tag:blogger.com,1999:blog-17232051.post2758550745015186441..comments2024-03-28T03:16:14.104-04:00Comments on Noahpinion: A few words about mathNoah Smithhttp://www.blogger.com/profile/09093917601641588575noreply@blogger.comBlogger112125tag:blogger.com,1999:blog-17232051.post-90065527774933633222013-11-30T00:49:26.860-05:002013-11-30T00:49:26.860-05:00I always feel like Im making a little toy that kin...I always feel like Im making a little toy that kind of acts like a person or country, maybe.I think a lot of times, the necesssity of writing down a model leads people to oversimplify issues. Building a model is tough work, and including lots of features in an elegant way is even more difficult, so what often happens when a "researcher" sets out do "research" on topic X is that they spend 90% of their time building a model on topic X and 10% of their time <a href="http://www.ipracticemath.com/" rel="nofollow">Learn</a> about topic X. As a result, their paper contains a long boring model about a topic on which they essentially know nothingLearnhttp://www.ipracticemath.com/noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-51252538404023656082013-09-08T13:33:24.162-04:002013-09-08T13:33:24.162-04:00As one trained in physics, I would like to comment...As one trained in physics, I would like to comment on this most interesting history of math and economics, and the difficulties which economists have with the understanding of the proper application of math in the field. I think that what is important to keep in mind about physics is that its goal is to understand the inanimate world, and that this is an endeavor driven by the curiosity of the physicist. This curiosity led physicists ( by whom I mean anyone with an interest who does work investigating the inanimate world) to make observations about the world and to notice regularities in the world. Only then did attempts to apply math appear reasonable. The progress of physics may have evolved without the use of mathematics. That is, there is no a priori reason to believe that mathematics is related to the effort to understand the inanimate world. The fact that mathematics has played such an important role in physics is quite a marvel to physicists. Eugene Wigner gave a speech which summed up the relationship of physics and math quite nicely, which I highly encourage others to read. You can find it here: http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html <br />I think the title captures the ideas nicely: "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". In other words, math is used in physics not because physicist want to use math, but because it is so dramatically effective in describing the laws of nature.<br /><br />Physics, at its root, is based on a belief system. That is, physicists believe that the universe is governed by immutable physical laws, and that we can discover these laws by making systematic observations of our world. That human beings can divine these laws through these methods. The language of mathematics has been found to be exceptionally effective in describing these natural laws. But not all of mathematics is applicable to physics, rather the physicist picks and chooses carefully what works from what is irrelevant. Wigner makes a key point that most mathematics used in physics was derived by the physicist as a necessary part of the investigation. Only later is it often realized that a description of the math was previously made by a mathematician. Efforts to relate and manipulate the values associated with the physical world led inevitably to new mathematics which were explicitly suited for that purpose.<br /><br />The mathematical descriptions of natural laws are called theories, and the key property of these theories is that they can be used to make predictions about the phenomena that they describe. This ability to make predictions is what leads to the belief that the natural laws are immutable and are regular and continuous. We test these theories using experiment. If this were not true, then we would be left with empiricism, which is the merely cataloging of events and values. These events and values may then repeat themselves in the future, but we have no way of knowing this just from the past events. This confidence that we will continue to find laws of nature Wigner calls the "empirical law of epistemology"<br /><br />Economist seem to have been guided to some extent by the success of physicists in using math to create theories, and have sought to emulate this success in economics. This is a valid course to attempt as the payoff would be so great. But the caution here is that economist must also evaluate the applicability of mathematical descriptions to the laws of economics that they seek to create and be willing to reject those that don't stand up to testing. Perhaps even abandon attempts to use math as the language of economics if it is not appropriate.David W. Vielhttps://www.blogger.com/profile/16559249540276639324noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-76973340112650004972013-09-05T09:50:43.644-04:002013-09-05T09:50:43.644-04:00this days many young peoples are facing more troub...this days many young peoples are facing more trouble with mathematics since they are having more stress in <a href="http://www.seolinksubmission.com/my-classified-sites.html" rel="nofollow">thinking</a>rahulhttp://www.seolinksubmission.comnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-20437314765018099252013-08-31T20:39:44.505-04:002013-08-31T20:39:44.505-04:00A naive person might expect that any intelligent p...A naive person might expect that any intelligent person would leave an economics PhD program after the 1st year, as , obviously, the education offered is phlogistonism.