tag:blogger.com,1999:blog-3046071861494986299.post2102645708353313585..comments2017-07-31T01:20:41.657-07:00Comments on Magic, maths and money: Oedipus and the difficult relationship between maths and economicsTim Johnsonhttp://www.blogger.com/profile/06952723922503939504noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-3046071861494986299.post-37749208191695112932017-05-29T06:27:09.230-07:002017-05-29T06:27:09.230-07:00thanksthanksAnonymoushttps://www.blogger.com/profile/16945480422986632992noreply@blogger.comtag:blogger.com,1999:blog-3046071861494986299.post-54324325508689986922014-11-05T02:12:09.993-08:002014-11-05T02:12:09.993-08:00I can see that you are an expert at your field! I ...I can see that you are an expert at your field! I am launching a website soon, and your information will be very useful for me.. Thanks for all your help and wishing you all the success in your business.<br /> <a href="http://badassmendating.com/" rel="nofollow">tao of badass</a><br />Anonymoushttps://www.blogger.com/profile/16906058993154949909noreply@blogger.comtag:blogger.com,1999:blog-3046071861494986299.post-49446421287306169462013-09-07T12:40:12.686-07:002013-09-07T12:40:12.686-07:00As 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.<br />David W. Vielhttps://www.blogger.com/profile/16559249540276639324noreply@blogger.comtag:blogger.com,1999:blog-3046071861494986299.post-885627448727404392013-08-24T11:20:55.094-07:002013-08-24T11:20:55.094-07:00This is simply not true. Try any of the following:...This is simply not true. Try any of the following:<br /><br />Sarah Otto & Troy Day<br />'A Biologist's Guide to Mathematical Modelling'<br /><br />H van den Berg<br />'Mathematical Models of Biological Systems'<br /><br />NF Britton<br />'Essential Mathematical Biology'<br />Unknownhttps://www.blogger.com/profile/17892825493311278789noreply@blogger.comtag:blogger.com,1999:blog-3046071861494986299.post-36837741264782747912013-08-24T09:42:04.054-07:002013-08-24T09:42:04.054-07:00"The critical distinction for Greek science a..."The critical distinction for Greek science and its descendants was that mathematicians dealt with pure abstract objects while natural philosophers and engineers work with the concrete, messy, qualities of physical objects [9, p 65]."<br /><br />This is pure drivel of a generalization http://en.wikipedia.org/wiki/Aristarchus_of_Samos<br /><br />Aristarchus_of_Samos first defined the heliocentric system and made measurements of the size of the sun and distance to the moon.<br /> <br />Eudoxus is another example of someone who developed mathematics to deal with planetary motions. <br />http://en.wikipedia.org/wiki/Eudoxus_of_Cnidus#Eudoxan_planetary_models <br /><br />Apollonious was the inventor of conic sections Newton later used without giving any credit to describe planetary motions http://en.wikipedia.org/wiki/Apollonius_of_Perga<br /><br />All of the above math and much more intended to be used to “save the phenomena”. equating all ancient Greek science and phisolophy with Aristotle is a straw man. <br /><br />It is true that Aristotle said was that motion should cease when the cause is removed. Some interpreted that to mean that he said F = mv, as opposed F = ma, the Newtonian consequent (but not so clear how it arises from the Principia). <br /><br />However, it is quite puzzling to anyone with a little brain that motion can continue when there is no application of force. Of course you could, as Galileo and Newton later did, define a universe where motion continues at constant speed when the force is zero. But that is purely axiomatic. There is no way to prove this experimentally and in any way Aristotle would like during his time. To understand why, just try to find any place in the universe where there are no forces. How do you know that forces are not present? Since we can only measure forces from their effects, can we really say that motion at constant speed is the effect of a causeless, zero-force- condition? <br /><br />Now, this puzzled Aristotle. Of course, people with a shallow understanding of physics and philosophy are driven to easy conclusions such that Aristotle was wrong, blah, blah, blah... Try to understand that our physics nowadays are essentially metaphysical commitments that agree with some limited experimental observations. Quantum mechanics and general relativity, the two most accepted theories are two examples. There are at least 12 interpretations of quantum mechanics. In some locality is violated, in others