Wednesday, March 20, 2013

How to Mechanically Calculate an Inverse and Integral

Just watched a neat series of videos on "mechanical computers" that were used to aim warship guns in realtime, using up to 25 input variables like speed, direction, enemy speed, wind, etc.


One simple example is adding using a differential, made clearer with two linear racks:

The position of the center gear is A + B / 2. You can see rack Ahas been moved to 4, which caused the gear center to move to 2, since rack B stayed still. If rack B moved to 4, too, the gear center would move another 2 units to 4 (4 + 4 / 2 = 4).

The same idea applies to a differential, where the racks are two bevel gears. Note that the middle gear spins freely on its shaft, and that the output is the rotation of that whole middle block as shown with the arrow. The outer two gears are locked to the outside shafts, but not the middle.


To do things more complicated than adding or multiplying (which can all be done with gears), a cam and follower, or pin and slot are used. As the wheel rotates, it pushes the pin down at exactly a 1/x rate. By cutting the path in different ways, you can express just about any y = f(x) using this technique, as long as the slope isn't too step I imagine. Arbitrary functions using wheels and slots!

If you make the pin follow the curve cut on the surface of a cylinder, you can provide two inputs: z = f(x,y).


Hold on to your pants, you can even integrate with these chunks of metal. Imagine you want to know the total distance a ship has traveled, and your only input is the speed over time: s = f(t). On paper, you would need to calculate the area under the speed curve, or you could pull out one of these bad boys.

That bottom platter is rotating constantly, which rotates the balls above it through friction. The location of the balls can be shifted left and right. If the balls are positioned directly above the platter, they won't move since the speed is 0 in the center. At the edge of the platter, the speed is max. By adjusting the balls' position along with speed, you're effectively calculating the total distance (d = speed * time), or integrating the speed. It's basically just an adjustable gear ratio, but neat regardless.

Thursday, March 7, 2013

2 Basic Things about the Supreme Court You Thought Were in the Constitution

The Constitution Text (Article III Section 1)

The judicial Power of the United States shall be vested in one supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish. The Judges, both of the supreme and inferior Courts, shall hold their Offices during good Behaviour, and shall, at stated Times, receive for their Services a Compensation, which shall not be diminished during their Continuance in Office.
There's some more, but it's just some technicalities about which court can hear which case. Actually, except for the part about "there shall be a Supreme Court," there's not much in Section 1, either. All that stuff you learned in elementary school was decided by Congress or just sort of happened and stuck. Am I missing something here??

9 Justices

No where in the constitution does it say anything about 9 justices. And it only mentions a Chief Justice in passing when talking about how to fire the President. Congress gets to decide the numbers, which begs the question of how separate the Judicial branch of the government really is.

It went from 6 to 7 in 1807, to 9 in 1837, to 10 in 1863, and back to 9 in 1869, where it's stayed since--but just barely.

Roosevelt didn't appreciate the court overturning a bunch of his New Deal laws during his first term, so he proposed a law that would "pack" the court with up to 15 judges. This law didn't make it through congress, but a retirement and death allowed Roosevelt to pick two new justices anyway. Before that, however, the court suddenly decided in favor of one of Roosevelt's laws, perhaps to play nice before something drastic happened... you can't always count on the rest of the government to play fair.

As Jackson was supposed to have said, "John Marshall has made his decision; now let him enforce it!"

Judicial Review

Congress and the President pass laws, and the Supreme Court rules them unconstitutional. Nice and balanced "separation of powers," except the fact that the constitution doesn't say anything about ruling laws unconstitutional, ie, "Judicial Review."

Tuesday, March 5, 2013

Top 4 Awkward Everyday Moments

Meeting someone when your right hand is full.

Checkout Line, Waiting on the Receipt, you and the cashier have run out of small talk.

The double-goodbye: You've said your farewells, the person leaves, but then comes back in to grab a forgotten item.

Talking to someone while trying to figure out if you've met them before.

Saturday, March 2, 2013

A Bunch of Clever Product Ideas (RedDot awards)

The RedDot awards are some sort of design awards. Here are a few products that won in 2012.

Lady Shifting
The patient leans onto a carrier that functions like dolly so someone much smaller can maneuver them to sit on the bed.

A little triangular kink gives you enough room to get the cutter blade under the tie wrap.