Ship of Theseus Paradox

The greek historian Plutarch wrote in the year 75 that the ship of the legendary Theseus was preserved by the people of Athens for hundreds of years. Whenever some part got too worn out they would replace it. Eventually, it was not clear if any part of the ship was still original  And if every part had been replaced, is it still the same ship?

And what if you found and gathered all the original, replaced and discarded parts and reassembled them into a boat - which of the two would be the true Ship of Theseus? 

Similarly, we know our own bodies are always replacing parts. How much of you is the same as the you that existed when you were a small child? Enough to say that you are the same person?

The answer, of course, is that we are the same person. And most would say the Ship of Theseus is the same ship, but it's instructive to think about why. It seems a thing does not derive it's thingness from it's parts alone. It's the relationship of those parts that is important, and the persistence (and evolution) of that relationship through time. 

The Block-Stacking Problem

The scenerio: you have some rectangular blocks all stacked at the edge of a table. Just by nudging blocks over, how far can you get the stack to reach beyond the edge of the table?

Well, we know that if the center of mass of a block is over space, it will topple and fall. So one block can be pushed halfway out over space before falling. It is also true that if the center of mass of any group of blocks taken together as a unit is over space, they will topple as that unit. Now it's just a matter of calculating those centers of mass. The result is that the top block, Block 1, can reach over 1/2 the length of a block (let's call the length of a block 1 lob). The block below Block 1, Block 2, can overhang 1/4 lob. Block 3 can overhang 1/6 lob. There is a pattern here. If n is the block number, it's overhang is 1/(2*n) lob.

n	Overhang (lob)	Total overhang (lob)
1	1/2	0.5
2	1/4	0.75
3	1/6	0.917
4	1/8	1.04

Note that at four books, you can overhang by a whole block, so the top block is not over the table at all anymore. Can we reach two blocks over? The overhang is getting smaller each time, but each added block still gets us a little farther. Incidentally, those incremental overhangs are related to the harmonic series (1, 1/2, 1/3, 1/4, 1/5...). It turns out that to reach 2 lob would take 21 blocks. Theoretically, any overhang can be achieved with enough blocks, but practically there will be limits. We're assuming the blocks are perfectly rigid, actually they will flex some small amount and topple sooner. Also, the numbers quickly blow up. To make it 3 lob would require 227 blocks, and 4 lob would require 1,674 blocks. For five lob: 12,367. 

Velocity

Velocity is usually treated as interchangeable with speed, but in the context of science, velocity is used to refer to a combination of speed and direction. There are a few different ways to express velocity. You might say you were driving 50 mph at 37 degrees from north per your compass. Or you might say, equivalently, that each hour you’re 40 miles farther north and 30 miles farther east. So, where with speed you could just give a single number, velocity requires a set of numbers that together give speed and direction. We call the former a scalar, and the latter a vector. Scalars are just normal numbers, but vectors are usually expressed like <50, 37°> or (40; 30). The symbols vary, it’s the grouping that’s important. 

The word, velocity, comes from the Latin vehere - to carry. This meaning is better preserved in biology where a vector is a disease carrier like a rat or mosquito. But the first recorded use in English was actually the mathematical version discussed above. It came about as astronomers were analyzing the elliptical lines that seemed to carry the planets around the sun. The velocity of the planet is, at each point, tangent to that elliptical line.

Crepitate

To crepitate is to make a crackling or popping sound. Like electricity.

From Latin crepare, to crack, creak, or rattle.

The Magnus Effect

The Magnus effect is a name we've given to the phenomenon of an object curving away from a straight line because it is spinning while passing through a fluid. The most ready example is a curve ball. A pitcher achieves a curve ball by putting spin on the ball. The spin causes the curvature, and this is the Magnus effect. It can similarly be seen in table tennis, and it is responsible for long drives in golf (the curvature is upward due to backspin).

The name comes from Gustav Magnus even though Isaac Newton observed it almost 200 years earlier. That's fine; Magnus is a pretty cool name, and Newton get's plenty of recognition (and deserves it)

Let's try to understand how it works in the case of a golf ball with backspin. As the air encounters the ball, it would normally tend to part around it and meet on the other side. It may be stirred up into turbulence  but on average it's following about the same path it did before. The Magnus effect works by deflecting the path of the air. Because of the backspin, the underside moving forward and the top backward. The side on top is moving along with the air, and the air on that side is able to move farther along the face of the ball before meeting the air from the bottom side and continuing on it's way. Likewise, the bottom face is going forward  against the fluid and impeding it. On average the path of the air has been deflected downward, and by pulling the air down, the ball pulls itself up getting extra time in the air and extra flight distance. This helps us understand why golf balls are dimpled: that texture enhances the Magnus effect.

There have been attempts to use this effect to propel vehicles. Butler Ames made a prototype airplane that derived its lift from a horizontal spinning cylinder using the Magnus effect in 1910. It was able to lift off while being towed by a boat, but didn't make it any farther than that.

There have also been attempts to use a vertical spinning cylinder on a boat for propulsion. It would work as a sail replacement, interacting with the wind through the Magnus effect to push the boat in the desired direction. This was called a rotor sail, and the boats, rotor ships. These worked perfectly well, but it turns out the energy you use to spin the cylinder can be more efficiently used to turn a propeller in the water. However, there has been some limited use of smaller, horizontal spinning cylinders in the water used to stabilize boats against rocking.

Could Not Care Less

It is fairly common to hear someone dismissively say that they could care less. Think about what has been said. If they could care less, than they do care. They may care a great deal for all we know, then it would be very easy to care less. 

Napoleon could not care less

Of course, we understand what they mean, but why not say "I couldn't care less." Or "I could not care less," which has a better rhythm to it, I think. In any case, there's no reason to say the exact opposite of what you mean by going with "could care less."

Trilithon

A trilithon is a formation of three large stones, usually two upright and one over top as seen at Stonehenge.

That is the most common usage (not that it is used commonly), but it could refer to other formations, manmade or natural. The main thing is that there are three (tri) stones (lith).

The Spoked Wheel

A spoked wheel, as seen on a bicycle, is a familiar sight to all. You've used them, but perhaps you haven't thought much about how they work. It may not be what you expect.  

Let's think it through: The weight of the bike and rider (the red arrow) needs to get to the ground. The most obvious path for the that load would be though the spoke below (red). We would say that red spoke is compressed, pressed in from either end. But that spoke is very thin, and very long compared to it's thickness. If you think about compressing anything similar, such as a thin strip of paper, you know that it immediately buckles out to the side without taking much force at all. This is true of the spoke as well. So that must not be how it works.

Actually, the weight is hanging from the top of the wheel. The blue spoke is holding it up by tension. It is being pulled at each end. Even your thin strip of paper can stand quite a bit of force pulling at each end. Now pulling down on the top of the wheel like this would tend to squash it into a flatter oval, but the green spokes are there to hold the sides in; they, too, are in tension. The wheel is a tension structure, with the top spokes under the greatest tension, the sides under less, and the bottom carrying very little load at all.