Have you anytime sat bottomward with yourself in a quiet abode and anticipation about how best of what we apperceive is fabricated up? We body our aggregate ability aloft huge, baggy abstractions and you accept to alcohol an abominable lot of Koolaid appealing aboriginal in activity to accumulate up.
Take for example, the accepted cardinal line:
It seems like a appealing simple, not nuanced affair until you try to explain it to a kid who’s been larboard out of the bend aback about 4th grade.
“Right so, it’s aloof a representation of all the counting numbers, or absolutely all the numbers from aught to beyond in either direction. We can use it for a lot of things: to represent the advance of data, to actuate the ambit amid two points, and it additionally serves as our x-axis on a alike plane.”
“Let’s think, what are some examples of some capacity we’ve covered this year that accomplish use of the cardinal line?”
***crickets and mumbling***
“Okay, so maybe inequalities? Definitely graphing. But mostly, it’s aloof an abstraction we accept to accumulate in our arch aback we’re ambidextrous with numbers. Like aback you’re abacus 10 and -2, for example, you appetite to anticipate of the about adjustment of those numbers on our cardinal line. -2 and 10 are 8 units afar so aback we add them together, we should get 8. If you anticipate about abacus and adding as ambit and difference, you’ll be beneath acceptable to accomplish baby mistakes aback analytic algebra problems.”
If this is all authoritative faculty to you, again congratulations, you drank the Koolaid aboriginal and didn’t attending back. But try to brainstorm the alertness of audition for the aboriginal time about this conga band of numbers addition on and on into abstract space. And add to that the abstraction that aloof because we say so, one adaptation of beyond should go endlessly up and the added endlessly bottomward with annihilation in the middle. Now anticipate about all the dash we accept to add to attack with these numbers in affiliation to one another. There is an adjustment that we’ve authentic and commutual with accent that cannot be breached. We charge additionally accept that we can zoom in and out at our discretion, that added infinities abide not alone in either direction, but amid every accomplished cardinal as well. And that at some point, numbers become so baby or so ample that we accept to alpha talking about them differently, but you could still leave off one decimal and abort to accelerate a rocket to the moon.
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