Posts by ivan_llaisdy 2 publicly visible posts • joined 14 Feb 2014
"There's nothing preventing someone writing a markov model algorithm that takes account of more than one hop" People do do this, but such a model is no longer a Markov model. It wouldn't be a model of a Markov process. In a Markov process, future states of the process depend only on the current state.
Models that take account of more than one hop would be more general graphical models like Bayesian networks, or neural networks.
Here are some ideas toward my fantasy curriculum, for late juniors (i.e., age 8ish to 11ish).
I think intelligence (as in "what IQ tests measure") can be thought of as "pattern recognition" --- an always-on facility or habit of noticing patterns. The main force of an early curriculum should be to promote this habit by looking at and learning about patterns of different types. So, the central subjects will be maths, music and language.
Maths: If the early juniors can establish basic numeracy (and literacy), then yes I think 7 or 8 is a good time for simple set theory. This will open up topics like functions as mappings between sets, type theory, and propositional logic (which is just set theory really). There is a lot of scope for fun lessons through quite challenging terrain.
(as far as computer programming goes, 11 or 12 year olds with this background could be happily getting into scheme or haskell, and if senior schools are to teach programming generally, scheme is by far the best choice of language).
Music: playing: explorations in tonality; listening: Haydn.
Language: learning a foreign language is an exposure to another type of pattern. I don't think it matters much which language(s). French seems to be traditional in Britain, mostly I think because of the weather and the food (and wine) (oh and the culture of course); the language itself is probably quite difficult for first language English speakers (weird sounds and spelling, hideously complicated tense system, ...).
In maths and music, and in English lessons, the children will also be learning rhetoric. Aristotle called rhetoric the art of making oneself understood. I think of rhetoric as mapping a logical structure onto spacetime: setting out a maths problem on a page; playing out a scale as a melody. This laying things out is another kind of pattern.
Apart from music, this is pretty much the traditional trivium. The next most central layer would be sport (fitness, teams, athletics) and art/craft (splashing paint around, making things). Finally, "science" (lots of experiments, finding out what happens, explaining) and "humanities" (history, geography, general knowledge).
Thanks
Ivan
p.s. I like that Maths is fun site too!
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