counterfactual definitiveness is violated. Also all of our experiments are local in spacetime. This is why the strongest principle throughput the ages has been Pessimistic Meta-induction, i.e. that sooner or later all theories will be trashed. <br /><br />Philosophy of science is a very complicated subject and not for easy conclusions. <br />Anonymoushttps://www.blogger.com/profile/06787200197343589571noreply@blogger.comtag:blogger.com,1999:blog-3046071861494986299.post-65793517100283943062013-08-24T07:16:14.318-07:002013-08-24T07:16:14.318-07:00In a large sense, the question is: should economic...In a large sense, the question is: should economics attempt to be deterministic, as proper (classical) physics is, or to be non-deterministic? Each approach implies its maths. Making explicit my biases, physics should be deterministic via a proper geometry; economics should NOT attempt determinism beyond toy models. But, this should be a debate in both sciences as mainstream physics is now largely non-deterministic and mainstream economics is largely deterministic.Anonymoushttps://www.blogger.com/profile/14466785184416801339noreply@blogger.comtag:blogger.com,1999:blog-3046071861494986299.post-74018736270125247692013-08-24T06:32:07.842-07:002013-08-24T06:32:07.842-07:00Totally agreeTotally agreeAnonymoushttps://www.blogger.com/profile/14466785184416801339noreply@blogger.comtag:blogger.com,1999:blog-3046071861494986299.post-31136644647485824602013-08-24T06:28:48.242-07:002013-08-24T06:28:48.242-07:00Totally agreeTotally agreeAnonymoushttps://www.blogger.com/profile/14466785184416801339noreply@blogger.comtag:blogger.com,1999:blog-3046071861494986299.post-91640899148288638922013-08-24T04:31:21.816-07:002013-08-24T04:31:21.816-07:00You go into a financial crisis with the math you h...You go into a financial crisis with the math you have, not the math you might want. I think that macro is more like biology than physics and the appropriate math for bio is in its infancy.Anonymoushttps://www.blogger.com/profile/01548916487126464717noreply@blogger.comtag:blogger.com,1999:blog-3046071861494986299.post-20500616093657866452013-08-24T02:35:27.050-07:002013-08-24T02:35:27.050-07:00Economists do not necessarily need new mathematics...Economists do not necessarily need new mathematics, they just need the right mathematics; dynamics and statistical mechanics.<br /><br />Engineers and biologists (as well as physicists) have lots of dynamic models that could sensibly be moved across to economics. At the moment the the post-Godley Stock-Flow-Consistent research strand, along with Steve Keen, are the only economists who use a genuinely dynamic approach. If every ungraduate economist was forced to read Strogatz's 'Non-linear Dynamics & Chaos' macro would be solved within a decade.<br /><br />As the example above of Bachelier, a statistical mechanical approach has been used in finance for many years. The Black-Scholes equation is after all just the diffusion equation; and by usage certainly the most successful equation in the history of economics/finance. Econophysicts have produced much useful work in finance on the basis of stat-mech.<br /><br />Statistical mechanics is the obvious framework for many-bodied systems such as economics, yet despite its use in finance stat-mech has been resolutely ignored by economists.<br /><br />Ian Wright's 'Social Architecture of Capitalism' uses simple stat-mech models that produce dozens of the regularaties that are seen in real economies. Despite this his papers have been resolutely ignored. Pascal Seppecher has independently produced ABM models that produce many of the same results as Wright's. My own stat-mech based work has mirrored the work of these two.<br /><br />For an in depth expansion on the failed relationship between maths and economics read Mirowski's 'More heat than light'. The IS-LM diagrams, used for example by Nobel winning Krugman, are directly descended from field theory physics, a mathematical structure absolutely inappropriate for dynamic many-body systems such as economics and finance.<br /><br />Geoff Willis.<br />econodynamics.orgUnknownhttps://www.blogger.com/profile/17892825493311278789noreply@blogger.comtag:blogger.com,1999:blog-3046071861494986299.post-4902627244521368852013-08-23T08:34:58.386-07:002013-08-23T08:34:58.386-07:00This is among the most awesome blog posts I have e...This is among the most awesome blog posts I have ever read.Noah Smithhttps://www.blogger.com/profile/09093917601641588575noreply@blogger.com