hehe. Is there an echo in here? Not going to deal with shadow, but this caught my eye?
Youshutup the Vile wrote:
Yeah, I'm sure that'll work out great ten years down the line when you get a bunch of engineers whose bridge was built to "almost" exact specifications, or a nuclear technician who was "reasonably" sure the rays wouldn't make it through that lead wall.
Actually, in practice, the exact opposite happens more often then not.
The problem is that when you do "exact" math, it's extremely hard to tell if you got the answer right. This becomes doubly problematic when dealing with complex engineering problems. A dropped decimal point or trasposed number sequence is a far more likely error. And if you don't have a tool for checking if your answer is "about right", then you wont catch it.
Without estimating of answers as an error correction device, there'd be no way to catch those kinds of mistakes. The result? Bridges that fall down because one guy goofed when doing some math. Reactor shielding that doesn't block all the radiation because one guy goofed on the math. And both not caught because no one eyeballed the thing and said: "Hey! That doesn't look quite right. Are you sure that's thick enough?...".
And that's without getting into things like calculus and such. If we did nothing but "exact math", the space program would *never* get off the ground. Even ignoring things like how much fuel to put in a rocket, how do you think space vehicles are guided? Do you honestly think that we calculate their exact position for every second of the entire trip? We don't. We calculate ranges of possible positions based on likely ranges of error in thrust vectors from a given burn at a given angle. Those are stored in tables. The computer then constantly alternates between high and low values to "guesstimate" the middle range. As they move from one point to another, they shift from table to table, adjusting their calculations as they go. The computer does not have to know exactly how fast it's going, or exactly what direction. It only needs to know that as long as it's speed is between a particular pair of values and it's direction is between another set of values, it can compute what alterations it needs to make to arrive at the target destination. Trying to do it "perfectly" would be impossibly complex (and impossible to do in real time). Estimating allows for the trip to work.
Heck. How do you think people navigated back in the day of sailing ships? They didn't know where they were at every moment of every day. They took readings at set periods of time and based on the readings, made course corrections. Amazingly, despite not knowing exactly where they were at any given moment, they could navigate across an ocean the size of the Pacific and reliably arrive on a tiny island. How'd they do it? Estimation. They knew *about* how fast they were going, and *about* what direction. And a series of such measurements could allow them to follow a path to where they needed to go.
Trying to argue that estimation is a bad thing to teach to kids is really ridiculous. It's one of the most important math skills you can have. It's how you know what you're doing is right. Following rote formulas is great, but if you don't know what the answer means or why it's right or wrong, you haven't really learned anything.