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10/30/07

20-year UnderGraduate Proved Simplest Universal Turing Machine


Stephen Wolfram is the author of the book "A New Kind Of Science", and the founder of the software "Mathematica". He postulated in his book, that the 2,3 Turing Machine is universal.
This has now been proved by 20-year Alex Smith, an undergraduate from Birmingham university. He thereby won a prize of $ 25,000 set by Wolfram.

The idea of a universal machine originated from Alan Turing in 1936. He defined a machine now called Turing machine, capable of computing anything that is computable at all. The machine is only conceptual, not a hardware. It has an infinite 1-dimensional tape, and a read-write head which can also move left or right.

Digital computers are also universal in a sense that it can be programmed to compute any computable function. The difference with a Turing machine is that a Turing machine has infinite storage (tape), whereas digital computers are finite, so digital computers are not really universal.

People have asked what is the simplest possible Turing machine. A 7,4 machine is found to be universal. The numbers 7,4 refer to the number of states of the head (7) and the colors of the tape (4).
Wolfram later discovered a smaller 2,5 machine, and postulated that a 2,3 machine is universal, which according a 40-page proof by Alex Smith, indeed is.

This machine has only 2 states and 3 colors, and it is amazing that such a simple machine can compute (in theory) complex differential equations, make weather predictions and financial calculations. In theory of course, since the Turing machine is not known to be (time) efficient. Still it is more powerful than computers with highly dense electronics.

So, what is the practical application of the new discovery? Wolfram said "Perhaps one day there'll even be practical molecular computers built from this very 2,3 Turing machine.
With tapes a bit like RNA strands, and heads moving up and down like ribosomes.
When we think of nanoscale computers, we usually imagine carefully engineering them to mimic the architecture of the computers we know today."

Wolfram thinks the philosophical implications are also important, "that above a very low threshold, all systems will be exactly equivalent in their computational capabilities."

Background information:

10/22/07

Einstein and "The Old Man"

Because Einstein was a highly respected figure, what he said about God and religion, are often quoted to support various views from atheism to all shades of religions or beliefs.

What is actually his relation to God, or "The Old Man", a term he sometimes used to refer to God?

A way of speaking.
To begin, it seems stupid to point out that when he says "The Old Man does not play dice", he does not in any way imply that God exists, any more than implying that God is male. It is just a way of speaking common with many. This much is obvious, yet there are people who uses such quotes in discussions to imply that Einstein believed in God, instead of reading it as meaning that the universe is deterministic, not random.
I used the word "I" quite often, although I believe in non-self, because it is convention in communication.

Being religious.
One of his often quoted statements is "Science without religion is lame. Religion without science is blind."
As a scientist, he expressed the importance of religion and beliefs in general.
But religion does not necessarily mean God, and God does not necessarily mean a personal God who has a child, gets angry, and generally interferes in human affairs.

Being religious for him means "To sense that behind anything that can be experienced there is something that our minds cannot grasp, whose beauty and sublimity reaches us only indirectly, this is religiousness."
And "Try and penetrate with our limited means the secrets of nature, and you will find that, behind all the discernible laws and connections, there remains something subtle, intangible, and inexplicable. Veneration for this force beyond anything we can comprehend is my religion. To that extent I am, in fact, religious."

In other words, being religious is some form of incompleteness (Dukkha) of science.
Religion is like a hypothesis to be verified - then it becomes science - or refuted and discarded, while humbly accepting that there are always things we don't understand.
It is not dogma. It is not absolute.
Einstein also rejected religious rituals, just as J. Krishnamurti did.

Rejects Personal God.
His rejection in a personal God began already when he was in school, and he repeated this rejection many times later.

"I cannot imagine a God who rewards and punishes the objects of his creation, whose purposes are modeled after our own -- a God, in short, who is but a reflection of human frailty."

"The idea of a personal God is an anthropological concept which I am unable to take seriously."

"I do not believe in a personal God and I have never denied this but have expressed it clearly. If something is in me which can be called religious then it is the unbounded admiration for the structure of the world so far as our science can reveal it."

