I stand with my feet planted securely on the shoulders of giants, and my head in the clouds.

Francis Heylinghen
Douglas Hofstadter
Sydney Lamb
Mariusz Nowostawski
Heinz Pagels
Cosma Shalizi
Herbert A. Simon
Richard Dawkins


"... there is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things. Because the innovator has for enemies all those who have done well under the old conditions, and lukewarm defenders in those who may do well under the new." Machiavelli (1515) The Prince

"God grant me the serenity to accept the things I cannot change, courage to change the things I can, and the wisdom to know the difference." Alcoholics Anonymous version of The Serenity Prayer by Reinhold Niebuhr (c. 1940)


  • that a Turing machine must halt but that life must not.
  • that dictionaries define words in terms of other words, and not axioms.
  • that Gödel's incompleteness result closed the door on Hilbert's program but did not open another.
  • that a cartoonist can capture a person, and their mood with just a few lines.
  • that music can do all that it does.
  • the musical and mathematical prodegies are so starkly different to the rest of us.


  • "Despite considerable and continuing efforts, no clear and compelling role for sleep has been identified." Eichenbaum in Sleep and Brain Plasticity pg v.
  • We don't have a definition of the word 'game', and we don't need one, because even without the definition, we use the word successfully. Wittgenstein in Philosophical Investigations.
  • "The practical value of mathematics over common sense is that: 1) mathematical arguments remain sound even if they are long and complex, 2) axioms stake out an area within which patterns of reasoning have a reproducible, objective character, and 3) mathematics allows an immense variety of intellectual structures to be elaborated." Schwartz in Mathematics Today
  • Cellular Automata rule 30 is of special interest because it is chaotic. Wolfram in "A New Kind of Science" pg 871.
  • “Measurement of spoken languages show a different result. Although the loudness fluctuations retain a 1/f-spectrum, pitch fluctuations for spoken English show a Lorentzian behavior with white or independent variations for time scales longer than the spoken phenome. Oriental languages, on the other hand, show an increase in spectral density of pitch fluctuations at low frequencies corresponding to increased correlation (but less than 1/f). The 1/f-spectral density seems to occur for measured quantities that are more closely related to “meaning” (musical melodies, spoken loudness)." The Science of Fractal Images pg 41.
  • "How can I tell what I think till I see what I say?" E.M.Foster Aspects of the Novel