Food for Thought

Curious

• 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.

Observations

These are some observations made by others that I find particularly interesting.

• "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

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