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.
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.
I was just considering posting some jokes as an entry. Many of the jokes I like are, to some people, offensive. Blonde jokes, dead baby jokes, religious jokes, racist jokes -- these don't go over well with everyone. And I want readers, lots of readers. So, unsurprisingly, it occurred to me that posting the jokes might be a bad idea. Of course, if I don't post anything that might be offensive, I'll never post anything interesting. So what should I do?
There is a moral principle that tells us, if we imagine some stone-age people, who want a society with lots of washing machines, their best bet is not to campaign for them, and try to invent them, but rather to become capitalists and try to act morally. Similarly, the Arab world, if it focussed more on acting morally than acquiring weapons, would have more weapons than it does (just like the US has lots). Of course, in that case, the Arab world also would not want to use them to kill civilians... Also similarly, if one wants to be happy, one should not focus on trying to become happy directly, but should try to act morally, and happiness will come as a side effect.
If I want readers, I should not focus on how to get readers, but rather on creating a good blog, which means writing what I want and like.
Even if we imagine in the limit cases with perfect foresight and calculation, a focus on morality would still be superior to a focus on readers. Either, they would be the same, or the readers approach would result in more readers ... at the cost of acting badly, and I certainly don't want readers that much.
As to jokes, as I'm ambivalent about posting them, I won't for now, but may later.
Humans live by their creativity, not by devouring limited resources.
People twist their factual views to fit their moral views, not vice versa.
Some people don't value anything. (This is often associated with the left wing. Offense intended, but not to any particular person.)
These people often adopt pseudo-values to hide this, from themselves and others. Pseudo-values have an appearance of being values, but are not. One way to spot pseudo-values is they can be applied without thinking. An example is pacifism, which states that all violence is wrong, period.
Pacifists, of course, oppose a war on Iraq. In Iraq, every day, people are tortured, which pacifists must consider to be wrong. Yet they refuse to do anything about it. The problem is, if they did not turn a blind eye to such suffering, their "values" would fall apart. They would have to support a war, and could no longer be pacifists. But they also cannot be good people, who support freedom and liberty and such, because they do not value those things, or anything else, and do not understand how any else can either. And so they cling to their pseudo-values.
Here are some other "values" that are often (not always) shams:
- Save the environment
- Feed the hungry
- Equality for all
- Loving one's family (Notice how mechanical it is. Simply determine if someone is family to decide if there is love.)
- Collateral damage is always wrong, because it hurts people (A pacifism variant. Easy to apply mechanical, just determine if anyone will be hurt as a result of action X, then oppose X.)
- Guns kill people
- Raise school standards
- Won't someone please think of the children!?
- Save the sea snails from extinction!
- All actions have to be UN approved.
- Curse words are bad.
- TVs ruin our minds
My intuition claims Inverse and Anti theory are closely related, but I can't explain why it is, so they will get different titles for now.
Coercion is a state of enacting one theory while another active theory conflicts with it. All emotional pain, amounts to coercion.
People with one of the in the limit, stable, complete worldviews (empty, good, inverse), will never be coerced. Because they have no contradictions in their worldview, and no unanswered questions, they will always wholeheartedly go for some single course of action.
As people approach one of these complete, stable views, they will find it easier to avoid coercion, because they will be closer to having a unified, contradiction-free view. Which means that sufficiently bad people (near inverse view) will be difficult to coerce. Perhaps this helps to explain suicide attacks.
There is a very pernicious idea in epistemology, called induction. It's an imaginary, physically impossible process through which, supposedly, justified general theories are created from observations. It's still popular with some philosophers. Others realise it does not work (it was refuted by Hume hundreds of years ago), then wonder how we can know anything, and get stuck on the Problem of Induction (solved by Karl Popper, who should be super famous, but isn't). And, normal people hold many inductive ideas as common sense, too.
The primary claim of induction is that a finite set of observations can be generalised into a true predictive theory. However, any finite set of observations is compatible with an infinite number of predictive theories.
To see this, just imagine a paper with dots (observations) on it. We're going to draw a line from left to right (with the flow of time), and it has to connect the dots. The line is a predictive function, that gives values at all the points, not just the dots. So, how many ways could we draw this line? Infinitely many (go way up or down or zigzag between points). What inductivists do is pick one (whichever one feels intuitively right to them), and declare it is what will happen next. And people with similar intuitions often listen...
If you want a real-world example, think about the sun. We know it will rise tomorrow because it is a good explanation of reality (via our physics). Not because we saw it rise yesterday (and the day before).
I tried to write an entry that would be more helpful to people who don't understand, and it didn't go well. I have doubts about how helpful this will be to most people. I can answer stuff in the comments section.