Math Vs Economics
Math Vs Economics[Moved from MasterOfBusinessAdministration]
This is in serious need of taking apart and putting back together again in a coherent DocumentMode page. There's a lot of potentially interesting material here.
I think the below needs refactoring in order to separate out the arguments that I think are:
I think just about all of these are questionable. Market failures are hardly unknown or unstudied by economists. The South Sea Bubble and tulip mania were some time ago, after all.
Caveat emptor is an appropriate maxim for financial markets. Those gullible investors didn't have to invest, and blaming "economists" entirely for the cattle-like rush to throw money away on bad business plans is too much.
''No, Maths and CS don't teach you about economics but they do teach about Mathematics. ...
Economists proclaimed that a trillion dollars(or more) were lost in the market crash of the 2000. But this assertion is as stupid as it can get for a mathematician, since no 20$ bill was ever burnt on the Nasdaq, money just changed pockets from the gullible "investors" (including individuals, banks, pension funds), to some smart assed who created the buble, and in the case of some .coms even to some employees who took advantage of the opportunities to actually steal money in a legal way. Here I mean stealing from an ethical stand point. A trillion dollar or so, were not lost but actually stolen. Do those MBAs actually discuss those things? I suspect they do not.
The economists as a profession have not been able over a hundred years or so to establish a sound mathematical and ethical basis for accounting and markets, as shown by the latest Enron (and others ) happening. Now many economists proclaim that accounting needs to be reformed, markets need to be reformed. The latest Nobel prize I think it's about "markets with unbalanced distribution of information" - a gentle way of naming the actual frauds and scams that happen in the extreme cases. Were they really doing scientific research before, if it took catastrophes like Enron (or Nasdaq), to slap them in their face and tell them that something is not quite right ?
Straight off the bat, the author is confusing macro and microeconomics. Or intentionally using problems with macro to beat on the whole subject. It's like saying failures in cloning mean the whole of biology must be suspect.
Perhaps the most concise disproof of the above rant is the large number of economists who also have math degrees - it is very common for people to get a B.Sc. or masters in Math and then a PhD in economics. It is also not uncommon for economists to occasionally prove purely mathematical theorems, either on the side or as part of their economics work.
As a PhD in PureMathematics myself, I can assure the rant's author that the average mathematician believes none of the many (false) things he/she asserts they do. This is particularly so if they had ever taken Econ 101 and taught the difference between values, prices, and currencies.
I'll end with a story that I think points out a more true relationship between economics education and MBA education: a friend of mine was pursuing an MBA at MIT's Sloan school and for her electives took a number of economics classes. Occasionally, she would be confused by the disparities in the viewpoints the MBA and economics classes took in discussing ostensably the same subjects, until as she said, "One day it all made sense: what they call market failure over there" (pointing to the econ building) "is what they call strategy over there" (pointing to the Sloan school). -- ThomasColthurst
Ok, so I wasn't aware of such differences between Economics degrees and MBA degrees. My appologies if I offended anyone unnecessarily. The rant was written in a context relating MBA degrees to engineering and science degrees, and the current page title was attributed by someone else.
However, what were those guys in the autumn 99/spring 2000, proclaiming on all business related TV channels and shows essentially bogus numbers ? I believe they weren't, by large, mathematicians, nor engineers. I believe they had an essential problem with either mathematics or ethics or both. Several accounts from insiders do tell about serious ethical problems. Maybe they also had problems with economics 101, in which case it kind of proves the point.
What's fundamentally wrong with the above rant? If markets are to function correctly, there has to be a relatively strong correlation between prices and other (not easily quantifiable but nevertheless real) values. If the GDP growth is linear, and the average growth of the stock price tends to be exponential for quite a long time, well how do we put all of that into an equation ?. Either the GDP isn't measured correctly (unlikely), or we're about to have an explosive growth in the GDP (again unlikely), or the financial markets do sell illusions (a serious ethical problem). Ethically I equate selling illusions with stealing. I'm open to other hypothesis. What I expressed at that point in time when everything looked rosy for the average MBA, and what I still believe now to be the essence, is that they were selling illusions.
