Wednesday, December 13, 2006

How Random?

SEE THE ARTICLE Start-up generates random numbers from space from CNET News:
British start-up Yuzoz has announced that it will be launching its beta service in the next two weeks--an online random-number generator driven by astronomical events.

Working with data from satellites and observatories, Yuzoz will use the solar wind, the clouds of Venus, the Northern Lights, Jupiter's shortwave emissions and other cosmic events to generate 200 choices per second.
This web site will provide random numbers to the general public: such numbers are of great importance in cryptography and in simulations of games of chance. The company hopes to make money by selling random numbers to online casinos.

So this service will offer continuous, live sequences of random numbers: 8485739532053023847543953452345623468345325.... This may seem either trivial, or dull, but this leads us to an example of science getting dangerously close to theology.

After all, what is a random series of numbers?

A pragmatic person can say that a series of numbers is random if they can't reliably predict the next number in a sequence, having been given all the previous numbers in the sequence. Now this doesn't mean that there is no method in generating these numbers, but perhaps it just means that we are ignorant of the method.

As it so happens, many deterministic systems, like for example, a roulette wheel, produce a series of seemly random (that is, unpredictable) numbers. Even though the systems are simple, they are "chaotic", having wildly different outcomes depending on initial conditions. We humans can't predict where the roulette ball will land, so the outcome is considered random. However, there is a (perhaps apocryphal) story of a group of scientists who developed a computer system that would analyze the throw of a roulette ball to reliably predict the outcome, and they made quite a bit of money at the casino before they were caught. Likewise, the random number generator software found in common computer systems is typically deterministic, but chaotic: there is a strict, predictable method of generating the numbers, but we are simply ignorant of its initial condition.

Data encryption methods usually use random number sequences to make breaking these codes more difficult. Now spy organizations, such as the National Security Agency, are in the business of cracking codes. The NSA often uses a 'brute-force' technique to break codes, using the largest and fastest computers available to try every combination of code to find something meaningful. More typically, it will exploit the fact that the random number sequences used in codes really aren't random: for example, most passwords are words found in the dictionary, and even better, most people use passwords that are meaningful to them. So if you know a lot about a person, you can more easily guess their password.

Good encryptions will use random numbers that are as unpredictable as possible, such as perhaps a combination of the barometric pressure with the closing number of the Dow Jones Industrial Average. Of course, these numbers are not really random, but we certainly can't predict them accurately. Scientists have even developed random number generators that use properties of Quantum Mechanics, which is very unpredictable indeed.

But we really haven't defined "random" in a good, solid, sense; we just have a practical definition based on our own subjective ignorance.

For a humorous and profound meditation on the meaning of the word "random", here is a famous little fictional philosophical dialogue between a computer scientist and a seventeen-year old student back in the 1960s:
In the days when Sussman was a novice, Minsky once came to him as he sat hacking at the PDP-6.
"What are you doing?", asked Minsky.
"I am training a randomly wired neural net to play Tic-tac-toe", Sussman replied.
"Why is the net wired randomly?", asked Minsky.
"I do not want it to have any preconceptions of how to play", Sussman said.
Minsky then shut his eyes.
"Why do you close your eyes?" Sussman asked his teacher.
"So that the room will be empty."
At that moment, Sussman was enlightened.
(Marvin Minsky and Gerald Sussman are famous early experts in computer Artificial Intelligence (AI).) This dialogue is in the form of a Zen Buddhist koan, which is a short question or dialogue that attempts to develop intuitive wisdom. The concepts of intuition and paradox should be quite familiar to an orthodox Catholic, while to the modern mind, which divorces faith and reason and has a restricted concept of reason, they are quite strange. The reason why Zen has become popular among scientists will be considered later.

Catholicism synthesizes faith and reason into a whole: God is the author of all reality and does not contradict Himself. However, the Reformation divorced faith from reason, by rejecting philosophy as a means of finding the truth. Likewise, in the Enlightenment, reason was restricted to the scientific method and could no longer contemplate the angels; so this is why today we have so many fundamentalists and secular rationalists. Further, modernism led to the divorce between logical and intuitive reason, giving us either cold-hearted rationalists or dopey New Agers.

