Second Chances

Why is it that we believe in second chances? Or at least, some of us. The phrase is a strange one; it is as if, not content with taking our chances once, we are taking another gamble.

The problem with second chances is that they aren't first chances. This is not as trivial as it sounds: the difference between having no chance and a single chance is like the gulf between zero and one, or between nothing and something. But a second anything is just more something, a superfluity.

And then, having opened the door to superfluity, why not a third, or a fourth, or any nth chance? This is the difficult thing — the line between nothing and something is obvious, the line between something and something else is always less so. And that difference actually decreases the more you have of something; you can't see so clearly the difference between a 1,201st chance and a 1,202nd chance.

Atheism as a Subset of Religion

Of course, the previous post was also connected to other curious arguments I've been having of late. There are a lot of math and science majors out there with funny ideas.

In one of those arguments, I said that atheism is a subset of religion. A famous atheistic pseudo-argument or joke goes like this: "A monotheist claims that Occam's Razor must reduce the total divinity of a viable religion to one. An atheist merely reduces this number by one."

As an admirer (though not adherent) of Bertrand Russell, I can only say that just as the null set is a subset of all sets, so atheism must be a subset of theism. Since theism is a subset of religion, it follows that atheism must be a subset of religion.

However, many atheists contend that atheism is the logical complement of religion, i.e. not-religion. That's plainly not true — atheism is the '0' to monotheism's '1', you might say, but that doesn't mean 0 and 1 are not both values. Neither belief can be proven uncontroversially to be true, and any 'falsification' argument fails simply because of the fundamental asymmetry between 'yes' and 'no'; 'no' is not 'not-yes'.

So, yes, all these controversies are in the end to be avoided. They waste a lot of effort, as the Good Book says.

The Bonfire of the Vanities

"Vanity of vanity, all is vanity," saith the Preacher, king in Jerusalem. "Man is born unto trouble as the sparks fly upwards." And much of this wisdom was the profit of painful years, for the Preacher pondered much, and the words of the wise are as goads.

I long ago figured out why religion is trouble. The stakes are very high. If religion describes reality ontologically, then disciplines like the sciences and mathematics, which limit their outcomes and scope of knowledge by their own rigour, cannot claim a monopoly on truth.

And yet, it is by their obvious stranglehold on description, manipulation, prediction and control of reality that science and mathematics have gained their hard-won prominence and domination over the souls of men. A scientific or mathematical theory, absent a 'falsifying dream' (as Hughes's Hawk Roosting has it), has great powers to describe, explain, or predict. It is on the basis of these powers that we are masters over reality as we know it.

But mastery over reality as we know it is never 100%. As the old school joke goes, "The more we know, the less we know we know." Science and mathematics are the guiding daimonia of technology and engineering, and humans will gladly forsake those daimonia for these material fruits of application.

That is why science as religion and mathematics as technology are uncomfortably true to life. No scientist knows anything except what he knows — this is the curse of the empirical and the rule of epistemology; no mathematician knows anything except by what he believes through the working of his rules — this is the curse of the logical and the rule of rationality.

It is only the religious who believe that not only do they not know, but that they cannot know, and what they cannot know is nevertheless of the greatest significance. And if they are right, the brightness of science and mathematics is like a light without lenses or augmentation; it is like using nothing but the visible spectrum and calling it 'diagnostic radiology'. In fact, it is worse; it is agnostic radiology.

This is why there are more and more people willing to blacken religion with the radiation of reason. It is the only way to preserve the new monopoly — by destroying the old one. But which one sees more? Which one is of greater value to humanity? Both might contend that they are the only truth. But the key question we have to ask is, "Can anything be supernatural and still be true?"

Responses 010 (2011-2012)

Well, after being more cryptic than usual for this round of responses to the latest list, I am happy to be at the end of yet another season of Fun With Epistemology. Kidding... but I will still leave a complete link-list at the end of this post for everyone's greater ease-of-use.

Here's Question 10, the last of the season: " 'Through different methods of justification, we can reach conclusions in ethics that are as well-supported as those provided in mathematics.' To what extent would you agree?"

Ah, this one is a tricky one, make no mistake. Note the phrase 'different methods of justification'. Immediately, this centres the question around the issues of how one supports conclusions in different areas of knowledge, supports them in different ways, and yet is able to claim that they are conclusions that are equally well-supported.

First, we need to define 'ethics', something which is vaguely and variously defined no matter how you look at it. The problem with defining 'ethics' is that we speak English, but 'ethics' came from the Greeks. Roman culture produced 'morals' as a sort of synonym, but the two are not the same. A simple test shows this to be true: we speak of medical ethics, but not medical morals nor medical morality; we speak of legal ethics, but not legal morals nor legal morality.

I first said something about ethics in the context of such discussions here. The last paragraph of that post talks about how the grounds for an ethical basis arise. A better place to look is this post, in which I clearly outline the difference with support from an empirical (frequency-of-usage) approach.