"I have repeatedly said that in my opinion the idea of a personal God is a childlike one, but I do not share the crusading spirit of the professional atheist whose fervor is mostly due to a painful act of liberation from the fetters of religious indoctrination received in youth. I prefer an attitude of humility corresponding to the weakness of our intellectual understanding of nature and of our own being."
In this last quote, he preferred the agnostic attitude, and rejected atheism.

What kind of God?
If not a personal God, then in what kind of God did he believe in?
"I believe in Spinoza's God who reveals himself in the orderly harmony of what exists, not in a God who concerns himself with the fates and actions of human beings."

The closeness of Spinoza's God and Buddhism, both believing in a cosmic religious feeling, led him to say:

“The religion of the future should transcend a personal God and avoid dogma and theology. Covering both natural and spiritual, it should be based on a religious sense arising from the experience of all things natural and spiritual as a meaningful unity. Buddhism answers this description…If ever there is any religion that would cope with modern scientific needs it would be Buddhism.”

Science and religion.
The distinction between "what is" and "what should be" describes the all important difference between science and religion. The boundary of "what is" and "what should be" is not strict, there is interaction between the two:

"Yet it is equally clear that knowledge of what is does not open the door directly to what should be. One can have the clearest and most complete knowledge of what is, and yet not be able to deduct from that what should be the goal of our human aspirations. Objective knowledge provides us with powerful instruments for the achievements of certain ends, but the ultimate goal itself and the longing to reach it must come from another source. And it is hardly necessary to argue for the view that our existence and our activity acquire meaning only by the setting up of such a goal and of corresponding values. The knowledge of truth as such is wonderful, but it is so little capable of acting as a guide that it cannot prove even the justification and the value of the aspiration toward that very knowledge of truth. Here we face, therefore, the limits of the purely rational conception of our existence.
But it must not be assumed that intelligent thinking can play no part in the formation of the goal and of ethical judgments. When someone realizes that for the achievement of an end certain means would be useful, the means itself becomes thereby an end. Intelligence makes clear to us the interrelation of means and ends. But mere thinking cannot give us a sense of the ultimate and fundamental ends. To make clear these fundamental ends and valuations, and to set them fast in the emotional life of the individual, seems to me precisely the most important function which religion has to perform in the social life of man. And if one asks whence derives the authority of such fundamental ends, since they cannot be stated and justified merely by reason, one can only answer: they exist in a healthy society as powerful traditions, which act upon the conduct and aspirations and judgments of the individuals; they are there, that is, as something living, without its being necessary to find justification for their existence. They come into being not through demonstration but through revelation, through the medium of powerful personalities. One must not attempt to justify them, but rather to sense their nature simply and clearly. (The World as I See It)"

This is how conflict often arises: "For science can only ascertain what is, but not what should be, and outside of its domain value judgments of all kinds remain necessary. Religion, on the other hand, deals only with evaluations of human thought and action: it cannot justifiably speak of facts and relationships between facts. According to this interpretation the well-known conflicts between religion and science in the past must all be ascribed to a misapprehension of the situation which has been described."

The world would be more peaceful if we all adhere by the limitations of both science and religion.

Related:

10/14/07

A Different View of Mother Teresa



It is hard to understand how Mother Teresa, in the last 50 years of her life, could not feel the presence of God, "neither in her heart or in the Eucharist", yet she said that Christ is everywhere. She called her smile a "a mask" or "a cloak that covers everything," and she wondered if she was engaged in verbal deception and hypocrisy.

Simplistic explanations, that she has given up God, or that it is normal for people and saints to have dark spiritual moments, do not tell the whole story. How could she be in dark spiritual moment for so long, and how could she have the strength to go on with her work of helping the poor and the dying if she had lost her faith?

It is known that leaders, and Mother Teresa was one, often can see, and understand further than their followers. This includes cases when the leader knows that a change of direction is due. Anwar Sadat was such a leader who saw the necessity of making peace with Israel, and did so, even though he knew that many Egyptians and Arabs would consider him a traitor.

