No wonder my blog has caught on with the public
Here’s Nobel Laureate Tom Sargent:
Mr. Sargent says his most important work is spoken “in the beautiful language of math.” He knows it’s not widely understood.
“The kind of work we do, that real economists do, will never catch on with the public,” he says.
Unfortunately I’m buried in work right now. Not much blogging in the near future.
Tags:
7. December 2011 at 20:00
The sad thing is, and maybe the good thing is, he’s right. Real economists use models rather than waving their hands. A lot.
7. December 2011 at 20:40
Until “models” have empirical grist worthy of their mathematical intricacy, they’re nothing but silly toys.
7. December 2011 at 21:00
Math and intricate models are nice but people cannot forget to include economics and wave away the messy parts of life. Economics is so much more than physics with people instead of particles.
8. December 2011 at 01:08
All economists would do well to read and reread that other “Nobel” prize winning economists lecture “The Pretence of Knowledge”.
8. December 2011 at 04:40
ugh. what nonsense. I spend a significant amount of my time with math (mine and other peoples models these days, and empirical fit of those models), have degrees in it. I am old school: it does not matter what is in your head if you can’t communicate it. Second, I have seen a lot of models in my day. garbage in, garbage out. Putting together a model is no trick. Putting together a model that allows one to test an assumption (or reduce the set of likely assumptions to a smaller set), now THATS a trick. It’s pure hubris and arrogance to think that models are reality unless they explain the data. There is way to little of that going on in the econ modeling world, IMO. Also IMO, in the old days, the best modelers were in academia. Nowadays, most of the strongest quants work for (or consult with) Goldman Sachs or some other bank. The first thing I learned out of graduate school was that the best research going on would probably not be made public as long as it made the firm money, or until there was a much better model that made the firm MORE money.
8. December 2011 at 04:57
Math is only as good as the assumptions behind it. Besides the lack of constant relationships in the social sciences makes math a particularly bad tool for studying them. “Real” economists can keep wasting their time. When these two guys were asked about the US economy after winning the Nobel; they had nothing to say. When they were asked about the European situation they had nothing to say. So we have our best economists knowing math with nothing to say about the worst economy since the Great Depression. Why do we pay these guys?
8. December 2011 at 05:37
Amazing hubris.
8. December 2011 at 06:08
Chicagoist, You are right that economists should use models. I certainly do. But that’s not what he’s saying.
Neal and Peter, I see lots of people here are linking models and math. Keynes had a model in the General Theory, but almost no math. Friedman and Schwartz had a model in the Monetary History, but almost no math. I’ve noticed that both books were pretty influential. Of course F&S had lots of empirical evidence, which supports Neal’s point.
Hayek had models too.
Perhaps I’m obsessing too much about the model-math distinction. I certainly agree with the thrust of your arguments.
Nevorp, Good point.
dwb, That’s what I think too.
John, Good point.
Joe2, I should add that this post isn’t a personal attack on Sargent. If you read the entire article he seems like a really good guy–very modest. It’s just that I think his vision of economics is too limited.
Of course I could have put names like Paul Krugman and Tyler Cowen in the title–economists who communicate to the public far better than I do. I suppose that would have made Sargent’s comment look even sillier.
8. December 2011 at 06:16
Even as recently as five years ago, many people thought that economic issues had nothing to do with them. To go around talking about the importance of economics in what was happening could get one some blank looks in the middle classes (not so much in the lower classes). Why was that? Perhaps the person who thought “everything’s okay” assumed, if the models are working, why should we even worry about them? But now that people are concerned about what lies behind the screen, they are unprepared in their need to think fast on their feet. That’s the sad part, so many people don’t even know what lay behind the screen in the first place, that they need to work with in the present. That’s what made the dialogue so incomplete in the Tea Party. They knew that the government could not keep spending indefinitely, but because they only started paying attention when housing crashed, their arguments simply were not ready. In some cases their relevant dialogue got shut down altogether, when they realized they did not yet have ways to fill the vacuum that would be created by taking away the ability of government to spend.
8. December 2011 at 07:03
“Perhaps I’m obsessing too much about the model-math distinction.”
I don’t think you can obsess enough about it, before you know it people will confuse the math for the model and recommend raising the interest rate to prevent deflation as the natural rate rises 😛
8. December 2011 at 09:12
There’s no math at all in The Theory of the Firm or the Problem of Social Cost, nor in The Use of Knowledge in Society. Not much in the Permanent Income Hypothesis or the idea that ‘Inflation is always and everywhere a monetary phenomenon’.
