Re: Math
Greetings Economists, CB (Charles Brown) writes, (first), ...Math, grammar and logic are all sets of rules on how to use symbols then CB writes, ...logic is mathematical and linguistic, but I am curious on the essential distinction between linguistics and mathematics implied here To which JD (James Devine) replies, ...it's possible that math might be part of Chomsky's transformational grammar, i.e., the structure of human language that is inborn (built-in) in the human brain? In that case, math is linguistic, but not merely so Doyle, Chomsky's transformational grammar? This is still a debate about what exactly is inherited. A better discussion about the issue of inheritance is found in Gould's book, The Structure of Evolutionary Theory, Belknap, Harvard press, 2002. Chapter eight, Species as Individuals in the Hierarchical Theory of Selection, pages 638 through 644 discuss some of the problems that Dawkins has with the idea of rule based inheritance. Since you seem to think grammar is inherited, Let's try to make a distinction here that most people could understand. Logic has been treated as part of mathematics for awhile. So I won't distinguish between them. Grammar structures language as is the commonplace. We might go to Wittgenstein to get an odd ball view of grammar (Philosophical Grammar, Wittgenstein, Blackwell, 1974) which parallels JD's conflation of mathematics and language. However, mathematics doesn't appear to grammarize symbols. There is a case for a low level math instinct in the sense of babies can count before they can think language. That is called subitizing. To understand the difference then between grammar and subitizing it is best to consider the difference in the labor processes. The basis for language is joint attention. That is at some point babies learn to look at a parents face and follow their gaze. So if mom looks at something like a toy the baby understands something about the object which is a toy. Or food, or whatever. Sharing attention means more or less mind reading. That is states of the brain are shared and understood to be shared. Mom does her brain work in her old familiar ways. That is incoming to the occipital lobe mainly for vision, naming things in the temporal lobe, doing things in the parietal lobe, and organizing and planning what to do with stuff in the temporal lobe and parietal is done in the frontal lobe. The baby does roughly the same sort of stuff. Babies vary in how they do things from their parents for various reasons. The baby learns how to use their mind from the example of the parents. Habits of brain work. Not necessarily there in terms of a grammar. Grammar is variable within bounds. Chomsky like the enlightenment thinkers he has always sprung his own thought from thinks of this as a universal essence. However, Gould and others see this differently. We may have a tool that can do certain things, the brain. But what emerges in how we do things must certainly vary. How can the brain anticipate email? A general purpose theory of the work process of brainwork that grammar implies, presumes that we understand what exactly the brain is doing word by word. George Lakoff the linguist looks at where Mathematics comes from. Like many linguists Lakoff broadly uses metaphor as the basic mechanism of thought and therefore of mathematics. In his book, Where Mathematics Comes From,. Lakoff, Nunez, Basic Books, 2000, gives an extended examination of all levels of mathematics to trace down how metaphor might be the basis for mathematics. Metaphor stands in for field states in the brain. So for example at a given time, various fields are connected in the occipital lobe, temporal lobe, and frontal lobe. That being the metaphor. Returning to grammar, language is a representation of between a parent and child the basic way to use the face and hands to do work in the world. Mathematics is not confined to that metaphor. Math does not function in brain work like plain language acts. Grammar is not mathematics. They are both metaphorical in the sense that sheets of neurons interconnect in patterns. But the labor processes are different. Nor is it possible in my view to say grammar is inherited. As most evolutionary theorists would say there is a wholeness of environment and human beings that does not reduce to rules. Let's try to envision that. If I write this piece I am using a linear script to describe brain states or metaphorical activity in the brain. However, the brain states are not linear. So in the sense I write anything linearly I am not conceptualizing the process of thinking. If I conceptualize thinking that is create symbols that work like thinking, I might then find ways to do non-grammatical language. That is not restrict myself to an a priori limitation to what can be done. Thanks, Doyle
math
[was: RE: [PEN-L] absolute general law of capitalist accumulation] Charles writes: CB: I want to go dialectical on y'all and say logic is mathematical and linguistic, but I am curious on the essential distinction between linguistics and mathematics implied here. it's possible that math might be part of Chomsky's transformational grammar, i.e., the structure of human language that is inborn (built-in) in the human brain? In that case, math is linguistic, but not merely so. It seems to me that math represents the abstract aspects of reality. But since it leaves out the concrete, it must be incomplete. (oops, I'm going Johnny Cochrane on y'all.) jd
math
Math, grammar and logic are all sets of rules on how to use symbols. CB by Devine, James [was: RE: [PEN-L] absolute general law of capitalist accumulation] Charles writes: CB: I want to go dialectical on y'all and say logic is mathematical and linguistic, but I am curious on the essential distinction between linguistics and mathematics implied here. it's possible that math might be part of Chomsky's transformational grammar, i.e., the structure of human language that is inborn (built-in) in the human brain? In that case, math is linguistic, but not merely so. It seems to me that math represents the abstract aspects of reality. But since it leaves out the concrete, it must be incomplete. (oops, I'm going Johnny Cochrane on y'all.) jd
Degrees of Freedom Fw: Re: Eco-Math
[A lesson worthwhile for those engaged in political economy-ecology. From the Ecological Society of America...] - Original Message - From: Patrick Foley [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Friday, July 18, 2003 5:48 PM Subject: Re: Eco-Math Warren, Mathematics is very powerful in physics because the laws of physics are simple. Ecology, while ultimately dependent on physics, is far too messy to follow simple axioms and provide exact results. As Burnham and Anderson point out in their 2002 book, Model Selection and Multimodel Inference, the actual number of degrees of freedom in ecological models is so large that it might as well be infinite. Our attempts to use parsimony as a guide are often just dumb (that's me speaking not B and A, I think). Often the most elegant and beautiful theory is the correct one in physics. Not so, in ecology. Patrick Foley (ecologist and recovering mathematician) [EMAIL PROTECTED] Warren W. Aney wrote: How useful and basic is mathematics in the field of ecology? I'm not talking about just using mathematics (and statistics) to describe, model, and test. I'm talking about the basic idea posed by Edward O. Wilson that there is a natural body of mathematics that will serve as a natural language for biology and hints that mathematics may even provide a bridge that unifies all sciences (Consilience, pp. 103-104, 212-214). An article by Max Tegmark in the May issue of Scientific American discusses the correspondence between mathematics and physics (and, presumably, natural sciences in general) and how it goes back to Greek philosophy: According to the Aristotelian paradigm physical reality is fundamental and mathematical language is merely a useful approximation. According to the Platonic paradigm, the mathematical structure is the true reality and observers percieve it imperfectly. (page 49) Elsewhere in the article Tegmark says that scientists discover mathematical structures rather than create them and quotes physicist Eugene P. Wigner: the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious. I guess I tend to have an Aristotelian view of mathematics, but E. O. Wilson probably has advanced to the Platonic view. I could expand on this, but I'd like to hear other viewpoints instead. Warren W. Aney Senior Wildlife Ecologist
CEPR: Paying the Bills in Brazil: Does the IMF's Math Add Up?
