[Order] Is logic the best problem-solving tool?

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Yvain Wintersong
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[Order] Is logic the best problem-solving tool?

Post by Yvain Wintersong »

A spinoff thread from "I'd like to start a religion". Benkern and the Kaiser said that logic isn't always the best way to answer hard questions Since logic is the foundation I'm basing the Order on, let's make this the topic of the first discussion.

I'm wary about starting a discussion here since most discussions on online forums degenerate into shouting matches between really intelligent people desperate to prove their superiority. I want to write a Code of Discussion for the Order, and I probably will later, but for now just use common sense.

One thing I DO insist on, to paraphrase a comment from the Overcoming Bias blog:
A duel is a struggle to show personal dominance. A discussion is a struggle to discover truth.
That's why I hate college debate clubs. They get people in the habit of "debates" where the point is to "win" - i.e. to convince the other person to your point of view. Those are duels. This is a discussion. If someone who disagrees with you is obviously right, instead of fretting about how to beat them, change your position.

No personal attacks, keep things clear, try to avoid fisking (thanks benkern), support everything you say, and, when in doubt, do the exact opposite of everything they're doing on this thread.

I'll post my position in a few minutes.

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Re: [Order] Is logic the best problem-solving tool?

Post by Yvain Wintersong »

My position is: Logic is always the best problem-solving tool. To put it clearer:
1. If a question has an answer, answering the question logically will be more likely to get the right answer than answering it any other way.

2. If you have to make a decision, making the decision logically will work better than making it any other way. By "work better", I mean whatever it is you want from that decision, you'll be more likely to get it by using logic.
When some people hear "logic", they think of a sci-fi robot saying "I compute probability of success at 93.5014%!". But logic also includes wearing a jacket because it's cold out, or not playing loud music because your flatmate's trying to study, or believing trolls probably don't live in your closet.

Logic is basically just believing something if there's a good reason to believe it, and not believing something if there's a good reason not to believe it. Lots of very smart people have found ways to put this into mathematical language and define what "good reason" and "belief" and so on mean, but that's the basic principle. So to rephrase the box above:
1. If you want to know whether or not something's true, you should look at the evidence for and against it.

2. If you want to make a decision, you should look at the evidence, use the evidence to find which way is better, and then do whichever way is probably better.
I'd spend several paragraphs supporting this, but I don't think anyone really disagrees. If you do, say why you disagree below and I'll see if I agree with your objection. But I'm kind of at a loss for this whole first discussion because it's hard for me to imagine someone seriously thinking logic sometimes doesn't work. I guess I'll finish by thinking up a few situations where people might think logic doesn't work, and responding to them.

Objection 1: Logic can't tell me what art to like, what music to like, what girl to date, etc! No, it can't. Neither can anything else. "What art should Yvain like?" is, in my opinion, a meaningless question. Yvain can like any art he damn well pleases, and there's no "should" about it. But logic can have a bearing on these sorts of questions by helping make things clear. For example, if you're allergic to cigarette smoke, logic can tell you that you'll probably be less happy dating a girl who smokes than a girl who doesn't, all else being equal.

Objection 2: Logic is too hard to use for everyday life. I don't want to have to write a three page proof about why I eat toast instead of donuts this morning. Okay, fine. In that case, logic should be able to tell you that using logic too often will make you unhappy, and in that case, from the point of view of someone who wants to be happy, using logic too often would be illogical.

Objection 3: People aren't logical. No, they're not. It's too bad, isn't it? If they were, they'd probably be better off. I'm not asking you to treat other people as logical, just suggesting you'd be better off if you were more logical yourself. You can then do the logical thing and deal with people exactly as they are.

Objection 4: It's impossible for a human to ever be 100% logical. Yes, it is. It's also impossible for a football player to get a goal on 100% of kicks. That doesn't mean football players shouldn't try to get better at football, and it doesn't mean people shouldn't try to get better at logic.

