Thursday, February 13, 2014

Which Celebrity Pet Are You Most Like?


You are most like Jane Seymour's cat.


Jane Seymour and Max

Now that we have that out of the way...

I've written several posts expressing disdain for "unscientific" thinking. Now, don't get me wrong - I fully understand that life is full of problems you can't solve by science alone. Science might help you with the nutritional aspects of whether to eat steak or beans, but the final decision is going to involve other concerns that science isn't going to help with.

But what bugs me is when the science is there but people refuse to use it. Today's target is economics. Many people consider economics to be a science, and people who have subordinated themselves to the advice of economists, expecting that advice to be scientific, have suffered terribly.  How scientific is it? Let's find out.

By science, I mean the exact sciences - ones that write laws in the form of mathematical equations. There are other sciences like biology that don't do much of this. But biologists only claim to explain certain interesting aspects of plants and animals. Other than that, they mostly leave you alone. Economists go around advocating rules that you personally must live by, such as paying a 25% tariff on pickup trucks.

To put economics in perspective, I have to describe some characteristics of an exact science. I'll use classical mechanics as an example. Let's consider the important equation

F = ma

What does it mean? It means that the net force on a body equals the mass of the body times its acceleration. But it contains much more than that. It contains (among others) the following definitions and assertions:

- A body is a fixed quantity of matter.
- Force and acceleration have directions, but mass doesn't
- Forces and masses are the same regardless of whether we're moving when we observe them.
- The acceleration may appear different to different observers, so there must be some restriction on the kinds of observers who will find this law to be correct.
- It makes sense to talk about the motion of a body even though there may be several points on a body that all have different motions

I could go on, but the idea is that you have to know what it is you are talking about before it makes sense to put it into an equation. If you don't know the general properties of acceleration, this equation makes no sense. If you use mass in more than one equation, it has to be exactly the same thing in all respects. Not similar, not analogous, but exactly the same. There is no way to distinguish one electron, or one water molecule, from another.

I'm not talking about metaphysical questions of what mass "really is". I'm talking about stating carefully that mass has certain logical-mathematical properties that limit how it can appear in a physical law.

Carefully collecting all the assumptions underlying a law of physics is called "axiomatization". Not many laws of physics have been completely axiomatized, but the point is to try. Sometimes in the process of axiomatization, it is found that a law is logically inconsistent with other laws we are more confident in. Then, changes have to be made.

The laws of physics have a pretty good track record of being useful for making predictions, so this business of carefully stating assumptions is probably the right thing to do.

It would seem that economics could be developed in the same way. You start out by saying we are going to study money. Before you write down any laws, you have to talk about the properties of money. Can it be created? Destroyed? Is its location important? Can you talk about the speed of money? Does money appear to act the same way to different observers?

One problem that arises right away is that while we can exchange dollars for yen or gold at a certain rate, there doesn't seem to be an underlying unit of money with fixed properties. The same is true of speed; different inertial observers see the same object traveling at different speeds. Because of this, speed can only be used in certain ways in a law of physics. If someone proposed a new law of physics saying that the force was proportional to the speed, you would know right away he was wrong, because force is a vector and speed is a scalar, and vectors can't be proportional to scalars.

It seems to me that, not having defined the properties of money (or any other thing economists talk about, like unemployment) very carefully, economists are never going to be able to write down any really useful laws. Instead, you have professional economists arguing with each other and having to stop and ask: are you talking about nominal dollars or constant dollars? It's like physics was in the 16th century, when people were still having trouble with the difference between mass and weight. All economists can come up with are rules of thumb, like the price of a good is influenced by supply and demand.

The classic rejoinder to all this is that the "real economy" is too messy to subject to such logical treatment --- which is another way of saying that economics isn't a science. Somehow, in the physical sciences we managed to come up with laws that describe the real, messy world - not exactly in every case, but pretty close. You economists can do it too, if only you try.

  


Friday, February 7, 2014

How a Rocket Doesn't Work

This is a science post, but there won't be any numbers, just concepts.

When I had my consulting business, the website included a post about Newton's Laws and how they apply to rockets. The business and the website are history, but people really seemed to like that post, so it deserves to be revisited here.

