If you read this post, then you will understand basic logic.

I want to talk about a strange math related topic.

The moment anyone starts seriously studying mathematics they immediately come across a few terms (all related to logic) that are very related. I specifically picked them because they are very applicable in even every day logic. They are:

1) Sufficiency and necessity.
2) logical implications (i.e. ⇒, ⇔, iff, etc.)

I'll start with the first.

Now, the first time someone studying mathematics comes across this is probably in mathematical optimization (necessary and sufficient conditions for maximization and minimization). Yet, it springs up constantly from there on. What does it mean?

Well, I'll start with an example.

Let's say that I want to prove that I'm a human being. Showing that I have blood is necessary, since human beings have blood, but not sufficient. Many different creatures have blood. Likewise, let's say that I want to prove I'm a male. Since my name is Brandon, that's sufficient, but not necessary in order to prove it. Certainly, there are many men who aren't named Brandon, but if you're named Brandon you're most certainly a male.

The distinction is very important. In these examples something that is necessary is exactly that, necessary, but that doesn't mean it completes the proof. Sufficiency, on the other hand, can prove it, but that doesn't mean it's necessary, since there may be examples where it's true that aren't related to it.

However, they can be taken together, and that's when it's the strongest. Let's say all males were named Brandon, and only males were named Brandon (no dogs, creatures, women, etc.). Well, showing that my name is Brandon is both necessary AND sufficient since it's sufficient to prove I'm a male, but at the same time for me to prove it it's necessary that my name is Brandon.

 This leads right to logical implication which is directly tied to this (and makes it much more intuitive). The first time you come across these would be in mathematical logic, which may be in early calculus, or as late as real analysis.

Here are the implication arrows. They are:

P⇒Q
Q⇒P
P⇔Q
 
Although the first two seem redundant, I'll use them with my previous examples. Let's say the statement P is "My name is Brandon" and Q is "I'm a male". The first says, essentially, "If my name is Brandon, then I'm a male." Which means the fact that my name is Brandon implies I'm a male. Let's switch the world around a bit, and say that all males are named Brandon, but so are some females. Then, the reverse statement would be true. "If I'm a male, then my name is Brandon", but then the previous statement would no longer be true since some females would be named Brandon. So now being named Brandon isn't enough to prove I'm male.

Notice how this works. With the first two implication arrows, you can take the previous statement and imply the latter, but you can't go back. My name is Brandon, therefore I'm a  male. However, if I'm a male that doesn't mean you can show my name is Brandon, since it's certainly not always true.

The last example follows necessity and sufficiency. I'll just restate my example of both necessity and sufficiency (the world where all men are named Brandon, and everyone named Brandon is a male), which is "If my name is Brandon, then I'm a male", and "If I'm a male, then my name is Brandon." In other words, I could take either fact and it would lead me to the other.

This is very simple, but incredibly powerful with logic. My name is Brandon⇒I'm a male. I'm a human being⇒I have blood. I'm from planet Earth⇔I'm from the third planet from the sun.

The first leads me to the second in all of those, but only in the last one can I go both directions.


Strange topic. Feels weird. I'll try something different next time.

I feel your pain, Appleby.

Taken (stolen?) from "Catch-22"

"Appleby was as good at shooting crap as he was at playing Ping-Pong, and he was as good at playing Ping-Pong as he was at everything else. Everything Appleby did, he did well. Appleby was a fair-haired boy from Iowa who believed in God, Motherhood, and the American Way of Life, without ever thinking about any of them, and everybody who knew him liked him.

'I hate that son of a bitch,' Yossarian growled."


I feel an urge to read that book again. Why does he bring up ping-pong? Who cares.

Update: I think it's a state law in Iowa now that you need to post this video every time you mention Iowa.

They run these advertisements all the time in the United States..

Here's some ideas to get the ball rolling in Britain. With slogans like "We hate ourselves-we'll probably hate you too", "Grey Britain", and "Go to Australia instead", how can they lose?

