7 ms·

I don't think it would be hard to do, in fact, they reverse the whole point of a CAPTCHA. A CAPTCHA is supposed to be a task that is easy for humans, but diffi

by mvalle 16y ago

I don't think it would be hard to do, in fact, they reverse the whole point of a CAPTCHA. A CAPTCHA is supposed to be a task that is easy for humans, but difficult for computers. High-level mathematics is difficult for humans but easy for computers. They do have some success of telling computers and humans apart, though.

mrspeaker 16y ago
Precisely the reason I wrote the very useful "human.txt" captcha: http://www.mrspeaker.net/2010/07/15/humans-txt/ http://www.mrspeaker.net/2010/07/15/humans-txt/ Stops those pesky humans wasting precious robot bandwidth and is quite a bit harder than the Quantum Random Bit Generator captcha ;)
- deleted 16y ago
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iy56 16y ago
High-level mathematics is difficult for humans and provably impossible for computers.
- timtadh 16y ago
  Correct. For those that don't agree see the Incompleteness Theorem. It was once thought (by Hilbert no less) that computers would one day be able to derive all mathematical truths for us. Alas, G\:{o}del came along and ruined all of those grand plans by proving such an endeavor was in possible. He also showed the limits of human reason. Computers may or may not be "dumber" than humans, but we know that they can't be "smarter."
- ekidd 16y ago
  What kind of high-level mathematics is provably impossible for computers, but merely difficult for suitably-trained humans? If you're thinking of either of Gödel's incompleteness theorems, you may be slightly mistaken about what they say. In general, a human operating by rigorous standards of proof is no more able to prove the completeness and consistency of certain formal systems—using the tools provided by those formal systems—than a machine can. If, as a human, you somehow prove the consistency of these particular formal systems, you run smack into Gödel's second theorem: For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent. Thus, any proof of consistency is self-defeating, whether it's made by neurons or silicon. Really, math doesn't care what parts of the periodic table you use to prove things. :-)
jonnathanson 16y ago
If the math problem were squiggly and hand-drawn (i.e., as if on a chalkboard), we might have a more effective CAPTCHA.

by mvalle 16y ago

mrspeaker 16y ago

Precisely the reason I wrote the very useful "human.txt" captcha: http://www.mrspeaker.net/2010/07/15/humans-txt/ http://www.mrspeaker.net/2010/07/15/humans-txt/ Stops those pesky humans wasting precious robot bandwidth and is quite a bit harder than the Quantum Random Bit Generator captcha ;)

deleted 16y ago
[deleted]

iy56 16y ago

High-level mathematics is difficult for humans and provably impossible for computers.

timtadh 16y ago
Correct. For those that don't agree see the Incompleteness Theorem. It was once thought (by Hilbert no less) that computers would one day be able to derive all mathematical truths for us. Alas, G\:{o}del came along and ruined all of those grand plans by proving such an endeavor was in possible. He also showed the limits of human reason. Computers may or may not be "dumber" than humans, but we know that they can't be "smarter."
ekidd 16y ago
What kind of high-level mathematics is provably impossible for computers, but merely difficult for suitably-trained humans? If you're thinking of either of Gödel's incompleteness theorems, you may be slightly mistaken about what they say. In general, a human operating by rigorous standards of proof is no more able to prove the completeness and consistency of certain formal systems—using the tools provided by those formal systems—than a machine can. If, as a human, you somehow prove the consistency of these particular formal systems, you run smack into Gödel's second theorem: For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent. Thus, any proof of consistency is self-defeating, whether it's made by neurons or silicon. Really, math doesn't care what parts of the periodic table you use to prove things. :-)

jonnathanson 16y ago

If the math problem were squiggly and hand-drawn (i.e., as if on a chalkboard), we might have a more effective CAPTCHA.