Critical Thought Experiments

cannabineer said:
Then I am stumped. I see no way (shy of cheating, which would ruin this as a puzzle of critical thinking and reduces it to a mere riddle, and riddles have always mightily annoyed me by their sly ways of cheating language) that the outcomes could have been fixed. Please tell me if this is indeed a logic puzzle and not a riddle ... I was going on that basic premise since I have not once seen Heisenberg stoop to sophistry.
But if it is a logic puzzle, i am hung on what appears to be an internal contradiction.

I could use the "no chance it was chance" as my starting point, decide that means "the whole thing was rigged", which would moot the question of the sender's psychic prowess. But that would be ugly and inelegant and unsatisfying, an answer worthy of a riddle but not a puzzle, which isn't Heis' way. So I reject that. cn
Click to expand...


I did call this thread 'logic puzzles' for about 10 seconds and changed it, because I realized it involved critical thinking. I apologize if you saw the original title and was lead astray.

I suppose I would have to call it a riddle that stresses critical thinking principals. It is not a logic puzzle, as in your were supplied all the information and need only to reason your way through. You must make assumptions, which is where critical thinking comes in. I was actually going to use this as an example for the Chief, but realized it would be wasted on him. I thought it would be fun for us instead, and we might learn something. Just as when I did the 'name that logical fallacy" thread, it teaches me as much as anyone else.

Fist let me explain how it was done, then I will explain how I think it relates to critical thinking.

I choose only situations where there is a 50/50 outcome. In sports, a team either wins or it doesn't. Stocks either rise or fall. I choose races with no more than 6 contestants and which give prizes for 1st 2nd and 3rd place, so the chance of winning a prize is still 50/50. (unrealistic to find races which award half the contestants perhaps) I wait till the apprentice is down to 2 people, choose elections with only two candidates, ect. Knowing my outcome will be either-or with each prediction, I start out with millions of letters and send half the either and half the or. After the event I predicted, I drop the half that missed from my mailing list, and send the next prediction to only the hits. I do this for 6 months until 1 person remains on the list, and then I hit them with my car.

The first thing I think this suggests is that we should always search for and consider alternate explanations. This seems elementary to most of us, but obviously not to all who participate here. It is in fact a basic principal of critical thinking, not to favor any explanation at the total exclusion of others, or because we lack of a better one. We must always consider that the information we have is limited, and that there could be more to the picture than what has been supplied. This is especially true when we seem to reach a logical impasse or extreme improbability, such as the one I attempted to present here.

This also demonstrates the usefulness of parsimony and Occam's razor. People often confuse Occam's razor as saying the simplest explanation is most likely to be correct. Here, the explanation of psychic seems to be much less complex than the convoluted explanation I have provided. Yet, proper application of the razor favors the convoluted in this case. That is because Occam's Razor is about parsimony, and not simplicity. It's true that each new assumption offers room for error, but what is more important is the size of the assumption. Although my explanation is complicated, it's still working within the known laws of the universe. The psychic route may offer less assumptions, but the ones it does offer are huge paradigm breaking leaps.

So my intention was not to fool or deceive, it was to demonstrate and inform. Perhaps riddles aren't the best vehicle for what I wanted.
 
So my answer was correct, a variation on the stock tip scam. I actually posted that as a clue rather than an answer since I wasn't sure how many people would know what I was talking about. Tyler obviously caught on. My only concern was how was the scammer supposed to hit so many people with their car, especially if they were already convinced and became so paranoid after your 'prediction,' they kept their car in the garage.
 
It would be virtually impossible to predict a a car wreck and front fender damage to a specific area..even if tens of thousands of letters were sent out.
 
Corso312 said:
It would be virtually impossible to predict a a car wreck and front fender damage to a specific area..even if tens of thousands of letters were sent out.
Click to expand...
If I predict you will have a house fire this week, then I come over and start a fire in your garage, my prediction came true.
 
mindphuk said:
So my answer was correct, a variation on the stock tip scam. I actually posted that as a clue rather than an answer since I wasn't sure how many people would know what I was talking about. Tyler obviously caught on. My only concern was how was the scammer supposed to hit so many people with their car, especially if they were already convinced and became so paranoid after your 'prediction,' they kept their car in the garage.
Click to expand...

I suspected maybe you had restrained explaining yourself for the sake of other's fun. This is indeed my attempt to adapt the stock tip scam to demonstrating critical thinking. I also didn't want to make it so similar to the stock tip scam that people could simply look it up.

I suppose we have to confine our first millions of people to only those with cars, but great point that they may be so fooled by the scam as to take measures to protect their car. In fact, if the scam is going as well as intended, they probably should be that convinced. Guess we would have to change it to something more likely to be in our favor. Something that is personal and seems accidental. Something we would seemingly have no control over. Where's a mentalist when you need one. ;)


What do you guys think would be an ironclad clincher for the final prediction? Something that would seem totally random, but leave nothing to chance.
 
Heisenberg said:
I did call this thread 'logic puzzles' for about 10 seconds and changed it, because I realized it involved critical thinking. I apologize if you saw the original title and was lead astray.