But Mother Teresa did not want her doubts to be publicly known (she asked the letters to be destroyed). She continued to wear her "mask". I can't think that Mother Teresa lacked intellectual integrity and courage to openly publish her doubts. The reason must be something else.

In other cases, such as in the Soviet Union during the heyday of communism, some leader had "revisionist ideas" but they often had to hide their ideas for fears of being chastised and fall from grace.
Again this could not be the case with Mother Teresa, she was not in any danger at all.

Could it be, that she had discovered the "God delusion" but not the "Self delusion"? Was she too much attached to her work, her success and fame? Reading from what people wrote about her character, I don't think this was the case either.

More plausible is that she had seen that "all in empty". Even her work was "empty". Yet she continued her great work to lessen suffering in the world, without hoping for rewards, earthly or otherwise. What she did was like the Tonglen "abandon all hopes of fruition", and Wu Wei action/inaction. She must have seen that helping people in their suffering is all that matters, even when there is no God to reward her. All her beliefs or non-beliefs, faith and religion do not matter in comparison with the actual work of compassion.
In this light, her already great work looks even greater.

The long periods of her agony, indicates that it was not easy for her to come to terms with "emptiness", or the "vanity of all vanities".

'Vanity of all vanities, all is vanity, what profit hath a man of all his labour which he taketh under the sun' The Book of Ecclesiastes

Links:

10/10/07

Discovery of Giant Magnetoresistance gets 2007 Physics Nobel Prize

The discovery of Giant Magnetoresistance (GMR) which makes tiny hard-disks, like the one used in iPods and MP3 players possible, gets the Nobel Prize in Physics 2007.

Two European scientists, Albert Fert from Université Paris-Sud; Unité Mixte de Physique CNRS/THALES, Orsay, France, and Peter Grünberg from Forschungszentrum Jülich, Germany share the $1.5 million prize.

They discovered GMR simultaneously and independently about 20 years ago.
It is based on the large effect of small magnetic differences on electric resistances. Previously magnetic induction was the technology used to read and write to magnetic disks.
In magnetic induction differences in magnetic field lead to electric currents. GMR can detect much smaller differences than magnetic induction.
The use of Giant Magnetoresistance is regarded as the first major application of nanotechnology.
Hard-disks for home use now reaches a Terabyte, or one thousand billion bytes.

Downloadable Pdf documents from Nobelprize.org:

10/9/07

An Appeal to all Bhikkhu Sangha by Karen Monk Union

Here is statement from the Karen Monk Union, reproduced in full from BuddhistChannel.tv:

The most venerable all Bhikkhu Sangha of all sects of Union of Myanmar.
The Pattanikujjhana Sangha kamma done by you is in accordance with Vinaya Pitaka. All Bhikkhu Sangha of the seven States (all ethnic minority Sangha) also support you very strongly. All you have to do is to go ahead only.

At present, as the army has also started to divide among themselves, the divisional army chief of middle region division, General Ko Ko (Bogyut Ko Ko) has expressed on 25/9/07 that the father of the army is not Cr. Gen Than Shwe, but Late. Bogyut Aung San only. Therefore, he has requested the army not to follow the command given by Cr. Gen. Than Shwe.

1,037 Bhikkhu Sangha and over 8000 people from Kyondoe town, 578 Bhikkhu Sangha and over 1000 people from Kyaikdon region and 758 Bhikkhu Sangha and over 1000 people from Phah-pya region in Karen state have also been staging on the street in support to your righteous struggle.

It is sure to succeed if we, all monks of 9 sects of Myanmar Bhikkhu Sangha, are united and have four dominating factors ( Sandadhipati - will, Viriyadhipati - Effort, Cittadhipati - consciousness and Vimansadhipati - Wisdom).

From truth to success.
Karen Monk Union

Earlier: Myanmar crackdown on protesting monks

gPhone is not a Phone

Speculations about Google's gPhone can roughly be divided between those that say that gPhone will be a device like Apple's successful iPhone, and those that say it will be just a operating software for mobile devices.