On the other hand, a guy who has proclaimed that he’s a mathematical economist first and foremost makes silly, undergrad errors in logic on a regular basis on the Op-ed page of the NY Times.
Maybe Marshall was on to something about ‘burn[ing] the math’.
8. December 2011 at 09:18
I agree there’s a distinction to be made between models and math. My disdain is reserved for the sort of narcissistic model that’s so abstruse it doesn’t make any predictions. Call them the string theory of economics.
I suspect that the models in General Theory or F&S or Hayek could be expressed mathematically, but in simple terms which make easy, coarse, robust predictions* that can be verified by observation. My point is that I suspect economic observations are not nearly precise enough to distinguish between mathematically complicated and mathematically simple models.
8. December 2011 at 09:20
You know what da Vinci said “Simplicity is the ultimate sophistication”.
8. December 2011 at 09:41
Patrick,
You can add arbitrage to your list of important economic ideas that don’t require much math to understand. And while calculus helps in understanding things like why marginal revenue has to equal marginal cost for profit maximization, it can be understood without the math.
But math becomes important when you’re trying to do more complicated “complete” models with budget constraints, transversality conditions, intertemporal optimization, and so forth. You can’t do this stuff in words, you have to use math.
8. December 2011 at 13:11
In the supermarket checkout line today, I was browsing Time magazine and came across an economics column by Rana Forooha on the case for inflation and it mentions NGDP level targeting so you’ve been mainstreamed. (I’m coming from the Yglesias-DeLong-Krugman commie-pinko axis.) Anyway good to see.
The link is subscriber only:
http://www.time.com/time/magazine/article/0,9171,2101016,00.html
My father gets Time magazine and is always going on about the gov. running the printing presses, so I’m planning on tweaking him by pointing out the column.
The voting public doesn’t need to know macro if the technocrats do their job, but they haven’t been doing their job lately.
8. December 2011 at 13:16
Any math that argues with “all growth comes from productivity gains” is not math.
Once the eggheads are in that box, that can do any math they want.
8. December 2011 at 13:18
As such, Obama can’t do math…
“However many jobs might be generated by a Keystone pipeline,” he said, “they’re going to be a lot fewer than the jobs that are created by extending the payroll tax cut and extending unemployment insurance.”
http://campaign2012.washingtonexaminer.com/blogs/beltway-confidential/obama-more-jobs-jobless-benefits-keystone/244871
8. December 2011 at 13:20
‘You can’t do this stuff in words, you have to use math.’
You certainly can economize on ideas with math, but it has its limitations too. In the end, you have to use words. To be obvious, legislation isn’t written in math even if a lot of ‘mathematical economists’ want their work to be the basis for legislation.
8. December 2011 at 13:26
Here’s what von Mises said about mathematical econ; “This is not a dispute about heuristic questions, but a controversy concerning the foundations of economics. The mathematical method must be rejected not only on account of its barrenness. It is an entirely vicious method, starting from false assumptions and leading to fallacious inferences. It’s syllogisms are not only sterile; they divert the mind from the study of the real problems and distort the relations between the various phenomena” (Human Action 347).
His basic point is that experience of economic history is an experience of complex phenomena. Stats can present historical facts but it can’t form a theory the way a laboratory observation would. No one can observe ceteris paribus changes in the real world. All the empiricists and mathematicians are working off an aprioristic theory anyway whether they know it or not.
Furthermore, plugging any type of price into an equation is misleading because that would treat money as a univeral standard of measurement when in reality the value of money is always fluctuating. You can’t measure goods in prices the way you could measure length with a yardstick. To quote Mises again, “Prices aren’t measured in money; they consist in money” (The Theory of Money and Credit).
Probably my biggest objection to the way guys like Sargent study economics is that they pay no attention to the market process. Math is not a suitable tool for describing how a market moves from point A to point B. That requires logic and verbal reasoning and without that foundation, economists are simply compiling volumes of useless equations and wasting countless hours of labor that would have been better spent by them working at McDonald’s.
