3-3 invasion takes teritory at the expense of influence (future potential).
I think I improved a lot when I stopped 3-3ing (it opened up different style of game for me)
Noobies love 3-3 (I definitely did), because it’s kind of simple and familiar move. (Especially at the start of the game, when board is empty, there is gadzilion of possibilities and most of them unknown and possibly risky)
If not discouraging 3-3, I would still recommend starting without it, to learn that way of play (if for nothing else, to deal with 3-3 invasions)
Lets start with best country of the world that is made of 300 million consumers and 1000 factory owners (also known as polluters) each of which has identical share of the market.
To reduce pollution, factory owners would need to use less polluting means (i.e. less profit) and produce less (again less profit).
What happens if 999 factory owners do adhere to pollution-reduction, while 1 of them is polluting a bit more than others? (Answer: The polluter increases his share of the market, as more profits can be reinvested; and with more market share the profit will grow even more)
The point: consumers incentivize factory owners to polute, if consumers buy stuff despite polution.
This exercise ignores legislation, but law will not change until enough of consumers/voters start to care of the topic and will be ready to pay more for less and demand for it.
Why are owners of capital deemed to be innocent when subject to the invisible hand and not the consumer? Answer is probably due to media influence paid for by the profits I alluded to earlier
I would like to label guilt/innocence as irrelevant.
The scenario above, describes the dynamics of how incentives work.
As long as consumers expect stuff to be cheap, somebody will step up to provide that (reaping profits). Only highly conscious society or totally authoritarian one can make these changes (though probability of dictator caring about environmental effects is low, and probably not sustainable).
Edit: guilt/innocence are irrelevant in the sense that they do not change the outcome. If human gets into a tigers cage and gets eaten (or seriously injured), outcome was predictable without the need to know who is at fault (tiger or human).
Whatever policy you implement, end result must be that stuff costs more and people live with less: virtually no personal cars, no for-fun-flights (vacation), force people to wear same pants for years and repair them when they get damaged.
That is hard pill to swallow for many, even for somewhat environmentally-aware beings.
Assuming no free energy is invented.
Related: exponential growth (x % each year) is not sustainable (approx 2500 years to consume whole universe converted to energy on 5% yearly growth); effectivity increases only multiply exponential function by a constant.
> Whatever policy you implement, end result must be that stuff costs more and people live with less: virtually no personal cars, no for-fun-flights (vacation), force people to wear same pants for years and repair them when they get damaged.
> That is hard pill to swallow for many, even for somewhat environmentally-aware beings.
You’re not wrong but I think adding some context would be helpful here.
That appears to be the situation now but it didn’t necessarily have to be this way. If effort in earnest was started earlier to develop the technologies necessary for transitioning off hydrocarbons, develop renewable energy generation, and so on the transition may not necessarily be so severe. And the policy which enabled this delay did cost consumers any way due to the active funding of a pro hydrocarbon influence campaign. Though I would guess the total cost of that policy is still much lower than actually trying to transition.
I think transitioning is a much easier pill to swallow if you realize that the decision will be made one way or another eventually and that it’s better to be proactive rather than reactive when trying to solve such an existential issue. That is, if one believes the science and cares about the future beyond just one’s self. Unfortunately that influence campaign I was mentioning earlier did a good job of denying the issue, used bad science to deceive, delayed climate action, degraded efforts of those fighting against it, etc. However I do acknowledge the ability to care beyond just one’s self is, to a certain extent, a financial privilege.
Incentivizing having less children is also another long term approach to limit emissions as technology becomes more efficient. Though it seems this has already been accomplished unintentionally in many places.
I’ve gone on kind of a rant but my point is yes the necessary policy decisions are more severe today but it absolutely did not have to be this way. And that is important to keep in mind because that campaign is still actively at play today.
Wording like “game is more complex” overal seems incorrect. Game is not complex by itself (for example go rules are extreemly simple), all the difficulty and challenge depends on the skill of your oponent.
Game only allows the opponent to demonstrate the skill.
Those are all meaningful measures of complexity, but it's worth noting that all of them are a function of the number of legal positions (among other things as well).
That would be quite a strange function. For example, Tic-Tac-Toe has 26830 possible games on 5478 possible positions, while 2x2 Go has 386356909593 possible games on only 57 possible positions.
The major difference of course being that Go allows stones to be captured.
I don't see what's strange about that, different functions grow at different rates. That's like saying it's strange that exp(x) is a billion for x = 21 while sqrt(x) is merely ~4 when x = 21.
Go's complexity grows much faster than tic tac toe's complexity as a function of legal positions, but the complexity is still a function of the number of legal positions (among other things, as I pointed out).
You can define a procedure that reaches 2 very trivially. e.g. you generate all possible 1 digit numbers, then 2 digit numbers, then 3 digit numbers, etc.
This is how natural numbers work in the first place. You're just adding a decimal point to all of the possible places it could go.
Well, you have to ask yourself what is PI really? You've been taught it is a number with infinite decimal places, however, practically speaking when you use PI you actually round. Practically speaking this doesn't matter because it's not actually possible to have a shape with infinite points in reality so you only need to approximate to whatever fidelity suits you.
How is this? This is because PI is not actually a number. It's a procedure that generates digits for approximating things about circles.
This is the same with sqrt(2). The sqrt procedure emits digits just as the procedure to find all real numbers does.
You can't "reach" PI for the same reason that a natural number can't reach "f(x) => x + 1". That is, natural numbers aren't procedures or functions.
What about 1/3, 1/7, …?
Previously outlines recursive procedure doesn’t generate those.
But yeah, if you deny existance of irrational numbers, and redefine Real:=Rational, then you can generate these “real” numbers recursively and it does follow that all infinities have same cardinality here.
Btw. what is the diagonal of a unit square formed by 4 objects at the corners? I assume it is a rational number.
Btw2. If you take that answer and multiply by itself, what do you get?
1/3 is also a special kind of procedure. It's 1 divided by 3. Either you use the isomorphic 0.3 repeater procedure where you recursively add 3 digits until you get bored or you have enough, or you use division to generate the number sequence. The fun thing about fractions is that we've worked out some ways in which fractions can be multiplied with natural numbers and rational numbers to generate new fractions, and also some fractions conveniently are isomorphic with rational and natural numbers.
Important to note: When ggp asked for a recursive procedure to generate real numbers, they wanted that exactly same proceedure would generate all reals (not special procedure for each number)
If we have special procedure for each number, then procedure to generate 1/3 is just 1/3. …of course naively assuming notation of 1/3 is as valid as 0.33333…, and that base 10 is not the only possible base.
Once you drop infinity as an axiom you have to think about fractions and repeating decimals differently.
1/3 isn't a real, it's a fraction. Fractions can be used to generate reals, and they can be used in algebra along with reals.
0.(3) is also not a real. It's also just representative of a procedure that can generate reals.
Both 1/3 and 0.(3) can still be used in algebra in the same way as before. You don't lose any capability because you can't practically expand 0.(3) to infinite decimal places in the first place.
You can have as many different symbols as you like, so long as you can actually write them on paper. As soon as you tell me that one of those symbols is a number with infinite digits I will disagree with you, given that you are unable to tell me what those digits are before the universe ends.
I can tell you that the number is 0.1 in base 3, which defines the number precisely. Or I can tell you that it in base 10, it has an infinite representation, and all the digits are 3. There, I told you what they all are, and the universe has not ended yet.
> Or I can tell you that it in base 10, it has an infinite representation,
Does it really have an infinite representation? I can't imagine an infinite representation fitting on a page. I'm pretty sure you're representing it as 1/3 or 0.(3). Neither of those representations are infinite. They're only a few characters really.
It seems to me that this comes at the price that now in your geometry the diagonal of a unit square does not have a defined length. Only an approximate one of 1.41421, but what does this approximate?
What price? In an algebraic setting you are never going to convert sqrt(2) into a real number, and in any practical setting you're going to have to round because nothing real actually has infinite precision.
It would appear that sqrt(2) does not have a meaning now, as sqrt(-1) in R. So it does not seem to matter if you do not convert it in an algebraic setting. There is no such number that you can reach with the enumerative approach, which will only give you the rational numbers. There are lots of proofs that sqrt(2) is not rational.
But in all probability we are discussing the wrong thing here. Our difference it's likely at a deeper conceptual level than this.
I think I improved a lot when I stopped 3-3ing (it opened up different style of game for me)
Noobies love 3-3 (I definitely did), because it’s kind of simple and familiar move. (Especially at the start of the game, when board is empty, there is gadzilion of possibilities and most of them unknown and possibly risky)
If not discouraging 3-3, I would still recommend starting without it, to learn that way of play (if for nothing else, to deal with 3-3 invasions)