A few weeks ago, Taiwan's Digitimes said that Google "will definitely launch its own branded handset."

The International Herald Tribune, according to Slashdot's "Google Hopes to Disaggregate Carriers with gPhone" however said that gPhone will be like Microsoft Windows Mobile operating system for mobile devices. gPhone will be free, and it will help Google distribute its services like advertising to phones.

It is expected to be launched later this year.

Meanwhile, Microsoft's Bill Gates doubts that Google could become a successful competitor in the smartphone software market, where Microsoft has about 10 percent market share.

Earlier: Bill Gates dismisses Google phone

10/4/07

What Makes Decision Making Hard

We make decisions all the time, some of them we call easy, hard and not so hard. What makes a decision hard?
The following looks at some conditions of a hard decision, and some of the tools available to help us.

Broadly, there are three categories of reasons why decision making can be hard.

Firstly, there is uncertainty.

This includes non-determinism as well as insufficiency of knowledge and information. It also includes complexity of the computing resources to obtain information.
For example, risk of a stock is associated with standard deviation, which is a statistical parameter of a probabilistic variable. However, the standard deviation is only approximated by looking at the historical data of the stock. Data may not be available, and computing resources may limit what can be calculated.
We have already seen this in relation to bounded rationality .
Another aspect of uncertainty is volatility, the uncertainty with respect to changes associated with the passage of time. Historical data may be useless if the system is changing very fast.

Secondly, structural complexity.

Structural complexity refers to the degree of entanglement of the situation. Structural complexity may imply computational complexity as well.
Many cases involve quantitative as well as non-quantitative relations among variables. One variable is likely to influence another, e.g. decrease in one variable will increase the other, but the relation cannot be quantified (see systems thinking and systems dynamics).
The number of variables and the relation and interactions among variables determine structural complexity.
We have seen how in Buddhist Economics , many more considerations such as Ethics and Ecology must be considered in addition to traditional Economics. This increases the structural complexity of the problem.

Finally, conflict.

Conflict refers to conflicting goals, interests and opinions.
Decision making with multiple goals is easy if the different goals can be weighted numerically and thus reduced to a single goal. In general, conflicting goals cannot be so treated.
Conflict can come from internal as well as external sources. It is interesting, that according to Minsky's "society of minds" theory , there are multiple minds inside us, including thinking and emotional minds, beliefs and desires, mostly in conflict with each other.

People found that our decisions are not rational, but instead we make decisions according to which mind happens to be strongest, and afterwards construct narrative rationalizations around them.

The combination of uncertainty, structural complexity and conflict makes decision making hard.
Some tools have been developed to assist us. For example Robert Clemens in his book Making Hard Decisions: An Introduction to Decision Analysis (Business Statistics) listed decision trees, cash flow discounting, probability and statistics, sensitivity analysis, Monte Carlo simulation, and utility theory.
These are useful, but often inadequate.

Systems Dynamics would be good for modeling, if everything is numerical. The system could be run under various what-if settings to produce simulations.
When numerical values are not available, Systems Thinking can be used for modeling. But the model cannot be "executed" by a computer program.
An alternative is FCM (fuzzy cognitive maps ), which uses fuzzy logic to express relations. Fuzzy logic has a natural way of resolving conflicts, allowing various "expert" opinions to be combined.
All three modeling methods have disadvantages. What is needed is perhaps a modeling method where the relations are can be partly numerical, partly fuzzy, and partly qualitative.
The model must be executable, at least for some of the sub-models.
Models must also be decomposable into top-down hierarchies to allow different levels of details.

10/1/07

`Tiger from Madras` is chess world champion

India's Vishwanathan Anand, known as the "Tiger from Madras, was crowned world champion of chess after winning the Mexico tournament.

He took over the title from Vladimir Kramnik of Russia.

Kramnik was second, followed by Gelfand and Leko.

Photos and games to download: