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hkmaly

Story, Wednesday, Oct 23, 2019

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12 hours ago, Darth Fluffy said:

The name of the band is a reference to the notion. (Flip side, I passed a LARGE flock of crows or ravens driving past the parking lot of the New Mexico Fair Grounds in Albuquerque; did not notice them at first, they blended in with the asphalt. They would have been difficult to count; they were just a sea of feathery blackness, and it was difficult to spot individual crows.)

I'm pretty sure the crows themselves don't know how many of them are. Nor do they care.

12 hours ago, Darth Fluffy said:

Re: "Four legs, duh :)" - Yes, centipedes are the brain trust.

Centipedes don't need to count their legs. Their method of locomotion works ok even with significant percentage of legs missing.

12 hours ago, Darth Fluffy said:
22 hours ago, hkmaly said:

The stuff we are made of are essentially probability waves.

At a more fundamental level, yes, but at the scale of discussion, the pieces are objects, Legos, so to speak.

At the scale of discussion, even atoms are too small.

12 hours ago, Darth Fluffy said:
22 hours ago, hkmaly said:

It's not complete ... however, which other SUBJECT in elementary/high school teaches logic? It's not that they couldn't. You could teach history in way of explaining strategical decisions rulers made, you can explain greek philosophy along with their poetry, I already mentioned physics ... It's that they don't.

There are definitely people like that lady too, but unless U.S. schools are worse than I though, I don't believe they form a majority.

... although maybe if I read that book I would find that U.S. schools ARE worse than I though.

I don't think you can teach history well without covering rationale, lest you end up making your students memorize the dry pointless lists that have been alluded to. The list of US presidents for example; dry and pointless, unless you incorporate what each man stood for, how it fit into the context of the day, what it lead to, and such. Decades of compromise over slavery did not preclude eventual conflict; the same kind of elitist a-holes who caused the Great Depression may be doing it again ...

My (US) teachers gave generally sufficient rationale, with little being presented as just rote, although there was some of that. Also, I asked questions and did outside reading.

Well, it's true there were several cases where I managed to get through exam with actual description of strategy instead of the dates. However, too often the question asked for date ; and I got the feeling the ones who just memorized the dates got quite good grades.

And, yes, it's quite obvious that teaching those pointless lists is not teaching history well.

12 hours ago, Darth Fluffy said:
22 hours ago, hkmaly said:

It doesn't hold in physics and other sciences, that's true. And even in math there are things which, while true, are later declared "not as important as though". However, you may notice that while most of what Aristotle said about physics is obsolete, Pythagorean theorem was actually already known to Babylonians and is still true.

Or the other way, how so much way out there abstract math tends to have real practical application.

More that you would expect, if you realize that practical applications include spacecraft, modern computers ... and modern CRYPTOGRAPHY. On the other hand, most of the maths dealing with infinities has little practical application, that's true ...

12 hours ago, Darth Fluffy said:
22 hours ago, hkmaly said:

Seriously: most of math university education is taught in term of statement - and how to prove it's true. The fact that mathematicians are only one who actually care about difference between what's true and what can be proved also speaks a lot.

That has not exactly been my experience; as an engineer, I was sometimes introduced to a new math topic in the course of an engineering application; however it was less satisfying; it helped to  learn it again in a more rigorous setting.

Another surprising thing in that regard was that often the math department professors were out of touch with their topic beyond the abstract. I asked our diffy q professor, who taught is topic very well, about the applicability of a topic he was teaching, and it wasn't just that he drew a blank, it was more like my words were foreign.

I found that the best math courses that I took at a higher level were rigorous, but taught by an engineer.

Hmmmm ... so perhaps my university experience is better than average. Granted, it wasn't for engineer.

12 hours ago, Darth Fluffy said:
22 hours ago, hkmaly said:

We don't NEED to experience all numbers. We KNOW how they will behave.

Fair enough in many cases; we will never see more than a tiny sliver of renderings of the Mandelbrot set. We know pretty much what it all looks like.

Sometimes misleading. We sample the low end of things and draw global conclusions. 2, 3, 5, 7, ... I guess all odd numbers are prime. ... 9, nope, 11, 13, ... with occasional exceptions ....

Well, obviously, that's what math is about. You don't find out how numbers will behave by taking few examples. Even taking countably infinite examples is not enough. But with math, you can make the prediction regardless. For example, we know what is the likehood that number is prime, although we don't know all primes.

12 hours ago, Darth Fluffy said:
22 hours ago, hkmaly said:

Well, the species in our own back yard seems to not want to make the effort in creating sum of own knowledge surpassing the memory capacity of individual. You can't really build civilization without that, unless you have individuals with MUCH better memory than humans have.

“For instance, on the planet Earth, man had always assumed that he was more intelligent than dolphins because he had achieved so much—the wheel, New York, wars and so on—whilst all the dolphins had ever done was muck about in the water having a good time. Curiously, the dolphins had always believed that they were far more intelligent than man—for precisely the same reasons.”

That's why I specifically said "civilization". Yes, there are some who think that civilization wasn't that good idea, but I personally think it was worth it.

12 hours ago, Darth Fluffy said:
22 hours ago, hkmaly said:

... I guess personal belief is technically religion but yes I was thinking more about organized religions ...

I'm guessing that's an oxymoron. Maybe Scientology, they seem sufficiently Machiavellian and monolithic to qualify.

Quite a lot of people disagree. Although it might be similar case as military intelligence, which is not oxymoron just because it means something little different than it seems on first look.

12 hours ago, Darth Fluffy said:
22 hours ago, hkmaly said:

Might depend on how you measure "much", obviously, but there is big core where everything is provable. Sure, you don't get prizes for core: those are for boundaries and often specifically for PROVING something which is already suspected to be true.

Calling out a similar concept to the hugeness of numbers; there's always way more that you don't know than that you do know. You know, sufficiently advanced, blah, blah, blah, magic.

I agree though, that we have a nice, functional core.

Yeah, but are not comparing with what we don't know. We compare what we know and can prove to what we suspect but can't prove.

And yes, any sufficiently analyzed magic ...

12 hours ago, Darth Fluffy said:
22 hours ago, hkmaly said:

Not that much. There were encyclopedia before computers. And most of that information is very rarely useful in practical life, so it doesn't matter that hardly any student will remember it longer than he needs for the exams.

Yes, but Oh, God, research is soooo much easier and quicker today.

Definitely. Also, it's much more distracting. :)

Doesn't change the fact that stuff like "Who was 36th president" is better answered using external memory than internal.

 

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10 hours ago, hkmaly said:

I'm pretty sure the crows themselves don't know how many of them are. Nor do they care.

They are quite social and fairly effectively communicate.

 

10 hours ago, hkmaly said:

Centipedes don't need to count their legs. Their method of locomotion works ok even with significant percentage of legs missing.

I can picture making a cartoon where one section missteps like the guy that screws up marching, and throws the rest off.

 

10 hours ago, hkmaly said:

Well, obviously, that's what math is about. You don't find out how numbers will behave by taking few examples. Even taking countably infinite examples is not enough. But with math, you can make the prediction regardless. For example, we know what is the likehood that number is prime, although we don't know all primes.

It's related to summation(1/x), which is roughly asymptotic to Ln(x) (I think it was base e; if not, there's a scaling factor, perhaps a small offset); interestingly it continues to diverge, even though it is sparser than 1/x.

There is a weird factoid about how that works. if you start with 2 and work up, each prime reduced the remaining primes by (p-1)/p. You see this almost immediately with (2-1)/2=1/2, but taking them in order, each new prime does not contribute to this reduction until p*p; before that it is composite with smaller primes. So beyond how you'd expect that primes are weighted toward the low end, they are even more so because the contribution of each new reduction takes a while to manifest.

 

10 hours ago, hkmaly said:

That's why I specifically said "civilization". Yes, there are some who think that civilization wasn't that good idea, but I personally think it was worth it.

Or like when Ghandi was asked, "What do you think about Western Civilization?", replied, "I think it would be a good idea."

 

10 hours ago, hkmaly said:

There are a lot of people that play the lottery. There are a lot of people that smoke cigarettes. There are a lot of people that drive too fast in inclement weather, with their headlights off, no less!

 

10 hours ago, hkmaly said:

Definitely. Also, it's much more distracting. :)

Hear, hear!

 

 

Edited by Darth Fluffy
typo

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6 hours ago, Darth Fluffy said:

There are a lot of people that play the lottery. There are a lot of people that smoke cigarettes. There are a log of people that drive too fast in inclement weather, with their headlights off, no less!

Not to mention a steady flow of applicants for the annual Darwin Awards.

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On 11/1/2019 at 7:47 PM, hkmaly said:

It's definitely useful, but there is even MORE important stuff math is supposed to teach you: logical way of thinking. The fact lot of people fail at that endangers not just them but whole world.

On 11/2/2019 at 0:18 AM, hkmaly said:

From the general point, yes. But if you look specifically at education, math is ONLY class until university teaching logic and deduction. Every other subject, including physics (which is closest to math from all sciences taught at school), can be just memorized and memorizing is big part of what is necessary to do in them. At least that was true in schools I visited. I've heard that in US, there is much more emphasis on talking ... which, while likely more useful than memorizing, is again NOT logic and deduction.

I don't remember my math classes ever teaching much logic, at least prior to high-school. It was mostly just "here's the procedure" followed by endless sets of equations for us to practice the procedure on.

I mean I suppose word problems required a bit of logic to figure out what numbers you needed, but very few of my teachers ever bothered to explain how you figure out which numbers to use (and even they usually thought explaining just once or twice was good enough). Not surprisingly, a lot of students had a hard time with word problems and wound up hating them. Personally, I rather liked word problems, but unfortunately many of my math teachers seemed to think they were doing us a favor by not making use of them much or at all.

On 11/2/2019 at 0:18 AM, hkmaly said:

Most people claiming to hate math in school actually hate to think.

On 11/2/2019 at 4:36 PM, Darth Fluffy said:

I know a lady that edits sci fi for Baen Books. She is a good conversationalist, tends to be well versed. She says she "can't do math". I know she can think; seems more phobic than not willing to put forth effort. My hypothesis is "bad experience in school".

I almost had this myself, it might be more toward your point. I had trouble remembering the times tables because I did not want to put effort into memorizing. This could have gone bad two ways, either I was left to my own devices, and would have struggled. or my Dad, hearing about it in a conference with my teacher, would have done his usual and belted me, ruining math for a lifetime. Fortunately for me, my teacher must have guided him, because he became uncharacteristically involved, got flash cards, and worked with me to get me past this hump.

I hated math class because I did math so slowly that I almost never got what I needed done in class... And my math homework took so long that it felt like it was using up almost all of my free time (other homework usually wasn't a problem).

My parents tried flash-cards to help me memories my multiplication tables, but there were some I was never able to memorize no matter how hard I tried. (Heck, I never even managed to memorize all the single-digit addition equations; to this day a lot of my "math" involves counting.)

That said, I did enjoy algebra classes, despite how time--consuming they still were.

 

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On 11/3/2019 at 8:23 PM, hkmaly said:

... wait, WHAT is exported from Australia not by air or water and how? Did someone build a tunnel between Australia and U.S.?

 

On 11/4/2019 at 6:01 AM, ijuin said:

Digital exports?

Nowadays digital exports are usually done electronically - but if you need to transfer a yottabyte or so from Syndey to Seattle, probably the fastest way is to put a large crate of SSDs (or thumb drives or microSD cards) on a plane.

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On 11/3/2019 at 10:23 PM, hkmaly said:

... wait, WHAT is exported from Australia not by air or water and how? Did someone build a tunnel between Australia and U.S.?

Keppel Earl "Kep" Enderby QC, was an Australian member of Parliament who, in 1974, famously observed "Traditionally, Australia obtains its imports from overseas."

Just one of the little quotes I keep in mind to remind myself no matter how ridiculous American politicians may seem, the rest of the world can be just as insane

If Australia has imports that don't come from overseas, then they probably have exports that don't go overseas either

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6 hours ago, Pharaoh RutinTutin said:

Just one of the little quotes I keep in mind to remind myself no matter how ridiculous American politicians may seem, the rest of the world can be just as insane

They went into politics. That in itself is sufficient evidence to prove that they are either insane or evil (and possibly both).

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On 11/5/2019 at 4:06 AM, Darth Fluffy said:
On 11/5/2019 at 3:15 AM, hkmaly said:

I'm pretty sure the crows themselves don't know how many of them are. Nor do they care.

They are quite social and fairly effectively communicate.

That's not in conflict with what I said.

On 11/5/2019 at 4:06 AM, Darth Fluffy said:
On 11/5/2019 at 3:15 AM, hkmaly said:

Centipedes don't need to count their legs. Their method of locomotion works ok even with significant percentage of legs missing.

I can picture making a cartoon where one section missteps like the guy that screws up marching, and throws the rest off.

So what, there are lot of cartoons where characters only fall when they notice they don't have anything under legs while running.

On 11/5/2019 at 4:06 AM, Darth Fluffy said:
On 11/5/2019 at 3:15 AM, hkmaly said:

That's why I specifically said "civilization". Yes, there are some who think that civilization wasn't that good idea, but I personally think it was worth it.

Or like when Ghandi was asked, "What do you think about Western Civilization?", replied, "I think it would be a good idea."

Very true, however different meaning of the word.

On 11/5/2019 at 4:06 AM, Darth Fluffy said:
On 11/5/2019 at 3:15 AM, hkmaly said:

There are a lot of people that play the lottery. There are a lot of people that smoke cigarettes. There are a lot of people that drive too fast in inclement weather, with their headlights off, no less!

You have a point. Considering most of people calling the religion organized are IN it, it can be considered more wish than statement.

On 11/6/2019 at 4:46 PM, ChronosCat said:

I don't remember my math classes ever teaching much logic, at least prior to high-school. It was mostly just "here's the procedure" followed by endless sets of equations for us to practice the procedure on.

I mean I suppose word problems required a bit of logic to figure out what numbers you needed, but very few of my teachers ever bothered to explain how you figure out which numbers to use (and even they usually thought explaining just once or twice was good enough). Not surprisingly, a lot of students had a hard time with word problems and wound up hating them. Personally, I rather liked word problems, but unfortunately many of my math teachers seemed to think they were doing us a favor by not making use of them much or at all.

... I would add this into the heap of "the teachers should teach better".

Yes, apparently sufficiently bad teacher can teach math without teaching logic.

10 hours ago, Don Edwards said:
On 11/4/2019 at 4:23 AM, hkmaly said:

... wait, WHAT is exported from Australia not by air or water and how? Did someone build a tunnel between Australia and U.S.?

 

On 11/4/2019 at 2:01 PM, ijuin said:

Digital exports?

Nowadays digital exports are usually done electronically - but if you need to transfer a yottabyte or so from Syndey to Seattle, probably the fastest way is to put a large crate of SSDs (or thumb drives or microSD cards) on a plane.

The alternatives are to use satellites by sending the data into air on radio waves or the cables in water, on bottom of ocean.

3 hours ago, Don Edwards said:
10 hours ago, Pharaoh RutinTutin said:

Just one of the little quotes I keep in mind to remind myself no matter how ridiculous American politicians may seem, the rest of the world can be just as insane

They went into politics. That in itself is sufficient evidence to prove that they are either insane or evil (and possibly both).

Yes. Anyone who ever enters politics is not qualified to rule a country.

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32 minutes ago, hkmaly said:

That's not in conflict with what I said.

I know, right?

 

32 minutes ago, hkmaly said:

So what, there are lot of cartoons where characters only fall when they notice they don't have anything under legs while running.

Given that we are in a forum discussing a comic, this should have some relevance.

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1 hour ago, Darth Fluffy said:
2 hours ago, hkmaly said:

So what, there are lot of cartoons where characters only fall when they notice they don't have anything under legs while running.

Given that we are in a forum discussing a comic, this should have some relevance.

EGS has more standard set of physical laws ... which says something considering it allows magic :)

 

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6 hours ago, Don Edwards said:

They went into politics. That in itself is sufficient evidence to prove that they are either insane or evil (and possibly both).

That is, if they are Democrats, of course. </sarcasm>

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1 hour ago, hkmaly said:

EGS has more standard set of physical laws ... which says something considering it allows magic :)

I wanna live in your universe. Hovering sounds cool. Also flying for no aerodynamic reason.

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12 hours ago, Don Edwards said:

They went into politics. That in itself is sufficient evidence to prove that they are either insane or evil (and possibly both).

 

5 hours ago, The Old Hack said:

That is, if they are Democrats, of course. </sarcasm>

I offer no such qualification.

My father said his uncle told him that anyone who gets elected twice is a crook. This was, supposedly, during said uncle's 8th term in the Indiana state legislature.

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33 minutes ago, Don Edwards said:

My father said his uncle told him that anyone who gets elected twice is a crook. This was, supposedly, during said uncle's 8th term in the Indiana state legislature.

The main problems with this attitude are 1) it generates immense cynicism towards the democratic system and 2) the people who most want to do something about it tend to sort themselves out of the political equation, leaving only those who don't care about it.

In Denmark we had an extremely principled politician named Preben Wilhelm who firmly believed there should be a seven year term limit for all politicians. At the end of those seven years he retired, leaving us one very rare honest elected representative poorer.

I do not see any simple solution to this, I fear. All I can think of right now is rage against it.

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17 hours ago, Darth Fluffy said:
19 hours ago, hkmaly said:

EGS has more standard set of physical laws ... which says something considering it allows magic :)

I wanna live in your universe. Hovering sounds cool. Also flying for no aerodynamic reason.

Wait, what?

I meant relatively to the cartoons. Note that there are plenty of stuff which fly for other reasons than aerodynamic - in case you probably refer to, the reason is obviously magic.

(Hovering is easy. There is nonzero probability you will hover just due to random Brownian motion. Ok, it's VERY small probability but it's nonzero :).)

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8 hours ago, hkmaly said:

Wait, what?

I meant relatively to the cartoons. Note that there are plenty of stuff which fly for other reasons than aerodynamic - in case you probably refer to, the reason is obviously magic.

(Hovering is easy. There is nonzero probability you will hover just due to random Brownian motion. Ok, it's VERY small probability but it's nonzero :).)

Somehow, the notion that the random molecular motion of the air molecules in my room might shove me up or down, left or right, does not occupy a significant portion of my daily thought process. Perhaps this is another manifestation of the difference between those of a practical bent vs a more rigorously logically, yet hypothetical, approach.

I heard an anecdote years ago that may help illustrate this. A mathematician and an engineer were given a test. They were on one side of a room and a prize was on the other. (In the original story, the prize was a beautiful woman, but my point here is not to offend anyone, and the notion of a person as a prize could indeed be offensive. So substitute anything you think would be more appropriate.)

The conditions of the test were thus, "You may go half way toward the prize, then you must stop. At the next phase, we will repeat this process, you may proceed half of the remaining distance, but then must stop. We will repeat this again in the following phase, and so on."

The mathematician, recognizing Zeno's paradox, left in disgust. "I can never reach the prize."

The engineer proceeded with the test, thinking to himself, "I can get close enough."

But it all worked out, because the mathematician met a stray unattached sheep on the way home, and they lived happily ever after.

(Confession, I added that last part to the story. Was that baaaaaad?)

 

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1 hour ago, Darth Fluffy said:

I heard an anecdote years ago that may help illustrate this.

Speaking of tests.

I just read the following story. A group of adventurers faced the old conundrum with doors they had to go through and two guards, one who always lied, one who always told the truth.

Wizard: Oooh, I know this one. You have to ask --
Barbarian: <brutally murders one of the guards with his axe>
Barbarian: <asks the other guard> This guy still alive? <points at the corpse with his blood-dripping axe>
Guard: Yes.
Barbarian: <jabs thumb at the surviving guard> This one liar.

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1 hour ago, The Old Hack said:

Speaking of tests.

I just read the following story. A group of adventurers faced the old conundrum with doors they had to go through and two guards, one who always lied, one who always told the truth.

Wizard: Oooh, I know this one. You have to ask --
Barbarian: <brutally murders one of the guards with his axe>
Barbarian: <asks the other guard> This guy still alive? <points at the corpse with his blood-dripping axe>
Guard: Yes.
Barbarian: <jabs thumb at the surviving guard> This one liar.

Nice. I think I posted this link before.

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8 hours ago, Darth Fluffy said:

Somehow, the notion that the random molecular motion of the air molecules in my room might shove me up or down, left or right, does not occupy a significant portion of my daily thought process. Perhaps this is another manifestation of the difference between those of a practical bent vs a more rigorously logically, yet hypothetical, approach.

There was a reason that example ended with smiley.

8 hours ago, Darth Fluffy said:

I heard an anecdote years ago that may help illustrate this. A mathematician and an engineer were given a test. They were on one side of a room and a prize was on the other. (In the original story, the prize was a beautiful woman, but my point here is not to offend anyone, and the notion of a person as a prize could indeed be offensive. So substitute anything you think would be more appropriate.)

The conditions of the test were thus, "You may go half way toward the prize, then you must stop. At the next phase, we will repeat this process, you may proceed half of the remaining distance, but then must stop. We will repeat this again in the following phase, and so on."

The mathematician, recognizing Zeno's paradox, left in disgust. "I can never reach the prize."