Objection 5: Sometimes you have to just take things on authority Absolutely, and this is logical. I don't understand fluid dynamics, and if an airplane engineer tells me the most important equation for fluid dynamics is pr=tn^2, I'll believe him. Not because I have no evidence, but because my evidence is that a guy who thinks this is true can make airplanes fly, and get a degree in airplane engineering from a prestigious university, et cetera. If, later on, I become an airplane engineer myself and run experiments that show the equation is different, I'll have more evidence that the guy is wrong than I do that he's right, and I'll change my opinion. None of this, however, suggests that I should believe the authority of a random person on the street who says "Planes fly because of gremlins!"

Please post your thoughts, opinions, objections, and clarifications! I want everyone in Shireroth agreeing on this issue by (Yvain checks his watch) the end of time.

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Re: [Order] Is logic the best problem-solving tool?

Post by Maksym Hadjimehmetov »

No
Because human behaviour and life in general are not logical!
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Re: [Order] Is logic the best problem-solving tool?

Post by Yvain Wintersong »

You mean Objection 3? :)
Seriously, please explain what you mean, and what method you think works better.

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Re: [Order] Is logic the best problem-solving tool?

Post by Neike Taika-Tessaro »

I think logic is the best problem-solving tool, as long as it recognises it's own limits.
Objection 1: Logic can't tell me what art to like, what music to like, what girl to date, etc! No, it can't. Neither can anything else. "What art should Yvain like?" is, in my opinion, a meaningless question. [...]
Logic will never be able to determine the outcome of "Is Apollo Four Forty superior to Destiny's Child?" [Don't answer that.] Now, you might argue that this, too, is meaningless, but an inherit issue with humans is that they seek meaning in everything, which in turn means that questions like that crop up. People want to like things that have objective value.

Now, I have a generally nihilistic approach to all that, and so most of the time I'm not bothered. I do, though, make an exception with @440 because I feel my emotional side needs some leeway, lest it whither away and die, and I bite when poked (as in, when other people start to pull the subjective 'superior' nonsense on me, such as, ZOMG, tabbed browsing is teh shitz!!! LOL@u, not using it!!!, which just makes me want to beat them across the head with something sufficiently blunt).

Of course, I like to think the answer to that lies in the premise itself.

"Logic is the best problem-solving tool."

If it ain't broke, don't fix it, and since I conveniently don't believe everyone has to get along with everyone else, the entire thing is moot.

Though, I do want to point out one thing: someone who would honestly not find logic the best problem-solving tool would not come here with logical arguments, which you then likely wouldn't accept. :) Which, by the way, really isn't supposed to be criticism - I expect it'd require something like logic allowing for infinite regression from itself before that would work.
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Re: [Order] Is logic the best problem-solving tool?

Post by Prodigy Almighty »

Sometimes, logic helps. Okay, most times, logic helps. But there are some situations that make ABSOLUTELY no sense, and if you try to use logic to solve/comprehend them, you'll just fail evn harder.
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Re: [Order] Is logic the best problem-solving tool?

Post by Braden Indianensis »

In my humble opinion, if something is beyond the grasp of human logic and reason, then it is not a problem: a problem is something which may be solved, and reason is man's only active means of solving problems. Something which is beyond human comprehension is a conundrum or something else.
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Re: [Order] Is logic the best problem-solving tool?

Post by Yvain Wintersong »

I think I agree with Braden, but I want to know what sort of situations Prodigy's talking about.

Neike, you put that much better than I did :) Philosophy of art is tough for me. I realize that, looking at it logically, it's completely a matter of taste. But it's hard for me to shake the feeling that there should at least be some way of saying that Beethoven's Ode to Joy is better than a monkey banging on a keyboard (or the latest crappy pop single). The only thing I've found that comes close to satisfying me is something Eliezer Yudkowsky called "objective subjectivity". That's basically subjectivity minus the free will - the superiority of the Beethoven song is all in my mind, but I didn't CHOOSE to prefer it, aspects of the music just interacted with aspects of my brain/mind in a favorable way. Since most people's brain/minds are built pretty similarly, the same song might also interact with another person's brain/mind in a favorable way, and so on. So Ode to Joy really IS better for me and people who have brains/minds like mine, but it's not because of any objective feature of the music or something that has to carry over to a very different person.