September 25, 2002 Center for Economic and Policy Research Paying the Bills in Brazil: Does the IMF's Math Add Up? By Mark Weisbrot and Dean Baker Executive Summary (full paper is at www.cepr.net) The IMF has recently approved a $30 billion loan to Brazil, with the idea that the government should eventually be able to stabilize its growing public debt burden at a sustainable level. This paper looks at the trajectory of the country's debt to assess whether such an outcome is likely. The evidence indicates that Brazil is extremely unlikely to reach a sustainable level of debt service, and return to a normal growth path, until a partial default has allowed the country to write off some of its debt. Brazil's public debt rose from 29.2 percent of GDP in 1994 to nearly 62 percent of GDP at present. (See Figure 1). The budget deficit is currently running at about 6 percent of GDP for 2002. The real interest rate on Brazil's debt has averaged 16.1 percent over the last eight years (1994-2001). With interest rates at this level, deficits quickly grow through time; as this year's deficit increases next year's interest burden, the debt burden becomes explosive. The paper examines several possible scenarios for Brazil's debt (see Figure 2): ·Assuming a 16.1 percent annual real interest rate for the future, the same as its average over the last eight years: This scenario is explosive, with the debt-to-GDP ratio quickly reaching implausible levels.[2] By 2009, the debt is projected to exceed 100 percent of GDP. It would be more than 188 percent of GDP by 2016. Of course these levels would not be reached; along this path, financial markets would demand ever higher risk premiums, which would raise the interest rate to higher levels yet, and default would cut short the process of accelerating debt accumulation. ·The implicit real interest on the public debt for the first six months of 2002 was 15.5 percent, or 33.5 percent at an annual rate. If we take an extremely conservative estimate for the 2nd half of the year, and project an annual rate of 21.0 percent for the year 2002, the debt is rapidly explosive. If we assume annual interest rates at the (underestimated) 21.0 percent rate for 2002, the ratio of debt-to-GDP would reach more than 100 percent in 2007. By 2012, the ratio of debt-to-GDP would pass 200 percent. On this path, which may best represent Brazil's current situation, the financial markets will very quickly give up hope that Brazil will be able to repay its debt in full. ·Assuming, as an optimistic scenario, that the real interest rate falls to 10 percent over the next two and a half years and stays at this level (real rates this low were achieved only once in the last eight years): the debt-to-GDP ratio will still rise to extremely high levels. By the end of 2010 it would reach almost 80 percent of GDP. By 2016, it would have grown to almost 90 percent of GDP. As in the other scenarios, these projections assume that the interest rate does not rise, even though the debt-to-GDP ratio grows substantially. This is almost impossibly optimistic, as investors would surely become increasingly concerned about the probability of default as the debt-to-GDP ratio continued to rise. The paper also considers the possibility of stabilizing the debt-to-GDP ratio by running larger primary budget surpluses (see Figure 3). This would require such huge primary budget surpluses that it would not be potentially achievable. There is also the possibility that the central bank could switch to a much lower short-term interest rate policy -- the nominal rate is currently still high at 18 percent -- and thereby eventually lower the interest burden of the debt. This would be difficult for a number of reasons, including the exchange rate risk, and the risk of default -- which is difficult to reverse now that the debt-to-GDP ratio is so high. But in any case, a trajectory that includes a new central bank policy with much lower short-term interest rates is not on the agenda, and is definitely not part of the IMF's current loan agreement. Therefore the projections included in this paper would cover the range of possibilities that could be expected if Brazil continues its current policies. On the basis of current policies, as well as past and present economic data, a scenario under which Brazil's debt burden stabilizes at a sustainable level would have to be regarded as an extremely low-probability event. It would depend on Brazil's economic and fiscal policy meeting targets that could not be regarded as plausible, and/or a world in which international financial markets behaved very differently than they have in the past. If the IMF cannot produce a credible intermediate or long-range projection under which Brazil could stabilize its debt service at a sustainable level, then the purpose of this $30 billion loan agreement is questionable.
Re: Do the math. I
Max Sawicky wrote, But suppose it is the ratio of net of tax income? In Walker's example, the ratio changes from (9/8)*(rich inc/poor inc) to (91/82) * (rich/poor). The latter is smaller, which could be taken to mean "more" progressivity. Or less inequality. The dictionary definition Roger gave didn't say anything about the ratio of net of tax incomes nor did it say anything about the ratio of changes in rates. The principle of progressive taxation was introduced in economics, I believe, by Boisguilbert from the perspective of the revenue collecting state. Boisguilbert argued that revenues would be more bountiful and less oppressive if taxes were assessed according to the ability to pay. The ratio of net of tax incomes Max brings up is a secondary effect, but as Max's example shows, one doesn't need a progressive tax rate structure to lower the ratio. Whether a lower ratio of after tax incomes is "progressive" in some other sense is a question I won't go into. It is not progressive taxation. Since in the after-tax case the two are getting the same electricity, while the ratio of rich after-tax to poor after-tax has declined, it is reasonable to say a rate cut is progressive because the result is "more" progressive I assume Max means the two are consuming the same amount of electricity as before -- which is only the ceterus paribus assumption. It could be that the change in rates also changes the consumption patterns, depending on the elasticities of demand. The two are NOT "getting the same electricity" in the sense of the wealthy and poor customer consuming the same amount as each other. I repeat, progressive taxation has to do with rate structures, not the ratios of after-tax income. To extend the label of progressive to the latter is to argue by analogy, but the analogy is flawed. The progressivity of the rate structure is FROM THE PERSPECTIVE of the revenue collecting state, which is a single entity. The analogical "progressivity" of after-tax incomes is from the separate perspectives of the rich and poor consumers. Thus to label the latter "progressive" is to impose an interpersonal comparison of utility. It is a violent simplification of a much more complicated case. Progressive taxation is a simple matter of arithmetic. Progressive second order effects is not. The Tricky Devil
RE: Do the math. II
Roger Odisio wrote, The clearest way to see the effect . . . The key word here is "effect". The illustration you gave, Roger, is not of a flat-rate reduction but of a lump-sum rebate. Under the circumstances, a lump-sum rebate _would_ be progressive in the strict sense that I use. Unfortunately, it doesn't illustrate the case we've been talking about. In a tax system with two tiers, which do you think is more progressive--when the poor pay 1% of their income and the rich pay 40%, or when the poor pay 2% and the rich pay 80%. Or are these the same because the ratio of rates stays the same? This two tier tax system is too abstract for me to touch. Say the "poor" earn $10,000 a year and the "rich" earn $15,000. Neither tax system could be considered progressive because neither respects the principle of ability to pay. Your underlying point here is a valid one: that judging progressivity simply by the ratio of rates is an over simplification. But I don't think one corrects for the over simplification by adding false analogies and even more over simplifications. Tom Walker
Re: RE: Do the math. II
Tom Walker wrote: Roger Odisio wrote, The clearest way to see the effect . . . The key word here is "effect". The illustration you gave, Roger, is not of a flat-rate reduction but of a lump-sum rebate. Under the circumstances, a lump-sum rebate _would_ be progressive in the strict sense that I use. Unfortunately, it doesn't illustrate the case we've been talking about. An electricity price reduction is the same thing as a lump sum rebate in this context; each has the same effect on disposable income. And a price reduction/lump sum rebate is precisely what we *are* talking about. Gene asked whether it was correct to claim that a reduction in electricity prices would be progessive as to to income. I said yes, and I see you agree. Case closed? RO
Re: Do the math. II
Roger Odisio wrote, An electricity price reduction is the same thing as a lump sum rebate in this context; each has the same effect on disposable income. No. The lump-sum rebate in your example was without regard to levels of consumption. The poor consumer received the same $200 as the rich consumer, even though the rich consumer consumes more electricity (although a smaller proportion of the rich consumer's income). And a price reduction/lump sum rebate is precisely what we *are* talking about. Gene asked whether it was correct to claim that a reduction in electricity prices would be progessive as to to income. A price reduction would distribute savings according to the quantity of electricity consumed. Thus, as Gene pointed out, the wealthy consumers -- who, it is assumed, consume more electricity -- would save more money in absolute terms. To my recollection, Gene did not ask if the reduction would be "progressive as to income" (whatever that means). He asked whether it would be like a progressive taxation. I said yes, and I see you agree. Case closed? See my next message, "Fuck the math, do the history." Tricky Devil
Re: Re: Do the math. II
Tom Walker: Roger Odisio wrote, An electricity price reduction is the same thing as a lump sum rebate in this context; each has the same effect on disposable income. No. The lump-sum rebate in your example was without regard to levels of consumption. The poor consumer received the same $200 as the rich consumer, even though the rich consumer consumes more electricity (although a smaller proportion of the rich consumer's income). And a price reduction/lump sum rebate is precisely what we *are* talking about. Gene asked whether it was correct to claim that a reduction in electricity prices would be progessive as to to income. A price reduction would distribute savings according to the quantity of electricity consumed. Thus, as Gene pointed out, the wealthy consumers -- who, it is assumed, consume more electricity -- would save more money in absolute terms. To my recollection, Gene did not ask if the reduction would be "progressive as to income" (whatever that means). He asked whether it would be like a progressive taxation. While it is of course true that wealthier customers get more savings because they consume more electricity, that changes nothing about the conclusion. Do you know anything about the difference in electricity consumption by income group compared to the spread of the income distribution itself? Poor families typically consume roughly 400-500 kwh/ mo., while on average wealthier families use about 500-800 kwh/mo. (one point being that more sophiscated buyers usually make better use of ways to conserve electricity and use it more efficiently, thus preventing usage gaps betwen rich and poor from widening further). I'll assume you know something about the fact the spread in income difference between rich and poor is much larger than that. (And, no, I don't mean between $10,000 and $15,000--the last bit of bullshit you used to avoid addressing which tax system I posited was more progressive.) The point being, that yes, a price reduction will mean more dollars to wealthier customers, but, in considering possible progressivity, that effect is swamped by the larger spread between the income of the poor and wealthy. The savings for the wealthy are less as a percentage of income, which was my point and leads to the answer of the question Gene asked. RO
Re: Fuck the math. Do the history!
Tom Walker: I sense a lot of associative confusion on the issue of "progressive" taxation. There are two connotations of progressive that are being mixed up here. There is also an intimate historical connection between the uses of the two connotations. One meaning of progressive is the arithmetic one in which rates become higher as ability to pay increases. The other has to do with the distributive justice that presumably results from a system of progressive taxation. What Roger, Max the two neo-classical economists and others seem to be arguing is that the hypothetical rate decrease increases distributive justice, therefore it is progressive (in the latter sense). I won't have anything to do with that argument because it brings in too many undefined variables. We might as well discuss the Laffer curve -- because that's where shoot from the hip backformations take us. Typical email gambit, I see. Create a strawman position (Max, I, and others aren't merely answering the "arithmetic" question about progressivity, but "seem to be arguing" for some claim of distributive justice), attribute it to others, and whack away. But you've added a novel twist, at least. That strawman you've created is so unworthy, you say, you refuse to talk about it! I can't think of anything further I could possibly want to say on the topic of progressivity, Tom, including in response to whatever it is you can dream up to say about my last two messages. Bye. RO
Re: Do the math. II
Roger Odisio wrote, mean between $10,000 and $15,000--the last bit of bullshit you used to avoid addressing which tax system I posited was more progressive.) Getting testy now, are we? Max has an income of $100. Roger has an income of $10. I give Max $2 and Roger $1. Roger thinks this is a progressive distribution because the $1 I give him represents 10% of his income but the $2 I give to Max represents only 2% of Max's income. Roger is happy because he believes that now he is 'relatively' better off. Max is happy because he _is_ absolutely better off. The income gap between Max and Roger has now grown from $90 to $91 but Roger's income is now 10.78% of Max's instead of only 10%. That's progress, folks! The point being, that yes, a price reduction will mean more dollars to wealthier customers, but, in considering possible progressivity, that effect is swamped by the larger spread between the income of the poor and wealthy. The savings for the wealthy are less as a percentage of income, which was my point and leads to the answer of the question Gene asked. Ignoring for the sake of sophisticated analysis the inconvenient piece of tricky Tom Walker devil bullshit that the income spread has become even larger AFTER the "progressive" redistribution than it was before. Tom "bullshit" Walker
email gambit (was fuck the math . . .)
I haven't had so much fun since a bunch of latter-day Anarcho-Pagans called me provocateur and police agent. O.K., O.K. I can see I'm not welcome here. Unless I get positive feedback from other subscribers, Pen-l won't have me to kick it around anymore. *That's* my gambit. I'm not in it for the gratuitous abuse. Roger Odisio wrote, Typical email gambit, I see. Create a strawman position (Max, I, and others aren't merely answering the "arithmetic" question about progressivity, but "seem to be arguing" for some claim of distributive justice), attribute it to others, and whack away. But you've added a novel twist, at least. That strawman you've created is so unworthy, you say, you refuse to talk about it! I can't think of anything further I could possibly want to say on the topic of progressivity, Tom, including in response to whatever it is you can dream up to say about my last two messages. Bye. Tom Walker
Re: email gambit (was fuck the math . . .)
Tom, don't go! Behind the original question I posed about "progressive taxation" was a motive. In preparation for someday attacking the analysis that is going to defend the California de-regulation as a form of "progressive taxation." I wanted to check to see if there was any basis for claiming, as the economists are, that a drop in electric rates was progressive because small users spend more of their income on electricity than do large users, and thus were going to get a more "progressive" impact from the (supposed) future drop in electric rates. I thought that was a ridiculous claim, and still do, but wanted to check about the definition of "progressive taxation" used by mainstream economics. For my purposes, which is to attack a forthcoming report, I've learned that I should attack on the substance of what they are doing rather than on the basis of a single, unequivocal, well-agreed-upon definition of progressivity. It seems to me that a change that widens the dollar gap between money in the hands of the poor and the rich is not "progressive." (By the way, I never suggested that it is bad for the poor to cut their electric rates -- seems as if somebody erroneously inferred that.) I opened my Schumpeter's History of Economic Analysis and learned that there are even worse positions available to those who see things differently than I do in this discussion. Nobody has yet brought up the marginal utility of money as a reason for calling such a change progressive. The marginal utility of money for the rich is much lower than for the poor, hence one would have to give them a huge electric rate cut to give them a sum of money than would have the same marginal utility as a small rate cut for the poor. How did we miss getting that argument? There are other bases for attacking the forthcoming study, and I will use those. One thing the authors do is produce forecasts of the increase in electric consumption for various classes of customers, and for the state as a whole. They only produce numbers for rate cuts. I asked them if they were assuming fully reversible preference functions -- which baffled them. They had no idea of the assumptions behind elasticity studies. Surely, I said, consumption wouldn't go back to its original level if any rate cuts were reversed. After a little discussion they replied "We're only looking at rate cuts, not increases." So much for Berkeley Ph.Ds in economics off to another prestige department and looking for publications. Just run regressions and get the grants. Gene Coyle Timework Web wrote: I haven't had so much fun since a bunch of latter-day Anarcho-Pagans called me provocateur and police agent. O.K., O.K. I can see I'm not welcome here. Unless I get positive feedback from other subscribers, Pen-l won't have me to kick it around anymore. *That's* my gambit. I'm not in it for the gratuitous abuse. Roger Odisio wrote, Typical email gambit, I see. Create a strawman position (Max, I, and others aren't merely answering the "arithmetic" question about progressivity, but "seem to be arguing" for some claim of distributive justice), attribute it to others, and whack away. But you've added a novel twist, at least. That strawman you've created is so unworthy, you say, you refuse to talk about it! I can't think of anything further I could possibly want to say on the topic of progressivity, Tom, including in response to whatever it is you can dream up to say about my last two messages. Bye. Tom Walker
RE: Re: Do the math. II
Over on LBO they're arguing about who is more psychotic. I think both sides are winning. So this debate compares well. I would be sorry to see either TW or RO go. Neither of them has called me an insect yet. On the substance of the matter . . . TW said: Max has an income of $100. Roger has an income of $10. First thing I want to know is who told Walker my income. . . . I give Max $2 and Roger $1. Roger thinks this is a progressive distribution because the $1 I give him represents 10% of his income but the $2 I give to Max represents only 2% of Max's income. Roger is happy because he believes that now he is 'relatively' better off. Max is happy because he _is_ absolutely better off. The income gap between Max and Roger has now grown from $90 to $91 but Roger's income is now 10.78% of Max's instead of only 10%. That's progress, folks! There are different ways to measure equality and progressivity, some pretty arcane. An issue in these measures is comparability, part of what has been discussed here. They can easily give contradictory results. The metric upon which TW casts aspersions is one such. It is often used because it is simple. If there's a better one, especially if it is equally simple, I'd be thrilled to learn of it. Or equally thrilled to learn something new, like why such measures are unimportant. The income ratio in the example is ten to one. Suppose the incomes were $10,000 and $100,000. Then following the example, the poor person gets $1,000, the rich $2,000. Does anyone doubt the well-being of the poor one is enhanced more than the rich, or that the outcome is less unappealing? Suppose we went backwards. The poor income goes from $10K to $9K, the rich from $100,000 to $98,000. Who has suffered more harm? A relative closing of the gap looks good when incomes are increasing, even though the higher income goes up more than the lower, unless you use tiny numbers. Then it looks like an exercise in triviality. But it's the direction that matters. More problematic is when the gap narrows (however you like -- relatively, absolutely, etc.) when incomes are going down. How worthwhile is distribution in the context of declining real incomes? This is not necessarily far-fetched. Let a hundred turds fester. mbs
RE: Do the math II
Max, you butterfly, you. I would agree that the outcome in the example you give seems "less unappealing". That is perhaps because we can imagine what it is like to have an income of $10,000 and what it would feel like to get a $1000 boost. We can also imagine how unimportant a $2000 windfall might seem if our income was $100,000. But we can play another numbers game and say that an allocation of $300 to Roger and $2700 to Max is still, just barely, "more progressive" than the original income ratio. And then we could argue (as Gene suggested) that given the difference in marginal utility of income between Roger and Max, the latter distribution would be subjectively "fairer" but still "progressive". Where do we want to draw the line on this? So far, it's 4-1 for me to stay. Unless the nays rally for a comeback, I'll stick around. The income ratio in the example is ten to one. Suppose the incomes were $10,000 and $100,000. Then following the example, the poor person gets $1,000, the rich $2,000. Does anyone doubt the well-being of the poor one is enhanced more than the rich, or that the outcome is less unappealing? Tom Walker
Re: email gambit (was fuck the math . . .)
