I've heard of intelligence failures to explain the Iraq war, now this author says it was confirmation bias which caused a completely erroneous justification for the invasion of Iraq. I think the author has confirmation bias in too easily using the term to explain government and corporate policy choices which have been based on false justifications.
A Quick Puzzle to Test Your Problem Solving
191–200 of 311 posts
Re: A Quick Puzzle to Test Your Problem Solving
#192My mathematical logic is rusty, but if I recall correctly, Gödel's incompleteness theorem basically states that it is impossible to solve this kind of question. No matter how many tests you run, there will always be an uncertainty. An incredibly stupid example is that the rule could be "yes for strictly increasing, OR if one of the numbers is -18273192783127897981." You'll never know. I understand this is contrived,…
Remotely related: I've been interested for awhile in how the same initial terms of a sequence could possibly be generated by multiple rules.
For example, you might have
2,3...
And the rest of the sequence might look like either
2,3,4,5,6...
or
2,3,5,8,13...
or
2,3,5,7,11...
or even
2,3,5,10,20...
Clearly, on some level those sequences are all much less complicated than one defined as "The first term is 2, the second term is 3, the third term is 919243, the fourth term is -1234..."
It's unclear to me how one might rank them in complexity, though. The maximum amount of memory necessary to get an arbitrary nth term? The number of operations necessary to get to the next term?
Another interesting question to me: if there is an ordering of ways to generate a sequence of numbers, given the first couple terms of a sequence of numbers, what are the simplest N ways to generate the full sequence?
Re: A Quick Puzzle to Test Your Problem Solving
#193I guess I'm the opposite: I got more No's than Yes's. My immediate sense was to find No's. I guess that's why I like 1 star reviews.
Re: A Quick Puzzle to Test Your Problem Solving
#194Typical NYT psycho-babble: I got the right answer but with several Yes answers and also several No answers and without their confirmation bias and other nonsense. And, I do know about "problem solving", thank you, with some of my solutions responsible for my peer-reviewed published papers and Ph.D. in some STEM work at a world class research university. Sorry, NYT: I don't regard your organization as able to "test" "…
Have you considered that you missed the point entirely? It's hard to see how you consider this an insult and not an interesting "live" experimental result. "Test your problem solving skills" is merely the experimental set-up and the purpose isn't to actually measure problem solving skill, but rather to demonstrate confirmation bias on a population. Your alligator tears and perceived insult add nothing to the conversa…
There's no question that
what the NYT wrote is, to
put is mildly, junk.
I believe that they should be called out on such junk.
Maybe you agree that they should be called out, and maybe not. Maybe you like that I called them out, and maybe not.
Still, what they wrote was junk.
Maybe you should take what I wrote as a call for the NYT to up their game by several notches. You've just got to agree that the NYT has room enough for improvement to stack all the US national debt in one column of pennies.
Re: A Quick Puzzle to Test Your Problem Solving
#195Veritasium, a pretty interesting youtube channel, posted a video on this experiment a while back. I found the discussion afterwards to be more thought-provoking than this article.
Re: A Quick Puzzle to Test Your Problem Solving
#196Earlier quoted context omitted.
Did you try floating point numbers? I didn't see anything in the text that said integers only.
I tried floating point numbers. Also, at 28 decimal places, the test breaks; it's not arbitrary precision. So, technically, the answer isn't simply "any ascending sequence of numbers".
I actually avoided going that far to avoid getting bad data. I was trying to answer the question, "What does the experimenter THINK his rule is?" rather than what will the computer do. Since the computer can't be infinite, it will inevitably fail with overflow, underflow, and such.
I was relieved, in fact, when it worked with negatives and floats in a "safe" range.
I also tested with 1,1,2 and 1,2,2 to make sure that the required increase applied to ALL of the values, not just a specific pair.
Re: A Quick Puzzle to Test Your Problem Solving
#197My mathematical logic is rusty, but if I recall correctly, Gödel's incompleteness theorem basically states that it is impossible to solve this kind of question. No matter how many tests you run, there will always be an uncertainty. An incredibly stupid example is that the rule could be "yes for strictly increasing, OR if one of the numbers is -18273192783127897981." You'll never know. I understand this is contrived,…
Remotely related: I've been interested for awhile in how the same initial terms of a sequence could possibly be generated by multiple rules. For example, you might have 2,3... And the rest of the sequence might look like either 2,3,4,5,6... or 2,3,5,8,13... or 2,3,5,7,11... or even 2,3,5,10,20... Clearly, on some level those sequences are all much less complicated than one defined as "The first term is 2, the second…
Take a look at Kolmogorov complexity. It's uncomputable.
Re: A Quick Puzzle to Test Your Problem Solving
#198My mathematical logic is rusty, but if I recall correctly, Gödel's incompleteness theorem basically states that it is impossible to solve this kind of question. No matter how many tests you run, there will always be an uncertainty. An incredibly stupid example is that the rule could be "yes for strictly increasing, OR if one of the numbers is -18273192783127897981." You'll never know. I understand this is contrived,…
Remotely related: I've been interested for awhile in how the same initial terms of a sequence could possibly be generated by multiple rules. For example, you might have 2,3... And the rest of the sequence might look like either 2,3,4,5,6... or 2,3,5,8,13... or 2,3,5,7,11... or even 2,3,5,10,20... Clearly, on some level those sequences are all much less complicated than one defined as "The first term is 2, the second…
I think you might enjoy the book Fluid Concepts and Creative Analogies, by Douglas Hofstadter [1]. The first chapter is on (what Hofstadter argues is) the fundamental nature of recognizing patterns in number sequences.
[1] http://www.amazon.com/Fluid-Concepts-And-Creative-Analogies/...
Re: A Quick Puzzle to Test Your Problem Solving
#199Math person here. I'm curious to know if anyone used decimal numbers in their tests and if negative numbers were used. The rule is increasing real numbers and one can guess that the rule is increasing numbers without realizing this includes all real numbers and not just integers. In addition to getting it right did you use an exhaustive set of tests?
Yes and yes. It wouldn't activate the "check" button with complex numbers.
There isn't a way to check order for complex numbers in any reasonable way.
Re: A Quick Puzzle to Test Your Problem Solving
#200Math person here. I'm curious to know if anyone used decimal numbers in their tests and if negative numbers were used. The rule is increasing real numbers and one can guess that the rule is increasing numbers without realizing this includes all real numbers and not just integers. In addition to getting it right did you use an exhaustive set of tests?
I wonder if somebody tested the rule to be deterministic by entering same number over and over. But I think the rule a<b<c is too simple to invite to use creative tests.