Friday, June 4, 2010
Huh?
Yesterday it was so hot,and I went visiting. Cakes..biscuits...cookies...YumYum.. :)
I woke up diz morning and found out I had a mosquito bite on my arm..Dang!
Tommorow I'm going back 2 kuching..can't wait to hangout wif the guys..
Pergi tengok2 org..Haha.
I wanna eat waffle...peanut butter+milk+chocolate....Waaa....
Sooo nice...:)
Stacey,bla U mok sampe Kuching,I wan ice-cream bha.
Lucia,sorry cannot go your open house,still at kampung. Hehe.
I'm gonna hav fun today..eat n eat n eat...:)
Wednesday, June 2, 2010
About Randomness...
In ancient history, the concepts of chance and randomness were intertwined with that of fate. Many ancient peoples threw dice to determine fate, and this later evolved into games of chance. Most ancient cultures used various methods of divination to attempt to circumvent randomness and fate.[3][4]
The Chinese were perhaps the earliest people to formalize odds and chance 3,000 years ago. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the sixteenth century that Italian mathematicians began to formalize the odds associated with various games of chance. The invention of the calculus had a positive impact on the formal study of randomness. In the 1888 edition of his book The Logic of Chance John Venn wrote a chapter on "The conception of randomness" which included his view of the randomness of the digits of the number Pi by using them to construct a random walk in two dimensions.[5]
The early part of the twentieth century saw a rapid growth in the formal analysis of randomness, as various approaches for a mathematical foundations of probability were introduced. In the mid to late twentieth century ideas of algorithmic information theory introduced new dimensions to the field via the concept of algorithmic randomness.
Although randomness had often been viewed as an obstacle and a nuisance for many centuries, in the twentieth century computer scientists computer scientist began to realize that the deliberate introduction of randomness into computations can be an effective tool for designing better algorithms. In some cases such randomized algorithms outperform the best deterministic methods.
Randomness...
Randomness, as opposed to unpredictability, is held to be an objective property - determinists believe it is an objective fact that randomness does not in fact exist. Also, what appears random to one observer may not appear random to another. Consider two observers of a sequence of bits, when only one of whom has the cryptographic key needed to turn the sequence of bits into a readable message. For that observer the message is not random, but it is unpredictable for the other.
One of the intriguing aspects of random processes is that it is hard to know whether a process is truly random. An observer may suspect that there is some "key" that unlocks the message. This is one of the foundations of superstition, and is also a motivation for discovery in science and mathematics.
Under the cosmological hypothesis of determinism, there is no randomness in the universe, only unpredictability, since there is only one possible outcome to all events in the universe. A follower of the narrow frequency interpretation of probability could assert that no event can be said to have probability, since there is only one universal outcome. On the other hand, under the rival Bayesian interpretation of probability there is no objection to the use of probabilities in order to represent a lack of complete knowledge of the outcomes.
Some mathematically defined sequences, such as the decimals of pi mentioned above, exhibit some of the same characteristics as random sequences, but because they are generated by a describable mechanism, they are called pseudorandom. To an observer who does not know the mechanism, a pseudorandom sequence is unpredictable.
Chaotic systems are unpredictable in practice due to their extreme sensitivity to initial conditions. Whether or not they are unpredictable in terms of computability theory is a subject of current research. At least in some disciplines of computability theory, the notion of randomness is identified with computational unpredictability.
Individual events that are random may still be precisely described en masse, usually in terms of probability or expected value. For instance, quantum mechanics allows a very precise calculation of the half-lives of atoms even though the process of atomic decay is random. More simply, although a single toss of a fair coin cannot be predicted, its general behavior can be described by saying that if a large number of tosses are made, roughly half of them will show up heads. Ohm's law and the kinetic theory of gases are non-random macroscopic phenomena that are assumed to be random at the microscopic level.