I haven't had so much fun since a bunch of latter-day Anarcho-Pagans called me provocateur and police agent. O.K., O.K. I can see I'm not welcome here. Unless I get positive feedback from other subscribers, Pen-l won't have me to kick it around anymore. *That's* my gambit. I'm not in it for the gratuitous abuse. Roger Odisio wrote, Typical email gambit, I see. Create a strawman position (Max, I, and others aren't merely answering the "arithmetic" question about progressivity, but "seem to be arguing" for some claim of distributive justice), attribute it to others, and whack away. But you've added a novel twist, at least. That strawman you've created is so unworthy, you say, you refuse to talk about it! I can't think of anything further I could possibly want to say on the topic of progressivity, Tom, including in response to whatever it is you can dream up to say about my last two messages. Bye. Tom Walker I'll provide some positive feedback... Brad DeLong
Re: email gambit (was fuck the math . . .)
Our system has been down. I have not been able to follow this thread. The mail I am reading is also out of order, but it seems that Roger is going over the top with Tom. please stop. Timework Web wrote: I haven't had so much fun since a bunch of latter-day Anarcho-Pagans called me provocateur and police agent. O.K., O.K. I can see I'm not welcome here. Unless I get positive feedback from other subscribers, Pen-l won't have me to kick it around anymore. *That's* my gambit. I'm not in it for the gratuitous abuse. Roger Odisio wrote, Typical email gambit, I see. Create a strawman position (Max, I, and others aren't merely answering the "arithmetic" question about progressivity, but "seem to be arguing" for some claim of distributive justice), attribute it to others, and whack away. But you've added a novel twist, at least. That strawman you've created is so unworthy, you say, you refuse to talk about it! I can't think of anything further I could possibly want to say on the topic of progressivity, Tom, including in response to whatever it is you can dream up to say about my last two messages. Bye. Tom Walker -- Michael Perelman Economics Department California State University Chico, CA 95929 Tel. 530-898-5321 E-Mail [EMAIL PROTECTED]
Re: Re: email gambit (was fuck the math . . .)
Michael Perelman wrote: Our system has been down. I have not been able to follow this thread. The mail I am reading is also out of order, but it seems that Roger is going over the top with Tom. please stop. Could you please explain what you mean by "it seems that Roger is going over the top with Tom'', Michael, so I could at least try to understand what you are accusing me of, or find objectionable? Particularly since you admit you haven't followed the thread and have only read things out of order. Perhaps I could (gently) suggest that you read the thread in sequence before you reach judgments like this. And then, at least, please make a clear statement of the problem. Seems elementary, doesn't it? Moreover, you don't seem to have noticed that I had already said I had said all I was going to say on the topic. Your asking me to stop was unnecessary. RO
Do the math.
Roger Odisio wrote, By my reading, only a couple posts by Tom Walker seem to quarrel with it. (the definition of progressivity) I don't quarrel with the definition, only with applying the term to a situation where it doesn't apply. Be humble. Do the math. "Increasing in rate as the taxable amount increases: a progressive income tax." The definition refers to the rate and the taxable amount. Not to the _change_ in the rate as a proportion of the taxable amount. Speed and acceleration are different things. Size and growth are two different things. A rate and a change in a rate are also two different things. As the example I just posted shows, a.) 18% is twice as much as 9% and b.) 20% is twice as much as 10%. By the way, you can pick any numbers to do the illustration because it's the relationship between the numbers that stays the same. Tom Walker
Spinhead math 101: lesson two
It may not be immediately clear to everyone why taking a ratio of a ratio is not an acceptable way of assessing the "progressivity" of a rate change. So let me give another example: Sometimes governments announce tax or spending changes relative to a previously projected change. Thus, the diminution of a previously announced tax increase might be announced as if it were a "tax cut". Suppose deregulation would enable the utility companies to forego rate _increases_ that otherwise were projected? Suppose those foregone rate increases were of the same magnitude as the rate decreases projected in Gene's question. The effect of such a non-change in rates would be EVEN MORE PROGRESSIVE (using the two economists' logic) than the decrease in rates that they were talking about. Imagine that! More progress from standing still. Using these kinds of subtle spin techniques one can easily cook up a "progressive" rate change that is structurally regressive but nominally "progressive" because it is less regressive than another projected rate change. In plain language: compared to a banana, an orange is an apple. Not. Tom Walker
teaching math (or maths to Mig Fiona) (fwd)
Forwarded message: From [EMAIL PROTECTED] Fri Mar 27 14:08:56 1998 Delivered-To: [EMAIL PROTECTED] Delivered-To: [EMAIL PROTECTED] Date: Fri, 27 Mar 1998 09:07:27 -0500 (EST) From: Gunder Frank [EMAIL PROTECTED] To: Sing Chews [EMAIL PROTECTED], D Shniad [EMAIL PROTECTED], whitney howarth [EMAIL PROTECTED], Michael Perelman [EMAIL PROTECTED], Marianne Brun [EMAIL PROTECTED], Wally Goldfrank [EMAIL PROTECTED], Albert J Bergesen [EMAIL PROTECTED], Pat Lauderdale [EMAIL PROTECTED] Subject: teaching math (or maths to Mig Fiona) (fwd) Message-ID: [EMAIL PROTECTED] MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Status: X-UID: 575 ~~ Andre Gunder Frank University of Toronto 96 Asquith Ave Tel. 1 416 972-0616 Toronto, ONFax. 1 416 972-0071 CANADA M4W 1J8Email [EMAIL PROTECTED] My home Page is at: http://www.whc.neu.edu/whc/resrchcurric/gunder.html ~~ -- Forwarded message -- Date: Fri, 27 Mar 1998 12:35:17 +0100 From: Paulo Frank [EMAIL PROTECTED] To: Mig [EMAIL PROTECTED], Fiona Godfrey [EMAIL PROTECTED], gunder [EMAIL PROTECTED], nancy [EMAIL PROTECTED], Gabriel Gutierrez [EMAIL PROTECTED] Subject: teaching math (or maths to Mig Fiona) From: Andrea Hoffmann [EMAIL PROTECTED] Teaching Math in 1950: A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit? Teaching Math in 1960: A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price, or $80. What is his profit? Teaching Math in 1970: A logger exchanges a set "L" of lumber for a set "M" of money. The cardinality of set "M" is 100. Each element is worth one dollar. Make 100 dots representing the elements of the set "M". The set "C", the cost of production contains 20 fewer points than set "M". Represent the set "C" as a subset of set "M" and answer the following question: What is the cardinality of the set "P" of profits? Teaching Math in 1980: A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Your assignment: Underline the number 20. Teaching Math in 1990: By cutting down beautiful forest trees, the logger makes $20. What do you think of this way of making a living? Topic for class participation after answering the question: How did the forest birds and squirrels feel as the logger cut down the trees? There are no wrong answers. Teaching Math in 1996: By laying off 402 of its loggers, a company improves its stock price from $80 to $100. How much capital gain per share does the CEO make by exercising his stock options at $80? Assume capital gains are no longer taxed, because this encourages investment. Teaching Math in 1997: A company outsources all of its loggers. They save on benefits and when demand for their product is down, the logging work force can easily be cut back. The average logger employed by the company earned $50,000, had 3 weeks vacation, received a nice retirement plan and medical insurance. The contracted logger charges $50 an hour. Was outsourcing a good move? Teaching Math in 1998: A logging company exports its wood-finishing jobs to its Indonesian subsidiary and lays off the corresponding half of its US workers (the higher-paid half). It clear-cuts 95% of the forest, leaving the rest for the spotted owl, and lays off all its remaining US workers. It tells the workers that the spotted owl is responsible for the absence of fellable trees and lobbies Congress for exemption from the Endangered Species Act. Congress instead exempts the company from all federal regulation. What is the return on investment of the lobbying costs? - Anyone want to speculate on Teaching Math in 2000? :-) -- Michael Perelman Economics Department California State University Chico, CA 95929 Tel. 530-898-5321 E-Mail [EMAIL PROTECTED]
[PEN-L:11533] Re: Intuition in Math Reasoning
Wojtek Sokolowski wrote: Therefore, the mystification of mathematics in modern economics can be compared to cargo cults that spread on some Pacific isalands after World War II. The Americans established air bases on those islands, and to buy the aborigines' loyalty, they showered them with goodies which, of course, they transpored by air. After the war, the Gringos left, and the trickle of goodies dried up. To reverse their fortune, the aborigines started to emulate what the Gringos did -- building aircraft carrying the goodies to the islands. Except that lacking the proper materials, the aborigines built those aircraft from sticks and straw. I like very much the metaphor above. Actually, it suits the economists. All attempts to construct an original axiomatic basis in economics remain still uncompleted, and mainly the marxist one. The 28th january 1884, Engels wrote to Lavrov: "The Third book, capitalist production taken as a whole, exists in two draftings which have been written before 1869 ; later, there are only a few notes and a notebook full of equations to calculate the numerous ways of surplus-value rate changing into profit rate." So, 14 years before Marx's death, "The Capital" was already, and for ever, an uncompleted work. If his pages of equations had enabled their author to transform the "Mehrwertsrate" in a "Profitrate", the mathematical notebook would have been followed by new writings concluding or rectifying the "Third book", and by a publishing. Not only Marx didn't go on writing, but he died without having told anyone about the state of his work. The 2nd april 1883 (Marx was dead the 14th march), Engels wrote to the same Lavrov: "Tomorrow, I'll have at last some hours to spend on revewing all the manuscripts the Mohr has left us (...) But he always hided from us the state of his works ; he knew that once aware of what was ready to be published, we'd have violeted him until he consents." And this silence lasted 14 years! Due to dogmas and neuroses accompanying the value accumulation process, to the merchants struggle for contending with the political institutions for power, and to the awfully effective scholastic and working consensus by which the ad hoc ideology can reproduce, neoclassical economists are unable to overcome the lesser epistemologic obstacle. But because of a paralyzing devoutness, Marxists never tried, too, to go beyond the conceptual contradiction against which Marx came up. Except Rosa Luxemburg (by the way, a woman who readily confessed she was hopeless at mathematics... ) But all that doesn't mean that an economic science, using mathematics, can't be. It only means that an original economic tool, taking place beside the other social sciences (and no more above them), is still ahead ... Sincerly, Romain Kroes (Warning : Engels letters translation here is of mine, and from a french version, the only one I had handy)
