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Since numbers are infinite and the ways we can manipulate them are infinite (or at least large) doesn't it mean that unlikely or strange things happen all the t

Since numbers are infinite and the ways we can manipulate them are infinite (or at least large) doesn't it mean that unlikely or strange things happen all the time? I would be more surprised if they wouldn't happen.

Totient 12y ago
Speaking analogously, "If we gave everyone one in the world a device that randomly shot paint at the wall, I would be more surprised if no one ended up with an interesting pattern." I agree, but whatever that pattern (or patterns) turned out to be is still an interesting question.
jks 12y ago
Yes. This is sometimes called The Strong Law of Small Numbers, see e.g. http://mathworld.wolfram.com/StrongLawofSmallNumbers.html http://mathworld.wolfram.com/StrongLawofSmallNumbers.html and https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Guy697-712.pdf https://www.maa.org/sites/default/files/pdf/upload_library/2...
tel 12y ago
It means that it would be weird for there to not be interesting patterns all over the place, as you suggest. This is, however, subtly different from there being such patterns. In particular, the first one is stated independent from the effort it would require to find them, while the latter includes it. In other words, maybe the right want to understand this is via intuitionistic logic where not (not A) is not convertible to A. So, it's certainly not the case that there are no interesting patterns... but you must show me one before I believe that they actually do exist.
draugadrotten 12y ago
> Since numbers are infinite and the ways we can manipulate them are infinite (or at least large) doesn't it mean that unlikely or strange things happen all the time? They do. If you haven't seen it already I can recommend a movie about this topic. It can be enojyed for other reasons as well. Pi: "A paranoid mathematician searches for a key number that will unlock the universal patterns found in nature." http://www.imdb.com/title/tt0138704/ http://www.imdb.com/title/tt0138704/
- ivan_ah 12y ago
  +1 for the movie Pi recommendation---it's proper good stuff.
- lutusp 12y ago
  I like the movie, it deserves its fame, but there are some errors in the script that could have been easily avoided. For example, at one point a character says something to the effect of, "Surely they've printed out every 216-digit number?" No, not likely. :)

Totient 12y ago

Speaking analogously, "If we gave everyone one in the world a device that randomly shot paint at the wall, I would be more surprised if no one ended up with an interesting pattern." I agree, but whatever that pattern (or patterns) turned out to be is still an interesting question.

jks 12y ago

Yes. This is sometimes called The Strong Law of Small Numbers, see e.g. http://mathworld.wolfram.com/StrongLawofSmallNumbers.html http://mathworld.wolfram.com/StrongLawofSmallNumbers.html and https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Guy697-712.pdf https://www.maa.org/sites/default/files/pdf/upload_library/2...

tel 12y ago

It means that it would be weird for there to not be interesting patterns all over the place, as you suggest. This is, however, subtly different from there being such patterns. In particular, the first one is stated independent from the effort it would require to find them, while the latter includes it. In other words, maybe the right want to understand this is via intuitionistic logic where not (not A) is not convertible to A. So, it's certainly not the case that there are no interesting patterns... but you must show me one before I believe that they actually do exist.

draugadrotten 12y ago

> Since numbers are infinite and the ways we can manipulate them are infinite (or at least large) doesn't it mean that unlikely or strange things happen all the time? They do. If you haven't seen it already I can recommend a movie about this topic. It can be enojyed for other reasons as well. Pi: "A paranoid mathematician searches for a key number that will unlock the universal patterns found in nature." http://www.imdb.com/title/tt0138704/ http://www.imdb.com/title/tt0138704/

ivan_ah 12y ago
+1 for the movie Pi recommendation---it's proper good stuff.
lutusp 12y ago
I like the movie, it deserves its fame, but there are some errors in the script that could have been easily avoided. For example, at one point a character says something to the effect of, "Surely they've printed out every 216-digit number?" No, not likely. :)