A completely useless post as the name suggests 😛
So, if you have noticed, I have changed the theme of the blog, I was kinda bored with the greenish springish theme…this one’s completely the opposite and I kinda like it. Simple, a bit too plain, literally on the verge of boredom 😛
You might also notice a new page named Blissful Marriage which lists the whole series for easy access. I dont know if I have missed out on a particular topic, if I have, please leave a message there so that I can do a post on that wenever I can.
Other than that, I was hoping to make some money from the blog. Any bright ideas? I mean I know of adsense, but does it let you make enough money? People, I need ideas to make this blog more useful for myself than just venting out and/or using it as an extended version of twitter.
I hated Dijkstra. I really did.
But soon after his death in 2002 while I was only in the second year of my undergraduate degree trying to make sense out of the Dining philosphers problem, I started to search the various aspects of his life and realized how truly amazing he was. In merely 72 years, he gave so much to the world of computer science: be it the harmful effects of GOTO statements or the concept of Semaphores, we are all grateful to him for his generous contributions that he made, all of them neatly written by him with his ink pen. Isnt it just amazing that one of the greatest computer scientists of all time did not consider it ultimately important to use computers himself?
Today, on his 7th death anniversary, could you please pay homage to this great man by visiting this website and reading some of his greatest gifts to the beautiful world of computer science?
My quest to make some sense out of randomness, logic and Islam led me to the Theory of Incompletion. It is a beautiful theory on its own. It says how any theory or any law that we might have now can be nullified with new discoveries and invention and goes on to state that logic in itself does not exist: which did not lead to randomness (randomness itself had been known for a long time) but made it completely unavoidable in modern day Physics.
I hope, if you are still reading this, know that you can not predict exactly what’s going to happen because nature itself is non-deterministic: you can only predict probabilities. Thats where randomness becomes just so important. Poor Einstein, he was never able to prove that there are some hidden variables which could perhaps bring back the good old days of deterministic Newtonian Physics. Einstein was a physist, he was never scared of randomness but he still firmly believed that there must be something that could eliminate randomness, a true challenge to the Theory of Incompletion.
My own research that I have often been whining about is about randomness in time series and I somehow stumbled upon something else which can possibly be used to quantify the Theory of Incompletion: The number of wisdom.
So what is the number of wisdom? Chaitin discovered a number (called Ω, ‘Omega’) with the amazing property that it is “perfectly well-defined mathematically, but you can never know its digits, you can never know what the digits in the decimal expansion of this real number are. Every one of these digits has got to be from 0 to 9, but you can’t know what it is, because the digits are accidental, they’re random. The digits of this number are so delicately balanced between one possibility and another, that we will never know what they are!” (OK, I myself dont know wat I just said!!! 😛 )
Lets track back a lil and see what it actually is: In simple words, Chaitin is only trying to say that if we can find the exact digits of the ‘number of wisdom’, all sorts of randomness can be eliminated and also prove that mathematics has no limits (we already know that Theory of Incompletion says that mathematics is incomplete and has boundaries: wat is true within one boundary will be false in some other boundary)
I am intrigued, fascinated, to say the least! 😀
Anas was talking about this quiz and I just couldnt resist…I just had to take it. And, I am jealous of him now, he’s 88% geek while I am only 86% 😦 But khair, wat made me feel good was the fact that girls, on average, only score 38 😀
When we talk about mathematics, we talk about logic, conciseness, completeness and abstraction. So that means, everything in this world, can be described in terms of mathematics? Even religion? Atleast thats a common belief of a lot of atheists that if something cant be proven through logic or lacks empirical evidence, it shouldnt be believed. Have they tried proving mathematics to be correct? Hmmm…so thats where the problem starts because of Gödel’s incompleteness theorems.
In 1931, the Czech-born mathematician Kurt Gödel demonstrated that within any given branch of mathematics, there would always be some propositions that couldn’t be proven either true or false using the rules and axioms of that mathematical branch itself. You might be able to prove every conceivable statement about numbers within a system by going outside the system in order to come up with new rules and axioms, but by doing so you’ll only create a larger system with its own unprovable statements. The implication is that all logical system of any complexity are, by definition, incomplete; each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules. He proved it impossible to establish the internal logical consistency of a very large class of deductive systems – elementary arithmetic, for example – unless one adopts principles of reasoning so complex that their internal consistency is as open to doubt as that of the systems themselves.
The proof of Gödel’s Incompleteness Theorem is very simple, a lil confusing but surely makes it clear that even logic can be illogical. His basic procedure is as follows:
- For instance there is a machine, UTM, that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all.
- Lets call the program P(UTM) for Program of the Universal Truth Machine.
- Gödel writes out the following sentence: “The machine constructed on the basis of the program P(UTM) will never say that this sentence is true.” Call this sentence G. Note that G is equivalent to: “UTM will never say G is true.”
- Now the UTM is asked whether G is true or not.
- If UTM says G is true, then “UTM will never say G is true” is false. If “UTM will never say G is true” is false, then G is false (remember G = “UTM will never say G is true”, point 3). So if UTM says G is true, then G is in fact false, and UTM has made a false statement. So UTM will never say that G is true, since UTM makes only true statements.
- We have established that UTM will never say G is true. So “UTM will never say G is true” is in fact a true statement. So G is true (since G = “UTM will never say G is true”).
- So we finally we know something that although G can be true, it cannot be universally true!
G is a specific mathematical problem that we know the answer to, even though UTM does not! So UTM does not, and cannot, embody a best and final theory of mathematics!
A very interesting post that shows “as soon as you update the master, the other places automatically get the update.” Facebook Status was used to apply this concept. A must read!