Mankiw Reviews Skidelsky on Keynes

Count Dracula,

Get your stinking corpse back in the crypt.

Daniel,

But you people have been telling me that "math was the international, universal language of logic" and plain English inadequate to its needs.

And now you tell me that you need English, the language of logic, to understand the math, and I'm the one who's behind?

Lord Kuehns,

You and I have had this discussion many times before. The outcome has always been the same. You fought and ran away, so you could live to fight another day. But, as far as I'm concerned, you were slaughtered a long time ago, and I don't go on fighting ghosts.

That's all for you.

RE: "And now you tell me that you need English, the language of logic, to understand the math, and I'm the one who's behind?"

No, I'm telling you you did us the favor of finishing your thought in English. You didn't finish your thought in the math statement. How do you expect us to respond? If I provided you with a sentence that had no verb and mangled grammar and spelling and offered it as proof that pure prose economics isn't ideal, how convinced would you be?

RE: "Lord Kuehns,..." etc. etc.

First, I like my new name a lot. Second, notice it's not just me that thinks you're wrong on this. And nobody is saying that prose is a bad way to do economics either. We're just saying that, as with everything, there are tradeoffs you make by relying exclusively on prose.

To all you mathematical economists:

Here is a quotation from a very famous economic treatise.

"V sub script 1, O subscript 1 + P subscript 1 = M subscript 1, and T subscript 1."

Can you tell me if it's right or wrong, and, why?

Here, from a not so famous one:

"There's demand for apple pies, but none for mud pies, so they won't be worth a red cent, no matter how much labor has gone into them."

Can you tell me if that's right or wrong, and why?

dg, quit while you're not too far behind.

You're asking us to compare a complete, contextualized statement in the vernacular to an incomplete, uncontextualized mathematical statement. What the hell do you expect the answer to be? Once again, you're posing the question in a way that assumes your own conclusions.

RE: "Once again, you're posing the question in a way that assumes your own conclusions."

And note that with mathematics you have to clearly state all your assumptions or else they stand out like a sore thumb. When you abuse language like this you conceal those assumptions - which is a huge part of the reason why lots of economists prefer a heavy dose of mathematical formalism.

Dave,

Sorry, but here I am, 77 years old, and still can't resist the temptations of a 12 year old.

I'm like the John Carradine character in The Grapes of Wrath, Casey, the preacher, confessing his sins to the Henry Fonda character, Tom Joad.

"Why, I had the girls so glory shouting they about passed out. Go to comfortin' 'em, and wind up lovin' 'em. Knowed I shouldn't a done it, but, next time, do it again."

That's me, an incorrigible juvenile.

Sorry, and thanx for your forbearance.

Yet Another Idiot,

Confusing human beings with atoms and molecules, and economics with physics, the mathematical economists would apply the analytical method of physics to human action. But there are no equations in economics. If you and I exchange my A for your B, it is only because I value your B more than my A and you value my A more than your B. If we both valued A and B equally, there would be no exchange, for nothing could be gained by it.

If mathematics and logic lead to the same conclusions in economics, they are redundant, and, the foreign language of mathematics, pointless. If they lead to different conclusions, you must choose between them, and acceptance of the one is rejection of the other. And since mathematics is simply an abridged form of counting, mathematical economics implies counting in place of thinking. But there is nothing to count, for the passing data of economics is irrelevant to its eternal truths. There is nothing to calculate, for there are constant relations between cause and effect but not between the magnitudes of the causes and effects.

Without examples of any of the actual numbers in their alleged calculations, the mathematical economists hide behind symbolic allusions to them, or reference to an isolated number, such as the number of dollars circulating at a given time. But one number by itself is not mathematics. Mathematics implies at least two yielding a third. Without them, they must finally pretend that they are somehow counting without numbers or measuring without magnitudes. To such absurdity is “mathematical economics” finally reduced.

Nullifying distinctions nullifies meaning and is an admission that you don’t have any. To those who cannot see a difference between mathematics and non-mathematics, I can only say that I see it, and regret that I cannot give sight to the blind.