Lots of different sorts of people were saying all sorts of different things at the immediate turn of the century. Some were merely saying that future prospects for their company or industry looked very very good. N o doubt, some or these people were deliberately lying when they said this. But certainly not everyone was, and it certainly wasn't just restricted to MBA or managerial types - cthulu knows I had any number of electrical engineering friends back then who read Wired too much and started believing their own hype.
Other people, including some economists, were saying more general things like "there will never again be any recessions" or "the dow will soon reach 50,000" or "the economy will henceforth grow at 5% a year". Whatever you might think of such statements, they were almost certainly not deliberately fradulent, if only because there wasn't really anything to be gained.
I also think that such statements, while false, aren't the sort of tautological falsities that can be disproven though pure math. Economists have bunches of theories about recessions, and some of them are better than others, but none are so certain as to be able to prove the existence of a future recession. Likewise, we really don't have a theory so good as to tell us why GDP growth for the last half century has been stable at around 3% and not at around 5%.
I'm not sure what your point about GDP and stock prices is, as both grow in approximately the same way: GDP at an average of 3% a year, stocks at an average of 10% a year. Both grow exponentially, or at least have in the past. They don't grow at the exact same rate because the GDP measures the entire economy, including government, nonprofits, and non-publicly traded companies. -- ThomasColthurst
I believe it should be provable that if in any one year, "out of the blue" the Nasdaq index doubles while the GDP growth is 4-5%, something is wrong in the markets. Either a doubling of the GDP is to be expected within a decent horizon, or the market is flawed (it is selling illusions). That's my "math" instinct, sorry, I'm to burried into programming problems right now, and I can't take time to come up with a reasonable justification (mathematically speaking).
But here's the deal, stock prices are "evaluated" in dollars. That's their measure unit. So is the market cap of a company -- let's take Microsoft for example. The figures were (still are) astronomical. Only that the market cap is an accounting/statistical fiction. The problem is to determine if those "dollars" that are owned in stocks are real dollars or fictitious dollars, that may evaporate over night. Let's assume, for a brief moment, that all the dollars in the stock market are as real as the thing you get at ATMs and you have in a bank account. Who knows, if the markets get to work really bad, even the money in a bank account are kind of a fiction. Let's assume a 0% inflation just for the sake of discussion, and let's focus on a frozen moment in the life of the whole society -- a perfectly static picture, we can see how we account for the dynamics of time later. So, the money in the stocks are perfectly real. The money in my pockets are perfectly real. What should all the money in circulation represent? They should represent, I believe, a measure of the total goods and services produced by the society. I have 5$, I can buy a hamburger, I have 1000000 I can buy a house in Malibu (maybe). So let's compare in that very moment the actual situations with the situations that happened the same instance of 1 year ago. How did the total amount of money available evolved, and how did the available goodies evolved. Well, if the theoretical money in the market doubled, and the goodies didn't growth as spectacular by far, there is a certain imbalance. Let's assume that the guys with governement issued dollar bills are one set, and the guys with only money in the stocks are another set. The two sets are disjoint. We can mark up the real money with the green collor and the stock money with blue collor. I own green dollars only and you own blue dollars only. One year ago we'd had considered perfectly equitable for both of us to trade 1 gren dollar for 1 blue dollar. If the time were to stopped the goods produced by the society would have been shared proportionally with the number of green or blue dollars each one owned. Right ? Well, we're one year after. The number of green dollars is far from double what was last year, but the blue dollars are certainly at least double (Nasdaq index doubled, but there were some spectacular IPOs also). What do we do now ? If we are to divide proportionally with the exchange rate 1blue$= 1 green$, your piece of the (only) slightly larger pie more than doubled.