[PEN-L:11534] Re: Re: Intuition in Math Reasoning
Romain Kroes writes: ... because of a paralyzing devoutness, Marxists never tried, too, to go beyond the conceptual contradiction against which Marx came up. what specific conceptual contradiction are you talking about? the "contradiction" of the so-called "transformation problem"? neoclassical economists are unable to overcome the lesser epistemologic obstacle. what obstacle? how do they overcome it? As for "paralyzing devoutness," assuming that you're talking about the "transformation problem," you should look at: _Marx_and_Non-equilibrium_Economics_ (editors: Alan Freeman, Guglielmo Carchedi; Cheltenham [England] Brookfield, Vt.: Edward Elgar, 1996). This book defends Marx's approach to the transformation without any devoutness at all. In fact, they attack the devoutness of the neoclassical and neoclassical-Marxist belief in equilibrium. in pen-l solidarity, Jim Devine [EMAIL PROTECTED] Econ. Dept., Loyola Marymount Univ. 7900 Loyola Blvd., Los Angeles, CA 90045-8410 USA 310/338-2948 (daytime, during workweek); FAX: 310/338-1950 "As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they really do not refer to reality." -- Albert Einstein.
[PEN-L:11547] Re: Re: Intuition in Math Reasoning
James Devine wrote: what specific conceptual contradiction are you talking about? the "contradiction" of the so-called "transformation problem"? neoclassical economists are unable to overcome the lesser epistemologic obstacle. what obstacle? how do they overcome it? As for "paralyzing devoutness," assuming that you're talking about the "transformation problem," you should look at: _Marx_and_Non-equilibrium_Economics_ (editors: Alan Freeman, Guglielmo Carchedi; Cheltenham [England] Brookfield, Vt.: Edward Elgar, 1996). This book defends Marx's approach to the transformation without any devoutness at all. In fact, they attack the devoutness of the neoclassical and neoclassical-Marxist belief in equilibrium. Why didn't Marx succeed in transforming his surplus-value rate in a profit rate ? Because he had postulated that the profit issued of productivity gains (the "relative surplus-value") were globally nil. That is global accumulation were impossible, from a growing productivity. Now, what are we observing, today ? A poursuit of profit related to the lowering of the work sharing part in the product unit. The contradiction is : work is actually the only supply of wealth, but capitalist accumulation of value depends on the productivity gains. What Marx gave as a "surplus-value rate" is a relative one, and what he gave as a "relative surplus-value" is globally capitalizable. So Marx could not explain the "enhanced capital reproduction", as Rosa Luxemburg realized it (Die Akkumulation des Kapitales, 1913). That's the reason why I put forward the idea of an "epistemologic obstacle", since we are facing a conceptual inversion. As for equilibrium, I don't think it's a matter of believing or not. Equilibrium is a concept : the decretionary reference to stability. For exemple : the equilibrium can be defined as being the zero price index. But it's from the capitalist point of vue. If, on the other hand, one prefers the employment rate and the welfare state, as references of equilibrium, one has to consider that price index has been invariably positive for more than fifty years, and to explain that both equilibriums (money and growth) have become incompatible. And this is the point where we meet Rosa Luxemburg intuition... Salut et fraternite Romain Kroes P.S.- Although that discussion and your company are highly fascinating, I must move away from my computer, up to 25th august. But I'll come back on the Pen-L.
[PEN-L:11439] Re: Male Chauvanist Math
In a message dated 97-07-24 02:01:53 EDT, you write: 1. Marx tended to minimize concerns for the immediate adverse impact of capitalism on women and children because he focused on what he believed to be the inherent impact of capitalism dynamics in the long run on their situatio Bob, Read the stuff on the working day - hardly a concern with LR dynamics! Also, my sister was a math major at Queens College in the early 1970's. On the first day of a Differential Calculus class, the prof turned to my sister (and the 3 other female students) and said, "what are you doing here? your never going to need this stuff while your raising your kids!!" More to the point: The use of econometrics in is to emphasize central tendencies and often long run tendencies. This "makes sense" if one can ignore the immediate situation or the deviations from the central tendencies. I work for an insurance company and do econometric forecasting/research. I don't consider myself an "econometrician" but I know how to use the tools. The strenghts of econometrics are also its weaknesses (which neither radicals nor NCs nor others who use the stuff pay attention to): its a flexible set of tools that are capable of giving "soft" and "hard" results. For example, when I want to establish "credibility" in a rate trend, I can use a host of techniques. The point is that math, stats, and other quant techniques are systems of knowledge that are made to be manipulated (but also need to be understood). Unfortunately, I'm not paid to be concerned with "long run central tendencies," rather I need to get a short run projection for a defined objective. Finally, I object to the characterization of my wife as the "Willie Mays" of hospital accounting: Mays had to endure overt racisim from a crowd of people that was in his face everyday. My wife's situation - while difficult - was no where near as traumatic (even though in the beginning of her career she regularly worked 80 hour weeks) Jason
[PEN-L:11417] Male Chauvanist Math
Jay Hecht wrote: "In fact, it was quite evident that the hospital practice at this particular Big 6 succeeded because the women supplanted the incompetent males!" This can be explained in a simple Becker (neoclassical) manner: Prior to the hiring of women, incompletent males were hired. However, once access was extended, capitalist accounting firms were able to hire the most productive workers which included many women. Generally, in the first stages of integrating the workforce, very talented women are hired. Not surprisingly, just as in baseball in the 1950s, this would include some exceptional players. In a sense, Jay's wife may be the Willie Mays of hospital accounting!! More to the point: The use of econometrics in is to emphasize central tendencies and often long run tendencies. This "makes sense" if one can ignore the immediate situation or the deviations from the central tendencies. Professional men have a greater willingness to do this because they rarely experience (though they may empathize with) the downsides -- adverse side effects -- of public policies. A few examples: 1. Marx tended to minimize concerns for the immediate adverse impact of capitalism on women and children because he focused on what he believed to be the inherent impact of capitalism dynamics in the long run on their situation. While I believe he was absolutely correct in his prognostications, it is unlikely that many of his contemporary working class woman would have been so focused on long run dynamics. 2. Paul Krugman makes a somewhat similar point about the present dynamics in newly emerging industrialized countries where women are being exploited in the capitalist process rather than in the more feudalistic structures that previously dominated their employment. There is a certain logic and "truth" in what Krugman states because as a central tendency capitalism on average is improving the economic wellbeing of women. However, within this dynamics there are women who will necessarily experience not the central tendency but the worst abuses. Again, it is more likely that men will focus on the central tendency rather than the worst abuses. This is the same when we look at economic analysis which posits a "typical" household or "typical" firm. Here an example could be NAFTA where it may be true that on average a typical household would benefit from the increased world specialization with lower consumer prices. However, it makes a difference whether the typical household is comprised of upper-income professionals or lower-income blue collar workers when we look closely at the employment effects (which in the aggregate may net out to zero). Again, do we focus on the central tendency (male professionals??) or on the adverse consequences to particular subgroups (female blue collar??). Robert Cherry/Brooklyn College
[PEN-L:11402] Re: Intuition in Math Reasoning