What prompted the post was the many confusing and/or wrong websites claiming to explain how a rocket can be propelled in the vacuum of space. They typically go like this:

1. Rockets produce thrust by expelling hot gases out their nozzles.


OK so far.

2. Newton's Third Law explains why a rocket can accelerate in space, where there is nothing to push against.


Nope. The Third Law says, To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. It doesn't say anything about motion. All it says is that when Body A exerts a force on Body B, Body B exerts an equal and opposite force on Body A. It's true that the exhaust and the engine exert equal and opposite forces on each other, but this accounts for only a small part of the thrust. The reason is discussed below. 

Some really bad sites will say that the expelled gases are the action, and the forward motion of the rocket is the reaction. This is way off, because "action" in this law means force, not motion or momentum. You may think this is trivial, but anyone who doesn't know the difference between force and motion is going to have a rough go in physics class.

Additional note for geeks: Not only does the Third Law not explain why a rocket works, there are electric rockets that are in strict violation of the Third Law but work just fine

3. Well, maybe it's Newton's Second Law that explains it. 

 

Not really. The Second Law does talk about motion, implicitly as momentum. Momentum is mass times velocity. The Second Law says, The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed. But what is a body? It's a fixed quantity of matter. There is no fixed quantity of matter that corresponds to what we think of as the rocket. The best definition of "the rocket" is "the stuff the engine has to push forward." That includes both the airframe and the fuel it holds. But at the next instant, some of that fuel has been burned and blown out the nozzle, and is no longer part of the rocket. The rocket's mass is rapidly decreasing, so it isn't a body and hence is not described by the Second Law.

The fact that the rocket isn't a body also explains why the Third Law has little to do with the total thrust. If you draw an imaginary boundary around the rocket, no matter where you draw that boundary, somewhere, fuel or exhaust is pouring across the boundary. That fuel or exhaust exerts pressure on the stuff on the other side of the boundary, which accounts for a small part of the thrust. But the vast majority of the thrust comes from the fact that mass is crossing the boundary. 

To understand the motion of a changing quantity of matter (an "open system"), we need a generalization of the Second Law that didn't come along until some time after Newton. He was mainly thinking in terms of planets, which are about as close to the strict definition of a body as you can get. 

It is true that Newton phrased the Second Law in terms of momentum, so some people think it accounts for momentum change due to mass change as well as velocity change. But it says, and means, that it applies only to bodies.



You may have noticed that one of the websites I called out above is a NASA site! Here's one that is just horrible; they have an equation at the end that is plain wrong. I am going to resist the urge to make a NASA joke here. I know a lot of people at NASA and they're all pretty sharp. My guess is that those websites were made for NASA by "education contractors" that were chosen based on some criteria other than technical competence. NASA ought to have some of their real rocket scientists review them. 

If you want the equations in all their detail, check out this site from MIT. Notice that the word Newton never appears on that page.

In conclusion, any explanation of rocket motion in terms of Newton's Laws is going to turn into a mess, because in fact they are insufficient by themselves to do the job. Because rockets change their mass, they're probably the worst possible way to try to introduce the laws of motion to a beginner.  


Wednesday, February 5, 2014

Principles Suck

I started to write a post about arguments over principle versus arguments over numbers, but it turned into this screed about rigid thinking and free speech.

Now I'm going to start over and try to stick to the topic.

The vast majority of political debates center on principles. This is why such debates are pointless and infuriating. Let me explain.

In the engineering world, if we made decisions the same way political compromises are worked out, it would go something like this: Jim and Tim are designing an airplane and need to decide what kind of engine to use.

Jim: Propellers are the best choice. They have a long tradition, and have been used on many successful planes. In fact, every plane should have a propeller. When jets were introduced, it was a great disaster for the airlines. Didn't you see that a jetliner crashed last year and killed 200 people?

Tim: But propellers are old-fashioned. They're heavy and they could be a danger to people near the airplane. No airplane should have a propeller. People who like propellers are just afraid of change.