I don't like it. Well, here's the deal: you cannot actually get the piece of pie unless you actually own green $. If you don't, you can only eat proportionally with other blue$ owners (aka shareholders) from what piece of pie your blue dollared business did output from last year til today. Trust me, you'll get hungry. Some blue$ businesses did have a negative output, so if you were to abide by the rule, you'd have to stay hungry for the next couple of years :). What you can also do, is convince me to trade green dollars for blue dollars. Do you think I'm gonna pay still 1 green$ for 1 blue$, so that you can happily enjoy your double piece of pie ? No way, dude.
Therefore your equation 1green$=1blue$ looks fictitious to me. When you convince me to trade 1green$ for 1 blue$ you are selling me an illusion.
Enough for today, sorry for the long story. If you or anybody else are interested, we can try to account for what happens in a permenently moving system. Please do point the flaws, or wrong suppositions in the argument so far. Of course, we should introduce orange$ for Dow Jones dollars, yellow dollars for real estate possessions and a few others. But one thing should be clear: in a properly run system of markets (cause there are so many markets you get dizzy), nobody's share of the pie should double over the year, unless the guy did something spectacular, or is expected to do something spectacular -- like produce twice as many automobiles, find a cure for the cancer, or things of that nature.
Here's an observation that neither of you will like. As soon as you realize that the stock market (actually, the entire paper economy) is an illusion, you have to account for that illusion's existence and the laws that govern its behaviour. And there's only one way to explain illusions / delusions; psychology.
Now, as it happens, there's a group of psychologists who do have a good theory about why recessions occur. And that theory proves that they will occur, with probability 1, for a long time yet.
Well, the good news (I say to the unknown italics poster who started this discussion) is that you are using in your analysis many of the same tools economists use when they think about economics: simplified assumptions, freezing things at certain moments at time, marking different types of currencies and seeing how they interact, etc. The bad news is that you still have many things to learn.
First is a simple piece of math that explains why changes in the NASDAQ index are not expected to be directly proportional to changes in the GDP. For this illustration, we'll assume Microsoft is the only company in NASDAQ, that Microsoft's stock is valued at $100, that Microsoft is believed to grow at 10% a year, and that unlike in the real world, Microsoft returns all of its growth back to its investors in the form of dividends. In this imaginary world, there is no inflation, Microsoft's stock stays at $100 (the stock price grows in our world because Microsoft doesn't issue dividends and instead reinvests its growth into the company), and every year issues dividends of $10 per share. Now imagine that something happens to make everyone believe that Microsoft will henceforth grow at 20% a year -- some new market for them to dominate opens up, or they invent some new technology that everyone is going to want. Then, all things being equal, Microsoft's share price will probably double: if everyone was willing to pay $100 to get something that pays out $10 a year, they should be willing to pay $200 to get something that pays out $20 a year (which is what we're assuming Microsoft shares will do in the future). The NASDAQ (= Microsoft, in this example) doubles overnight, while the GDP doesn't: at best (if Microsoft is the entire economy), GDP growth will double overnight (from 10% a year to 20% a year).
Another thing this example illustrates is how share prices are entirely bound up in people's beliefs about the future. This is why your whole project of trying to distinguish "true" values or prices from "illusionary/fictional" values or prices is doomed: while it might be possible to get people to agree as to the "true" value of Microsoft's current assets, people are almost always going to have differing opinions as to how Microsoft is going to do in the future, and as we just saw, it is that information which primarily determines Microsoft's stock price.
Another "proof" that separating "true" value from "fictional" value is probably impossible is this: if it wasn't, you could make millions on the stock market by buying companies whose true values was greater than their fictional value and shorting the rest.
There are many other errors in your analysis (the amount of currency in circulation has almost nothing to do with the amount of goods and services and economy produces, for example); I really encourage you to pick up any introductory economics text to learn more. (Economics, much like philosophy, is often better at shooting down bad models than it is at coming up with good ones). -- ThomasColthurst
If Microsoft's P/E would be 10 your example and your reasoning would work. During the period which I was referring to the P/E was on average more than 100, not to count the negatives. So for those prices to be justified, it would have amounted to at least an order of magnitude growth in business profits. Which would have amounted to a significant growth in GDP that was nowhere in sight. For one single company, it is acceptable to say that even a P/E of 1000 is fair, given an expectation that something spectacular is going to happen. But for a whole economy to be "valued" at such ridiculous levels was unreasonable for any one with the least of mathematical intuition ( I acknolwedge here that many "intuitions" were proven wrong in Mathematics). The reality proved my intuition (which was also the intuition of several colleagues of mine), while I'd be curious if you can come up with (or point a link to), any reasonable mathematical model, that would provide a decent justification for what was happening in the markets in the period we're talking about. What was supposed to happen in the American economy for the markets not to drop big time, as they did ?
