We wish to sensitize the student to the obvious-but-hard-to-see truth that both language and arithmetic have slippery natures built into them and seeing this clearly is a part of deeper education, our mission here.
Take four simple statements and see that they’re entwined and “confusing.”
- You can count (i.e., numeracy).
- You can count (depend) on me.
- You don’t count (i.e., importance).
- Count (include) me in.
When a person says, “you can count on me” do they mean that you will be standing on me and then go, “one apple, two apples, three apples” (i.e., count in the everyday sense). No, obviously not. “On” in this context is not physical or locational, but figurative. Ask yourself: how is it that you know the difference and nuances of all these meanings given that the word count and the preposition “on” seem straightforward but are really “polyvalent.”
When Gadamer (Heidegger’s student) tells us that “man is a linguistic creature” he means, among other things, that man “swims” in this ambiguity ocean every moment and puns and jokes aside, handles these ambiguities automatically, somehow. How does a child acquiring language get the sense of all this? It’s difficult to understand and explain. Language is both our nature and somehow beyond our grasp.
The same slipperiness, in a different way, holds for arithmetic and numbers. You can immediately see that the square root of 16 is 4 (plus or minus) but if you are asked, “what is the square root of seventeen?” you’d be “at sea” without a calculator. If you’re now asked, what is the square root of -17 (negative seventeen), you would probably be lost.
These would seem to be very basic “operations” and yet are baffling in their way and parallel the “sudden difficulties” in language use and orientation and clarity.
Deep and “meta-intelligent” education, which we promote here, begins by seeing, among other things, that both our ability to function while “swimming” among words and numbers is puzzling if you look at them “freshly.”
When one glimpses the truth that we are surrounded by obvious things that are never really obvious, one pauses and thinks. This is where (self) “re-education” begins, especially if “enchantment” (genuine magical fascination) accompanies the thinking.