Obsolete Skills

[jackflashdrive]

Great OP, and some great responses so far. I'll note with glee that a sense of direction is quickly becoming an obsolete skill. This is great for me because I have the worst sense of direction of anyone I've ever met. This also illustrates the relation between evolution and environment. Ten-thousand years ago I would have wondered off with no hope of returning home the first time my mother took her eyes off of me (I have plenty of modern-day stories to this effect from when I was a kid). Now having a sense of direction just doesn't matter. In fact, I read an article a few weeks ago about someone developing a GPS belt you wear on your waist that vibrates at true north (e.g., a small vibration just above your right hip indicates that true north is in this direction), or that can vibrate in the direction of a preloaded waypoint. I need me one of them belts.

Edit: Jesus, do you realize how much money you could make selling these belts to Muslims with the waypoint for mecca preloaded? "When you are praying to Mecca X times per day, show the prophet your devotion and accept no substitutes."

[Borodog]

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By the way, if anyone doesn't know the simple techniques for taking square roots and logarithms in your head, I can explain it if you're interested.

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That'd be cool.

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Taking really quite accurate square roots in your head is pretty easy. You have to know the perfect squars, but most people know those (I hope). Say you want the square root of 70. Obviously 8.x (greater than 8, less than 9). Take the difference between the number you want the square root of (70), subtract the next lowest perfect square (64), and divide by 2 times the whole number part of the square root (8). So the square root of 70 is 8+(70-64)/(2*8) = 8 6/16, or 8 3/8, which is accurate to one tenth of one percent. It also works the same for the next highest square, too, if that is closer. So the square root of 78 would be 9 - (81-78)/(2*9) = 9 - 3/18 = 9 - 1/6 = 8 5/6. Accurate to about 2 one-hundredths of one percent.

Any time you want to take a square root of a larger or smaller number, just extract an even numbered power of 10 and repeat. So the squart root of 4200 is the square root of 42 times ten, or about 65. Accurate to three tenths of one percent.

Base ten Logarithms require a small amount of memorization, but the pattern is not hard:
log(2) = 0.3
log(3) = 0.5
log(4) = 0.6
log(5) = 0.7
log(6) = 0.8
log(7) = 0.85
log(8) = 0.9
log(9) = 0.95

Since log(ab) = log(a) + log(b), you can take any large number, like 3x10^8, and its logarithm is easily calculable: log(3x10^8) = log(3)+log(10^8) = 8.5 (recall that log(10^n) = n). Accurate to three tenths of one percent.

If you need to take logarithms of numbers where the lead number is 1 (where the log function rises most steeply), you can do it like this. Say you need the log(120). log(120) = log(3*4*10) = 2.1 (to about 1%). This works for other numbers if you need more accuracy. Like log(35). Instead of turning that into log(3x10^1) or log(4x10^1), just make it log(5*7) = 0.7+0.85 = 1.55 (to about 0.4%)

You can also take sines, cosines and tangents pretty easily and accurately in your head, or use the binomial expansion to raise numbers near one to high powers easily. All sorts of mathematical tricks that are lost on most kids these days.

[JaBlue]

more math tricks boro! I knew the square root one but not logs. How about quick sinusoidals?

When I took calculus, calculators were never allowed and I didn't even own one all year. My edge on my peers went up for sure. Yes, that is sad.

[TiK]

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using an abacus


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As obsolete as the abacus has become, those who are skilled at it use the skill on a daily basis. (When you get to be skilled with the abacus, you start being able to do all the calculations in your head by picturing an abacus) While probably more of a parlor-trick nowadays, I still use it to calculate pot odds, tax, tip, and other random calculations throughout the day. In my prime, I could probably do calculations of 5-7 digit numbers in my head, but these days, I can barely do 3 digits. I know people who used to be able to calculate columns of 7-10 digit numbers in their heads; it was pretty sick. Granted, this skill (calculating columns of 7-10 digt numbers) doesn't have too many applications in daily life, but it's still useful on occasion.

[gusmahler]

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2) Colleagues: can't calculate exponential half lives, square roots, awkward division in your head, etc... This is just [censored] pathetic. You are in graduate school. This tilts the [censored] out of me.

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What is your major? I was a EE and I don't think any of my colleagues would have even attempted awkward division or square roots in their head. We all carried calculators anyway, so why would we ever do awkward division in our head?

[sirtimo]

One social skill I can think of that has almost vanished is the art of discretion.

Being able to tactfully and politely correct someones error, or not 'seeing' an embarrassing faux pas used to be one of the marks of a gentleman.

[suzzer99]

Having to plan way ahead to meet someone in a certain place at a certain time, with no chance to call if plans need to change. Whenever I travel or something where we don't all have cel phones I'm reminded of what a PITA this is.

Changing your own oil - used to be pretty common. I don't know anyone who does it now.

[Borodog]

Well, here's how to do sines.

For small angles, less than 35 degrees, you can just divide the angle in degrees by 60. For example sin(15) = 0.25, to about 3%.

For angles greater than 30 degrees but less than 90, the trick is a bit harder, but gives great results. Take 90 minus the angle, divide by 60, square the result, and subtract half that from 1.

So, sin(75) = 1 - 0.5*[(90-75)/60}^2 = 1 - 0.5*[15/60]^2 = 1 - 0.5*[1/4]^2 = 31/32, to within 0.3%.

sin(45) = 23/32, to within 2%.

Since cos(x) = sin(90-x), you can use these same tricks to do cosines.

For small angles, tan(x) ~ sin(x), so you can use the same divide by 60 trick, but it's less accurate and becomes really inaccurate fast. For even 10 degrees, this method is off by almost 5.5%

Instead, you can use tan(x)=sin(x)/cos(x)=sin(x)/sin(90-x) and the above tricks. So, tan(15)= sin(15)/sin(75) = 0.25/(31/32) = 8/31, to less than 4%.

The most useful of these is obviously the first, for small angle sines.

[jeffnc]

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grammer

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Not of mentioning spelling.

[jeffnc]

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hm, ive never thought about math as an art form before. i dont think i agree though.

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Quick math estimations is an art form.