The Scientific Method is based on two pillars: math and experimentation. The Method assumes that mathematics is real, in a Platonic, metaphysical sense, and that it is a reliable means of finding the ultimate, absolute truth. The Method also assumes that the only way of determining the truth about nature is by direct observation: if you can't reliably and repeatedly measure something, then it ought not to have any part in your theories about the truth of nature.

(Some Postmodern educators reject the notion of absolute truth, and so reduce the study of mathematics to an experimental science. Students try to derive the Pythagorean Theorem by measuring cardboard cutouts of triangles and squares, and so reject more than 2,500 years of philosophy on the distinction between appearances and reality. They say they do this for the sake of women and minorities, who are oppressed by mathematics invented by dead, white, European males. Of course, much of our math comes from India and Islam. Graduates of these programs are unsuited for higher education, being unable to use mathematics as a tool of reason.)

The Scientific Method joins an absolutely true mathematics with the experimental method to avoid the trap of a pure epistemology of Empiricism: if you think that truth can only be derived from experience, then it is logically impossible to find cause and effect, you can show correlations only. Stuff just happens. (It ought to be noted that modern psychology attempts to show that experience is unreliable: this is why optical illusions were designed. Taken to an extreme, doubt in the truth of experience leads to solipsism, the belief that nothing outside of the mind is real. Folks who think like this are probably the most selfish people alive.) However, the Scientific Method is extremely successful when applied to its proper domain, and has good, philosophically solid foundations.

The Scientific Method assumes a really real, true mathematics. But when we get to probability and statistics, we run into trouble, for there are two interpretations, or schools of thought in the field! The Frequentist and Bayesian schools of thought are sources of deep heated debate and their results are often contradictory. We should recall that no mathematician will debate the truth of the calculus, or algebra, or geometry: theorems are either true or false, and there is a logical method that will invariably come to the correct conclusion. The fact that the field of probability is not solid, and is open to opinion, tells us that its use in the Scientific Method can be suspect, and that its truth value can be uncertain. (I recall the probability and statistics class I took in college: we used the best textbook available at the time, by William Feller. This book was full of errors, though. Not typographic errors, but really bad blunders in logical thinking. This field of study is problematic because much of its subject matter may not or cannot be objectively true, and it is hard telling what is reliably true and what is not)

The problem with the field of probability and statistics is that it assumes that randomness is really real, in a metaphysical, absolute, ontologically true, Platonic sense. But I can assume grass is orange and that the sun rises in the north, but that doesn't make it true. The fact that there is no unanimous, provable agreement on the subject, and that such disagreements are based on differences of philosophy, tells us that this is no longer mathematics, but something else, and that we must dig deeper into reality. No Catholic (or members of most religions for that matter) can accept this theory of a metaphysical randomness, because we believe in Divine providence, predestination, or fate. We can, however, accept the notion of randomness due to ignorance, but it always has a cause, either due to extreme natural complexity or from the sublime Will of God.

The physical theory of Quantum Mechanics accurately describes nature, particularly with very small objects. Like the closely allied subject, Statistical Mechanics, both of these theories are based heavily on probability and statistics. But unlike Statistical Mechanics, which merely posits randomness due to our ignorance of complexity, one popular interpretation of Quantum Mechanics actually posits a real, ontological, irreducible, true randomness in nature. Note that I said "one interpretation" of Quantum Mechanics: there are at least eight other interpretations of the theory, and this tells us that we have left the Scientific Method behind and are now studying higher philosophy.

Quantum Mechanics is an accurate theory of nature, but it only predicts the probabilities of things happening: it does accurately predicts the probability distributions actually seen in nature. This theory therefore must have a high degree of truth. This quantum randomness is used in data encryption devices to generate unpredictable random numbers.