On the other points, let me tell you a some fictional and some real values. The fictional value was the value Sun Microsystems stock when it was around 80. It was based on a fiction. The theoretical "wealth" of Bill Gates is also fictional, you can read about it expressed in billion$ in Forbes magazine.
For example of real values, here you have it: the bread you buy at the grocery store. The services provided to you by your doctor. Those are real values. You can come up with some examples yourself.
As a matter of fact, I consider that you proved the point for me: "share prices are entirely bound up in people's beliefs about the future". Yep, exactly tight. That's what I was saying. They sell beliefs. When those beliefs predictably fail to materialize on a large scale I legitimately call them illusions. So they were selling illusions, and they still do.
From dictionary.com:
illusion
1.
An erroneous perception of reality.
An erroneous concept or belief.
So why aren't you rich? You claim that you can predict when people's beliefs about the future will fail to materialize, you claim that you "intuitively" knew that stocks were overvalued in the late 1990s, so why didn't you then or currently now make a killing on the stock market?
Similarly, if you know what the true P/E ratio for the entire market should be, why aren't you making lots of money by shorting a diversified portfolio of stocks that are over your one true value?
Simply because the market as a whole is overvalued, and is based largely on fictions. Add to that the fact that you can't get any decent mathematical idea about the current and past activity of an enterprise, because economists and accountants made a lousy job. You're asking me something fallacious here. The fact that I understand the math behind California's state lottery, doesn't allow me to win money at lottery. Do you expect me to?
Or is it just possible that no one, including you, can predictably predict such future events like how well Microsoft will be doing in 10 years?
In the lottery example, I can't predict any particular ticket, but I can predict where the whole phenomenon is going. With markets, I can't predict whether MS will be 10 times bigger next year, 10 times lower next year. But I can reasonably predict that the whole economic output of American society will not double by next year.
My example was merely trying to demonstrate that a stock's price is linked to a company's expected future earnings, and thus changes in the overall stock market evaluation need not be immediately reflected in the GDP. The reasoning works no matter what the specific P/E involved is.
Let me tell you why the specific P/E does matter. Say, you're a single owner, you invested 1000000$ in a business. What is the expected output (profit) you want to make in a year. A reasonable figure should be around 100000 or better (10 P/E). You can't make profits in a single year, you first have to ramp up investments. You expect to be paid back later by bigger profits. But if when averaged over the whole years, and taking into account that "money now is better than money later", you do expect over the next 10 years the average equivalent of a 10 P/E or even better. Otherwise you just lost money and opportunity. Let's say that the average 10 fails to materialize, what do you do ? You sell your investment to others making sure they are illusionned that the firm will grow explosively. The others will not reasonably expect a 10 P/E anytime soon, but they will expect that others will bail them out, at their turn. In the end somebody will predictably have to pay the bill for what essentially is a combination between a pyramidal scheme and a lottery. Let's say, when you decide to sell to others the P/E was 1000. Others may (reasonably believe) that productivity doubles, costs wil be cut, etc. By next year the P/E will be 500. But business will still not stand on its own (it will be loosing money and opportunity). But because of the earnings growth, other in the market will be illusionned and jump and bail the second round of investors out, and so on so forth, until the earnings growth predicatbly hits a ceiling and the P/E is still showing that the business is loosing money for the current investors. And the stock price predictably drops. What this example shows is that what is sold is not essentially beliefs about when and how much the company will be making money for its current investors, but beliefs about what the next round of investors will believe.