At 02:56 AM 7/23/97 -0700, you wrote: It's relevant that Keynes doesn't condemn, here, the use of mathematics in economics (as for him, he rather liked to have recourse to them up to tautology), but that he implicitly accuses the lack of a conceptual basis in economics, so much so that "the back of the head" is nothing but a rough substitute for it. Economics aren't yet a true science, although such a tool has never been so necessary as nowadays. That's the reason why econometrics ask mathematics to fill the conceptual gap. This matter is economically the most important one, but I'm afraid it doesn't interest the most of economists... In this context, it is revealing to examine the etymological roots of the word "mathematics" - it derives from the ancient Greek and means "what is already known" - based on Heidegger's interpretation, that suggest mere cataloguing of information acquired through other means, rather than discovering new information. Intuition or insight, on the other hand, denoted in classical philosophy a cognitive faculty of direct acquisition of new information. In that aspect, it was comparable to experience, except that intuition was more valuable than experience because it allowed the inquiring mind to directly access the 'essences of things' rather than their appearences. This distinction between formal deduction (as in mathematics) and intution forming the basis of deduction (that's how we comprehend axioms) was still present in post Kartesian thought (cf. Baruch Spinoza). In essence, formal deduction was considered a vastly inferior to intuition form of knowledge, until modern times, when it became a tool of natural sciences perceived as successful. Therefore, the mystification of mathematics in modern economics can be compared to cargo cults that spread on some Pacific isalands after World War II. The Americans established air bases on those islands, and to buy the aborigines' loyalty, they showered them with goodies which, of course, they transpored by air. After the war, the Gringos left, and the trickle of goodies dried up. To reverse their fortune, the aborigines started to emulate what the Gringos did -- building aircraft carrying the goodies to the islands. Except that lacking the proper materials, the aborigines built those aircraft from sticks and straw. regards, wojtek sokolowski institute for policy studies johns hopkins university baltimore, md 21218 [EMAIL PROTECTED] voice: (410) 516-4056 fax: (410) 516-8233 POLITICS IS THE SHADOW CAST ON SOCIETY BY BIG BUSINESS. AND AS LONG AS THIS IS SO, THE ATTENUATI0N OF THE SHADOW WILL NOT CHANGE THE SUBSTANCE. - John Dewey
[PEN-L:11395] Re: Intuition in Math Reasoning
It's relevant that Keynes doesn't condemn, here, the use of mathematics in economics (as for him, he rather liked to have recourse to them up to tautology), but that he implicitly accuses the lack of a conceptual basis in economics, so much so that "the back of the head" is nothing but a rough substitute for it. Economics aren't yet a true science, although such a tool has never been so necessary as nowadays. That's the reason why econometrics ask mathematics to fill the conceptual gap. This matter is economically the most important one, but I'm afraid it doesn't interest the most of economists... Sincerly Romain Kroes Laurence Shute wrote: Does this help any? From the General Theory (pp 297-98): "It is a great fault of symbolic pseudo-mathematical methods of formalising a system of economic analysis, such as we shall set down in section VI of this chapter, that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed; whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep 'at the back of our heads' the necessary reserves and qualifications and the adjustments which we shall have to make later on, in a way in which we cannot keep complicated partial differentials 'at the back' of several pages of algebra which assume that they all vanish. Too large a proportion of recent 'mathematical' economics are mere concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose4 sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols." In 1940 Keynes was greatly worried that his American disciplices "were more orthodox than the master," in the sense that they failed to keep the necessary reservations "at the back of their head."
[PEN-L:11381] Re: Intuition in Math Reasoning
Does this help any? From the General Theory (pp 297-98): "It is a great fault of symbolic pseudo-mathematical methods of formalising a system of economic analysis, such as we shall set down in section VI of this chapter, that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed; whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep 'at the back of our heads' the necessary reserves and qualifications and the adjustments which we shall have to make later on, in a way in which we cannot keep complicated partial differentials 'at the back' of several pages of algebra which assume that they all vanish. Too large a proportion of recent 'mathematical' economics are mere concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose4 sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols." In 1940 Keynes was greatly worried that his American disciplices "were more orthodox than the master," in the sense that they failed to keep the necessary reservations "at the back of their head." Larry Shute Thanks for your message at 07:06 AM 7/22/97 -0700, [EMAIL PROTECTED] Your message was: In a message dated 97-07-21 10:04:11 EDT, Anders writes: At 07:35 PM 7/20/97 -0700, Maggie wrote: Nope. This is why ( as I pointed out) other types of debate are more It may not have been phrased exactly this way, but what I say in the rest of my initial message is that one of the primary feminist critiques is that econometrics (models) are almost by definition inaccurate. In other words, they are parsimonious to the point where they can not possibly reflect social issues (power, gender, race, sexual preference, etc.). So even when power is added to a model, the model inaccurately portrays the exercise of power because the one dimensional nature of mathematics does not allow for the variable degrees of the exercise of power. Is that really the result of mathematics, or is it the result of a model that starts with the assumption that we don't have to worry about power (or attempts to change the rules of the game)? If you had a model that did start by putting power at the center, why couldn't you use math to talk about variable degrees of power? Wl, part of it is the assumptions on which the model is based--so, frinstance, Posner's recent work which "proves" that white men should receive a larger part of the medical research dollar because the loss of white men to ill health or death costs more is an excellent example of assumptions determining outcome. As long as we measure the value of life in terms of documented income from the market place, and do not place a monetary value on household labor, mainstream economists will always reach this conclusion. ***However even if one incorporates truly progressive values into econometric work--and I think that there is some really good work out there (frinstance, Australlian economist Gillian Hewitson did an excellent rational choice model for surrogate mothers) I question the ability of mathematics to portray the complexities of social interactions. Does racism or sexism or power vary with mathematical certitude even in exactly the same situations over time? I really don't think so. Further, econometrics is only one form of logic, generally associated with men, and its use as a legitimizing force to the exclusion of all other types of logic (artistic, intuitive) is in and of itself a form of bigotry. Two questions: -- Suppose econometrics gave us the answers we wanted. Would it be bigotry to say, that's what we're going to use to the exclusion of, say, artistic logic? I'm not sure I understand the question--but--I wrote in answer to Jim Devine that I am not completely convinced by this portion of the feminist argument. I don't think there has been enough of a separation between econometrics as a tool and the USE of that tool by the mainstream as a way of promoting all forms of bigotry. -- Are you arguing that econometrics doesn't involve intuitive and other forms of logic, or are you saying that when it's used as a legitimating force, it pretends that it doesn't involve intuition, etc.? The reason I ask is that I remember reading articles about the history of econometrics many moons ago that analyzed the shift in rhetoric, and they all argued that econometrics was an attempt to appopriate the images of "hardness" and "rigor" from physics while denying the role of intuition, etc. that physics takes for granted. All science begins with intuition. However, econometrics simplifies this intuition to a parsimonious skeleton and--at best--is useful as a compliment to intuitive explanations. Further, I question the definition of
[PEN-L:5635] Re: language math
On Tue, 20 Jun 95 [EMAIL PROTECTED] (Paul Cockshott) said: John asks All of the above is true but seems to miss the point of the Okishio Theorem. That is, Okishio points out that rattional capitalists make investments to increase their rates of profit or, at least, to keep them at their current level. Thus, why would a capitalist invest to bring about a fall in the rate of profit? This question was first raised by Tugan-Baranowsky using a one commodity model as Van Parijs pointed out. Paul The point is that in the real world, as opposed to equilibrium models, capitalists do not know what their profits are going to be this year let alone next. They do not know what the level of effective demand will be nor next years price level. I think that it is unrealistic to expect to be able to construct a theory of the rate of accumulation at this kind of micro level, since it is inherently a dynamic macroeconomic phenomenon, affected by interest rates, existing accumulation levels, changes in wages etc. The point about the declining tendancy of the rate of profit is that over long periods, the fall in profit rates relative to interest rates tends to act as a limiting factor on the rate of accumulation. It is this macroscopic limitation that is the interesting factor. John says Ok. Let me see if this question clarifies matters. Do capitalists invest in ne techniques which, using current prices, will reduce their rates of profit? -- John R. Ernst
[PEN-L:5626] Tendency of falling profit rate - was: language math