Thank God these aren't actual, prospective, advertisements. Just jokes. The idea isn't a joke, though.

I make Kleptomania look good.

One person gets this joke.

Alright, stealing one more from Beth, but it'll be quick.

 Unlike her usual self, she's brought up two stealworthy posts in a row. This time, She's brought up charity as a topic, and mentions some facts regarding popular charities. She brings up a great point:

 "With so many charities out there, if you're thinking of making a donation, it's important to know how to choose the right one."

I couldn't agree more with this. This is nearly the most important factor of picking charities, and most blatantly ignore it. In the United States it's very popular to text in a donation that bills your phone company. There's literally no information on how it'll be spent, where exactly, or how efficient it is. This is exactly what she's talking about.

However, I do disagree with one point she brings up later:

"For a charity to be considered as one that spends it's money well, two thirds, or 66.6% of donations should go directly towards programmes supporting the charities aims."

It's a very good indicator, but to bring up an analogy where it might not always work would be  educational spending. Many sources claim increases in educational spending as something desirable in and of themselves, but as professor Heckman would put it, spending is an input, not an output. So, I agree absolutely that we need to spend time and choose, but now it has become considerably more complex on how we choose.

If two charities, A and B, make $100,000 each, but A spends 10% on administration costs, and firm B spends 30%, then, superficially, it appears that firm A has more "bang for the buck". After all, 90,000 goes to the stated cause for A, but only 70,000 for B.

However, let's say B is more efficient than A. Let's say that, out of the money that goes, 1/4th of A's is spent efficiently, but firm B spends 3/4ths of it's money efficiently. Some examples would be that A spends more money on things that aren't used, or perhaps it spends it on projects that are relatively less helpful than B.

Well, now multiplying the money they have to the percentage of it that's used effectively, we get A has $22,500 going to the charity, and firm B has $52,500. The roles have reversed.

How do we know which charities are efficient? Well, I've heard of some estimates that mix Beth's definition with other efficiency measures, like this. If you want more rigorous studies I've heard of a whole slew of research coming from John List over at Chicago. Since I haven't gone over that, I'll cover one paper of his that I have, which is this. One part of the Abstract runs:

"We design a door-to-door fund-raiser
in which some households are informed about the exact time of solicitation with a
flyer on their doorknobs. Thus, they can seek or avoid the fund-raiser. We find
that the flyer reduces the share of households opening the door by 9% to 25%
and, if the flyer allows checking a Do Not Disturb box, reduces giving by 28%
to 42%. The latter decrease is concentrated among donations smaller than $10.
These findings suggest that social pressure is an important determinant of door-to-
door giving."

So, apparently part of the reason we give is social pressure. Could be pressured into doing worse things, I suppose.

Now I'll stop stealing for a while and be original.

Approaching light speed.

Over a hundred views? 3 different countries? 2 of which aren't my own? I'm worldwide mother fuckers.


Time to celebrate:

Enjoy the storm.

Beth being interesting? You be the judge.

A few posts back I mentioned “why people do things”. Now, the analysis was incredibly vague and inconclusive (which should be expected from me), but I’d like to go a little deeper with an example.

Over at Indecision, Beth lays out a great summary over the history of the English language. So I think this is a good opportunity to explain how exactly the structure of society has tangible effects on how people make choices, as well as how those decisions feed back into society.

I won’t cover everything that she brought up, nor speak about the more specific historical facts, but I will note some interesting things.

 Firstly:

“The first, Old English is defined as the period between 450 and 1100 AD.  The languages of the invading Germanic tribes were similar, and slowly blurred together as time passed, forming Old English…Middle English is defined as 1100-1500. The main difference between this and the former was the invasion of the Normans, who brought with them a type of French…Modern English is classes as quite a broad period, spanning from 1500 to present. Within this, there have been many dramatic shifts. The biggest alterations from Middle English were the invention of the printing press, which standardised the English language…Today, there still remains about 10,000 french words in the English language, as well as many German, Greek, Latin, Arabic and Scandinavian. A little known and interesting fact is that upon their journey across the Atlantic, many English words were "frozen" and terms we consider to be Americanisms such as "trash" and "fall" were actually first used in Britain.”