I reemphasize that many reasonable (and admittedly, many unreasonable) people in the late 1990s thought one or both of two things: (a) that the information revolution brought by computer technology was soon going to approximately double productivity rates across more or less the whole economy and (b) that stocks were and more or less always had been in the past undervalued relative to other less risky investments like bonds. [More precisely, stocks appeared to be undervalued relative to investments such as junk bonds that had almost exactly the same risk profile.] Taken together, these two beliefs could justify more than a doubling in the stock market.
You invest 1000$ in a company that will double its productivity. Currently the company is making only 1$ in earnings. Without waiting for others to bail you out, how much do you expect the company will be making next year as a result of productivity doubling (other things being equal), and can you be happy with it ? The doubling of productivity and the comparison with junk bonds could hardly justify those beliefs. They could only justify that the pyramidal scheme that stock market was in that period would go on another round (maybe another year), in which case we hit the ethical problem.
I'm curious about how you would classify the value of the following objects into real or non-real: an Eminem Show CD (I would pay $20 for it; my roommates would pay at least double that never to have to hear it). A bread making machine. The company that makes the bread. My doctor's education. The bet I make with my bookie for the Red Sox to win the World Series. A $100 dollar bill. A stock certificate worth $100 which my landlord lets me pay my rent with. -- ThomasColthurst
I won't classify them into real non-real, but I'd put them on a scale. And it also depends on the context. That's what markets are for, to provide the proper context, when they work. When they don't work, they will provide the wrong context, as it did happen over and over again. The doctor's education if it's solid and we don't have a hyperinflation of doctors in society is something very real. Ditto for the bread making machine if it's not outdated technologically and consumes more than it produces. The company that makes bread, it depends, here we enter into the fiction about predictions of future. But if it's profitable , by that including its accounting is in order, I'd say it's a real value. Your bet is a lottery, I'm not interested in lotteries and a society as a whole can't build anything on a system of lotteries, lotteries can only pass the buck around, they don't create values. If your landlord accepts stock certificates, it's his problem (sooner or later). Most of the landlords will not accept certificates, and I met some that don't accept even personal checks.
Finally, I request elaboration from the author of the non-italicized remarks above about the illusionary nature of the stock market and supposed ability of psychologists to explain recessions. For example, when you say that the whole paper economy is an illusion, do you mean in the sense of Parmenides, in which all of reality is an illusion? Do you mean it's one real big trick put on by Penn & Teller? Or do you mean that all values and prices are in a sense subjective, something economists have known for over a century? References to the work of this group of psychologists who can explain recessions are especially requested. -- ThomasColthurst
I mean that prices have no relation to value. And the psychologist in question is Lloyd deMause.
Cool. I take it then that you would be willing to sell me everything you own for $1? You can't say that you won't because you value your stuff more than $1, because you just asserted that prices (like $1) have no relation to value. -- ThomasColthurst
You assume that "value" is measured in dollars, or indeed that value is at all measurable. The fact that I value my stuff more than 1$ isn't the same thing as your claim that I assign a price higher than 1$ to it. So there isn't the slightest contradiction between the statements that value has no relation to price and that my stuff has higher value than 1$.
In fact, it is impossible for value to be related to price since 'value' is multi-dimensional. It is, at best, a partially-ordered set. OTOH, prices are singly-dimensional, and are a well-ordered set. And that's just value within a single person. Value between people is incomensurable. "Price" is a fiction invented by idiots to compare the incomparable.
I most emphatically do not assume that value is measured in dollars, or any of the other things you say. I do assume that prices are (sometimes!) measured in dollars, and offered to buy everything you own for the price of $1. I think you are making the mistake of assuming that all relationships are the equality relation ("equals", in math talk). You valuing everything you own more than the price of $1 is an example of a relation between a value and a price.
It is true that economists often make the simplifying assumption that values are a well-ordered set. They do this in the same spirit that physicists sometimes use Newtonian gravity rather than general relativity to do calculations: they know it's false, but boy does it make the math easier, and for many problems of interest, the simplifying assumption makes no difference in the answer.
