Stephen Downes

Knowledge, Learning, Community

Nothing could be more basic than language and math, right? And these are built on solid foundations that form the basis for literacy and numeracy, right? Well - no. Today I have two cases in point. The lead item points to "three different foundational ideas can be identified in recent syntactic theory: structure from substitution classes, structure from dependencies among heads, and structure as the result of optimizing preferences" (my italics). In another post, Daniel Lemire notes that in most programming languages, 0.2+0.1 does not equal 0.3. Why? "The computer does not represent 0.1 or 0.2 exactly. Instead, it tries to find the closest possible value. For the number 0.1, the best match is 7205759403792794 times 2-56." Wait - what? Lemire explains that a computer could perform the operation the way humans do, but it's a lot slower. Now, note: none of this shows that math and grammar are wrong per se, only that they are much more complex phenomena than are generally supposed, and that there is more than one way of looking at them, and the way we actually do look at them might not be the best or most efficient.

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Stephen Downes Stephen Downes, Casselman, Canada
stephen@downes.ca

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Last Updated: Oct 21, 2020 11:18 p.m.