Tavis Barr says: ..if there is no tendency of the profit rate to fall, why has it been on a downward trend for the last 25 years or so? First: Are economists in agreement on this? I have economist acquaintances who say otherwise. Just asking. Secondly: If this rate really has been falling, it could perfectly well do so without being caused by mechanization/automation. Even a static economy (static in the sense of negligible technical change and productivity growth in the period considered) will experience long run financial crisis symptoms simply due to accumulation of assets. As long as all sorts of returns (from loans, bonds, stocks) are re-invested, aggregate net assets (mirrored by net debts) will grow, regardless of productivity growth and technical change. Sooner or later the net assets holders (and I am not only talking of the financial sector here, also any economic agent who holds dividend-giving assets - including firm owners who behave as rentiers towards their own firms) will have trouble upholding a return flow that is proportional to net assets. Thirdly: Imagine a future class society with 5% of the workforce in manufacturing, and where physical production is undertaken 90% by robots and automated processes with the workers as overseers and maintenance personnel. Since this is a class society the workforce will be dependent on selling their labour power to capitalists on the market. This extremely productive society will therefore employ the majority of workers in a huge service sector, which to a great degree is employed with catering to the needs of the capitalist class. This service sector will - being a service sector - have a lower organic composition of capital than industry, and therefore give good possibilities for exploitiation of employees. The capitalists will exploit those service workers as hard as possible, and accumulate as today. If returns to capitalists in the automated industrial sector are lower than in the service sector, the industrial sector will shrink. But this will increase prices for products from this sector until profitability there is comparable to that of the service sector. So my conclusion is that as long as a society is divided into two main classes: Capitalists and wage labourers, there will be the same possibilities for harvesting profits as today, or for that sake 50 years ago. The average rate of profit doesn't depend on level of automation/mechanization, but on the power balance between exploiters and the exploited. And back to my second point: To the degree one observes a some-decades long path towards stagnation and crisis in capitalism (a "long wave"), this is explained by accumulation due to compound returns, not by increased organic composition. Futhermore to the third point above: If I am right here, any marxist who believes that socialism and then communism is inevitable in the long run because capitalism is doomed due to a profit rate tending towards zero because of automation/mechanization, must be in error. Capitalism can continue indefinitely as long as one class has the power to coerce the majority to work for them by control over their means of living. Incidently I _do_ believe that socialism and some sort of "asymptote" towards communism is bound to come in the long run. But this belief is based on the relentless and gradual increase in average workforce education level and the communication technologies that the capitalists themselves need in the global competitiveness rat race. In this sense they are themselves bringing forth the tools that will mean their future demise. But this is another discussion. All this, IMHO, of course. I may be wrong. cheers, Trond - | Trond Andresen ([EMAIL PROTECTED]) | | Department of Engineering Cybernetics | | The Norwegian Institute of Technology | | N-7034 Trondheim, NORWAY | | | | phone (work) +47 73 59 43 58 | | fax (work) +47 73 59 43 99 | | private phone +47 73 53 08 23 | | private mobile phone +47 90 16 69 30 | | | | http://www.itk.unit.no/ansatte/Andresen,Trond | -
[PEN-L:5608] Re: language math
On the other hand, looking at interactive behavior, things could go either way depending on expectations (i.e., dynamic strategies), for which the Folk Theorem says pretty much anything interesting goes. Successfully choosing not to make an innovation might happen in more mature markets where entrepreneurs are more sure of their competitors' profits versus newer markets (e.g., computers) where somebody is bound to enter the market with the new technology fairly soon. In any event, in the latter case (which I would argue is probably more the norm; few markets are entirely fixed from entry) I think it's pretty straight forward to illustrate Shaikh's response to Okishio with a Cournot example (for which Shaikh with his aversion to anything vaguely neoclassical would be none too happy). I'm trying to use "reasonable" numbers here. Suppose two firms face a demand function p = 10 - q and two possible technologies with constant marginal costs 5 and 2.5. Ignore sunk costs for a second. The Cournot equilibrium for the first technology is q = 5/3 for each firm, p = 6 2/3, and each firm has profits 2 7/9. In the second case, q = 2 1/2, p = 5, and each firm has profits 6 1/4. (the "reasonableness" so far is that the price elasticity of demand at the relevant point is just over 1, which is a little high but actually then only underscores the point since a lower elasticity would strengthen the effect. The thing I like about the two-player Cournot example is that it puts the individual firm's elasticity at about twice that of the aggregate elasticity, which seems ballpark right to me though I don't know of studies of this kind of stuff). Now, back to the sunk costs: Suppose all marginal costs are labor and all sunk costs are capital (it doesn't really matter for the Marxian questions since they are, by definition, variable and constant capital). Each firm would be willing to just over double its capital costs in order to maintain the same profit rate. Given that each firm raises its output by fifty percent, this seems excessive but not too excessive. I'm sure moving the elasticity up would create a 1-1 increase or even less in the break-even case. I do think this kind of game is a lot more reasonable than the typical neoclassical functions that Okishio considers for a couple of reasons: (1) innovations more typically involve larger sunk costs and smaller marginal costs and (2) firms have a bit of room to manoever their prices as well as get into price wars or not get into them. The point is not that changes under these conditions _always_ lower the profit rate, but that under very reasonable specifications they may. Either way, it illustrates Marx's point pretty well: I leave it to the reader :) :) to show that in the break-even case (i.e., the same profit rate in the two scenarios), the firm that stays with the higher-MC technology while the other one switches will get really screwed. I haven't done the math but it seems pretty intuitive and not hard to compute just annoying. If a firm believes that it can switch technologies a "period" before its competitors do anyway, then the incentives will be that much greater. So expectational considerations can go a long way toward lowering the profit rate. In any event, I don't think this is the main justification for falling profits. Technical change seems to be correlated with higher profits, though I don't know of studies of this on a firm-level basis, with 3-5 year lags and using more "Marxian" estimates of these variables. But it does raise serious questions about the relevance of Okishio's theorem, even within the one side of the story of accumulation that it does address. Added to this, Gil, if there is no tendency of the profit rate to fall, why has it been on a downward trend for the last 25 years or so? Yours for the squabble after the revolution, Tavis
[PEN-L:5619] Re: language and math
This was Ricardo's argument for a declining rate of profit. Marx wanted to develop an argument that was internal to his theory of capitalist dynamics, i.e., not imposed outside the system. Not that Ricardo was wrong just that his argument was endogenous. David Levine discusses this in one of his early books. On Tue, 20 Jun 1995, John L Gulick wrote: Can't the rate of profit also fall when technical and organizational changes which increase surplus value extraction meet various "natural limits to growth" ? I adamantly am not talking a Club of Rome discourse here, merely referring to the conditioning of "revolutions in value production" by the uneven and unpredictable process of rationalizing and taming (an already socially modified) "nature". For example, socio-technical change in intermodal shipping -- containerization, concentration of capital, rationalization of routes, the building of huge supertankers and cargo ships -- has played a major role in the multinational- ization, transnationalization, and globalization of production. Given the high organic composition of capital in this sector, continued price reductions in ocean-going shipping services has depended a lot on reducing turnover times. But this is coming up against all sort of (socially modified) "natural limits" -- increased harbor traffic leads to congestion, channels must be dredged to accomodate the giant new-generation liners, increased speed of vessels leads to accidents, etc. Shippers internalize these costs and the price of shipping services rise. Rising prices for shipping services take a cut out of the aggregate social surplus created. (I recognize the limitations of the example, since it entails only a singular sector and kind of ignores the fluidity of investment across sectors). Any comments for this argument by a non-economist ? John Gulick UC-Santa Cruz Sociology Graduate Program research interest: eco-Marxist theory of the built environment
[PEN-L:5571] Re: language math
The discussion of whether the falling rate of profit is true under different assumptions of wage rates seems to me beside the point. What one should be looking at is not micro phenomena like that but macro dynamics. A sufficient condition for the rate of profit to have a declining upper bound, is that capital accumulates faster than the growth of the pool of exploitable labour. When this occurs the rate of profit does decline, and in periods of stagnation - when capital accumulation is often negative - it does not. The maths required to demonstrate this do not go beyond elementary differential calculus - but one does not even need this to see the argument.
