Paul Krugman: Noah Smith … on the role of math in economics … suggests that it’s mainly about doing hard stuff to prove that you’re smart. I share much of his cynicism about the profession, but I think he’s missing the main way (in my experience) that mathematical models are useful in economics: used properly, they help you think clearly, in a way that unaided words can’t. Take the centerpiece of my early career, the work on increasing returns and trade. The models … involved a fair bit of work to arrive at what sounds in retrospect like a fairly obvious point. … But this point was only obvious in retrospect. … I … went through a number of seminar experiences in which I had to bring an uncomprehending audience through until they saw the light.
The article says "But in fact academia research and teaching put a low priority on accurate useful conclusions, relative to showing off, and math is very helpful for that purpose." - exactly correct.
Both real numbers and money are false, because both are not objects of nature. Therefore, whatever you create using math or money, must also be false. Note that money is also a real number, and therefore must be false, since real numbers are false. Falsity of economics is obvious everywhere we look - we see wars, poverty, unemployment, pollution, migration etc. These are all happening because of money. Remove money, and create money-less economy (MLE) all these problems will vanish.
Invalidity of math is very subtle. If you know engineering, it will be obvious for you. For example 3+4=5, is the common case in engineering. This is so because all variables in engineering, and even in economics, are bounded by lower and upper values. In this example 5 is the upper bound. No matter what the result of addition is, the output must be clipped to the upper bound 5. This makes all applications non-linear, but math requires linearity, a very false assumption for nature. The issue is more complex with infinity, another false object of math. Take a look at https://theoryofsouls.wordp... for more details. Under MLE even math will change and become more meaningful.
Mathematical logic is a subject that happens to be useful. It tells you whether certain things are true and others are false. Logic doesn't need any numbers.
Statistics is a subject on it's own and a lot of mathematicians want to have nothing to do with it.
I do care that the garbage collector of my android phone runs well. That has something to do with math, but it's not about numbers.
The entire purpose of math, the reason why we use it is to quantify. An inordinate focus on the theorems and axioms without an ability to make predictions using real data makes for a truly useless framework.
If your mathematical framework is not applied to make accurate, repeatable predictions; then your framework is not useful.
Answer me this: can you explain why the Philips Curve has the statistical regression that it does? If you see oscillations in the relationship between inflation and unemployment rate, can your framework predict a-priori what the frequency of those oscillations are?
Or is the usefulness of your mathematical framework limited to making generalizations, truisms and successfully being manipulated to confuse the public and cause the next recession?
The formal econ I took was at Caltech so maybe me and my profs were a little happier with the math than the rest of econoworld. I realize Robin is Caltech also, but he has had an entire career to assimilate with the rest of econoworld, and my point here is that the math was very helpful in learning basic econ, for me and it seems for the others in my classes.
Based on my non-economic work now, R&D for cell phones, I'd say you should always use at least enough math to run a sim, at least a trivial "sim" which is to show some numerical curves of one thing against another. Not only does this serve as a great check on your intuition, but you can look at what you must assume mathematically and ask yourself what each piece means, enhancing old intuitions even developing new intuitions.
As to complex gobbledy-gook written out math, for me and apparently for most people that is sort of the 4th line of defense, there to check if you really get in to something but never the first step in figuring out what is going on.
" "I'm not going to put a number on it" is often short for "I don't want to formally structure my argument"."
That's not the kind of math Krugman and Caplan are referring to, if they were they'd be totally guilty of avoiding real argument like you say. They are talking about the (mostly unnecessary) use of bizarrely complicated calculus and such to show off, those articles sometimes make the average physics article look simple, but that's all they do, it's just about looks, not substance. If economists gave their lectures like that any half decent college would fire them on the spot because if they didn't no student would ever pass a course.
Economists who want to show off will find a way to use the description "the identity element of the abelian group of real numbers, except zero" to describe the number "1".
I find an unwillingness to go to maths is a good indicator of weak argument. "I'm not going to put a number on it" is often short for "I don't want to formally structure my argument".
"According to Caplan, he was first introduced to libertarian capitalist political philosophy through the writings of Ayn Rand and that it was his interest in philosophy that drew him to study economics."
"What about those made rich through government? Clearly they're out. "Why?
"Which rich people are being "told" they deserve it?"I think the point is not that rich people need to be told, it's the poor/middle class people who need to be told things such as "Inequality talk is about grabbing"
Even the ancients understood mathematics as a kind of filter to keep dumb people out of serious intellectual discussions. For instance, above the entrance to Plato's Academy, there was purportedly a sign reading "let no one inapt to geometry come in."
I think the ones with views that are most of a far stretch will reject mathematics the most.
Even simplified models can shed a lot of light on validity of intuitions. For example intuitively the richest must have some superpowers, which is why they are richest. But when there is a model exhibiting the same wealth distribution as the real world even when the "skills" are exactly identical, or when a monkey flinging poo at a chart performs as well as an economist, that really calls into the question our assumptions - now we know that mere shape of the distribution does not indicate corresponding distribution in skill.
Thing is, this sort of stuff is not kind to various absolutist ideologies that have fixed conclusions which need to be rationalized. Yes, its not perfect and you can make up assumptions as to arrive at the desired conclusion, and you can use the standard rhetorical tricks at the interfaces between the math and the world, but at the end of the day those other guys are going to have a model that actually fits real world data, and which gets in the way of your arguments, and you won't, especially if you haven't studied enough calculus to be able to model normally distributed intelligence. (Caplan's post about signalling theory of education).
The discussion of math models shows economics' lack of scientific maturity. That it still needs to deal with problems prior to quantification speaks to the field's level of development.
