logic and programming are the tools we use to build all kinds of simulations. Essentially, we are recreating the real world in a digital/mathmatical/logical(simplified) way. When people are talking about AI, machine learning, all kinds of algorithms, and sounds crazy concepts like AI taking over the world, mind uploading, maybe all these could be viewed in a different way: they all are simulations of the real world. Then they are not so mind blowing after all, they are in fact the very logical progression of human civilazition, we are in fact heading towards another new world which is created by ourselves based on abstractions of the pyhsical world.
5.how does it relate to the movie?
The movie introduced very advanced concepts like AI master control program, human digitalized into computer simulated world, they look fictional, they sound unreal. However, they are in line with the directions we are heading to. And it is in some sense definitive. I personally believe they are achievable, people say si-fi predicts the future, I think si-fi draws blueprints for the future and we humans create the future based on it. Anyway, I think this movie was so advanced and still relating till this day, we are heading towards all the ideas this movie presented.
HD