8. December 2011 at 13:31
As luck would have it;
http://www.voxeu.org/index.php?q=node/7402
I’m sure they’ve worked hard on the math, but this seems more than a trifle naive:
‘…a better policy would be to first close loopholes so as to eliminate most tax avoidance opportunities and only then increase top tax rates. With sufficient political will and international cooperation to enforce taxes, it is possible to eliminate most tax avoidance opportunities….’
8. December 2011 at 13:33
Peter K,
An economy is a complex ecosystem of individual decisions directed by individual value scales. It’s not something technocrats can run because it is impossible for any one man or group to know the individual value scales of other people. That’s why market economies where individuals have sovereignty consistently outperform planned economies. It would always work more smoothly to let individuals plan their own lives than to have other people plan their lives for them (even our seemingly benevolent technocrats like Bernanke are planning our lives for us in an economic sense).
8. December 2011 at 13:41
An even better example comes courtesy of the Falkenblog
http://falkenblog.blogspot.com/2011/12/private-sector-incentives.html
and this from a Northwestern grad student, attempting to show that the profit motive isn’t really an incentive for most workers:
http://afinetheorem.wordpress.com/2011/11/21/decentralization-hierarchies-and-incentives-a-mechanism-design-perspective-d-mookherjee-2006/
‘… it is just a couple lines of math to prove. Assume agents have information or types a in a set A. If I write them a contract F, they will tell me their type is G(a)=a’ where G is just a function that, for all a in A, chooses a’ to maximize u(F(a’)), where u is the utility the agent gets from the contract F by reporting a’. The contract given to an agent of type a, then, leads to outcome F(G(a)). If this contract exists, then just let H be “the function concatenating F(G(.))”. H is now a “truthful” contract, since it is in each agent’s interest just to reveal their true type.’
What’s beautiful about that?
8. December 2011 at 13:44
John,
You might as well forbid the use of German in economics if you’re going to ban math. Math is nothing more than just another way to express certain things. And like any ‘language’ it has its advantages and it has its disadvantages compared to other forms of expressions. Methodological strictures such as ‘no math ever’ are silly. Keep an open mind and use what is useful and persuasive. If it would help my argument I’d even resort to interpretive dance and considering Mises has not objected to that, so should you.
8. December 2011 at 13:56
“That requires logic and verbal reasoning and without that foundation, economists are simply compiling volumes of useless equations and wasting countless hours of labor that would have been better spent by them working at McDonald’s.”
Hey now, let’s not slam math. There is no logic nor verbal reasoning that is not at its heart math. The problem is not with the use of mathematics, the problem is with observational error and uncertainty.
8. December 2011 at 15:13
Neal there really isn’t observational error and uncertainty in econ. It is impossible to run experiments or make observations because the causal links are too dense. Data never definitively proves or disproves a theory in the social sciences. Understanding that is key to seeing why these issues are so ideological and controversial.
Here’s the Austrian answer to the epistemological problems of social sciences. Reasoning has to be deductive and start from simple basic assumptions. For instance people act in order to exchange one state of affairs for a more satisfactory one. Economics is an a prioristic science like geometry. The use of a similar reasoning to geometry is really what econ has in common with math.
The second very cool (to me) and important principle is methodological individualism. All effects in an economy of any size always trace back to individual action. I like this because tracing effects back to individual action always makes cause and effect seem so much clearer.
8. December 2011 at 15:16
Can anyone that reads this site show me an example of how math helps with the understanding of the market economy? Is there any situation where math has an advantage in this field over verbal reasoning? Usually I find that when I see a math equation in econ it greatly over simplifies in a way that leads to much greater confusion.
8. December 2011 at 15:42
Math seems to work better in economics for investigating the limits of economic models, than for creating models for complicated economic systems.
There are so many bad models, that showing that one produces ridiculous results is quite useful.
With all models, mathematical or otherwise, it is critical not to use them outside their domain of validity. This seems to cause some of the most aggravating problems.
Aggregate demand is a good example of this. It’s useless when you’re trying to model systems where people don’t all have similar preferences. Aggregating capital has similar problems.
Yet you see these models used every day without any discussion of why this use of the model is appropriate even when their provably necessary assumptions are not met.
Assume a spherical cow of uniform density is supposed to be the punchline of a joke, not a postulate for a theorem of bovine management.
8. December 2011 at 15:47
@John: Show that an increase in inflation expectations leads to increased inflation today. Do so entirely verbally, with no diagrams or equations and explain all of your transmission mechanisms.
