Other
Under construction - (A selection of random interesting things)
Interesting books
- "Information is beautiful" by McCandless
Interesting charts
- FB relationships and betweenness-centrality fb2.pdf
Interesting software
- vowpal wabbit (online machine learning)
- cplex - gurobi - ortools (combinatorial optimization)
- porta (integer polytope analysis)
- tesseract (an old-fashioned low level ocr)
- postscript (the postfix-notation programming language)
Interesting paradoxes
Some of my favourite "mathematical" paradoxes
- Counter-intuitive, but nonetheless true
- Braess : How adding an additional road (at a badly selected place) increases capacity, but can make traffic worse (non optimal Nash equilibrium).
- Newcomb : Intuitively correct versus obviously correct: when a problem is (deliberately) ambiguously underspecified.
- Simpson : Treatment A is better than B for group 1, and also separately for group 2, but the opposite is true for groups 1 and 2 combined. Can made to happen easily by adding imbalance between the two groups for each treatment.
- Harmonic mean : People use the average (a+b)/2 for situations where the correct way is to use the harmonic mean (the average of 1/a and 1/b, inverted). The harmonic is the correct way to average km/hour, miles per hour, dollars per kilo, miles per litre (gallon) etc, because in reality, one ought to be averaging (with the arithmetic mean) the hours/km, hours per mile, kilos per dollar, and litres or gallons per mile.
- Benford : the first non-zero digit of physics constants in any units, or numbers generated among [1,..,N] where N varies, has a 30% chance of being 1, 17% chance of being 2, etc, and only 4% chance of being 9.
- Friendship : On average, a person's friends will have more friends than the person.
- Spurious calculations - limitations of floating number precision : Eg prove that sum_n=0^infinity (floor((e^pi - pi)n) / 3^n ) does not equal 14.50000. NB the fist non-zero decimal digit after 14.5 is at the ~531th decimal digit.
- Hidden mistake paradoxes
- Various division by zero paradoxes (0=1 paradoxes)
- All horses are the same colour paradox (mistake in the induction)
- Logical or semantic paradoxes
- Russel paradox (set of all sets etc)
- Hilbert hotel paradox (double of infinity is infinity)
- Monty Hall paradox (both answers are correct, depending on assumptions)