Now the multitudes of different causes and effects here show exactly what I’m talking about. Notice that the geographical position largely affected the form of the language. If, for instance, England were located in the Pacific it would more than likely NOT have an alphabet that was a direct descendent of the Latin alphabet, but perhaps one similar to, say, the Chinese writing system. Furthermore, it would probably have a phonetic system similar to that of East Asian countries, and the influences of, say, the German, French, Scandinavian, etc., languages would be much less pronounced (if it would exist at all).

Notice other aspects of it. English moving in different directions once being separated by UK English and US English is another, as well as the effect of a printing press and the standardization of languages.

I could go deeper (especially with the printing press), but I’d like to move onto more contemporary effects of differing languages.

Today, if Germans wanted to travel to England, they wouldn’t have to create raiding parties and travel days and weeks by boat.

They fly.

Notice the importance of this. Globalization is affecting the choice of languages and whether or not people of differing languages meet. Now it’s much more common to get in touch with someone who speaks a different language. In fact, with the advent of the computer all you need is a public library.

However, barriers still exist, which is why the average European knows multiple different languages, and the United States is largely mono-linguistic. So geographical concerns still make a difference. If your own country is surrounded by neighboring countries with different languages, you have a tendency to speak more.

Which leads me to a few very interesting points. Here’s a paper from Edward Lazear, and an excerpt:

“Trade between individuals is facilitated when all traders share a common

culture and language. A common culture allows individuals to

trade with one another without intermediaries. In the case of language,

this is most clear. If two agents speak the same language, they

can negotiate a contract without the use of a translator. A common

culture allows the traders to have common expectations and customs,

which enhances trust.”

Which, empirically he verifies and finds that:

“The theory is tested and confirmed

by examining U.S. census data, which reveal that the likelihood

that an immigrant will learn English is inversely related to the proportion

of the local population that speaks his or her native language.”

Which is what you’d expect. For people who live in those areas, it’s much less tempting (and less vital) to learn a new language if people there can understand you and communicate with you.

Fuckin' interesting stuff.

But moving on. One point that’s similar to Lazear’s conclusion that I wanted to mention was actually very related to a seemingly unrelated topic. Why do we have money? Well, the reasons as to why it was started and why it continues are rather different, but most monetary economists agree that one major cause behind both is known as the “Double Coincidence of Wants”. In other words, in a barter system I’d have to have what you want, and you’d have to have what I want. Which is a double coincidence. Money eliminates one. Now, if I have money, you just have to have what I want, since people generally accept money in return.

What does this have to do with language? Well, consider the referees in FIFA. There can be very strange match ups, and the probability that they have referees that speak both Romanian and Japanese is tiny, not to mention the fact it may only be needed for one game. Solution? All referees speak English. Now they all share a common language in which they can communicate, but at the same time they can specialize in, say, Japanese. The referees that can speak both Japanese and English can be in used in every Japanese game, instead of the one where they speak both Romanian and Japanese, or Swahili and Japanese, or whatever. 

This isn’t the only example. Wonder how flying planes works in a multilingual world? If one plane flies from, say, England to Germany they don’t have to speak both English and German. Now, thanks to international laws, English is the common language. Which is incredibly helpful. If a plane malfunctions and needs to land sooner than it’s actual destination, it doesn’t have to worry about flying erratically into an airport where the people in the control tower can’t speak their language.

All interesting stuff, and if I find time I’ll post more about it later. Perhaps about the benefits and costs of a mono-linguistic society? Who knows. As for now food.


Update: I just wanted to stress the importance of how these different geographical positions, different turns in history, the double coincidence of wants, etc., are all structural aspects that affect languages, and also how languages feed into those structures. Also, I'd like to go into what Beth calls the "monopoly" at some point, but not now.

Stylized facts and over aggregation.

Back to science.


