Ideas
From Huben's Wiki
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These ideas are free to anybody who wants to use them. I don't need credit, but it would be nice. | These ideas are free to anybody who wants to use them. I don't need credit, but it would be nice. | ||
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| + | == The nature of individual knowledge. == | ||
| + | My Raft Metaphor. I came up with this independently, and recently have seen something similar. | ||
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| + | All human knowledge resides in individuals: the creators and interpreters of that knowledge. When we begin development of knowledge (well before birth), it is as if we are floating in a sea, studded with possible information, mostly floating trash. We start assembling this information much as we might assemble a raft from floating bits. The raft represents our knowledge. At first, we have very little choice in what we incorporate: our growing brains, the womb, and our parents dominate our incoming information. perception, language, various innate skills both physical and intellectual. We start being selective about what we incorporate into our raft, and also reorganize the parts of the raft: discarding some, shifting others. Presumably the graft grows larger, more complex, more integrated and possibly more stable and useful as a platform from which the activities of life are pursued. '''But there is no foundation or mooring for the raft or for knowledge. No islands of a priori knowledge.''' We can interconnect our rafts with our language skills, showing each other how to improve our rafts; starting with the development of language skill, observation of parents, social development, education, etc. As we form social alliances, we can revise and reconnect our rafts to reflect changes in our knowledge, including beliefs. Natural selection operates upon the rafts, selecting for the most robust and practical. As with life, we should expect a diversity of species of rafts, each specialized in niches. '''There is no one "true" knowledge.''' | ||
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| + | == Emergent Phenomena == | ||
| + | Emergent phenomena are simply phenomena whose prediction based on microfoundations is too complex to compute efficiently with the human mind. The behavior of the R pentomino in the game of life is characterized as emergent, but it is trivial to write a computer program to predict that behavior. Emergent properties are still theoretically predictable from the underlying parts: it just might be very difficult or impractical. Hence we make approximate "laws" describing them more tersely and computably. Ideas like temperature and pressure in physics, even though they really only boil down to energy of large numbers of particles. Thus reductionism is always justified in theory, but in practice it will not always work (greedy reductionism: see Dennett.) | ||
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| + | == There is no truth in mathematics. == | ||
| + | Of course it depends on your definition of truth. You could define truth (as in a proof) as having followed rules and axioms, but the axioms are only assumptions, not truths upon which you can found other truths. Nor does math correspond to the real world: that is the tail wagging the dog. Instead, sometimes the real world can be well modeled with math. For example, if I have a math where 1+1=1, the real world provides examples such as the coalescence of a water drop with another water drop into one water drop where this math might be applicable. A totally random sort of math (that may include 1+1=1) has the same sort of truth (probably none) as our favorite math. The difference is our perception of beauty in the math, which will include elements of simplicity and applicability to modeling the real world. | ||
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| + | == Why are humans so surprisingly good at math, given that there was no evolutionary selection for it? == | ||
| + | Our math ability evolved without the tools of writing, just like our physical ability evolved without modern tools. We don't marvel that we can move mountains with modern tools assisting us, but we do marvel that we can compute with the help of writing? | ||
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| + | == Science is not about truth: it is about honesty. == | ||
| + | Science is not about truth, the way philosophy and religion often claim to be. Instead it is about honesty: the humble claim that the evidence and reasoning can be confirmed by anyone through observation and experiment and supports a preferred model better than the other models. That's why scientific notation has basic ideas such as significant figures, and statistics has confidence intervals. Opponents of science often accuse scientists of pride, but it is actually about being humble enough to not lie. (Beware of different meanings of truth here.) | ||
== Homicide through the market. == | == Homicide through the market. == | ||
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* Ability to present both formula and results of a cell simultaneously (a feature missing in most spreadsheets.) | * Ability to present both formula and results of a cell simultaneously (a feature missing in most spreadsheets.) | ||
* Ability to graphically organize calculations outside of the constraints of rectangular arrays of cells. | * Ability to graphically organize calculations outside of the constraints of rectangular arrays of cells. | ||
| + | * Create groups of cells (maybe ranges) that all use the same calculation and/or formats, without copying the formula for the calculation or formats to each cell. | ||
* Ability to extend the list of functions beyond those of a spreadsheet. | * Ability to extend the list of functions beyond those of a spreadsheet. | ||
* Ability to preserve the view of the results of calculations or graphing for checking by teachers. | * Ability to preserve the view of the results of calculations or graphing for checking by teachers. | ||
