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.
I noticed a parallel.
Taking a reductionist view is useful in Physics when people make things up. It is easy to characterise made-up things on a human level (like describing what elves look like), but not easy to give a description in terms of atoms (without making the elves easy to refute via observation).
Taking a reductionist view is useful in Relationship Theory when people make things up. It is easy to characterise made-up things on a human level (like describing the effects of a supposed obligation), but not easy to explain what specific event created the made-up obligation.
Does God exist? Are there faeries? We cannot have certainty in the matter, so we will evaluate postulating such entities as a good or bad explanation.
There are two important varieties of claims. One postulates an entity that does something. Santa is actually supposed to deliver presents, and to visit every house. These claims are uncommon because they can be falsified by observation (like watching bad parents fake Santa's visit). Some of these claims, like the tooth fairy, fail because they are refuted by observation. But some do not. One might see a burning Bush, and say that it is God's work. Upon observation, the bush behaves just as the believer has said it will. The problem here, is that the "God" being observed hasn't got any properties other than those observed ... He's acts just like a bit of fire on a bush. Or, the believer might say He's up in heaven, but the bush acts as if He were simply a bit of fire, and this brings us to the second variety of claim.
The second variety of claim involves attributing something to an entity that functions exactly as if the entity did not exist. This approach fails because it adds a complication (the entity) to our explanatory framework, without explaining this complication. For example, we might wonder where the universe came from. And we might want something better than is offered by modern physics. So, we might postulate that God made the world, because this seems to answer the question. However, all it does is deflect the question. Now we wonder where God came from. And if God is a complex enough entity to create the entire universe, then this question is even worse than the previous one (that we had before we postulated God), because we now have even more complexity to explain than before. It also violates the Unexplained Complication rule -- why should there be a God rather than not? This is unexplained.
One strategy that can be useful is to ask someone postulating such an entity, "How can I differentiate you from someone who made up an entity?" All the believer can really do is tell you to have faith, which is not a valid reason to think something true.
Warcraft 3 r0xx0r3z
We reject theories for being bad explanations (of reality), and accept theories for being good ones. How do we know which are which?
The following properties make theories better:
- says more (deeper)
- explains what it purports to
- bold (exposes itself to refutation by all sorts of observations)
- supported by good arguments
The following properties make theories worse:
- contains unexplained complications
- is not consistent with some observation
- criticised by good arguments
Note the use of comparative words. There is no way to measure how good a theory is in absolute terms, only compared to its rivals.
I probably left out some important things, because I tend to do this very intuitively. Please comment on any glaring omission. (And yes I'm aware some items are a bit redundant -- redundancy doesn't hurt anything and can help.)
Parents often make their children say 'please' and 'thank you' and send thank-you cards. In effect, they make their children apply compliments mechanically. Certain politenesses are appropriate in certain situations, period. The merit of the people involved is irrelevant.
The same thing can be observed, say, on sports teams where players are told to cheer on their companions, and chastised if they do not, even if they didn't feel like it or considered the event unworthy.
Some people realise this mechanical approach is silly, and then reject compliments and saying nice things altogether. It's difficult to accuse such people of wrongdoing. They aren't hurting anyone. All they are doing is failing to take action to, possibly, help others in a somewhat minor way.
However, even if there is no burden on people to say nice things, they still should do it. It must be merit-based and applied when felt, to have meaning. But fanmail (even very short ala "nice post"), comments on blogs that say "keep up the good work" (hint hint), or telling a friend "I'm having fun," when deserved and true, is valuable. It is encouraging, and we should like to make our friends feel good.
One might not see why this is particularly important. However, one reason it comes up is that I am generally against, say, telling one's friend "I like you" (see previous post). So, in the absence of normal things like "you're my friend" and whatnot, it is especially important to be active in expressing genuine, useful information like "I'm glad we did X today" or "that thing you said was brilliant" or "you look beautiful today".
Setting The Stage: Jack and Jill see each other every few days, online if not IRL. They often chat, when something interests them both, and usually something does come up. They invite each other to do activities sometimes, and usually accept the offers, when they want to.
Thesis: Jack should not ask himself Do I like Jill? or Is Jill my girlfriend? and should not ask Jill Do you like me? or Why do you like me?.
Suppose Jack decides he does like Jill (romantically) -- what then? Won't he continue to do exactly what he had been doing before? And suppose he does not -- what then? Won't he continue to do exactly what he had been doing before? The same applies to girlfriend status.
Asking Why do you like me? has a bit of a different problem. Besides being useless, it forces Jill (if she answers -- she should refuse) to take a stance on what is good about Jack. Doing so can cause various problems. For example, if Jill gives reasons A, B, and C, Jack may become afraid to criticise those things about himself. Or Jack may be tempted to try and emphasise those aspects of his personality. Or Jack may become self-conscious about them. Or Jack may worry that they aren't all that good, and thus that Jill must not like him very much.
Before I close, I want to acknowledge that this isn't all completely true. Answering some of these questions can be useful for making (imprecise) long-term judgments for which the kind of approach I tend to recommend in the short-term is infeasible.
I was tired yesterday and my last post had no thesis. I have two Relationship Theory posts I intend to write today.
Everyone knows that if you hit someone on the head, s/he won't turn into a democrat (assume s/he wasn't one). The chances of causing just the right brain damage to do that are on par with the chances of making her/him think s/he's a cow. This is because political affiliations are the result of many complex theories, and to affect them in just the right way to become a democrat would require an extraordinary ammount of information (or luck).
So why is it that people expect that some other physical effect, like faulty neurotransmitters or chemical imbalances, would be able to turn a happy person into a sad person? (Cause depression). How one is feeling is governed, just like political affilliation, by a large set of complex theories.
Or why do people think alcohol, which does not contain very much information, can change someone's personality?
The truth is that alcohol changes someone's environment (s/he gets different sense data while using it). Then, s/he reacts to this new environment according to her/his theories. And a lot of people have weird theories about how to act in alcohol-type environments. Depression works much the same.