Or solve the same problem with the help of a few diagrams and equations. The second will be far clearer.
An economist ought to be able to explain their reasoning in words, in diagrams, and in equations. The exact combination of the three will depend on situation and context.
Or, to take a second example, it’d be very difficult to explain the arguments and conclusions of the Solow growth model entirely in words. A single equation and a single graph do wonders to help the argument. The intuition can be shown in words (“with diminishing MPK, sustained capital accumulation will not lead to long-run growth…”) but it becomes clearer, at least to me, with diagrams and mathematics.
A third example: Comparative statics (arguably the most important part of any model) are far easier to do mathematically than purely verbally. Even if you want to back away from “models” entirely, any time you are making policy prescriptions you’re implicitly doing comparative statics and I’d rather see the argument summarized in four equations than in pages of text.
An example where you’re right would be, say, supply & demand at the 101 level. There words are fantastic, diagrams slightly less so, and mathematics little more than obfuscation.
It is a great advantage of both this blog and Worthwhile Canadian Initiative that they stick to verbal arguments; but it’s also clear that one could formalize Rowe or Sumner in a simple model quite easily.
8. December 2011 at 16:06
Integral,
Or as Marshall said:
“(1) Use mathematics as shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This I do often.””
8. December 2011 at 16:18
It’s amazing how using 2 different equations with the same economic data set produces such radically different results.
8. December 2011 at 16:55
John, you wrote:
“Neal there really isn’t observational error and uncertainty in econ. It is impossible to run experiments or make observations because the causal links are too dense. Data never definitively proves or disproves a theory in the social sciences. Understanding that is key to seeing why these issues are so ideological and controversial.”
I am not so certain that your rebuttal is consistent. It is indeed impossible to run thorough experimental tests, but that hasn’t stopped other observational sciences like paleontology and astronomy and geology from gathering data from complex and causally difficult environments.
Likewise, I agree that it’s difficult to definitively prove or disprove propositions, but I contend that this difficulty is because it is difficult to gather data, not because it is impossible to gather data. Some propositions have enough data to be reasonably established: “centrally organized economies experience lower long-run growth than market-oriented economies, and the extent to which long-run growth trends suffer is roughly proportional to the extent to which the economy is centralized;” “imposition of a good’s price is correlated to increased illegal exchanges and surpluses or shortages of the good on the legal market;” and so forth.
You wrote:
“Here’s the Austrian answer to the epistemological problems of social sciences. Reasoning has to be deductive and start from simple basic assumptions. For instance people act in order to exchange one state of affairs for a more satisfactory one. Economics is an a prioristic science like geometry. The use of a similar reasoning to geometry is really what econ has in common with math.”
In other words, the Austrian answer to the difficulty of data gathering is … to reject the possibility of winning knowledge and embrace narcissistic navel-gazing? Forgive me, but I do not find capitulation in the face of difficult problems an appealing course of action.
Actually aiming to become like mathematics is to concede the central problem of the whole science, which is to describe what’s actually happening out in the real world. Mathematics is not a science! It’s the exploration of possible abstract patterns of ideas. If you’re an economist, it seems to me that you should care about how economies actually work, and your work should be directed toward figuring that out. Math should be a tool, not a goal.
Or, to paraphrase Feynman, “Math is to science as masturbation is to sex.”
“The second very cool (to me) and important principle is methodological individualism. All effects in an economy of any size always trace back to individual action. I like this because tracing effects back to individual action always makes cause and effect seem so much clearer.”
This also excites me! I wonder frequently about whether statistical mechanical methods could be used to derive useful models of market activity, since they play a similar role in physics transition from particulate models to aggregate models.
A paper I saw a while ago successfully modeled the corporate employee pay distribution under certain thermodynamic assumptions, then tested the model against actual recorded distributions. I thought that was a very interesting approach.
PS- I strongly suspect that economists actually butcher math. If they’re anything like the physicists, they don’t really understand the math they’re using. For scientists, math is (should be) a tool, not a goal!
8. December 2011 at 17:05
By the way, here’s a neat way math helps understand the real economy. My simple labor supply/demand model implies the Laffer curve is concave down, so I predict any change in taxes, up or down, will result in revenue below what static predictions would indicate. I also predict that as income taxes rise, the marginal increase in income with respect to tax falls.