Once we can define ethics, we can start thinking about how we reach conclusions about ethics. One of the most straightforward ways is some form of Kantian argument, in which we ask the question, "What if everyone in the world saw action X as a morally good thing compared to action not-X?" and figure out the consequences. This would make murder an unethical thing because if everyone committed murder, there wouldn't be enough of a society left to have any ethics. This is also true of many things, but it leads to logical consequences like thinking of contraceptive technology as morally evil — and also things like eating Big Macs. I'm sure you can see what else could be problematic.

However, if we don't say 'everyone', the problem goes away and is replaced by another one called 'relativism', in which we might have to argue that anything can be good if done in the right context, or that there are no such things as good or evil — merely optimal and suboptimal solutions. This was where utilitarianism led us, to the idea that something called a 'moral calculus' exists — a kind of situational mathematical solution for the determination of what the most moral action should be.

Lines of reasoning like this are not necessarily supported by mathematical approaches such as statistics, algebra, or formal logic. However, they can be treated (by philosophers especially) as equivalent in support to some areas of mathematics; just as math can have conjectures, so too can ethics.

One interesting way of comparing math to something related to ethics can be found here. In a way, that post suggests the possibility of treating areas in the two domains the same way.

I would conclude that conclusions in ethics can (not 'will') be as well-supported as some conclusions in mathematics. I'm not sure that this is extensively true; ethics is a less closed system than mathematics is, and it is hard to consider ethics without metaphysics.

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Here's the list of links:

Question List for 2011-2012

Response to Question 1
Response to Question 2
Response to Question 3
Response to Question 4
Response to Question 5
Response to Question 6
Response to Question 7
Response to Question 8
Response to Question 9

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Again, I have to remind everyone that these posts are just my personal responses, somewhat off the cuff and sometimes with loopholes I've overlooked. If you are going to quote any of my elegant prose (haha), please ensure you cite the material appropriately and check its validity by your own research. Thanks!

Radiology

I was listening to the car radio as usual with my 'peripheral hearing'. To my amusement, it was a Mandarin-language broadcast of rather soppy (and clichéd) content.

There was a woman who was obviously telling a man some home truths: "If I love you, I love you because I love you and not because you're wealthy; if I don't love you, I don't love you because I don't love you, even if you're wealthy. But I don't love you because in the depths of your heart all you care about is money and not love."

It's this kind of thing which leads me to believe that humans are basically irrational, and therefore when we invent things like science and mathematics and logic and so on, it's a sort of attempt to deny that fact. When we say 'human' we imply subjective and irrational; when we say 'mathematical' or 'scientific', we imply objective and rational.

A moment's reflection should disabuse you of these pretensions to rationality. Mathematics is only objective within the terms it has defined for itself; basically it says, "Here are my rules, and if we all play by my rules, I will always win." Science is less than that, because it says, "I assert the universe can make sense, now let's observe it and figure out what that sense is; I don't know what the rules are, but I am going to assume that all the games in the universe follow the same basic rules."

When humans attempt to use mathematics and science to solve problems, they can only solve the simple ones. That's OK, because if you build complex-looking problems out of simple ones, you can solve pretty complex-looking ones. It's like saying proteins are very complex molecules, and then asking someone to compare the molecular structure of haemoglobin to that of DNA, and then to that of a champagne diamond.

Then you take all that knowledge about molecular entities and say, "Yes, here is a cure for human stupidity, venality, and intransigence." Haha, so funny.

That's what I like about random radio shows. They have their own logic and it's not a very consistent one, but it shows human thinking. It's kind of radio-logical; you can use it to look into the human condition. In that sense, I suppose I can call myself a diagnostic radiologist...

Drawing Lines (Part IV): Mathematics and Theology

At first sight, this seems to be an odd choice of disciplines between which to draw a line. Surely it is obvious that the two have nothing in common? Well, not so fast...

Here's a list of what they do have in common. Both of them

• construct knowledge based on fundamental axioms which are supposedly self-evident but unproven and nevertheless taken to be true;
• use rigorous logic to derive secondary propositions from those axioms;
• claim to explain the underlying structure of reality;
• handle entities which the human mind cannot visualise nor find material analogy for;
• have been shown to have questions for which there are no answers;
• can be demonstrated to obey Gödel's Incompleteness Theorems (or at least, their extension to sets of logical propositions);
• seem to be obsessed with numbers and symbols;
• have a long tradition of philosophy and religious conceptualisation;
• have been considered necessary disciplines for the pursuit of an ordered life.

So... what don't they have in common? Actually, that part is pretty easy. Theology prefers words to numbers. Ha, yes, I was only teasing. Theology of course requires the existence of God as axiomatic. Mathematics requires the existence of a universe in which things remain consistent (but unprovably so). The two are not quite the same thing, I suppose.

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Afterword: As BL has pointed out, there is an entertaining episode in the history of mathematics, involving mathematicians David Hilbert and Paul Gordan. Hilbert's work on the Basis Theorem elicited Gordan's response, "Das ist nicht Mathematik. Das ist Theologie." If that were the case, Gordan was to recant eventually, for he later said, "Even theology has its merits."