(For a field (in psychology) that is more mature than economics, consider vision science.)
The article says "But in fact academia research and teaching put a low priority on accurate useful conclusions, relative to showing off, and math is very helpful for that purpose." - exactly correct.
Both real numbers and money are false, because both are not objects of nature. Therefore, whatever you create using math or money, must also be false. Note that money is also a real number, and therefore must be false, since real numbers are false. Falsity of economics is obvious everywhere we look - we see wars, poverty, unemployment, pollution, migration etc. These are all happening because of money. Remove money, and create money-less economy (MLE) all these problems will vanish.
Invalidity of math is very subtle. If you know engineering, it will be obvious for you. For example 3+4=5, is the common case in engineering. This is so because all variables in engineering, and even in economics, are bounded by lower and upper values. In this example 5 is the upper bound. No matter what the result of addition is, the output must be clipped to the upper bound 5. This makes all applications non-linear, but math requires linearity, a very false assumption for nature. The issue is more complex with infinity, another false object of math. Take a look at https://theoryofsouls.wordp... for more details. Under MLE even math will change and become more meaningful.
Mathematical logic is a subject that happens to be useful. It tells you whether certain things are true and others are false. Logic doesn't need any numbers.
Statistics is a subject on it's own and a lot of mathematicians want to have nothing to do with it.
I do care that the garbage collector of my android phone runs well. That has something to do with math, but it's not about numbers.
The entire purpose of math, the reason why we use it is to quantify. An inordinate focus on the theorems and axioms without an ability to make predictions using real data makes for a truly useless framework.
If your mathematical framework is not applied to make accurate, repeatable predictions; then your framework is not useful.
Answer me this: can you explain why the Philips Curve has the statistical regression that it does? If you see oscillations in the relationship between inflation and unemployment rate, can your framework predict a-priori what the frequency of those oscillations are?
Or is the usefulness of your mathematical framework limited to making generalizations, truisms and successfully being manipulated to confuse the public and cause the next recession?
The formal econ I took was at Caltech so maybe me and my profs were a little happier with the math than the rest of econoworld. I realize Robin is Caltech also, but he has had an entire career to assimilate with the rest of econoworld, and my point here is that the math was very helpful in learning basic econ, for me and it seems for the others in my classes.
Based on my non-economic work now, R&D for cell phones, I'd say you should always use at least enough math to run a sim, at least a trivial "sim" which is to show some numerical curves of one thing against another. Not only does this serve as a great check on your intuition, but you can look at what you must assume mathematically and ask yourself what each piece means, enhancing old intuitions even developing new intuitions.
As to complex gobbledy-gook written out math, for me and apparently for most people that is sort of the 4th line of defense, there to check if you really get in to something but never the first step in figuring out what is going on.
That's fair enough.
Looking at a distribution that you get by sampling the real world has nothing to do with math in the sense math is used in the discussion.
Math is not about putting numbers on things. Math is about having axioms and proving theorems.
in other words, you think it's overused but useful?
" "I'm not going to put a number on it" is often short for "I don't want to formally structure my argument"."
That's not the kind of math Krugman and Caplan are referring to, if they were they'd be totally guilty of avoiding real argument like you say. They are talking about the (mostly unnecessary) use of bizarrely complicated calculus and such to show off, those articles sometimes make the average physics article look simple, but that's all they do, it's just about looks, not substance. If economists gave their lectures like that any half decent college would fire them on the spot because if they didn't no student would ever pass a course.
Economists who want to show off will find a way to use the description "the identity element of the abelian group of real numbers, except zero" to describe the number "1".
I find an unwillingness to go to maths is a good indicator of weak argument. "I'm not going to put a number on it" is often short for "I don't want to formally structure my argument".
oldoddjobs Wikipedia is your friend: http://en.wikipedia.org/wik...
"According to Caplan, he was first introduced to libertarian capitalist political philosophy through the writings of Ayn Rand and that it was his interest in philosophy that drew him to study economics."
"What about those made rich through government? Clearly they're out. "Why?
"Which rich people are being "told" they deserve it?"I think the point is not that rich people need to be told, it's the poor/middle class people who need to be told things such as "Inequality talk is about grabbing"
Even the ancients understood mathematics as a kind of filter to keep dumb people out of serious intellectual discussions. For instance, above the entrance to Plato's Academy, there was purportedly a sign reading "let no one inapt to geometry come in."
missing from the last sentence: you may also need to put in more math if you suspect your clinging to an intuition because of ideology
tl;dr summary: use math iff your intuition about the appropriate model is stronger than your intuitions about appropriate conclusions
I think the ones with views that are most of a far stretch will reject mathematics the most.
Even simplified models can shed a lot of light on validity of intuitions. For example intuitively the richest must have some superpowers, which is why they are richest. But when there is a model exhibiting the same wealth distribution as the real world even when the "skills" are exactly identical, or when a monkey flinging poo at a chart performs as well as an economist, that really calls into the question our assumptions - now we know that mere shape of the distribution does not indicate corresponding distribution in skill.
Thing is, this sort of stuff is not kind to various absolutist ideologies that have fixed conclusions which need to be rationalized. Yes, its not perfect and you can make up assumptions as to arrive at the desired conclusion, and you can use the standard rhetorical tricks at the interfaces between the math and the world, but at the end of the day those other guys are going to have a model that actually fits real world data, and which gets in the way of your arguments, and you won't, especially if you haven't studied enough calculus to be able to model normally distributed intelligence. (Caplan's post about signalling theory of education).
The discussion of math models shows economics' lack of scientific maturity. That it still needs to deal with problems prior to quantification speaks to the field's level of development.
(For a field (in psychology) that is more mature than economics, consider vision science.)