There: from a very simple, almost trivial, mathematical observation (which is actually simpler to express mathematically than verbally, I might add!), I have made predictions about qualitative patterns in the graph of (OECD income tax/GDP) x (per-capita tax revenue) and I have made predictions about the change in tax revenue accompanying every tax change in history.
Or take, for example, Friedman’s criticism of discretionary countercyclical fiscal policy: http://marginalrevolution.com/marginalrevolution/2006/11/milton_friedman_4.html
I think this illustrates the utility of mathematics quite nicely.
8. December 2011 at 21:31
There is a higher fact than math…
All growth comes from productivity gains. Natch on your silly population response.
The problem occurs when certain mathy folk think they can argue around this fact.
If they eat it, if they admit than any math which argues with this is wrong, then they are doing math.
This is the base root experience of business and economics, how can I do it cheaper, faster better is where all the magic happens.
Math isn’t a big deal, if they admit it is #2.
9. December 2011 at 04:07
Exactly what I’m talking about:
http://www.nytimes.com/2011/12/09/opinion/krugman-all-the-gops-gekkos.html?_r=1&pagewanted=all
Here DeKrugman attempts to argue around and around to somehow say that destroying old weak companies isn’t a good thing… as if somehow trying to create laws that hold on to old dead past jobs is acceptable…
And he violates the PRIME DIRECTIVE of economics and business….
He’ll draw graphs and use math and squirrel every which way, but one cannot argue with God’s natural law.
9. December 2011 at 04:41
Continuing the lesson about the mind of God, we see Megan McArdle explaining why a $1500 food processor is genius:
http://www.theatlantic.com/life/archive/2011/12/in-defense-of-kitchen-gadgets/249624/
“After all, the new gadget represents hours, maybe years, of human ingenuity applied to the problem of making repetitive tasks easier, faster, safer, or more convenient. Which basically sums up 90% of human progress since the industrial revolution, so don’t give it short shrift. We should enjoy these things–their sleek design, their nifty features. I love machines of all types, from welding robots to 50-foot cranes, and when they are specially designed for my favorite room of the house, I love them even more.”
“And while I occasionally feel the pull of those loving evocations of laborious kitchen prep, it never lasts much beyond chopping that first onion. I don’t find it uplifting to spend half an hour prepping vegetables; I find it tedious. What I like about cooking is the planning, the tweaking, and the eating, not the labor of stirring at a hot stove, or the beautiful geometry of reducing carrots to an even dice. And no, it’s not that I don’t know how to do those things–it would be ore interesting if I did.”
This is what life is all about… and it is only if thousands of such high end inventions get built and marketed at the top of America, can the idiocy of bad design, pure unadulterated economic mistakes be the STUPID TAX paid by rich people….
So that the technology and inventions that actually work wash out in low cost $5 food processors for the masses below.
Productivity gains are the only real form of growth, and growth is always good.
That alone is Econ 100.
We should hold personal grudges and great social animosity against anyone who argues with it.
Burn the witch. Burn her.
9. December 2011 at 07:41
I did pretty good at math back in high school and managed to get through my differential equations class @ MIT….but it seems to me the mainstream economists use math as a tool to keep attention and real discussion away from the basic questions regarding our economy.
Can creating new money bring about prosperity?
Can the government “give” to anyone person without taking from another?
While I don’t agree with all of Sumner’s ideas, I am thankful that someone is asking why can’t monetary policy be done in this way or that way? There are many holes in the “logic” used for managing our monetary policy currently. Scott has brought a great deal of attention to one of the logical fallacies suporting today’s system of monetary manipulations. Now the fed and mainstream economics is discrediting itself in front of a wider audience….that is good.
9. December 2011 at 07:54
“All growth comes from productivity gains.”
productivity gains come from people being incentivized with a system of property rights…when people can count on being able to keep the product of their labor and whereas other people can count on NOT being able to use force to gain their wealth. Then all people are forced to focus on productivity gains.
Thus when government(organized monopoly of force) gets into the business of selling its plundering services to others you destroy productivity growth. Much of the population starts focusing on how best to convince governemtn to plunder for them, much of the population works for the leviathan parasitical plundering force…the productive population becomes more focused on protecting themselves from plunder and a rapidly decreaing percentage of the population is focused on actual productivity gains.
Math equations are great…I love them…you could make a system of equations conveying what I just said…but it would do much…you get good economist jobs by defending the federal reserve and promoting socialism.