I suppose I would have to call it a riddle that stresses critical thinking principals. It is not a logic puzzle, as in your were supplied all the information and need only to reason your way through. You must make assumptions, which is where critical thinking comes in. I was actually going to use this as an example for the Chief, but realized it would be wasted on him. I thought it would be fun for us instead, and we might learn something. Just as when I did the 'name that logical fallacy" thread, it taught me as much as anyone else.

Fist let me explain how it was done, then I will explain how I think it relates to critical thinking.

I choose only situations where there is a 50/50 outcome. In sports, a team either wins or it doesn't. Stocks either rise or fall. I choose races with no more than 6 contestants and which gives prizes for 1st 2nd and 3rd place, so the chance of winning a prize is still 50/50. (unrealistic to find races which award half the contestants perhaps) I wait till the apprentice is down to 2 people, choose elections with only two candidates, ect.
Click to expand...
I must say that that smacks to me of "oh I forgot to mention". I see nothing in the OP that compels a binary outcome. Example: court cases. These are not binary but quaternary: acquit, convict (or hold liable), dismiss, declare mistrial.
But a proper puzzle or riddle won't have such concealed premises. I see sophistry (unfairly declaring things like trophy races even odds. Neither the America's nor the Stanley Cup starts with a pool of two contending teams) in this, and it damages something that could have been fun. I am a rabid solver of puzzles, but generally deeply dislike riddles, because they cheat in just such a manner.

Knowing my outcome will be either-or with each prediction, I start out with millions of letters and send half the either and half the or. After the event I predicted, I drop the half that missed from my mailing list, and send the next prediction to only the hits. I do this for 6 months until 1 person remains on the list, and then I hit them with my car.

The first thing I think this suggests is that we should always search for and consider alternate explanations. This seems elementary to most of us, but obviously not to all who participate here. It is in fact a basic principal of critical thinking, not to favor any explanation at the total exclusion of others, or because we lack of a better one. We must always consider that the information we have is limited, and that there could be more to the picture than what has been supplied. This is especially true when we seem to reach a logical impasse or extreme improbability, such as the one I attempted to present here.

This also demonstrates the usefulness of parsimony and Occam's razor. People often confuse Occam's razor as saying the simplest explanation is most likely to be correct. Here, the explanation of psychic seems to be much less complex than the convoluted explanation I have provided. Yet, proper application of the razor favors the convoluted in this case. That is because Occam's Razor is about parsimony, and not simplicity. It's true that each new assumption offers room for error, but what is more important is the size of the assumption. Although my explanation is complicated, it's still working within the known laws of the universe. The psychic route may offer less assumptions, but the ones it does offer are huge paradigm breaking leaps.
Click to expand...

If we allow for a moment that i haven't shattered the binary-outcome hidden premise, I still can't see the fake psychic paying twenty million in postage (2E25 outcomes means 2E26 minus one letters sent at avg. 28¢ per mailing) for a much smaller prize. Overcritical thinking on my part? cn
 
cannabineer said:
I did notice a sentence in the opener about "the volume being such that it cannot be pure chance". I am unable to derive this as being so from what I understand of the rest of the setup. Volume of what, in any case? Tyler's solution relies on what i consider a cheat: saying that the recipient was not the only one. I can find no indication of other players in the opener. Having to presume them without information supplied would be ... inelegant. cn
Click to expand...

Then call me inelegant, wouldn't be the first time I've heard it ;) I did assume that if I'm getting a letter from someone I don't know with an improbable pitch, I can't be the only one. Where would be the money in that?
 
cannabineer said:
I must say that that smacks to me of "oh I forgot to mention". I see nothing in the OP that compels a binary outcome. Example: court cases. These are not binary but quaternary: acquit, convict (or hold liable), dismiss, declare mistrial.
But a proper puzzle or riddle won't have such concealed premises. I see sophistry (unfairly declaring things like trophy races even odds. Neither the America's nor the Stanley Cup starts with a pool of two contending teams) in this, and it damages something that could have been fun. I am a rabid solver of puzzles, but generally deeply dislike riddles, because they cheat in just such a manner.
Click to expand...

Please note my edit you may have missed.

So my intention was not to fool or deceive, it was to demonstrate and inform. Perhaps riddles aren't the best vehicle for what I wanted.
Click to expand...

I must say that critical thinking is not confined to proper puzzles, and the way I presented it, although perhaps not as articulate as I would have liked, is a realistic representation of how the human mind often presents it. The reason we need critical thinking is that life's situations are often duplicitous and misleading. At the end of six months, your brain is likely to forget details and be overwhelmed by the facade. Critical reflection of each case might reveal a binary pattern, but general recollection simply says, it's a lot of hits. This is the very mechanism of psychic cold readings and easy to exploit, as any magician will confirm. I thought figuring out the 50/50 pattern should be part of the riddle, since disguising the pattern is part of the scam.

If we allow for a moment that i haven't shattered the binary-outcome hidden premise, I still can't see the fake psychic paying twenty million in postage (2E25 outcomes means 2E26 minus one letters sent at avg. 28¢ per mailing) for a much smaller prize. Overcritical thinking on my part? cn
Click to expand...

