Math

After a comment on the last entry, I will now work out a bit about numbers in base -2. To start, I'll convert a random number to base 10. 101 would mean: 1*(-2)^2 + 0*(-2)^1 + 1*(-2)^0 or 5. From right to left, putting a 1 instead of a 0 is worth 1 -2 4 -8 16 -32 64

So, to get the number 2, we have to write -10. It seems very confusing, on a human level, that using a minus sign has nothing to do with whether the number is negative or not. I guess a computer wouldn't care about that, except that we often work in positive numbers, and can use unsigned numbers to save space.

Now I'll count to 10 in base -2:

0001 -0010 0111 0100 0101 -1110 -1001 -1000 11001 -1010 which is really jumpy, and a total mess for humans, and it's very strange to need more digits to write 9 than 10. I think it would be slow for computers to do addition with this. In positive bases, using digits from 0 to base-minus-one, adding is nice, because you just increment the one's column repeatedly (and each time it overflows, reset it to zero, and increment the next column). There are tricks, like if you have two numbers in the same base, you can add various other columns directly to each others. There may be tricks with base -2 also, but I still bet it's inefficient, because you can't just increment the next column when one overflows.

Math

In base 2, 19 is 10011. In base 1/2, 19 is 1.1001

In base 10, 19 is 19. In base 1/10, 19 is 9.1

The trick is to write the number in reverse, and in the fractional version, put a decimal point after the ones column. This is because decimals have negative exponents, so the fraction gets flipped.

Fractional bases that aren't 1/something seem like a real mess to use.

Also, I wanted to count in balanced base 3. I will use -, 0, and + for my digits.

+ +- +0 ++ +-- +-0 +-+ +0- +00 +0+

You'll notice that you *can* count be incrementing the one's column repeatedly. You just have to remember to reset things to - not 0, after they overflow.

Will count from -1 to -5 now:

- -+ -0 -- -++

Notice it's the same as positive, with the -'s and +'s reversed, and 0's untouched. And you can count by decrementing the one's column, and when it overflows, decrement the next column and reset things to a +. I guess I should point out that you can add as many leading zeroes as you want, which is how decrementing a column that doesn't exist works.

Morality

I hear there is a biology professor who won't write recommendations for creationist students. I wanted to comment in general:

If I ask Joe Dirt to write a recommendation letter for me, he is perfectly right to refuse. People needn't write letters for anyone they don't want to.

However, in a school setting, students are required to have these letters. And professors are expected to write them. Refusing to write students a letter hurts them. And such a blanket refusal is morally wrong.

Refusing letters over a student holding some theory, only makes sense if the theory directly interferes with the student's studies, and makes her/him significantly (meaning "enough to matter" not "lots") worse at them. This basically means refusing letters for incompetence (math major who thinks 2+2=5; politics major who thinks "democrat" is a type of fish).

So what about biology and creationism? Well, if you want to be a doctor, you learn how human beings are, and about medicine, and it doesn't matter. If you want to be a vet, and you disagree about why vestigial organs exist, but know the same facts about them, it again doesn't really matter. If you want to be a zoologist, and study the evolution of animals, it does matter.

So my view is, to be moral, the biology professor must refuse recommendations on a case by case basis, and only in very specific circumstances will refusal for belief in creationism be acceptable.

Morality

Reviled in Many Places Around the World, Americans Are Adored in Kosovo

"Two years ago, after a U.S. soldier's weapon accidentally killed a 6-year-old boy, the grieving father publicly forgave the soldier and said he considered him part of his family."

The father is a Muslim living in Kosovo. Although the accident is sad, it is very nice to see such reasonableness over a collateral damage issue, by the victim. And doubly nice to see a demonstration that Islam is perfectly compatible with morality.

Inverse Theory

One may wonder what view based on the theory "No other theories are true" approaches as it becomes a complete worldview. Prima facie, it cannot quite get to the empty view, because it, itself, will always remain. However, with no other supporting theories, it will be completely meaningless gibberish, because the person will not be able to understand it any longer. And so s/he will reach the empty view.

What about "No other theories but this one, and the ones necessary to understand this one, are true" (will refer to this as the flagship theory of a view)? This will include knowledge about not accepting false theories, and knowledge that truth exists, so it cannot go to the inverse or empty views. Can it go to the good view?

You may think it is not compatible with the good view, because the theory that the War on Terror is right isn't necessary to understand the flagship theory, only to avoid contradictions. Well ... knowledge is interrelated, so I'm going to take the position one couldn't claim full understanding without the complete good view.

Oh, also, for those people who like foundations: in physics we determine the truth of theories by how they conform to physical reality. In morality, we can now determine it by how they conform to the good moral worldview.

I learned a new HTML tag today.

Make that two.

Morality

There is a new yahoogroup called You Poor Dear. The purpose is comfort and support without problem solving, debate, or criticism. How will that work? Approximately like this:

You, my dear reader, are a brilliant person. You're good at everything you try, and always persevere through misfortune. You're witty and fun, and a pleasure to be around. If you have any problems right now, which seems unlikely, I'm sure they are nothing for one such as you. If you are in school, you have my sympathy.