You're probably shaking your head and saying that's something really obvious expressed really verbosely, and I guess it is, but I hadn't thought of it until it was pointed out to me.

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Re: [Order] Is logic the best problem-solving tool?

Post by Prodigy Almighty »

Yvain Wintersong wrote:I think I agree with Braden, but I want to know what sort of situations Prodigy's talking about.
I read too many books on existentialism and higher powers... the situations I'm talking about will (probably!) never happen. Just sayin'. :shrug emoticon which doesn't exist:
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Re: [Order] Is logic the best problem-solving tool?

Post by Neike Taika-Tessaro »

Braden Indianensis wrote:In my humble opinion, if something is beyond the grasp of human logic and reason, then it is not a problem: a problem is something which may be solved, and reason is man's only active means of solving problems.
Beautifully said. I was kind of trying to get at that with my last lines, there, but re-reading it, mine just looks like a disoriented brainfart. This is much better. ^_^
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Re: [Order] Is logic the best problem-solving tool?

Post by benkern »

Then you're wandering into the territory of the meaning of words.

Like when people say many universes, I don't like it, because I've always assumed by definition the universe is everything. There cannot be more than one everything, because they would be part of one big everything which would be the universe. In the same way, I don't agree with what Braden said because there are still things outside of human logic as you say but you loosely label them a conundrum or something else - a puzzle is a problem.
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Re: [Order] Is logic the best problem-solving tool?

Post by hypatias mom »

Many parts of human life don't reduce themselves to the realm of logic. It is hard to quantify and qualify things like appreciation, love, likes and dislikes, appetites, faith, and similar emotionally- or sensually-charged areas of one's life. One can feel many things that are not logical, and that is not a conundrum or a puzzle--it just is the way of human life. Once one is aware of sensations or emotions, one can try to reduce them to whether they are logical, but it is not necessarily appropriate to approach things of that nature with logic alone.

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Re: [Order] Is logic the best problem-solving tool?

Post by Yvain Wintersong »

Prodigy wrote:I read too many books on existentialism and higher powers... the situations I'm talking about will (probably!) never happen. Just sayin'. :shrug emoticon which doesn't exist:
And I still want to know what you mean! This is (kind of) philosophy - even if a situation's never going to happen, it's still important. I'm never going to be locked in a room full of instructions for transcribing Chinese characters, but that's still a great thought experiment.
...although if you get too existentialist on me, I'll have to shoot you.
Benkern wrote:Like when people say many universes, I don't like it, because I've always assumed by definition the universe is everything. There cannot be more than one everything, because they would be part of one big everything which would be the universe. In the same way, I don't agree with what Braden said because there are still things outside of human logic as you say but you loosely label them a conundrum or something else - a puzzle is a problem.
I have the same issue with the universes (though I've learned to accept it). But I'm not sure I understand your second point. What are some examples of these conundra?
Hypatia's Mom wrote:Many parts of human life don't reduce themselves to the realm of logic. It is hard to quantify and qualify things like appreciation, love, likes and dislikes, appetites, faith, and similar emotionally- or sensually-charged areas of one's life. One can feel many things that are not logical, and that is not a conundrum or a puzzle--it just is the way of human life. Once one is aware of sensations or emotions, one can try to reduce them to whether they are logical, but it is not necessarily appropriate to approach things of that nature with logic alone.
I agree with you. Emotions are, indeed, not logic. All I'm claiming in this thread is that logic is the best problem-solving tool. If I fall in love, that's not a problem, that's a feeling. If it becomes a problem (for example, "how do I win this girl's heart?" or "I don't want to be in love, what's the easiest way to stop being in love?") then it has a logical answer.

My thesis is that logic's really good at solving problems. To convince me that emotions disprove my thesis, you'd have to give me an example of a specific problem related to emotions that can't be solved with logic.

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Re: [Order] Is logic the best problem-solving tool?