<br />Yet, clearly, this doesn't happen.<br />Perhpas we should have more respect for the Scholars of Marxist Lennist thought in the USSR.<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-37281128558859265832013-08-30T21:30:47.670-04:002013-08-30T21:30:47.670-04:00Physics uses physical constants. Examples: The spe...Physics uses physical constants. Examples: The speed of light in a vacuum, electron mass, etc.<br /><br />Paul Krugman was quoted as saying, in defense of "macro-math," that "macro math is also useful for clarifying your thinking, checking your self-consistency, and exploring the implications of various sets of assumptions." <br /><br />What are the economic constants that Paul Krugman uses in his "economic math" to "clarify his thinking?" <br />Adamhttps://www.blogger.com/profile/00973885100689935280noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-7226505806110760972013-08-26T07:31:04.829-04:002013-08-26T07:31:04.829-04:00I definetly agree. I quit my econ master's pro...I definetly agree. I quit my econ master's program and graduated from applied maths, for similar reasons. (In Finland, you can do such a switch.) Guess, if I have been pissed off by this a few times? Now I'm completing my PhD, and I know that I would make at least 1,000 a month more as an econ PhD - notwithstanding the option of going into government as an economist after my master's. Man, I would be rich!<br /><br />On the other hand, I'm a little bit less cynical about econ math now. I believe that rationality may be the right description of *average* human action *in the long run*. Given the complexity of real-world economics, we should be grateful even for average long-run descriptions, I believe. They can be used as tools of thinking better than mere words, I would guess.<br /><br />Having said that, I would more or less put the economists' education upside down. (Through some friends, I know also what happens in econ grad schools.) I would put in much more economic and industrial history. I would also add much more econometrics. Not necessarily fancy models, but hands-on stuff with real data - preferably every week. And if this is too much to handle for some young guy, yes, I would cancel the more sophisticated micro and macro models. Because they do not give you so much, after all.<br /><br />MarkkuAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-15498981863781355392013-08-25T13:18:01.997-04:002013-08-25T13:18:01.997-04:00What fantastic comments! (I'm sure)What fantastic comments! (I'm sure)RebelEconomisthttps://www.blogger.com/profile/13241098878248190971noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-70089937970129053262013-08-25T04:48:50.725-04:002013-08-25T04:48:50.725-04:00The author is very kind in trying not to spell the...The author is very kind in trying not to spell the mathematical truth: economy is not a science, is a religion meant to lie to the people for the interesets of those in power.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-8850924646746336992013-08-24T23:40:06.851-04:002013-08-24T23:40:06.851-04:00This is the thing that separates maths from physic...This is the thing that separates maths from physics --<br /><br /> http://en.wikipedia.org/wiki/Dimensional_analysis<br /><br /><br />It is also the bit that most economists get wrong, especially macro economists. Which is strange, because it is such an easy thing to check, and economists don't even have a need for all those annoying units like electrical charge and stuff.Telhttp://lnx-bsp.net/noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-84665631362241017382013-08-24T23:32:43.337-04:002013-08-24T23:32:43.337-04:00And you sir, just explained why I didn't get a...And you sir, just explained why I didn't get an advanced econ degree. <br /><br />Having gotten a math and compsci minor while getting my econ BS, it was obvious to me just how preposterous most macro econometrics really is. <br /><br />It's only been in the last few years that I'm starting to see people using basic simulations to try to predict actual real world behavior. And some of the work being done in virtual economies is starting to give me hope that macro will come out of the dark ages.