Best Wishes,
Elliot Temple

If you're objecting that the above is rather meaningless, you're right. I don't have a clue who you are, I just made it all up. How will the list avoid this? Easy. The participants will give out personal information to a public internet forum. This is a safe way to meet people and make friends, and I highly recommend it extremely dangerous. The more personal information one gives out, the easier it is for the other posters to hurt her/him. (To hurt someone with words, one must know enough about the person to know which words will hurt. Also, giving out personal information tends to lead to being hurt accidentally, if people talk about what one does give out without knowing everything else, like one's sensitivities.)

Anyway, the group doesn't allow saying mean things anyway, only nice ones. So when people post support it will be genuine totally meaningless, because it was the only type of reply possible.

Morality

I just read this USS Clueless piece and wanted to comment on a few bits. Quotes in italics.

I simply don't believe that Germany and France would be willing to sustain, let alone cause, the kind of damage they have just for the sake of moral inhibitions.

and later

And they have now reached the point where they are seriously imperiling the process of creation of the European Union. I do not believe that they would have gone this far if their primary motivation was moral inhibition.

I agree they wouldn't do all this just to hold to pacifism. But pacifism is an absurd moral stance, that very few people take seriously. Perhaps it's really about some other moral stance, like anti-Americanism.

And Rumsfeld refers to their behavior as "beyond comprehension".

I don't like to believe that this may be the reason, but I can't think of any other explanation that makes any sense.

Let's examine the roots of anti-Americanism, and it's close relatives like Jew Hatred. As I'm not much on history, I'll do this in abstract:

Long ago, no one knew about morality, and success was mostly random. All cultures had some people who were good at things, and some who were not. But over time, one culture evolved some moral knowledge. It's members led better lives, and were more successful. And it wasn't just luck, they did this consistently.

The other people knew of no way to be consistently successful. They watched the moral culture, and could not figure out what the important differences were. As the moral knowledge was evolved, it couldn't simply be copied. So, they were faced with a few possible explanations. They could, while having almost no clue what morality even is, decide they were bad people. Of course, they did not. Alternatively, they could decide the successful culture was somehow cheating, and hate its members.

In a perverse way it makes sense: if we are fundamentally the same, with the same chances to excel at any given thing, and I always beat you, I must be cheating somehow. And that you do not know how, must make it even more infuriating.

So, over time, the immoral cultures evolve their own traditions. They learn to hate the successful, moral culture. Partly, they want to destroy it, because it is living proof of their own immorality. Partly, they want to bury their heads in the sand, and get on with life as it was before there were any moral people. Partly, they want to be successful, and are unable. And, above all, the very premise of the moral stance of the immoral cultures, is a denial that they are bad.

So, I feel the explanation that France and Germany are in the grips of an anti-American morality explains why they will go to such great lengths to oppose the US.

Here's two generalisations:

Right wing folk deny explicable, rationally discussable causes for human behavior.

Left wing folk do not value anything.

Parenting

Here are two generalisations (if you haven't already, read previous entry first):

Left-wing folk object to TCS because they view all sorts of things as coercive, and see parental coercion as miniscule in comparison, and a defense of children. For example, some lady got the word "gun" removed from her daughter's spelling test. One can imagine the reaction if her daughter wanted to get a gun, and write gun a bunch, and draw gun pictures. The justification? In essence "guns are coercive/bad". Another common one is "TVs are coercive/bad" and therefore must be kept from children to protect them. Also, not having a college education is coercive, and so are fatty foods, which justifies... Also coercive is capitalism, which justifies not letting children buy things (they'll be tricked into wanting more and being materialists).

Right-wing folk object to TCS because they don't understand causality in human behavior. Mindless causes are ok, but not rationally discussable ones. Hence, children have bad theories because kids are dumb, not because their parents mistreat them. And TCS is a waste of time, because children won't understand anyway. Children are dumb, you can see it if you just look around and watch some kids mess up. The solution is to discipline/spank them (notice this is a method that can be applied, unthinking, to any problem). Also, as behavior isn't caused in any rationally discussable way, people who say treating children as inferior messes up their theories can be ignored. Besides, do children even have any theories besides the ones we teach them..? And also, genes cause behavior and being naughty is human nature (but beatings can overcome human nature).

Thanks to Rachel Lucas for the gun link.

Epistemology

True and mutable is one of the wisest phrases I know. It means we should hold our best explanations true and act on them, not give in to relativism. Just because we may be wrong, does not mean any particular idea we have is wrong, or that we should not hold our ideas true. It also means that our ideas must be mutable -- they must be open to criticism and change and improvement. And being mutable does not make them less true.

When someone says something is true, s/he does not mean s/he's certain it is true. That, of course, would be absurd. So what does it mean to assert something is true? Simply that it is the best explanation.

There is a common fallacy that says fallibilism implies mistakes. The logic is that because we can't be certain, we are bound to make mistakes. The refutation is to look at a particular action or theory, and point out that, while it may be a mistake, fallibilism does not state it is, and all we can do is use our best explanations. So, fallibilism is not an argument against this specific thing. Then, we examine another action/theory. Then another. The point is, fallibilism does not imply any particular mistake, and cannot be used as an argument against the truth of any particular proposition.

Credit for the phrase true and mutable goes to Yehudit's LGF comment here.