故事可以追溯到2014年,当时上海的一个朋友建议我研究语法和语义。
“形式语言”和“有限自动机”的概念对我来说是全新的。虽然我接受了7年的理论数学教育,但我从未听说过逻辑和可计算问题的主题,这实际上是纯数学的一个重要分支。
这段简短的谈话给了我很多启发,我开始把我以前学习中遇到的数学理论和问题作为一个完整的知识图谱来对待。我想找到它们之间的关系。
一切都可以用数字来表示吗? 或者每个问题都可以用形式语言表达,并由自动机计算。
如果我们想构建整个知识图谱的轮廓,需要什么来完成这个建设?
要回答这些问题,我们必须了解更多关于我们的物理宇宙和抽象代数结构。
作为个人,我又能做些什么来加速这个过程?
当我告诉我的朋友这些想法时,他说我可以对问题进行分类,并判断哪种类型的问题是可解决的。
我认为我可以解决这个问题。如果我们能把所有现存的问题和未来可能出现的问题都分类,那将是一个很有前途的项目,但要实现这个目标需要很大的个人毅力。
而且,如何对问题进行排序的过程本身仍然是一个无法解决的问题。根据库尔特·哥德尔的理论,有些问题我们知道它是可以解决的,但我们可以提供解决方案。
这听起来很荒谬,但它是严格证明的。
在这种情况下,全局解决方案将不存在,为什么我们还要浪费时间对问题进行排序?
我对此很困惑,但我继续探索,在数理逻辑,计算理论和自动机。
由于一些个人问题,探索被打断。几年,我呆在家里。
在那段时间,我问他一个问题,一个非常基本但有意义的问题:如果我们想要两个大数字,我们如何在计算机语言计算。
“答案很简单,只要找到两个足够大的空间存储数字和它们的和。”
是的,计算是如此简单,即使你需要处理“巨型”数据。你所需要的只是足够的空间来存储信息和进行计算。
我们出生后就被教导技能来处理各种复杂的问题,但你有没有想过那些基本的概念?
什么是自然数,为什么数字可以加和乘?
为什么理解这些基本知识可以帮助你更好地理解我们生活的这个物理宇宙的构成?
让我们追溯一切回到它的历史开始。数学,物理,音乐,声学是如何发展的,我们如何从这些复杂的系统得到抽象的数字并进行计算?
一首音乐传达了什么信息? 它是如何用通过语言表达和在宇宙中传播的?
如果我们知道颜色是由光的波长决定的,那么我们听到的音乐是由什么组成的呢? 是什么产生了声波呢?
如果所有的信息,包括文章,数字,音乐,建筑都必须记录在有形之物上,比如石头,木头,二极管等等。
为什么我们不能跳过现有的乐理研究,直接去研究声音和波粒理论,看看是什么组成了不同的声音,哪种类型的声音会是和弦。
这样,电脑根本不需要人类在艺术上的知识,它只要直接去研究声音背后的物理学原理就能生成美妙的音乐。
The story could trace back to the year 2014, when a friend in Shanghai
suggest me to research on grammar and semantics.
The concept of "formal language" and "Finite Automata
Machine" were brand new to me. Although I had 7 years’ education in theoretic
math, I had never heard about the subject of logic and Computable questions,
which ,in fact is an important branch of pure math.
The short talk inspired me a lot, I start to treat math theories and
problems encountered in my previous studies as a whole knowledge graph. I want
to find their relations.
Could everything be presented by numbers? Or could every question be
expressed in formal language and calculated by an Automata Machine.
If we want to construct the whole outline of knowledge graph, what is
needed to accomplish the construction?
To answer these questions, we must know more about our physical universe
and abstract algebraic structures.
And, what can I do as an individual to accelerate this process?
When I told my friend these ideas, he estimated that I could classify
questions and judge which type of question is solvable.
It's a prospective program if we can classify all existing questions and
problems that might be raised in the future, but it require a lot of personal
perseverance to achieve this goal.
Also, the process about how to range questions in order itself remained an unsolvable question to discover. According to Kurt G?del’s theory, there are question which we know its solvable but we can provide solution.
It sounds absurd, but it is strictly testified.
In that case, the global solution will not exist,why are we wasting time to sort question in order?
I'm confused on this, but I kept on exploring, on mathematic logic ,computable theory and Automata Machine.
Due to some personal issues, the exploring was stubbled.For several years, I was stayed in home.
In that period,I asked him a question, a very fundamental but meaningful question: if we want two big numbers, how will we do this caculation in computer language.
"The answer is simple, just find two digits big enough to store the numbers and their sum."
Yes, caculation is so simple, even when you need to deal with big data. All you need is enough area to store information and do caculation.
We have been taught skills to deal with all kind of complexed problems, but have you think of the basic concepts?
What is natrual number, why number can add and multiply?
And why understanding these elementary knowledge can help you understand more about the construction of this physics universe we are live in.
Let's track everything back to the beginning of its history?How math, physics, music, sound theory developed, and how we get abstract figures from these complexed system to do caculation?
What information does a music convey? how is it expressed in language and disseminate in universe?
If we understand colors comes are determined by The wavelength of light, what made up the music we hear. What generates the sound wave?
If every information including articles,figures,music,architecture is recorded in solid body like stones,wood,diode and so on.
Why can't we skip the study of music, and directly go to sound and wave theory, to see, what makes up different sound and which type of sound is music.