Jim: You know, Hitler loved jets. He wanted to use jet planes as a weapon against democracy. Are you against democracy?

Tim: No, you are probably against democracy because your propeller idea will destroy the country and leave us open to foreign domination. But I have a compromise to offer. Let's design a plane with a propeller engine on the left and a jet engine on the right!

Jim: That's an idea I can get behind. Plus, we'll have to have two totally different fuel systems, which will double the design work and ensure that we both have jobs here at the airplane company for a long time.

Of course, any company that designed airplanes this way would soon be out of business. In reality, the laws of thermodynamics -- the numbers -- essentially force you to choose the engine based on the plane's cruising speed.

If you think this is an exaggeration, I encourage you to read up on one case in which a flying machine really was designed this way. You'll find out that the Space Shuttle had such big, heavy wings because it was politically forced to do a secondary job (once-around reconnaissance missions) that is very, very different from its primary job of transporting things to and from orbit - a secondary job that it was in fact never used for. The CIA and Air Force were able to foist the big wings on the Shuttle because NASA needed their political support, even though the AF already had its own big orbital launcher...don't get me started.  

Someone will argue that in politics, we don't have anything corresponding to thermodynamics. That is, there aren't any objective calculations that would help us make the best decisions. Books have been written debunking this claim. Just because we couldn't make exact calculations doesn't mean that some kind of quantitative reasoning would be a waste of time. We use inexact (sometimes really inexact) models all the time to design airplanes and they come out a lot better than if we'd just thrown darts at a list of choices.

But we never learn, maybe because deep down we like to argue, and if there's a rational basis for choosing, then we don't get to spew bile all over each other. The worst example inflicted on us has to do with immigration.

Because immigration policy is always argued in terms of principle and not numbers, you only ever hear two sides: open borders or closed borders. It doesn't take a Harvard Ph.D. to realize that the best level of immigration, however you define best, is somewhere in between the two. Our form of government forces a compromise, but it's a propellers-and-jet kind of compromise that satisfies nobody and makes no sense. The arguments are so soaked in principle that if you think there should be less immigration, you're called a racist, while if you think there should be more, you're called a traitor. It's like the guy on the freeway who thinks everyone slower than him is an idiot and everyone faster than him is a maniac.    

Of course, both sides can and do refer to reams of statistics and projections to bolster their side. It puts a gloss of rationality on their argument, but that's all. They don't use data like they ought to. If you believe a study that shows a million immigrants a year are a net drag on the economy, then surely that same study could be used to determine how much fewer immigrants are the right number. 600,000? 300,000? But all you'll hear is that the study says there's too many immigrants. Conversely if a study says a million is too few, then the same study should say whether 1,200,000 is enough. But no, all you'll hear is that a study said we need more immigrants.  




 


Sunday, February 2, 2014

Names and Places

The great thing about having Appalachian ancestry is that if your people were there before about 1870, you probably have a creek, road, town, fork, run, lick, mountain, hill, cave, holler, gap, or cove named after you.

My great-grandfather was a Conley and his place is Conley Flats Road, Greenup County, KY

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His mother was a Dysard and her place is Dysard Road, a few miles away
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Grandpa was adopted by Mr. Noah Henson who descended, I am almost certain, from the Hansons of Hansonville, Russell County, Virginia. Yes! I have been there.
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My dad's grandmother had Shannons in her line. They were at Shannon Branch Road, which of course runs along Shannon Branch off the Levisa River in Lawrence County, KY.
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But some other Shannon brothers were up in West Virginia, and their name is all over the place; for instance on another Shannon Branch Road where a Shannon Pocahontas Mining Company now operates.
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They spread out to West Virginia and Kentucky from "Shannandale" near Bluefield, Virginia
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On Dad's mother's side, we have the Edwardses of Yancey County, NC. I think about half the phone book of Yancey County still consists of Edwardses. With so many of the same name, there was no point using it as a place name, so it isn't really found there. Reuben Thomas, my 6th great grandfather, was on the Holston River in far southwestern Virginia before the American Revolution.
View Larger Map In fact, just about every little branch that runs south off South Holston Lake has a name that shows up in my family tree.