This is why the scenario was presented hypothetically. I only need to add on that the psychic is an insane billionaire. We don't ask why some people only speak in lies, and others only speak in truth in logic puzzles, it's irrelevant. I suppose I unconsciously geared this toward uncritical thinkers learning yet presented it as if it was for critical thinkers to flex their skills. I would love to include puzzles like that as well.
 
Sorry guys. I have had the sort of day which left me in sort of a mood. I came, found critical thinking puzzle, and practically salivated. I'm always doing found crosswords etc. (as i don't subscribe to the rural rag of a paper). I guess I remain unclear on just what disbelief to suspend in order to make this one sing. In any case, I've been a grouch. I'll stop. cn
 
Heisenberg said:
I suspected maybe you had restrained explaining yourself for the sake of other's fun.
Click to expand...
Yep, since I was the first, I didn't want to be so specific that if you had never heard of the stock tip scam, you wouldn't be able to make the connection to your scenario, but those that are familiar, would probably already have seen the connection.
Where's a mentalist when you need one. ;)
Click to expand...
I'm here, what can I help you with today? Hell, my audiences are impressed with choices that are 50:50. It's all on how you present them.

Take a look at how a master can make even a 50:50 proposition into a miracle.
[video=youtube;ei-Pw5KgE7k]https://www.youtube.com/watch?v=ei-Pw5KgE7k[/video]
 
Heisenberg said:
Very good!! and the car accident? Bonus question, assuming each situation had a 50/50 chance, how many letters did I send out?
Click to expand...

Ha! I thought the car accident was just a final layer, dropping the number of people to which the scam could apply close to single digits...
 
If we accept that the final accident is a unity-chance event, we have 2E25 binaries. So 2E25 letters were sent out as a first cut. Half each successive time, with only one recipient getting the final letter detailing the accident. he also received the final letter at the end of a convergent series, 2E25 plus 2E24 plus ... equals 2E26 minus one. Add the final letter, and I arrive at a (minimum) total of 2E26 letters sent, or 67,108,864. cn
 
cannabineer said:
If we accept that the final accident is a unity-chance event, we have 2E25 binaries. So 2E25 letters were sent out as a first cut. Half each successive time, with only one recipient getting the final letter detailing the accident. he also received the final letter at the end of a convergent series, 2E25 plus 2E24 plus ... equals 2E26 minus one. Add the final letter, and I arrive at a (minimum) total of 2E26 letters sent, or 67,108,864. cn
Click to expand...

Exactly right. If I send out one letter this week, 2 next week, 4 the week after, ect, I am sending 67,108,864 letters on week 26. So I had to start by sending out this many.
 
cannabineer said:
Sorry guys. I have had the sort of day which left me in sort of a mood. I came, found critical thinking puzzle, and practically salivated. I'm always doing found crosswords etc. (as i don't subscribe to the rural rag of a paper). I guess I remain unclear on just what disbelief to suspend in order to make this one sing. In any case, I've been a grouch. I'll stop. cn
Click to expand...

Not a problem at all. If I ever present this to a class or even just friends, I do not want them to feel the same feelings you had. I need to better construct the premise to hint at the 50/50 pattern so people have more of a chance to figure it out, and do not feel at the end they were duped from the start. Yet I still want to keep a representation of the muddled way in which the brain would reflect on the situation, the picture it constructs at the end of the 26 weeks.

I'll work on it.
 
I have been in dire need this last few years. I thew myself into puzzles. Stacking Children's Block by color was was a step up from picking only the dead leaves off a big bush for hours (only the dead ones).

Not kidding. Interferon therapy is mind boggling. TV or any type of entertainment, music, reading, etc, is gone. Cognition slowly and surely slips away, until only a minimal, fragile, confused survival stance is left. What to do?

Think about it....if you could not be interested or engaged with anything. Eat Ganga. It really helps.

IAC, I kept up with more and more complex puzzles, until I could get it together to, at least, hold my bass guitar. Then stand up. Then work on scales again.

Now, after 4 long years, I am still working Defense Grid on Xbox. And I get cognition gain every week. I'd say I'm actually better now, than when this first started close to 20 years ago.

Video Games, help the brain.
 
Doer said:
I have been in dire need this last few years. I thew myself into puzzles. Stacking Children's Block by color was was a step up from picking only the dead leaves off a big bush for hours (only the dead ones).

Not kidding. Interferon therapy is mind boggling. TV or any type of entertainment, music, reading, etc, is gone. Cognition slowly and surely slips away, until only a minimal, fragile, confused survival stance is left. What to do?

Think about it....if you could not be interested or engaged with anything. Eat Ganga. It really helps.

IAC, I kept up with more and more complex puzzles, until I could get it together to, at least, hold my bass guitar. Then stand up. Then work on scales again.

Now, after 4 long years, I am still working Defense Grid on Xbox. And I get cognition gain every week. I'd say I'm actually better now, than when this first started close to 20 years ago.

Video Games, help the brain.
Click to expand...

My anodyne is a book of Sudoku, with a familiar movie playing in the background. cn
 
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