Finally, the comensurabilitiy of values between people is an oft debated philosophical question which I wouldn't presume to know the answer to. I do however know that prices aren't fictional: the 50 cents I paid for this candy bar in front of me is as real as the candy bar's wave function. -- ThomasColthurst
Only a math geek, and I mean this in the most affectionate manner, could seriously state the equivalent of 'the number 2 and black holes are related'. By the mathematical definition of 'relationship', pretty much everything is related, if only by math, numerology or language. But since price and value are not significantly related, we colloquially say that they are not at all related.
Even non-math geeks agree that there are significant relationships that aren't "equals". Mass and weight, for example, are related but not equal. Values and prices are very similar: people value all sorts of thing, including money, and money is used to pay prices. If I buy something, then you can almost always infer, for example, that I don't value the money I payed more than I value the object bought. [In math talk, "willing to buy for" acts as a function mapping elements in the PO-set of values into downward pointing arcs in the completely ordered set of prices.] -- ThomasColthurst
That's a relation between value and money. And actually, since money only derives value from other things which have value, then it's a relation between different types of values through the intermediary of money. Can you specify any significantly useful (ie, correct!) relation between price and value?
Btw, you cannot infer (even "almost always") that what people pay for has more value to them than the money they paid for it. That assumes a rationality that does not exist in human beings. It assumes that coercion does not exist (which is probably why you made an exception). It assumes that the act of acquisition/paying does not by itself have value. It assumes that people value wealth over poverty (not true!). And even if all these assumptions were true, it would still be wrong because it automatically reduces value to a totally ordered set, which we know can't be done.
I did a quick web search on Lloyd deMause, and he seems like a real crank: see his webpage at http://www.psychohistory.com/ if you don't believe me. I didn't see anything about recessions, but his article on "Head and Tails: Money As a Poison Center" is full of sentences like "Ever since Freud pointed out the anal origins of money, it has been common knowledge that money unconsciously represents shit and reflects our ambivalent attitude toward our body products." If you honestly believe that this kind of psychobabble can help you analyze anything, you are almost certainly not worth talking to. -- ThomasColthurst
If you can't comprehend such a simple fact of economics as the difference between money and value, which you imply above you understand, there's not the slightest hope you can learn anything more advanced; like, say, the role of psychology in economics. But other people may want to read 'Reagonomics as a Sacrificial Ritual' (http://www.psychohistory.com/reagan/rp51x61.htm)
I'll leave it to our audience to decide which of us has the better grasp of the difference between money and value. I would like to state that I have no objection to the use of psychology in economics (and in fact, I am an enthusiast of the use of economics in psychology). I do however object to any use of Freudian psychobabble in any area other than humor. -- ThomasColthurst
The scary thing about deMause's essay 'Money as a Poison Container' is how accurate he is when you look at the practices of Scientology. Given how screwed up the human mind is, I don't object to anything to try to understand it, no matter how deranged it may sound at first.
Not to skew the subject too much from the above, but there is another factor that messes with the value of money, and which accounts for the number of different formulas for the "future value" of it and the different results obtained from these methods.
Banking, as it is practiced today, involves a monetary slight-of-hand in which imaginary money is loaned and real money is repaid on those loans. It's a kind of kiting scheme that depends on economic forward motion to keep it alive. Economics has to encompass banking in order to predict systemic behaviors. The math breaks down in trying to invent a formula that adequately gauges the effects of essentially arbitrary policy decisions by those who control the flow of money and interest rates.
It's not physics. There is no acceleration-of-gravity factor that can be applied to money. It's not chemistry. You can't predict that mixing this money with that set of social factors will produce these profits. It's not ... mathematics.
The best economic proofs are "educated" guesses. Heisenberg might have had some interesting thoughts on this, had he been an economist. Possibly someone with a better grasp of predictability in complex systems (chaos theory) might have a real shot at calling the outcomes, but I rather fear that economics, as practiced today, attempts to treat arbitrary human influences on the system as "natural law" in deriving the math to describe its patterns.
