Heh. I found this article:
http://mises.org/journals/liberty/Liberty_Magazine_March_1998.pdf#page=45
The author models government with a bit of integral calc and determines that government doesn’t oscillate but reaches an equilibrium point for any given level of pro-government sentiment.
Not sure that this has any real value, but I thought it was cute. If you know a bit about integral calc and logit functions then you might get a chuckle.
A warning about the erroneous page order would have been nice
Woops, yeah. Skip a page after the first page 
No worries…fixed now.
Actually… this is a remarkably good idea. It’s the old “fight fire with fire” idea. Dressing up sociological theories in mathematical equations is just a way to obfuscate and dazzle. Two can play that game.
Clayton -
Paper : There are many ways to explore this key question of how the state evolves in time. One of the simplest ways is to model the state as a dynamical system. The model might show that the state will bounce around in chaos or will fall into a cycle that bounces between patterns of high and low government. Or it might show that the system converges to a fixed level of government in steady state.
There are some accurate and appropriate assumptions here. For example, social groups are dynamical systems. The problem, and I think we all understand this, is that there are in fact mutiple dynamical systems in play within a social group, and that there are feedback connections between all of them.
Each individual is his own dynamical system, and in multiple ways. His knowledge state (content of the mind) and physical state (configuration of the body) are both dynamical and directly connected. The reality around him is also dynamical and providing feedback through his sensory data.
Subgroups that interact and construct their own localized schemas and models for managing the domain that unites them (think economists, programmers, politicians, managers, workers, parents, rebellious teens) are another type of dynamical system.
I’d make two points. We all know that you can’t get good predictive capability from such attempts, IF the goal is to know what’s going to happen tomorrow. However, as Austrians also know, if we do model these systems, we can know that certain effects generated in one part of the system can produce a known signal to other parts of the system. This is why for example Peter Schiff can say in 2k7 that the Housing Bubble will burst, and when it happens in 2k8 he looks brilliant.
So, I’d hope that Austrians look at those equations and laugh. Their predictive capability isn’t real in the traditional sense, but we may in fact be able to model some of the ways that signals flow in the system. That does have some predictive value.
I think we should remember that all action is speculative in nature, and anything that reduces the risk of being wrong, is valuable. The entire reason that knowledge exists, is in it’s ability to reduce risk by reducing uncertainty. The mistake of econometrics, as Nassim Taleb points out so eloquently in his books, is the misapplication and misunderstanding of the relevance and usefulness of statistical models. They aren’t useless, but you can’t overestimate what they are telling you. And as human’s we do overestimate what data tells us.
Also, there’s no guarantee that government follows a logistic growth pattern.
@DavidB: The problem with applying equations to human behavior (there are problems with applying them to any living system but human beings are particularly problematic) is that human behavior is not simply an input-output system. People get confused on this point because they conflate causality with intput-ouput systems. All well-defined input-output systems are causal but not all causal systems are input-output systems.
What do I mean by this? Consider the follow acme equation:
y=f(x)
The dependent variable (y) is the output of f; the independent variable (x) is the input of f. The function f is an input-output system. As long as it always produces the same y given the same x, it is a well-defined input-output system. I think you can see the problem, here… human beings do not always produce the same output given the same input even though we are a causal system. The problem is, of course, that we are not being given the very same input. But then we know that that is impossible… as the old proverb says, “you can never step into the same stream twice.” So, right from the get-go, we see that the application of mathematical functions to human behavior is worse than useless, it is misleading and obfuscatory.
The Austrians say it by saying “there are no constants in the social sciences” which is, I think, a bit opaque. Is not average body-temperature a constant, for example? The Austrians would object that body temperature is not a behavior but the distinction is lost on empiricsts, so it’s a moot point. The issue is that even if there were an input-output function, you could never give it the very same inputs. This means that the input-output function would be useless. In addition, if you don’t have an input-output function and you want to derive one empirically, you can’t for the simple reason that it is impossible to characterize human behavior. Characterization necessarily depends on measuring the outputs generated by a given input (e.g. characterizing a transistor).
Finally - to drive the final nail in the coffin - it is provably impossible (yes, provably!) to derive by analytical means an input-output function describing human behavior. This is a non-obvious consequence Godel’s incompleteness theorems which Chaitin’s work shows more clearly.
Clayton -
@Clayton, great points.
I think what you said was that for y = f(x) to produce the same y for the same x, one would have to actually get all of the relevan data into x, and the known universe is the only computational system with sufficient capacity to achieve that :).
I hope I didn’t sound like I was saying that. Here’s an example of what I mean.
Think of supply/demand and prices. A price that rises is a signal. My question is can you diagram the propogation of that signal? We don’t know that it will cause a person to stop buying the good, we do know that there is more demand or that there is less supply. We also know that it could be an effect of money.