One could however assume that there are mechanisms, which we can't see, in the sub-sub-atomic realm, which reduces Quantum Mechanics to just a simple case of Statistical Mechanics, where the randomness is just due to our ignorance. However, there is a theory, which seems to be experimentally proved, that
"No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics." And so, physicists have proposed an interpretation of Quantum Mechanics that states that this randomness is absolute and uncaused. Students of Saint Thomas Aquinas should find the concept of an uncaused cause familiar: in Thomas' Cosmological Argument, the uncaused cause is God.

Once we get into arguments about interpretations of a scientific theory, then we have gone far beyond the Scientific Method, and instead are arguing philosophy. By positing an uncaused cause, we are indeed coming very close to theology. Even as a student, I thought that obviously there is a Christian interpretation of Quantum Mechanics, but unfortunately, there are few Christians in the sciences, and fewer still that are orthodox Catholics. Most scientists come from a secular background with at best a liberal religious upbringing.

If you teach Quantum Mechanics, you can be an agnostic and claim ignorance as to the interpretation of the theory, or instead you can consider the wider philosophical implications of the various interpretations. The standard Copenhagen interpretation has a philosophy that the cosmos is random and ultimately meaningless, and this is a suitable theory for most scientists, who tend to be atheists and materialists. The Many-Worlds interpretation states that through our choices, we personally decide which parallel universe we live in: you make a choice, but in an alternative universe, there is an alternative "you" where "you" made the opposite choice, in a totally free, libertarian manner. The question as to which interpretation is the true one is a serious matter, that has profound philosophical and religious implications.

Most scientists have the Modern world view, which ultimately comes from the divorce between Faith and Reason that occurred during the Reformation. Most folks who have the standard Fundamentalist or Liberal religious views that come from Protestantism will avoid considering questions that overlap faith and reason, and will tend to err towards either overpowering grace or naturalism. Faith and intuition are sorely lacking in the modern sciences, and nature abhors a vacuum. Fundamentalist or liberal Western religion is useless in considering these questions, and orthodox religionists are rare in academia, so Eastern religion has rushed into the void.

As we have seen, the Scientific Method cannot answer all questions, and even some of what is called science actually violates the rules of the Method, leading to division and contradiction. Higher philosophy and traditional religion uses a broader definition of reason than what is found in the sciences: it can answer more questions coherently than just the Method itself.

Much of Eastern religion, like traditional Catholicism, is based on a philosophy of ultimate reality, where mere physical things are imperfect reflections of unchanging spiritual truths or forms, and both have a deep reliance on intuitive wisdom. Unfortunately, much of eastern religion has been garbled in translation, so instead we have fuzzy New Age thinking entering into the interpretation of the sciences, which can be disastrous (remember that the scientific eugenic theories which led to the Holocaust were just as much inspired by New Age religion as by Darwinism).

When scientists get to the edge of their sciences, when their Method fails, if they want to continue exploring, then they must expand their use of reason, and that usually means moving into a deeper world view, which is associated with traditional religions, but not most critically with post-Reformation religion. Psychologically, scientists often feel vastly superior to others, due to their knowledge of how things work. This perhaps is why some Eastern religions, or New Age theories, are so appealing: a notion of absolute morality is lacking, or is stripped from the religion, and so the scientist can believe himself to be a god in his cosmos, free from all moral obligation. Certainly traditional Catholicism has the expanded use of reason that is as good or better than the eastern religions, and is highly developed especially in the philosophy of science, but it also has a strict moral code, which is certainly unappealing to a mad scientist.

Catholics, as a matter of charity, must enter the debate on the interpretation of science. Unfortunately, the recent battles have been mainly waged in the field of evolution (where randomness plays a central role), and the debate is often badly framed as a fundamentalist vs. liberal dispute. There seems to be little Catholic activity in physics, which is a pity, for that field asks big questions and is closely concerned with fundamental material reality.

1 comment:

  1. It's strange how much we choose to ignore the importance of random, and the very concept of randomness, in the daily order of our lives and in our beliefs. For us, at Yuzoz, randomness is on the one hand--fun. Yet, by linking it to the beauty of outer space, we have chosen to elevate in ways that I think you can appreciate. We at Yuzoz believe we have not accept space as part of our lives, yet we live in the space age!Thanks.