Maximally Powerful, Minimally Useful
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Maximally Powerful, Minimally Useful
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Re: Maximally Powerful, Minimally Useful
#2While there is some truth to the author's point, and we can see the effect in in a lot in practice, he makes the mistake of confusing "useful" with "analyzable in FP terms".
This exact point (comprehensibility vs. power) is why Smalltalk is so amazing: it adds a lot of power while at the same time being more comprehensible, not less. That's no small feat, and IMHO one that is both under-appreciated and under-analyzed.
EDIT: Of course, see "The Power of Simplicity" http://www.selflanguage.org/_static/published/self-power.pdf
Re: Maximally Powerful, Minimally Useful
#3[deleted]
Re: Maximally Powerful, Minimally Useful
#4That link http://www.logicmatters.net/resources/pdfs/Galois.pdf (syntax - semantics as Galois Connections) in the comments seems pretty interesting.
Re: Maximally Powerful, Minimally Useful
#5I like what the author is suggesting. It's thought-provoking and is consistent with many experiences I've had in life.
An interesting analog in the arts is the notion that a chosen or imposed constraint can provoke creativity and open up new possibilities.
Re: Maximally Powerful, Minimally Useful
#6A familiar example is “goto” versus structured programming. “goto” is supremely expressive—conditional jumps are sufficient to express all of the usual structured programming constructs. But sacrificing “goto” enables much more powerful reasoning about programs because it restricts the shape of the control flow graph to common patterns: “while”, “do…while”, “for”.
One of the core features of functional programming is “recursion schemes”, that is, generalising patterns of data flow. While “goto” lets you manipulate control flow arbitrarily, it turns out that you don’t usually want arbitrary control flow—and the same is true for data, so rather than “for” loops, it’s often easier to think in terms of the common patterns: “map”, “reduce”, “filter”.
Re: Maximally Powerful, Minimally Useful
#7I like what the author is suggesting. It's thought-provoking and is consistent with many experiences I've had in life. An interesting analog in the arts is the notion that a chosen or imposed constraint can provoke creativity and open up new possibilities.
I’ve certainly been more impressed by creative expression in restricted media, and I’m not sure that’s only due to the restrictions—it seems people actually perform better when trying to circumvent limitations. Examples that come to mind include pixel art, sonnets, pointillism, and origami.
Re: Maximally Powerful, Minimally Useful
#8Seems related to the Rule of Least Power: http://en.wikipedia.org/wiki/Rule_of_least_power , http://c2.com/cgi/wiki?PrincipleOfLeastPower
Re: Maximally Powerful, Minimally Useful
#9This is really natural in mathematics and logic—it's the tension between consistency and completeness.
Essentially, you have a tension between laws a models. A larger number of laws means more reasoning power at the expense of fewer models (possibly 0 in which case you're inconsistent). A larger number of models means greater realizability but fewer laws (possibly 0 in which case you've gained nothing through this exercise).
It's always a game of comparative linguistics—does this abstraction pay its way? Well, without it we have this set of laws and with it we gain this new set. Are things in balance such that the abstraction is realizable and the laws are meaningful? That's your tradeoff.
Re: Maximally Powerful, Minimally Useful
#10Using this definitions, I think we can define technological progress as the discovery of new concept that are:
- More powerful than previous concepts but with the same useful properties.
- Or as powerful as the previous concepts but with more useful properties.