# User:Quietly/mirabile dictu

Mirabile dictu is a Latin phrase meaning "wonderful to tell". This page is a list of sourced facts I find particularly wonderful. (Feel free to tell me or correct any mistakes if I'm wrong about any of this!) Also, feel free to contribute your own interesting facts, just please cite them if possible.

## Mathematics & Computer Science

 The sum of all the positive integers, 1+2+3+4+... to infinity, is equal to -1/12. (See this or this proof.) The P versus NP problem in computer science asks about certain kinds of common problems for which a solution is easily verified whether or not there is also an easy way to find solutions. It is connected to the question of whether or not one-way functions exist, which has important implications for cryptography. It is considered an extremely difficult problem, and most of what we know about it is that most of the methods we use in proofs will not work here. One of the more interesting features of the problem is that if a proof were found that P is equal to NP it would be rather easy to verify it, whereas if they are not equal, the very fact that P is not equal to NP would imply the proof could be extraordinarily difficult to find, so the answer has strong implications to solving the question itself.

## Miscellaneous

I plan on growing this list significantly over time, and increasing the number and veracity of sources (both internal to wikipedia and external links). Feel free to contribute!

## Experiments

 Michelson-Morley experiment for refuting the luminiferous aether. Stern-Gerlach experiment for discovering the quantum nature of atomic nuclei. Fizeau-Foucault apparatus for measuring the speed of light. (In college I reproduced this experiment with my boss and got about 4% error; in class I was supposed to re-demonstrate the experiment but got something like 20% error.) Bell test experiments for demonstrating the violation of local realism in quantum mechanics. Millikan's oil drop experiment which measured the charge of the electron. (In college I reproduced this experiment and got 1.38% error(!), but in class demonstrating the experiment most students didn't seem to grasp what we were doing, and I don't think we got useful results. Students struggled to observe the drops.) Cavendish experiment for measuring the gravitational constant. Rutherford experiment for probing the atom. Lunar Laser Ranging experiment for measuring the distance between the Earth and Moon, and confirming the general theory of relativity. LIGO has now confirmed twice, detection of gravitational waves, in both instances seemingly caused by the merging of distant black holes, approximately 1.3 and 1.4 billion light years distant (and in the past).