Alan Turing and the Universal Machine - Part 1.

So I've been reading Alan Turing: The Enigma. I'm only about 1/3rd through, but really loving it so far, and thought of writing about it.

The part that interested me the most is the part where the development of the concept of the Universal Machine. Since I am unfamiliar with mathematic philosophy, I re-read the part many times and did a lot of background research. Below is a very rough explanation of the machine.

It all begin with the definition of Mathematics. Roughly speaking it splits into three stages.

Stage I. When mathematics became more than arithmetics, and numbers are treated as symbols and follows a set of rules.

Stage II. Is mathematics complete (ie, all the truth can be derived by following the rules), consistent (no contradiction) and decidable (can determine truth or false with standard steps) under the Formal System?

Stage III. The Universal Machine that aim the solve Stage II problem 3.

Gödel proved the first two problem as false, which is you will always find a statement you know is true but can not prove, and second, which is largely derived from the first, not all mathematical statement is consistent.

Math Stackexchange does a much better explanation than I do:

http://math.stackexchange.com/questions/453503/can-someone-explain-g%C3%B6dels-incompleteness-theorems-in-layman-terms

The more I study the more I understood that the Turing Machine is to solve a logical problem. Even though it is a "Machine", it only serve as a tool to visualize the concept to solve a fundamental problem in logic.

So how does the machine solve the problem of decidability?

First we imagine a machine that does everything a human can do when solving a problem. If we break down problem solving:

1. Read/Write symbols (ie numbers, operators etc..).
2. Execute steps based on certain rules, in the machine's case would be the "Configuration".
3. Conclude.

Therefore theoretically you can solve any problem a human can solve within the Mathematical system with the Machine, as long as you have the configuration. The Universal Machine, is a machine that is encrypted with all the configuration (which can also be a machine itself) of modern mathematics, therefore solving all the modern mathematical problem.

Turing called the results the machine able to churn out: computable numbers.

Turing proved that not all problems can be decided by giving a example of a paradoxical question: the halting problem.

First you imagine a machine that asks the question: does the machine halts?

And set up the configuration as below:

a. Yes: loop
b. No: halt

https://www.youtube.com/watch?v=macM_MtS_w4

If you really think deeply, you would see the configuration itself is a paradox can not be solved. Let's imagine if the input is:

1. Halt -> Yes, loop (Doesn't halt)
2. No -> Halt (but it is looping since the input is no halt)

Therefore creates a contradiction, and Turing determined that not all statements are decidable.

Ok. This is pretty much for part one. There's a lot of resource online for this question,  Udacity and Mathematics Stackexchange has been very helpful. Go check it out!

Anti-corruptions in China

So this post is really about the stories Hao heard from a Mr. Yu. Below is just a bit of a discussion we had, feel free to skip to the story part.


We began our discussion about the slowed economy in China, and Mr. Hao mentioned how locking up people does not that solve corruption, since it is a rather systematic issue. 

The rationale is that public servants in China typically have salary of 2 - 3 thousand RMB per month. "If you're a public servant, you're either politically well-connected, or you've studied very hard." , while the system itself is already a bit of a limbo, there is no clear roadmap for career advancement or whatsoever in the public sector.

To make ends meet, most people resort to taking under the table money, mostly from large infrastructure projects. The bribes gives the public servant incentives to push forward deals, and thereby more projects are build. By threatening people with jail time, you take away to incentives, and no deals are made, aka slows down the economy.

This argument may sound like a legit reason to take bribe. Coming back to the systematic issue, in my opinion, the first issue lies the lack of (or lack of execution) clear investment standards and procedures in SOEs (Stand Owned Enterprise), which thereby leave out grey area to influence and take bribes, the second, of course is the low salary.

Therefore in my opinion, the worst thing about this wave of anti corruption is because it's a personal fix rather than a system fix, and the effect is rather short-term than long term. In the end it serves more for Mr. Xi's political agenda, than structuring a more transparent and fair political system for China. 

Of course the above is a lot of hearsay and admittedly a very shallow analysis. I think I'll do a blog post later (or maybe never....) with a deeper research and analysis of the issue. 

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The background is we have a project in XXX province, and few of my colleagues went there to scout the project and had dinner with the head of the county Mr. Yu. 

Story 1. "I'm keeping you on file."

Ever since the anti-corruption started, authorities have been visiting Mr. Yu everyday, to "collect evidence". And after a while they told Mr. Yu "I'm keeping you on file.", then left. Mr. Yu doesn't know what's "on the file", but was pretty sure that one day if he's on the wrong side whatever is on the file will come back to haunt him.

Story 2. "The Text."

One day Mr. Yu received a photo of him and a naked girl in a motel room, with a note saying "Dear Mr. Yu, you're a good fella and certainly would be ashamed you lose your job and integrity over this, please transfer 150,000 rmb to XXX account.". 

Upon receiving the photo, Mr. Yu first panic for a while, but then thought closely "I'm pre---tty sure I've never sleep with this one". He did some research and found out the photo was photoshopped. Seems like they found his picture online and photoshopped his face with a naked girl.

Since it's a fairly small county, Mr. Yu phoned the head of the police department directly to try to get the blackmailer. Apparently someone within the police department was also blackmailed "Oh yeh, someone in our department received the same photo. The guy reported to me immediately. I asked him if he did it." 

"I'm really not sure........I must have!!"

  

Best storyteller on earth (at least top 5% anyways.)

I've befriended with the best storyteller on earth for 2 years now, and thought I should record some of the stories and topic we've discuss. Most are just random stuff, like some theories we developed, history, science, life, business, etc..

It's aim to be more a entertaining read than anything, hope the readers will enjoy!