[PEN-L:5600] Math 2
Math Language 2. The controversy between Newton and Leibniz over the "invention" of the calculus is interesting in this regard and sheds some light on the subject. The three greatest mathe- maticians of all time are generally considered to be Archimedes, Newton and Gauss. The crown probably belongs to Newton although he insisted that he "stood on the shoulders of giants" -- which is correct. It is said that Newton worked out his proofs using his newly invented?/discovered? calculus, but then restated or translated these proofs into the language of Euclidean geometry. Thus the great treatise called _... Principia Mathematica_(1687) is incredibly obscure because calculus is carried out in the language of Euclidean geometry. Why did Newton do such a thing? He said he wanted to make it difficult in order to avoid intellectual squabbling. However, I suspect that another more important reason is that he was first and foremost concerned to demonstrate without question the truth of his theorems. He couldn't do this at that time with "calculus" because arithmetic and calculus were not axiomatized until after centuries more work (eventually in axiomatic set theory this century). However, Euclidean geometry had been axiomatized by Euclid, was based on five "transparent" axioms (except the fifth wasn't so trans- parent) and hence Newton could demonstrate the truth of his theorems by "translating" calculus into Euclidean geometry, thereby creating an incredibly exact but obscure treatise. Later on there was a huge intellectual dispute over who "invented" the calculus, Newton or Leibniz. Leibniz was the one who invented the language of the caluclus that we use today. He took great pains in crafting the language. For the next hundred years English mathematicians, out of loyalty to Newton (English nationalism) attempted to develop the calculus along Newton's lines and failed. Rather, further development of the calculus was carried out on the continent because Leibniz had forged the superior mathematical symbolism. Point -- mathematical languages themselves undergo develop- ment. What motivates this development? The ease in carrying out proofs and performing calculations. However, such ease in one direction (proofs and calculations) does not make for an easy language to understand. Rather it makes for a new language to learn. On the other hand, the deepest mathematical results are very often most lucidly explained in ordinary language. There was a linguistic progression in the development of the symbolism (language) of mathematical logic also. The first work on this subject by G. Frege came out in 1879. The symbolism was hopelessly obscure. Thus Frege is obscure. Bertrand Russell studied under the Italian mathematician G. Peano for a few years and adopted Peano's symbolism as the symbolism of his _Principia Mathematica_ -- like Newton's tome, another obscure work that had to be gone over by scores of mathematicians and subsequent generations thereof. Gerhard Gentzen reformulated Russell's awkward "symbolic logic" into a system of "natural deduction," the way we (i.e., mathematicians) "naturally" reason, the mature form of mathematical logic today. However, this reasoning is not that "natural" to most of the species, but must be learned, just as you have to learn French if you're an English speaker. Math majors seem to be so natural- ly adept at this language that they don't need or bother to study it formally. It's sort of a sixth sense for them, even though it took Bertrand Russell his entire early career to codify the grammar. (Should this grammar be taught to everyone, like English grammar in grade school? Is this possible or is the subject too difficult?) But I have to get on to mathematics in economics. I am hardly an expert on this subject, but I did take a look at mathematical economics once in the 60s and formed an opinion on it. Which may be of interest. Curtis Moore [EMAIL PROTECTED]
[PEN-L:5549] Re: language math
In the midst of his very interesting and useful thoughts on math, Gil writes that "even if one doesn't agree with the premises of Okishio's theorem, who would have known that Marx's claim was inconsistent with those premises before Okishio's proof?" I think this example shows up some of the limitations of mathematics as often applied to economics, though they do not apply to math _per se_. The fact is that Okishio's premise (constant real wages) is _not_ the same as Marx's (constant rate of surplus-value), so that Okishio's theorem is not really a critique of Marx. Pen-l will be glad to hear that I am not criticizing Gil here, since I think he is familiar with the problems arising from the conflation of the two assumptions (with Marx's, real wages rise with productivity). What I'm commenting on is the fact that many or even most of the writings since Okishio ignored this confusion and even ignored John Roemer's generalization of Okishio to a case that approximates the constant rate of surplus-value assumption. The authors wanted to talk about, apply, and extend Okishio's math and how it "proved" Marx wrong. I hope that authors such as Dave Laibman (and Gil himself Frank Thompson) have gotten us away from the constant-real-wage assumption. The moral of the story is that one has to remember that math is a _means to an end_ (it's formalized logic) and should not become an end in itself, replacing scholarly discussion of the subject matter (such as actual reading of Marx) or other methods (such as dialectics). in pen-l solidarity, Jim Devine [EMAIL PROTECTED] Econ. Dept., Loyola Marymount Univ., Los Angeles, CA 90045-2699 USA 310/338-2948 (daytime, during workweek); FAX: 310/338-1950 "Segui il tuo corso, e lascia dir le genti." (Go your own way and let people talk.) -- K. Marx, paraphrasing Dante A.
[PEN-L:5551] Re: language math
Jim writes: In the midst of his very interesting and useful thoughts on math, Gil writes that "even if one doesn't agree with the premises of Okishio's theorem, who would have known that Marx's claim was inconsistent with those premises before Okishio's proof?" I think this example shows up some of the limitations of mathematics as often applied to economics, though they do not apply to math _per se_. The fact is that Okishio's premise (constant real wages) is _not_ the same as Marx's (constant rate of surplus-value), so that Okishio's theorem is not really a critique of Marx. Pen-l will be glad to hear that I am not criticizing Gil here, since I think he is familiar with the problems arising from the conflation of the two assumptions (with Marx's, real wages rise with productivity). What I'm commenting on is the fact that many or even most of the writings since Okishio ignored this confusion and even ignored John Roemer's generalization of Okishio to a case that approximates the constant rate of surplus-value assumption. The authors wanted to talk about, apply, and extend Okishio's math and how it "proved" Marx wrong. I hope that authors such as Dave Laibman (and Gil himself Frank Thompson) have gotten us away from the constant-real-wage assumption. The moral of the story is that one has to remember that math is a _means to an end_ (it's formalized logic) and should not become an end in itself, replacing scholarly discussion of the subject matter (such as actual reading of Marx) or other methods (such as dialectics). Right on! One minor comment: Marx phrased his argument under the assumption that the rate of surplus value is held constant, but I don't read him positing this as the economically relevant condition--rather it's a simplifying assumption stipulated as a point of departure. The economically relevant condition on wages would have to be supplied by a separate story about the impact of technical changes on labor market outcomes. Roemer's argument is that there is (to him) an economically plausible story which supports the Okishio assumption, and he doesn't know of one which supports the constant-rate-of- surplus-condition. In a recent paper to which Jim refers (still in submission limbo), I establish market conditions --something like a stationary-state competitive equilibrium in a dynamic market--which support this assumption. But the point still holds: if one replaces Marx's simplifying assumption with a demonstrably market-relevant condition (long-run wages constant at the subsistence level), there is no "tendency" for the rate of profit to fall--and this is a useful result. Gil
[PEN-L:5554] Re: language math
Gil, Other than as an exercise in gaining clarification concerning Marx's terminology and thus in extending his efforts, how is the Okishio Theorem relevant or "useful." Note that for Okishio not only is the real wage constant but all prices used in determining whether or not the rate of profit fall are "equilibrium" prices determined with the assumption that all capitals earn the same rate of profit. I find this result not only of little use but also one absent in Marx's CAPITAL. Note that the concepts of "market value" and of "market price" are both introduced prior to the discussion of "the law of the tendency of the rate of profit to fall." Thus, the question concerning the fall in the rate of profit should, at least, consider an "equilibrium" condition in which the rates of profit are not equal. In an earlier plan for the third book o CAPITAL, Marx actually planned to discuss the concept of rent prior to introducing the concept of the falling rate of profit. I realize that this may make mathematical exercises concerning the falling rate of profit somewhat more complex, but they may yield something that relates to Marx's work. Marx himself makes a slightly different point in Part III of Book III when he notes that if price reductions due to increases in productivity are uniform, the rate of profit will not fall. John