What is the purpose of blurring the distinction between logic and mathematics, other than to bury the one in the other?

This is just another part of the whole “progressive” assault upon traditional authority and convention, upon language, logic, law, morality, schools, churches, and even the family, upon anything standing between the self-appointed masters of our new educational and social order and those they wish to dominate.

Real economics is still the same simple logical and literary science as in the days of Smith and Ricardo, and, mathematization, not a “maturing” but a blurring of it.

Even the schools most steeped in it cannot start out with mathematical mystification. It is the last refuge of an artificial authority, running and hiding from logic, and, the prestige of its adepts, a demonstration once more that the best way to become an “expert” is by saying something with absolutely no meaning.

“What they are doing is vain playing with mathematics symbols, a pastime not suited to convey any knowledge.”

Ludwig von Mises

“What they are doing is vain playing with mathematics symbols, a pastime not suited to convey any knowledge.”

I hope you realize that is a condemnation of people, not of mathematics.

How nice - I was not at all rude to you and you respond with name-calling. Your parents must be proud. I was offering criticism because I think you have a good point that you’re trying to make about the dangers of relying on models (equations in this case) because they are abstractions containing assumptions. Of course, I can’t be certain because you obscure it with the anti-mathematics verbiage.

”…mathematics is simply an abridged form of counting…

…one number by itself is not mathematics. Mathematics implies at least two yielding a third…”

Thank you for proving me right about poor understanding of what mathematics is. It sounds like you are describing arithmetic, which is an extremely tiny portion of mathematics.

Lord Kuehns,

I'll give you this: Kuehnsian is still worth more than Keynesian economics, and you make Lord Keynes look like a commoner.

Daniel,

I was wondering when you'd chip in with your two cents worth, which, at that, overstates its value.

Well, you know - central bankers have consistently eroded its value over time. I think it really was worth two whole cents last week or so.

Twistavista,

You wrote,

"Take your illustration:

Q(A,B) = Vi(B,A) * Vj(A,B)"

That was not my illustration; it was yours, and a perfect example of what's wrong with translating a logical and literary science into mathematics. It's completely unintelligible.

Then you gave an example of mathematics that was perfectly intelligible: 1+1=2.

You will never find anything as simple as that in mathematical economics, for it defeats the purpose.

Nor will you ever find one plus one equals two in real economics, for there are NO EQUATIONS in real economics.

"It's completely unintelligible."

I'm sure you are quite capable of comparing it you your example and discerning the meaning of the symbols. Had I translated your example into Chinese, it would not have been any more or less an example of "what's wrong" with anything.

I'll let you sink your own ship DG, but attacking mathematics does not serve you--trust me.

All of the talk of mathematics in economics confuses the passing data of econometrics with the eternal truths of economics. Since there is none of the passing data in the eternal truths, there are no quantities, and no mathematics.

However essential to econometrics, it is irrelevant to economics, and, its only effect, to obscure it.

Sir, you seem to have a poor understanding of what mathematics is - logic and mathematics are inextricably linked. Mathematics is, in a sense, a language (one that many people throughout the world are familiar with even if you are not) and does not necessarily require numerical quantities. To the extent you have a point about mathematics it is limited to the truth that those who do not understand mathematics will not understand its application to economics. Of course economics is not unique here – those who do not understand mathematics will not understand its application to anything, so it’s not much of a point is it?

Your larger point about the non-validity of quantities in economics would be much more effective if you'd drop the anti-mathematics tirade. If you mean numbers don’t apply and aren’t required say so, don’t drag all of mathematics into it. People might still disagree, but at least they’d be discussing your point instead of your misuse of terms.

Vikingvista, or Mighty Intellectual Raider from the North,

As you said, mathematics is the language of quantities, and, as I said, there are none in economics. There is the concept of them, but no actual quantities themselves. You may illustrate the concept with actual examples of it, but there are still no actual quantities in the analysis itself.