It's not that I believe "math" is a better answer than "economics;" rather I believe that the application of math to any subject assumes (requires?) that there is not anyone tampering with the data or the rules that generate the data while the analysis is being done.
Of course ethics might have something to say about the whole tampering thing. Wow, wouldn't it be wonderful to be able to master the mathematics of a system in which the participants are all trying to bend the system's rules to suit their own ends.
Perhaps the white-lab-coat guys mentioned above have mastered all this and can give us the formula? Or maybe that would create a Heisenomics Distortion in which the members of the system being measured affect the outcome by being aware of the rules?
Note: Incidentally, the stock market is a game of its own. It would be a mistake to try to apply straight value exchange rules to that system. The motivations of the participants are different - and quite varied within the set. It's "related" to the world of value exchange, but only in a Rube Goldberg kind of way.
The best physics theories are educated guesses. As for economic theories, I agree you need scare quotes around "educated".
It is also not uncommon for economists to occasionally prove purely mathematical theorems
Only too often does mathematical economics resemble the children's game of hiding Easter eggs, great jubilation breaking out when the eggs are found precisely where they were hidden - a witty simile which we owe to the contemporary economist L. Albert Hahn.
I'm afraid that pretty much the same could be said about any mathematical science (and perhaps any science): people often invent problems just because they have the tools to solve them just because they need to write papers just because they want tenure. This happens in math, physics, statistics, economics, and every other field I've been unlucky to have to do research in. Still, it strikes me that the alternative - not having the tools to solve any problem - is worse. -- ThomasColthurst
What's striking about superstrings is precisely that people did not invent it just because they had the tools to solve it (or even sortof work on it). In fact, they still don't have the tools to solve it and they've been making new tools for the past two decades. Newton's physics was the same way. He had to invent the calculus in order to solve physics.
Similarly Einstein had to work out a lot of the math for general relativity. (Special relativity is more or less relativity without gravity, and was done in 1905. Adding gravity makes the math much hairier, and took until 1915 or so.) As I understand it, it turns out much of the math existed already in other fields, so that Hilbert was able to recreate a lot of it in a few months of work. But for Einstein it was definitely a case of making up (at least reinventing from scratch) math to work out the implications of the principles.
Yes, and good work in economics (for example, Walras' work on general equilibrium) invents the tools and math that it needs too. That doesn't change the fact that a lot of the work in both physics and economics proposes and then solves the problem of the easily nailed nail (which is what I believe the original comment by Hahn was addressing). -- ThomasColthurst (but just this paragraph).
The point is that physics is not like that; especially superstrings. Superstrings is a unique mathematical structure which it has taken more than two decades of research to discover even the most basic properties of. String theory was invented to solve the quark problem. It didn't. And one of the reasons it didn't was because physicists were unable to get rid of a spin-2 massless boson. It took a long time for them to realize that string theory was a theory of gravity. This is why they can legitimately say that string theory predicts gravity. It was never put in by hand and it couldn't be taken out no matter how much the researchers working on it tried to do so. Superstrings predicts gravity where General Relativity merely describes it.
Even for the simplest of problems, the equations in string theory are in no way simple. The mathematics is horribly complex and it's impossible to predict how or why superstrings solves a problem before actually solving it, sometimes not even then. There are no easy problems in superstrings; just solvable ones.
The real problem I see with economics is cause and effect. All economic predictions influence what they're trying to predict. The successful ones will cause the economy to move the way they say it will. The popular economic theories are those that make money for the people with predictions. The way to make money is to know what will happen before it does, and the choices that determine market movements are made by a relatively small group of people who all have about the same pool of information. So, if you know what tools the other members of the group are using, you know what tool you want to use to know what will happen. In order for an economic tool to be successful, it has to be popular with enough of this group that they base their decisions on it. And so now we have a collective action problem. We’re back to GameTheory which, while used by economists and biologists, is, at its core, math. So I believe math wins every time. Besides, Algebra doesn't have to be popular to work :-) -- BethanyAndresBeck
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