Post by Andreas the Wise »

So we agree that logic can not neccessarily help in every decision, but can help solve problems. I'd agree with that, but add that you need to use a degree of commonsense. Especially in matters involving emotions or the like, in which logic can help, but isn't necessarily the best way. I'm trying to think of an example but I can't think of a good one, the best might be the mathematical proof that 1.9999=2. 'Cept I can't remember the proof. The point of it is, though, that while each step follows logically, one step is still flawed and so the whole answer is wrong - and you have to have the common sense to know that 1.999 is not 2, and find the flaw.
You have to be careful that you don't make logic the unmistakeable ultimate, because if you did something slightly wrong, it could throw your whole answer out, and if you just say "I did it logically, it must be right," then you'd be making a big mistake ...


Which is not to say I don't happily employ logic whenever I can, but that's probably cause I did too much maths ... :demon
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Re: [Order] Is logic the best problem-solving tool?

Post by Neike Taika-Tessaro »

Psst, careful with that - 1.9999... is indeed equal to 2, in case you were referring to that; or someone thinks you were.
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Re: [Order] Is logic the best problem-solving tool?

Post by benkern »

Hey, don't get confused now Andreas. Whatever you call 1.9999, it's still just 1.9999, not 2.

Haha. I'll be making fun of that quote 'til my dying day...
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Re: [Order] Is logic the best problem-solving tool?

Post by Andreas the Wise »

Neike Taika-Tessaro wrote:Psst, careful with that - 1.9999... is indeed equal to 2, in case you were referring to that; or someone thinks you were.
There is a similiar proof there, but my math book used it to prove that it was WRONG ... how interesting (guess you can't trust everything Wiki says)
I think the catch was that, however many 9's you had on the end, when you multiply it by 10 it has one less than the original one, and so there;s 0.000000 ..... 0009 difference ...
So close as to be the same, or not?

Anyway, thought of a much better one. Lovely Greek problem - the turtle and the arrow.
You have a bow and arrow, and a turtle 10 m away. As you shoot the arrow at the turtle, the turtle starts moving. When the arrow reaches 10 m, the turtle has now moved 0.5 m further. When the arrow reaches that further 0.5m, the turtle has moved another 0.025m. When the arrow reaches that distance, the turtle has moved on again an even smaller distance and so on to infinity ...
Of course, commonsense tells you that the arrow should move to where the turtle's going to be ...
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Re: [Order] Is logic the best problem-solving tool?

Post by Neike Taika-Tessaro »

Andreas the Wise wrote:There is a similiar proof there, but my math book used it to prove that it was WRONG ... how interesting (guess you can't trust everything Wiki says)
I think the catch was that, however many 9's you had on the end, when you multiply it by 10 it has one less than the original one, and so there;s 0.000000 ..... 0009 difference ...
So close as to be the same, or not?
Not really. The question really is if the string of nines terminates - then it is not equal to 2 - or if it's an infinite string of nines - then it is equal to 2. I think the article on wikipedia describes it better than I could, though. It's a pivotal difference, mind you. See the section "Skepticism in education":
Some students interpret "0.999..." (or similar notation) as a large but finite string of 9s, possibly with a variable, unspecified length. If they accept an infinite string of nines, they may still expect a last 9 "at infinity".
Andreas the Wise wrote:<the turtle and the arrow>
Don't shoot me, but: How's that a problem? Plot the speed of the arrow in one function, and the speed and starting distance of the turtle in another, then calculate where they cross. Alternatively, playing that game, we're back at mathematical limits. Which, again, is 'easily' solved.
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Re: [Order] Is logic the best problem-solving tool?

Post by Yvain Wintersong »

[EDIT: Crossposted with Neike. Sorry for any inconvenience.]
I think the catch was that, however many 9's you had on the end, when you multiply it by 10 it has one less than the original one, and so there;s 0.000000 ..... 0009 difference ...So close as to be the same, or not?
I think what your math book was talking about was a large but finite number of nines, for example 1.999999, with six nines. That number is NOT equal to two, but using bad algebra could very easily lead you to believe that it was. With an infinite number of nines, no matter how many nines you remove, you'll still have the same number of nines left at the end (infinity's weird like that). The inifnite version, 1.99999..., is equal to two.
Anyway, thought of a much better one. Lovely Greek problem - the turtle and the arrow.
You have a bow and arrow, and a turtle 10 m away. As you shoot the arrow at the turtle, the turtle starts moving. When the arrow reaches 10 m, the turtle has now moved 0.5 m further. When the arrow reaches that further 0.5m, the turtle has moved another 0.025m. When the arrow reaches that distance, the turtle has moved on again an even smaller distance and so on to infinity ...Of course, commonsense tells you that the arrow should move to where the turtle's going to be ...
Yay people providing examples! Now you're speaking my language!