"mathematics is the language of quantities, and, as I said, there are none in economics. There is the concept of them, but no actual quantities themselves."

I hoped my example would preempt this reply.

More specifically, mathematics is the language of quantities--abstracted from actual quantities. E.g., you may experience 1 duck plus 1 duck, but mathematics is the abstraction that allows you to abstract out the duck and just think about 1+1. Or x+y.

If you value one thing more than something else, then you've created an ordinal system, and mathematics can help you deal with that.

I don't know of you think too much or too little of mathematics. Ultimately it is about the rational use of concepts--a consistent way of thinking. And mathematics is just a subset of that dealing with quantities.

Let me put it another way. Instead of decrying mathematics in general (a futile tactic, BTW), why don't you instead limit your attack those who claim that 2+2=5?

re: "but there are still no actual quantities in the analysis itself"

YOUR analysis, not THE analysis. Whenever anyone gives you an example you always say "well that's not a valid example because it has quantities and there are no quantities in economic analysis". Yours is always a proof by definition - a definition that you've concocted.

Mike Laursen wrote,

"Ask any Computer Science major, and they will tell you that math and logic do intersect."

I'm afraid that you fail to intersect with logic yourself when you try to tell me that math and logic are the same thing and that they intersect. How could something intersect with itself? Saying that they intersect acknowledges that they are different. And, if they are different, it doesn't necessarily follow that they "intersect" in economics. That is something that you must demonstrate.

Go ahead.

Boolean Algebra. Deals with logical "quantities" expressed as the numbers 0 and 1.

Is or isn't part of mathematics depending on your definition of what mathematics is (yours seems to be more restrictive than others, but you haven't actually defined what you mean by "math"). Thus, solution of the paradox of whether it can intersect with math -- I was trying to use your apparent definition of math when saying that it intersects.

In computer programs, Boolean and numeric quantities are commonly combined in the same expression, evaluated in the same artificial thought engine in the same manner.

"Name," or anonymous, wrote,

"Didn't Godel demonstrate that for even simple arithmetic operations we can't comprehensive(ly) list all the logical assumptions necessary to generate all possible conclusions? That is, that math is *not* completely logical in some sense."

I'm afraid I don't get the point of that. Math and logic are two different mental tools, and it’s logical to use math for mathematical problems and logic for logical problems, but not logic for mathematical nor math for logical problems.

As for what Mankiw is getting at, I’m not a mind reader. All I can say is that math serves the same purpose in economics as Latin in religion, bedazzling and controlling the flock.

It's up to the flock to have the integrity to admit when they don't understand, and up to the bedazzler not to expect their acceptance until he successfully conveys his understanding--if he really has any.

The goal is rational thought. Neither mathematics, nor logic, nor Latin, nor any mixture of the three is incompatible with that.

Ask any Computer Science major, and they will tell you that math and logic do intersect.

"those who fall into neither the pro- nor the anti-Keynes camp."

Psuedo-reasonableness. You have to hate it. Come on and give us a real opinion. Yuck.

Opinions on Keynes that differ from yours aren't real?

I think Mankiw is being a little inaccurate with his three groups. There are really only two (if we ignore the Skidelsky's of the world that are simply historians impressed with Keynes the man). Krugman, for example, is every bit as much the New Keynesian that Mankiw is. And who is the biggest uber-liberal "Keynesian" out there right now? Joe Stiglitz. Stiglitz laid the foundations of the New Keynesian school. New Keynesianism is all about a toolbox of frictions that can explain various things, and I'd guess about two thirds of those frictions have Stiglitz's name on them. The General Theory is still a nice nostalgic read and still makes good points, but the world is really not divided between Keynesian die hards, Keynesian detractors, and the sensible middle. The Keynesian die hards have learned a lot over the years and modified their perspective, and now it's largely divided between New Keynesian types and the detractors.

It’s easy to see why Greg Mankiw eliminated reader comments from his blog. For he would get eaten alive.