Labour Day (Redux)

A year ago, I wrote something about labour and surcease from it. It has always seemed to me that the end of labour is the fit ending to any endeavour.

For rest, the 'ground state' of being, is the baseline from which all things are measured. An object at rest remains at rest; an object in motion cannot be said to be in motion unless compared to an object at rest. If two or more objects are in motion, define one to be at rest, and the system remains unchanged as long as you haven't already defined the space they are in.

It is altogether fitting and beautiful that Labour Day should be made a day of rest, a day on which things normally in motion realise that without a resting state, their motion is in vain. It is like atheism; how can it be defined without the idea of God? And if it were to be defined as the lack of God, how sad should it be that it must be defined as an absence of essence, rather than an essence itself?

Rest defines the universe of motion and action, just as God defines the Universe. To say that there is no God is an assertion of faith equivalent to saying that things move without something to measure their movement by. To say that an atheist believes in one less God than a theist is to deny the difference between one and zero, and to say that all other numbers partake of the same essence that is 'one'. For 'one' is the first of something that is not nothing; of 'one' all other numbers are made, and their identity sustained. This is not true of any other number for that kind of process.

And so, we rest our case, and case our rest.

Prime Cuts

Family dinners are sometimes full of eccentricity. I have a family which puns all the time; it drives non-members and honorary members crazy once in a while. Last night though, the announcement that my siblings and I would be observing a rare occasion – the fact that we'd all be having prime birthdays (i.e., birthdays celebrating a prime number of years lived) in the same year – met with silence as people either tried to work it out or failed.

I have a sister who is ten years younger and a brother who is four years younger. If I were x years old, you'd be looking for a set of positive integers {x, x-4, x-10} such that these three numbers were all prime. The interesting thing about this set, of course, is that it seems impossible to prove how many sets there are which will meet the requirement.

Fortunately (as some people would say, God being one of them), we are not immortal and hence there is a limited range of possible solutions in the real world. And the real world offers at least one other benefit; many of you already know approximately how old I am and are thus able to narrow the search down considerably.

This is an example of reducing complicated problems to simple ones, a useful (but not always applicable) skill. Sometimes, life favours us with problems that are obviously and/or immediately reducible; sometimes, it doesn't. All I know is that we're glad we're in the primes of our lives.

A Sinister Dexterity

I was trundling around the workplace today when I noticed something decidedly sinister. The clients I was serving in one section were... hmm... displaying a preponderance of left-handed behaviour. I was intrigued. Was it a purely local phenomenon? Was the cosmic order under siege? I had to know more.

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I was ruthlessly empirical about my next step. Yes, one had to design an hypothesis and gather relevant data to disprove it! (Note: data have been rounded to prevent allegations of security violation.)

Null hypothesis: there is no significant statistical difference between the proportion of left-handers in population A and that in population B. All come from the same demographics, and are indeed selected for this. Despite the fact that population A has n=250 and population B has n=100, there should be no difference in terms of proportion.

Data gathering procedure: clients were examined by visual means; this examination was then crosschecked once by observation of tool location, limb preference and digital behaviour when at rest.

Data and Data Processing:

• Population A contained 20 LH plus one ambiguous out of 250, %LH = 8%
• Population B contained 10 LH out of 90, %LH = 11.1%

This meant that the two populations had different proportions of left-handers. Ah, but was this statistically significant? How would you know?

I shall skip the subsequent steps and keep the conclusion to myself. It is safer that way.

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At this point, it might be wise, lest I be overwhelmed by sinister forces, to say that I am the direct descendant, on both sides of my family tree, of ambidextrous people. It shows to this day: I play tennis left-handed, use my left hand when gathering information, use my right hand when transcribing or writing, use my left eye when aiming and under-use my right eye. All the tests I've taken so far place me as almost (if not exactly) halfway between left-brained and right-brained orientation (if these are valid descriptors at all). For fine work I use my left hand; for crude work I use my right. I can sketch with my left hand, but my right hand is aesthetically challenged. And so on.

Readers who can identify populations A and B, please note that a certain population C comprising about 10 individuals also contained 2.5 left-handers, for a %LH of 25%. Now, assuming that the three populations A, B and C are listed in order of mathematical ability (or preference for doing mathematics at a more rarefied level), which population do you think was most mathematically inclined?

Interesting what mental activity goes on when you have an ambidextrous mind...

Mathematical

I was walking down the avenues in the forest of shadows, the great hall of the people. Examinations were in progress, and they called to mind a host of images. I have always found mathematics to be a powerful ally, but never a friend. So I wrote poetry in my head, and here it is. (The hyperlinks are pretty random-associative; ignore them if you want.)

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The Battle of the Trees

it is verdant summer today
as the wyverns make their last stand
in the hall of their ancestors

resistance is made from writing
wire illuminates each row
towards a final solution

see them describe each airy arc
and branching combinatorial
spell out an algebra of grief

the wisdom of the scholar lies
with point and line, assent, decline,
maps out a geometry of pain

fractal and fallen are these leaves
do you still think that they conceal
an answer to the doom of worlds?