Can we diagram anything about the flow of information in economic systems? Can we diagram anything about the way in which information flows, or the effects of power and how they send signals in political systems?
An example of the same kind of idea in electrical circuits is here. The larger discussion is about potential alternative computing models that can be used to solve the kinds of problems we think of as involving intelligence. But at about 25:30, there’s a specific discussion about a computing concept called propogators, and he discusses the difference between how you teach a theory of circuits class and how engineers actually think about the circuit in practice. You might find it interesting, as I believe it might illustrate my point.
One of the points I’d make is that the price quantity, isn’t necessarily an interesting specific data. In otherwords, we don’t know anyway to quantify some mysterious thing called demand. But we can describe the affect on this mysterious thing, by propogating a known quantified value (or a relative relation) through the system. So, not only does a price NOW reflect a propogation of a change in demand or in supply from the past. We know that the change in the price also propogates back out to the system and acts as a pressure on supply and on demand. We can’t quantify D for a specific person, but we know if Pnow < Pearlier then for each Man M who receives the new information Dnow > Dearlier. Does that make sense?
I’m not sure if it does or not. Another point I’d make. One of the things we avoid is using mathematics to talk about economic phenomena, but there are versions of mathematics like set theory and logic, which can in fact operate in concepts of change and relative change, without requiring quantified change. And I think it’s reasonable to assume the human brain is actually setup to work that way, not to work off of quantification. We don’t think about how many feet it is down, we get a sense from historical data of “too high” or “safe” when we evaluate whether or not to climb down.
Anyway, not sure if I’m making sense. But I thought his point about circuit diagrams was spot on. We do similar diagramming in computer programming to think about the relationships between classes and objects in a system, and contstruct diagrams about signal propogation through a specific process.
Other computer modeling mechanisms like neural nets and others operate on similar principles. Where a specific input to a node conditions one or more outputs, but is not the only input that does so.
But to what end? I know why governments might want to track this sort of information but I can’t see how it will help a voluntary business run any more profitably. And we already do have industries that do something very much what you’re describing, they’re called futures markets. But rather than trying to distill real-world price information into a monster “God equation”, they simply use a wide array of tools (mostly boiling down to gut instinct/experience) to make predictions well enough to actually turn a profit, for those traders that don’t bankrupt themselves, that is.
Yes, there is definitely room for expansion of Austrian methodology with ordinal mathematics (even inequality-based mathematics could be useful). However, the primary difficulty will be choosing metrics that are meaningful and properly circumscribed with respect to subjective valuation and temporal variation in subjective valuation.
Clayton -
Hi guys I think it’s quit interesting the discussion is turning the way it is. I recently saw the UCLA interview Hayek gave with Jack High. When asked about whether he saw any role for mathematics in economics he responded in a most interesting way. He mentioned how most economists thought of mathematics as concerning quantity mistakenly, when really as according to a mathematician he cites, it is more broadly about the investigation of patterns. I think this might be a most interesting avenue to explore, especially once we consider the more elaborate avenues of economics, for instance in the patterns of inter-relations between price and capital structure.
Link?
Clayton : But to what end? I know why governments might want to track this sort of information but I can’t see how it will help a voluntary business run any more profitably. And we already do have industries that do something very much what you’re describing, they’re called futures markets. But rather than trying to distill real-world price information into a monster “God equation”, they simply use a wide array of tools (mostly boiling down to gut instinct/experience) to make predictions well enough to actually turn a profit, for those traders that don’t bankrupt themselves, that is.
I’m trying to figure out “to what end”. On one level, I’d say, “I want to.” There are many things man has done just because he wanted to. Many have little usefulness in the world other than to serve as data about what doesn’t work. However, if it has any value it might come form application that others put it to, that I’ve not imagined. If it’s useful. It could also be completely flawed and useless (think Marxism or econometric statistical models) and still be latched onto and misapplied and cause great destruction. A technology that has been misapplied would be nuclear physics with regards to nuclear weapons.
But the fact that someone might hit another man in the head more efficiently with a new and improved hammer, doesn’t mean a man might not try to build a hammer.
What’s been leading me there is some stuff I’ve done just to try to express relations that I hear, that can be hard to explain clearly in words. If only to express what we mean by valuing. Evaluating a set of potential actions is best described as a function, in that logically I put in a set of potential actions, and the function returns the most valued action. It becomes the action performed Now. So what can we know about what goes on here? Well we know the set of potential actions always contains “No action”, seems like that makes sense. Maybe it isn’t true, something to think on. We know that the action being performed is currently valued more than anyother action considered. We know that action aims at improving the expected conditions in reality at some point in the future. Therefore the discarded actions (or actions not taken) created realities that are valued less than the reality we are currently acting to create.