Assume the arrow's moving at 10m/second, and the turtle's moving at .5m/second. The arrow will reach the turtle's original position T1 after one second, at which point the turtle is at T2=10.5. The arrow will reach T2 after 1/20 second, at which point the turtle will be at T3=10.525. The arrow will reach T3 after 1/400 second. So it's clear that each step will take 1/20 of the time the last step took. So the amount of time it takes for the arrow to catch up to the turtle equals 1+1/20+1/400+1/8,000+1/160,000+.... and so on to infinity. Since there are an infinite number of numbers to add up, it might seem like the answer must be infinity, but it very often isn't! Here's an easy proof that this is true: 1+1/10+1/100+1/1000.... also has an infinite number of numbers, but since it's 1+.1+.01... the answer is clearly 1.11111111.... with an infinite number of ones after it, which isn't infnite at all and in fact is less than 1.2. This is called an infinite geometric series, and there's a quick way to calculate the answer: a/(1-r), where a is the first term (in the arrow example, 1) and r is the ratio (in the arrow example, 1/20). Plugging these in, we find out that the arrow will overtake the tortoise after 20/19 =~ 1.052 seconds, which is exactly what common sense would lead us to expect.

Zeno, the Greek guy you mentioned, has a lot of paradoxes like these, and they all work in the same way - they use "common sense" ideas about infinity to trip you up. Once you use the correct math, everything works out perfectly. So in my opinion, this is a perfect example of how real logic is never wrong.

But you do bring up a very good point - it's very easy to make mistakes using logic, and if you always trust the logical proofs you make you'll probably end up believing lots of false things. Logic itself is never wrong, but people are very often wrong when they decide that a certain proof is properly logical. So you can believe fully in logic while still not trusting a really good logical proof you thought up.

Here's how I would handle Zeno's paradox. I'd say "Well, this mathematical argument of mine seems to show that different speeds are impossible. But observation shows that different speeds clearly do exist. And I can also do math with time and distance to prove that speeds exist. So I have one piece of logical evidence (the paradox is deductive logic) against speed, and two pieces of logical evidence (the math is deductive logic, plus the observations are inductive logic) in favor of speed. Since the paradox goes against the other evidence, and is very complicated, and uses math I don't really understand, let me study it more closely to see if there are any errors. If I can't find any, I'll examine the other evidence to see if there's an error there, for example an optical illusion affecting my observations. If I can't find any errors anywhere, the evidence supporting different speeds is much more common and more direct, so I'll stick with that while continuing to try and figure out what's going on."

(Zeno, who first proposed the paradox, used it as proof of Parmenides' belief that the real world was just an illusion, which provides a convincing explanation for the reason why things do seem to move with different speeds. The only way I could argue against Parmenides without understanding infinite geometric series would probably be the claim that extraordinary claims require extraordinary evidence, or by using a Bayesian argument with a very very low prior.)

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Re: [Order] Is logic the best problem-solving tool?

Post by Neike Taika-Tessaro »

Yvain Wintersong wrote:Since there are an infinite number of numbers to add up, it might seem like the answer must be infinity, but it very often isn't!
I know, you pretty much disclaimered about this in the beginning of your post, but I feel compelled to point out that this is precisely what limits are about, and that I mentioned them. So, um... yeah...

^_^;
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Re: [Order] Is logic the best problem-solving tool?

Post by Andreas the Wise »

Don't worry Yvain, I know all about geometric sequences, did the top level of maths in my senior year (which I just finished, since in the Southern Hemisphere our summer break is of course Christmas).
I think that's a good point - logic works, but humans don't always. With that in mind, I'll concede logic is the best problem-solving tool.
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Re: [Order] Is logic the best problem-solving tool?