The engineer proceeded with the test, thinking to himself, "I can get close enough."

Of course, besides the issue with woman being prize, there is also the issue that desired distance between man and woman is negative.

4 hours ago, Darth Fluffy said:
6 hours ago, The Old Hack said:

I just read the following story. A group of adventurers faced the old conundrum with doors they had to go through and two guards, one who always lied, one who always told the truth.

Wizard: Oooh, I know this one. You have to ask --
Barbarian: <brutally murders one of the guards with his axe>
Barbarian: <asks the other guard> This guy still alive? <points at the corpse with his blood-dripping axe>
Guard: Yes.
Barbarian: <jabs thumb at the surviving guard> This one liar.

Nice. I think I posted this link before.

Yeah ... the idea behind the original test is nice, but can never be successfully applied in reality. Just like the other modification with three guards - one who always lies, one who always tells the truth and one who stabs people asking tricky questions.

Of course, that's nothing new. Alexander the Great practically pointed out this issue with theoretical problems and practical solutions with the Gordian Knot.

 

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6 hours ago, hkmaly said:

There was a reason that example ended with smiley.

Of course, besides the issue with woman being prize, there is also the issue that desired distance between man and woman is negative.

I do not understand why the distance would be negative, but Zeno works (or not so much) in either direction. Are you saying, "negative and small", like they are co-inhabiting the same space? Having been placed at the prize, there wouldn't be much test, would there?

I can imagine a similar scenario with a monetary prize. The test giver take out a small stack of gold coins, and turning to the engineer says, "Be a good fellow, take these to the other side of the room, and place them somewhere over there, then return here and our test shall begin." The engineer does as he is told. He crosses the room, slips the coins into his pocket, then returns.

:P<_<:o                                                                          :ph34r:

That's the engineer, the mathematician, the test giver, and a ninja who was going to steal the coins. Four smileys; do I win? :D

(Oops, five) :)

(Oops, six) :D

...

(OK, clearly, this leads to an infinite set of smileys; sorry, man, you are out-smileyed.) :lol:

 

6 hours ago, hkmaly said:

Yeah ... the idea behind the original test is nice, but can never be successfully applied in reality. Just like the other modification with three guards - one who always lies, one who always tells the truth and one who stabs people asking tricky questions.

I like that 3rd guard. I'll have to use that if I set up a puzzle like this for a game.

 

6 hours ago, hkmaly said:

Of course, that's nothing new. Alexander the Great practically pointed out this issue with theoretical problems and practical solutions with the Gordian Knot.

That is references in the last panel of the linked OOTS cartoon. Alexander's successes owe a lot to this kind of thinking. Facing innumerable Persian Immortals, he charged and killed the opposing commander. The now leaderless opposing troops gave up.

 

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4 hours ago, Darth Fluffy said:
11 hours ago, hkmaly said:

There was a reason that example ended with smiley.

Of course, besides the issue with woman being prize, there is also the issue that desired distance between man and woman is negative.

I do not understand why the distance would be negative, but Zeno works (or not so much) in either direction. Are you saying, "negative and small", like they are co-inhabiting the same space?

Considering this forum can technically be read by children I wouldn't be more specific.

4 hours ago, Darth Fluffy said:
11 hours ago, hkmaly said:

Yeah ... the idea behind the original test is nice, but can never be successfully applied in reality. Just like the other modification with three guards - one who always lies, one who always tells the truth and one who stabs people asking tricky questions.

I like that 3rd guard. I'll have to use that if I set up a puzzle like this for a game.

Remember the rest of discussion: in RPG, it's not hard to convince players they are NOT supposed to solve the puzzle without killing someone.

(Weird, I though this third guard is pretty famous addition.)

4 hours ago, Darth Fluffy said:
11 hours ago, hkmaly said:

Of course, that's nothing new. Alexander the Great practically pointed out this issue with theoretical problems and practical solutions with the Gordian Knot.

That is references in the last panel of the linked OOTS cartoon. Alexander's successes owe a lot to this kind of thinking. Facing innumerable Persian Immortals, he charged and killed the opposing commander. The now leaderless opposing troops gave up.

Yes, it was. Also note that Persian Immortals were already proven to be not, in fact, immortal by King Leonidas and his 300 warriors.

 

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The moniker “Immortals” was because the unit always survives and is brought back to full strength, not the individual soldiers.

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