He writes,

“Mr. Lucas, we are told, is following in the tradition of the ‘French mathematician Leon Walras (who) pictured the economy as a system of simultaneous equations.’ The very idea is made to sound slightly crazed.”

Crazed or not, it’s wrong, for there are no equations in economics. If you and I trade my A for your B, it is only because I value your B more than my A and you value my A more than your B. If we both valued A and B equally, no exchange would take place, for it wouldn’t be worth the bother.

Prof Mankiw then states that “mathematics is fundamentally the language of logic.”

In economics, it’s the language of a New Dark Age, with a new holy writ, statistics, and new priesthood, in academic rather than ecclesiastical robes, and chanting in mathematics rather than Latin.

He goes on,

“…why don’t firms adjust wages and prices quickly, to restore equilibrium? This is a classic question of macroeconomics that, despite much hard work, is yet to be fully resolved.”

Is it really so hard to understand that the market tends toward equilibrium and interference with it with its tendency toward equilibrium?

He concludes that Keynes was a “creative thinker.”

What did he create, but error and obfuscation?

"there are no equations in economics. If you and I trade my A for your B, it is only because I value your B more than my A and you value my A more than your B. If we both valued A and B equally, no exchange would take place"

I'm sensing an irrational bias against mathematics, rather than against the sophists who use it. Mathematics is an innocent language of quantities. Take your illustration:

Q(A,B) = Vi(B,A) * Vj(A,B)

"One and one are two" is not conceptually superior to "1+1=2".

"mathematics is fundamentally the language of logic.”

Didn't Godel demonstrate that for even simple arithmetic operations we can't comprehensive list all the logical assumptions necessary to generate all possible conclusions? That is, that math is *not* completely logical in some sense.

What's Mankiw talking about, then?

I agree with vikingvista incompleteness is different from illogical. But Godel addressed all logical systems, not just mathematics, right? In otherwords, incompleteness drags on dg's informal, inexact linguistic approach to economics as much as it drags on Mankiw's formal, exact, mathematical approach.

"Godel addressed all logical systems, not just mathematics, right?"

Wrong.

Great - thanks.

And after a little more googling, it doesn't even seem to be mathematics in general - it's specifically an arithmetic theorem.

But we shouldn't take this too far - it has been generalized to any formal semantic system. ie, "Not Wrong", in that regard at least.

"math is *not* completely logical in some sense"

Maybe not COMPLETE-ly logical, but incompleteness is not illogical.

He says it backwards. It's closer to say that logic is the language of mathematics--but only if you mean logical thinking, rather than formalism. It was a fun ride this century to see how much of mathematics could be founded on a formal logic, but historically--and in most people's lives, I suspect mathematics predates or at best parallels any language of logic (conditionals, conjunctions, disjunctions--and especially negations--are expressed at a pretty early age).

I am a keen observer of statistics and political anecdotes, and I can ask a bunch of hard questions. Does that make me a great macro-economist?

"If they can't predict, we must convict."

It's a very good review. I found it a pretty poor history. I quit reading consecutive pages of the book and began digging through the index but gave up even on that. Robert Skidelsky, like every biographer, loves his subject and can't get outside of that gravity well.

No matter what you think of Keynes you will not like this book. It's too shallow in economics and provides no real contrast with the era or other schools of thought. It's horrendous on discussing economic theories (look at the index and try a few passages if you don't believe me). Historical figures who didn't love Keynes are ignored and the third part of the book reads like a religious tract.

My copy's in the resale box, not on my shelves.

Ya - I bought the damn thing a day or two before Mankiw's review came out! Haven't read it yet - I still probably will at some point, but I wish I read Mankiw's review before hand :)

Mankiw is a master equivocator who lives by the philosophy that a man of wisdom can't possibly stand by logical principle but is in fact recognized by his indecisive, "Maybe."

So Don agrees that perhaps the pro-Keynes camp makes some valid points?

vidyohs comments on Boudreaux posting on Mankiw reviewing Skidelsky on Keynes.

This economics stuff makes my head hurt but I think I am getting the hang of it. :-D