Post by benkern »

Summer Break... Christmas... Can't get over that. No white christmases for you I suppose. :D

But at least it would snow rather than POUR DOWN on my birthday.
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Re: [Order] Is logic the best problem-solving tool?

Post by Andreas the Wise »

Benkern, in that last sentence you've shown you know very little about Australia.

For a start, snow is incredibly rare. We get it on a few mountains each year, but apart from that, it's a freak event. And rain ... it would be lovely to have some rain. I hear people in Britain, if they don't get rain for a month, fear it's a drought. We've been in a drought for, oh, say, 10 years? More, depending where you are ... rain is a very good thing, particuarly if it falls into the catchment areas for the dams, instead of flooding the coast ...
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Re: [Order] Is logic the best problem-solving tool?

Post by hypatias mom »

It sounds like your weather is even more strange than my state, California. We usually have rain from October or November until April or May (in good years). The rest of the year is usually totally dry, with a very occasional sprinkle sometimes in late summer. The hills are golden brown except in winter and early spring, and we often have a green Christmas. The mountains get snow, and over 70 % of our water comes from run-off from the snow pack--caught in reservoirs for drinking, irrigation, and all those other necessities. And, yes, our coastal areas get massive flooding and mudslides in the winter.

People who have rain year-round don't understand it doesn't do that where we live. I still find it interesting that southern continents have their seasons inverted from ours in the north. Merry hot Christmas and New Year down under.

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Re: [Order] Is logic the best problem-solving tool?

Post by Andreas the Wise »

Thanks, and the same (but colder) to you ...
*Is well aware this is getting heavily off topic, expects a moderator will split it soon*
Well, since Australia is of course very large, the weather differs from place to place. But a general tendency, apart from up north, which gets the monsoons, is to expect droughts and floods. Not that reguarly, necessarily, but they certainly happen. Where I am (Brisbane) has summer (ie now) as it's rainy season, but we haven't had proper rain in it for several years (the current cyclone induced floods aside). But in the south, they have rain in winter. And as a country, we're certainly a lot drier than most of America or Europe, but we've just adapted to it.
Bit worse in the drought of course, but hey. Just remember - if you can still legally use hoses more than 3 hours a week, count yourselves lucky :demon
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Re: [Order] Is logic the best problem-solving tool?

Post by Ari Rahikkala »

Andreas the Wise wrote:*Is well aware this is getting heavily off topic, expects a moderator will split it soon*
*Moderator action* to keep threads on topic? In SHIREROTH?!? Perish the thought! :knife
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Re: [Order] Is logic the best problem-solving tool?

Post by Liam conToketi »

Andreas the Wise wrote:Just remember - if you can still legally use hoses more than 3 hours a week, count yourselves lucky
Most of the summer, no, not recently...my county gets hardly any rain while the rest of the state gets too much. In my town we have no rain but the river will flood... :rolleyes

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Re: [Order] Is logic the best problem-solving tool?

Post by benkern »

Andreas the Wise wrote:Benkern, in that last sentence you've shown you know very little about Australia.
Hey, I know the essentials most people tend to pick up, that is when someone visits the country for a short time there's a window of opportunity for innuendo. :fish

Britain is known for its rain, yes - in a Walkers advert (the only place I get my information by the way) they said something like 250 days of rain a year. I bet you'd Aussies get pretty bored of it quite quickly even if you have been rainless for a decade. :p
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Re: [Order] Is logic the best problem-solving tool?

Post by Andreas the Wise »

Well, admittedly after a week in England at the end of last year it lost it's novelty ... I thought "Why not in Australia, not here?"
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Re: [Order] Is logic the best problem-solving tool?

Post by Yvain Wintersong »

Don't worry Yvain, I know all about geometric sequences.
Really? That embarrasses me - I had to check Wikipedia for the a/(1-r) formula :) If you can remember how to sum them more than six months after you take your last math class, I will stand in awe of you.

As for rain, I get it pretty often, but I kind of like it. It makes things more intense. Or intimate. Or something I can't really describe.

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