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-36576374733810332122013-08-24T22:27:31.138-04:002013-08-24T22:27:31.138-04:00Why make a special distinction for macro? I was ta...Why make a special distinction for macro? I was taught a fairly standard micro curriculum as an undergraduate: we learned the usual models for consumer choice, firm behaviour, general equilibrium information economics and so on with no attempt at any point to make us think about how we might test these models. I never studied economics at a higher level, but my impression is that graduate micro mostly just extends the mathematical precision and generality of what I studied. I'm still not sure why the "optimizing" paradigm is so dominant in all of economics and why more naive models based on, for example, simulation of rule-following agents are not investigated. In the case of models of competition and principal agent problems, the textbook approaches seemed particularly unrealistic and removed from reality. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-63577624394313789382013-08-24T17:30:03.610-04:002013-08-24T17:30:03.610-04:00Read some Steve Keen for Christ's sake! He is ...Read some Steve Keen for Christ's sake! He is doing real math in macro. Paul Krugman is a hack, doesn't even come close.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-22432068954894281972013-08-24T13:53:38.459-04:002013-08-24T13:53:38.459-04:00TBH this well-spoken rant gave me the impression t...TBH this well-spoken rant gave me the impression that you've come to the right conclusions for the wrong reasons. Your emotional satisfaction seems to be your baseline, and while that's rational (as a human being) this is not what math is ultimately about. Fuzzy math exists because people are obsessed with fulfilling their emotional needs at any cost, even at the expense of warping and outright denying reality. Math is not about getting high off of some pedantic power trip, it is instead as you surmised, about revealing deeper facets of reality that allow us to make better decisions. This is rarely (if ever) a pleasurable and emotionally rewarding experience since it predominantly countermands the shallow emotional impulses that are responsible for the happiness of the hedonistic junkie that lives in all of us.neotoyhttps://www.blogger.com/profile/13419656232431119124noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-80282817600227194022013-08-24T11:50:26.839-04:002013-08-24T11:50:26.839-04:00Okay Anon, but Kolmogorov is ubiquitous in contemp...Okay Anon, but Kolmogorov is ubiquitous in contemporary probability theory. You could say probability theory may be otherwise characterised, as it was when it wasn't done so rigorously, but TODAY probability is understood and actually taught as measure theory. The only place I've encountered other axiomatizations is in my person historical readings (Laplace) and in my philosophy courses (Carnap) which were arguably doing something quite different than the mathematicians. Anonymoushttps://www.blogger.com/profile/05932496549711542374noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-14666305324534569862013-08-24T09:34:50.415-04:002013-08-24T09:34:50.415-04:00Let's see: "probability theory is mostly ...Let's see: "probability theory is mostly measure theory under with concepts under a different name". No. You should read up on the background of Kolmogorov, who re-interpreted (some say rehabilitated) probability by re-defining as measure theory. So it's not so much that probability is hiding in some guise of measure theory. It is in fact entirely founded and formulated as measure theory - again based mostly on the work of the Soviet mathematician. His story is quite fascinating - how he developed as a mathematician in post-Revolution Russia, then the Soviet Union, his conflicts, his discoveries, and his contributions to so many areas of math. Good read - and, as a i say, you'll see how probability's foundation was re-constructed with measure theory.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-58224413538847749622013-08-23T23:05:11.628-04:002013-08-23T23:05:11.628-04:00Does that count as an AER? Or is that more like a...Does that count as an AER? Or is that more like a P&P?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-69334636799747246242013-08-23T04:40:27.401-04:002013-08-23T04:40:27.401-04:00Just because a quote is pithy, doesn't mean it...Just because a quote is pithy, doesn't mean it adds any value.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-77910267990797067712013-08-22T21:31:31.914-04:002013-08-22T21:31:31.914-04:00stating the conclusions as relevant when the assum...<i>stating the conclusions as relevant when the assumptions are false (or not even close to true).</i><br /><br />Agreed.Noah Smithhttps://www.blogger.com/profile/09093917601641588575noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-25753081155661023912013-08-22T21:07:50.861-04:002013-08-22T21:07:50.861-04:00For Anonymous,
I always find it amusing when some...For Anonymous,<br /><br />I always find it amusing when someone brags openly about their ignorance.<br /><br />The following is the blurb that Kenneth J. Arrow provided for the 2004 3 volume _Complexity in Economics_.<br /><br /> "The recognition of the importance of complex systems in physics and biology has led to the study in economic systems, usually characterized as governed by a large set of interacting nonlinear dynamic systems. It is clear that these phenomena are observable and are not necessarily inconsistent with standard economic reasoning. Professor Rosser has collected a large number of papers, some form not-easily-accessible sources, which show the application of complex systems theory to a variety of economic phenomena. This collection will be invaluable to the development of new and necessary thinking in economics."rosserjb@jmu.eduhttps://www.blogger.com/profile/09300046915843554101noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-48104260050838915242013-08-22T20:27:33.682-04:002013-08-22T20:27:33.682-04:00Thank you for responding.