9. December 2011 at 08:27
I don’t know why Morgan’s point is getting so much flak. It is the central observation of the Solow growth model – z-factor productivity drives all sustained improvements in living standards. Every other model is tinkering with short-term equilibria. The way we handle these short term disruptions can have long-term consequences, but that is ultimately captured in z-factor productivity.
What is z-factor productivity? It represents technology, the efficiency of our use of capital and labor, and the efficiency of our social organization (i.e. institutions).
9. December 2011 at 08:46
Well I finally found some proof that the US government creates terrorist. I even found a video of them doing it:
http://www.lewrockwell.com/blog/lewrw/archives/100312.html
Whose side would you be on in a fight…the little boy or those imperial troopers?
9. December 2011 at 13:17
Cthorn, now if we could just jump people from that to:
2. only savings can truly be invested.
we could get everybody focused on the re-investment of savings from productivity gains as the only form of improving the human lot.
John, to me Scott’s truly compelling thing is IF AND ONLY IF if would cause us to raise rates faster than we have historically.
His is the best dirty trick I’ve seen to literally use monetary policy to reduce the size of government… it is better than Greenspan molesting Clinton in Jan 1993.
9. December 2011 at 13:18
“… a better policy would be to first close loopholes so as to eliminate most tax avoidance opportunities and only then increase top tax rates. With sufficient political will and international cooperation to enforce taxes, it is possible to eliminate most tax avoidance opportunities…”
Thanks, Patrick. As one who’s worked professionally in the tax area for, er, mumbly mumbly years, that’s the funniest thing I’ve read all week.
First just close the all the loopholes and then we can increase top tax rates as high as we want. Easy! Especially internationally!
ROTFL! 🙂
9. December 2011 at 18:53
Everyone, With so many papers to grade I won’t answer each individual comment. I mostly agree with both sides of the argument. Math is fine and non-mathematical explanations are fine.
I’ll take a shot at Integral’s challenge:
“@John: Show that an increase in inflation expectations leads to increased inflation today. Do so entirely verbally, with no diagrams or equations and explain all of your transmission mechanisms.”
Inflation is (by definition) a decline in the value of the medium of account. If you expect future inflation, you expect the value of the medium of account to decline. This reduces the current demand for the medium of account, and hence reduces its current value. Thus expectations of future inflation produce current inflation. Is that right?
I’m puzzled by the fact that people differentiate between “math” and “graphs.” A graphical proof is a mathematical proof, as geometry is a part of math.
10. December 2011 at 12:59
I know my Turkish money will lose 20% in value over the next year, so I run out and buy a Gucci Silk shirt.
1. Gucci raises their prices.
2. The government of Turkey doesn’t fear anyone in the private sector amassing savings wealth to become powerful, so bureaucrats become less and less productive and get paid more and more. Cost of govt services goes up.
10. December 2011 at 13:04
A system without inflation has the added benefit of putting the screws to public employees making them productive, increases savings.
This fact is unavoidable: if public employees got only pay increases at inflation from 1998, they’d be making $1.2T a year, instead they are making $1.7T.
That lost $500B could be paying 20M @ $25K, and we could be forcing all of them to give us foot massages on command.
The ENTIRE problem is public employees.
Scott refuses to positively weigh the future benefits of the bashing they are taking, the lesson that is being taught.
Those benefits are HUGE.
10. December 2011 at 13:08
Morgan are you saying real public sector wages shouldn’t increase with growth?
10. December 2011 at 19:36
“Inflation is (by definition) a decline in the value of the medium of account. If you expect future inflation, you expect the value of the medium of account to decline. This reduces the current demand for the medium of account, and hence reduces its current value. Thus expectations of future inflation produce current inflation. Is that right?”
If you use “hence,” you’re making a mathematical argument. No exceptions 🙂
10. December 2011 at 22:17
[…] HT Scott Sumner. […]
11. December 2011 at 07:11
Morgan, I think public employees have been doing better than the rest of us during this recession.
Neal, If I say “You are being too picky, hence I will ignore your comment,” is that also a mathematical argument? 🙂
11. December 2011 at 07:47
Yep! (This is like the “If I say something I lose, if I’m quiet she wins” game my wife sometimes plays with me 🙂 )
12. December 2011 at 09:11
Neal, Can you write an assertion that’s non-mathermatical?