Recently, I've been coming across similar things in the more informal side of economic discussion (and, unfortunately, the formal). One is "stylized facts", and the other is, as I call it, over aggregation (many different ways of putting this one, but I like to use this).

Wiki defines "stylized facts" thusly:
 

"A stylized fact is often a broad generalization that summarizes some complicated statistical calculations, which although essentially true may have inaccuracies in the detail."

Well, you'd think that facts that are "stylized" are, by definition, not facts. Even if generally true, that does not make them "true", per se. However, it's surprising how often you see this in even formal and rigorous economic studies. Even if it's only used for convenience it can be detrimental. Even if it plays a minor role in your summary of a body of literature, it doesn't mean it won't have adverse effects.

This is all very related to another problem which, thankfully, is much more closely related to the informal side, but, alas, still found in even the most prestigious (pretentious?) journals.

Now, statistics is used to find causality and correlation in complex systems such as an economy. Good studies take into account everything about how their models and controls work. For instance, does increasing police officers decrease crime? The first wave of research suffered from an "endogeneity" problem. It just so happens that places that have more police officers are also more crime ridden. Can't get far with that. It'll tell you nonsense. So you have to go to more rigorous statistical methods to correct for this bias. That's what they did. They found that increasing police officers has an inverse relationship with crime.

That's how science is done. Want to see how it's not done?

I'm taking this from a review named "Real World Economics Review". They seem to be overcompensating with the name, right? Well, it's from a movement named "Post Autistic Economics", which, apparently, is aimed at people who use mathematical and statistical methods they don't know how to use.

Anyways, I didn't take it seriously. It was formed against the Neo-Classical side of economics which I don't think anyone fully subscribes to anyways, although they might find a great deal to agree with. Among other reasons it didn't seem serious. I think it could be easily countered with a movement of "Post-prepubescent-angst-economics", but I'll let you judge. 

I took this from the first article I grabbed, which was provocatively named "Neo-classical economics:A trail of economic destruction since the 1970s." Supposedly, this is "good" science from the next paradigm in economics:

This is the GDP of both Korea and Somalia. Well, it's obvious that they diverged. What could be the multitude of causes? And where's the sound empirical work in support? This is what the author had to say:

"Figure 1 illustrates the explosive growth of South Korea, starting only in the very late 1960s, as that nation diversified its economy away from agriculture and raw materials and into manufacturing industry. Through very heavy-handed industrial policy, Korea broke away from its ‘comparative advantage’ in agriculture. By comparison, Somalia – being richer that Korea until the mid-1960s – did not, and instead continued to specialize according to its comparative advantage in being poor."

This is awful science, and I will explain what I mean. When you step back and ignore nearly all the different causes and actions within an economy, you can get nearly anything to support what you claim. In this piece of nonsense, this is supposedly condemning evidence against "comparative advantage", which, anyone with at least a little bit of honesty would notice says nearly nothing about it (and more about nearly EVERYTHING). 

What are the effects of minimum wages on employment? Don't run around looking at aggregate data of different countries and their respective minimum wages. That's a small fraction of the economy that's absorbed by your over-aggregated data. You're basically absorbing every unrelated thing into a gigantic mess of data, and then focusing on two things going on in that mess. You need to do better.

To be fair, from what I've seen outside of this, most of the stuff in their reviews falls short of most peer-reviewed journals, which is by no means an insult. Some of this is completely helpful stuff. Such as his comment about increasing returns to scale which, if he had looked into the evidence, would notice economists do, in fact, study it. 

But outside of that it's essentially all of the teenage angst regarding the financial crisis and and an overbearing urge to revolt against the powers that be, but really aren't. This is glorified sociology, that reminds me of the half-assed historical studies of Marxists that were nothing more than glorified sociology. Not science. Politics. 

I have a feeling I'll be talking about them again, or at least another segment on bad statistics.

To sum up, stylized facts are exactly that, stylized. Looking at gigantic economies and using very aggregated data to prove, well, anything you want, isn't science.

Now sleep.