That's reassuring ...Thank you for responding. <br /><br />That's reassuring to know that that is probably what he meant. <br />Maybe I just missed it, but I couldn't find that anywhere; but I think you have a better idea of what he meant to say, so thank you.<br /><br />I don't know enough about the models he's talking about, but I still think the distinction I'm making should be the key point of his blog post, as this is one of the key errors I think many economists make- stating the conclusions as relevant when the assumptions are false (or not even close to true).ef17noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-13244260535781527422013-08-22T18:12:55.585-04:002013-08-22T18:12:55.585-04:00I think you're exaggerating in the post. Impla...I think you're exaggerating in the post. Implausible math and assumptions abound in micro as well as macro. Not sure you've got any real basis for making the distinction you do. How many facts are in Mas-Colell?<br /><br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-23374911704466540002013-08-22T17:14:40.214-04:002013-08-22T17:14:40.214-04:00The fact that this is being discussed is wonderful...The fact that this is being discussed is wonderful. Hopefully the insecurities of academia will not delay the process another hundred years before we get to the heart of the matter; establish what the real reasons are for human behavior (not referring to what has so far emerged in "Behavioral" Finance).<br /><br />Of course, typically, this type of exhortation will be dismissed by the "serious minded" practitioner as one of two things; far too sweeping and abstract or the opposite; it is too limited.<br /><br />The fact remains; until such a foundation is laid all the theories and accompanying math is but a game.<br />Kristian L. T. Blomnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-51050949728533151712013-08-22T16:01:06.732-04:002013-08-22T16:01:06.732-04:00I'm glad that that's your sentiment as wel...I'm glad that that's your sentiment as well. If you want to change things, you need to focus strengthening methodology in Economics, which requires the high discipline of making sure your theories are testable (exclude some possibilities, which you can specify), and testing and revising them openly when refuted. Testability is something that has to be actively sought as valuable, and refutations not evaded in an ad hoc way. This is something that's really fundamental, and even the best economists today, like Krugman and Stiglitz don't attempt the rigor of being testable. I heard your same complaint regularly from Edonomics students nearly 50 years ago in 1965 when I was a student at the LSE. I was a grad student in Philosophy, but that was the regular song I heard from Economics students. Only a new generation can do it, because the older ones have failed to take it seriously. You can do it! William Berksonhttps://www.blogger.com/profile/11116161633558655881noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-52091559026215919092013-08-22T14:44:28.310-04:002013-08-22T14:44:28.310-04:00Could you help me with this? I don't understan...<i>Could you help me with this? I don't understand how exactly it clarifies one's thinking</i><br /><br />Basically, math forces you to be precise instead of vague, because it makes you define terms and relationships. That's what people mean by "clarify", I think.<br /><br /><i>But with false assumptions, one certainly can't "arrive at" the point (i.e. you can't prove it happens in the real world).</i><br /><br />Yes.<br /><br /><i>I wonder if he's just being a bit unclear, and means that he showed that the conclusions he arrived at _could_ occur?</i><br /><br />Yes, although he might believe too strongly in that model.Noah Smithhttps://www.blogger.com/profile/09093917601641588575noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-47199440437494286442013-08-22T13:51:35.700-04:002013-08-22T13:51:35.700-04:00Could you help me with this? I don't understan...Could you help me with this? I don't understand how exactly it clarifies one's thinking, and Krugman's example for some reason doesn't help me.<br /><br />Krugman writes about his modeling that it "involved a fair bit of work to arrive at what sounds in retrospect like a fairly obvious point"<br /><br />But with false assumptions, one certainly can't "arrive at" the point (i.e. you can't prove it happens in the real world).<br /><br />I wonder if he's just being a bit unclear, and means that he showed that the conclusions he arrived at _could_ occur? If so, fair enough, it's a blog post, but it seems like a very crucial distinction to me.<br /><br />Any thoughts/help? Thank you,<br /><br />Eric<br /><br /><br />ef17noreply@blogger.com