In another thread I drew a diagram to try to explain a substantive difference between coercive social action and cooperative social action, in terms of how one parties actions create potential future conditions that the target of the social action is expected to perceive and value in very specific ways.
Meaning that pointing a gun at you takes away a future that you would have reasonably expected, and is used to compel an action you prefer to the threatened reality, but did not prefer to the unthreatened reality. But convincing you of something through argumentation is the same thing. If I accurately convey information you did not have and needed, it’s not coercion, even though the effect is the same. If on the other hand I deceive you through communication the offered future that I’ve substituted for the one you expected is a lie, that’s fraud, also the same effect, but in this case we consider it to be criminal. Again, I can diagram these out more clearly in some form of semantic logic language. I’m not sure one exists that works as is, but it’d be neat to try.
I’m not sure what all we can do with stuff like this, but modeling an exchange behavior in terms of this might be interesting. Anyway understanding value in this way and modeling some of the word explanations of Mises in a more formal manner might help clear up the edges and the arguments. It might be able to construct a more formal modeling of Marx’s theories and Mises’s theories such that proofs and errors could be demonstrated in a formal way, instead of as they are now with informal logic. I’d like for example, to find ways of expressing mathematically the role of labor in value, instead of letting the Marxists consistently go on and on about labor being the source of value.
From such logical theorems, I believe one could construct interesting models for doing simulations. It doesn’t mean that the simulations would accurately reflect specific events in reality. But one might be able to demonstrate the outcome of technical designs (laws, courts, norms, company structures, production methods, financial markets) such that one can understand how it might function in reality. Think of it like using CAD tools to design cars,and then running the models through aerodynamic simulations or crash simulations.
Just some thoughts, not saying I’m right, or that it’s doable. But as that video I linked mentioned, we need more models for computing.
If you watch that entire video, he draws into sharp contrast how weak we are at computation, when you compare what modern computers do, to what the human mind does. He then points out how the mind, uses multiple overlapping models in problem domains to arrive at “sufficiently confident” solutions instead of “right” solutions. That perhaps this is a clue to better computation. Which in the end is decision making.
An apodictic, apriori science is a great tool. I think it has more it can tell us about the world than we currently realize. Prehaps we figure out how to generate models it can actually say something about. Perhaps even trying and failing will give us interesting information.
What if the US CBO had to generate a signal model that demonstrated the economic forces generated by a specific budget plan for a program, and there was scientific verification and validation of that plan? Given price interference and pressures generated by Obama’s Healthcare plan, can you imagine any economist could support it?
I’m not saying it would effect anything, but if projections based on Austrian analysis of future impact (not in raw dollars but in distortions to the market) consistently came true 2-5 years after the plan came into effect, perhaps we would find that more and more members of the public, would start using such analysis in the decision making about programs and politicians to support.
I’m just grasping at straws about how to generate any additional tools for the libertarian toolkit that might undermine government interference in the market.
Bleh… another randomized brain dump
I’m going to have to watch these videos completely.
Hayek : That [has] led me to my latest development, on the insight that we largely had learned certain practices which were efficient without really understanding why we did it; so that it was wrong to interpret the economic system on the basis of rational action. It was probably much truer that we had learned certain rules of conduct which were traditional in our society. As for why we did, there was a problem of selective evolution rather than rational construction.
Hayek is referring to a fundamental difference between the way he and Mises viewed the rational thought and social behavior. I completely agree with everything in this statement. I would argue that rational thought more specifically is what we apply to understand why things go wrong. Think of it as a natural manifestation of Popper’s falsification theorem. Something we do because something failed, but have no need to do when things go right.
@DavidB: I’ll reply in detail later, just wanted to respond to this, “instead of as they are now with informal logic.”
I think you’re incorrect that Austrian arguments are informal. Formal versus informal has nothing to do with the use of non-Latin symbols or non-English words as any symbol only serves the function of distinguishing itself from other symbols. Rather, it is the rigid adherence to rules of definition, implication and conclusion as well as the use of an explicit set of axioms that distinguishes formal from informal reasoning. Austrian arguments are, in fact, formal logic.
Clayton -
Hayek again :
Another case where Mises and Hayek were thoroughly in agreement. I’m intrigued by suggestions by Hayek that they (Mises and Hayek) viewed the underlying epistemological foundations of Economics (social science) very differently. I’m going to have to look for the substance of that difference.
Clayton : Rather, it is the rigid adherence to rules of definition, implication and conclusion as well as the use of an explicit set of axioms that distinguishes formal from informal reasoning. Austrian arguments are, in fact, formal logic.
I’d simply reply that I’d like to see them structured as such, because in my discussions with Marxist proponents in this forum, I find myself trying to express these things in such formal ways, so that the implications are seen by pointing at the mathematical form and writing a simple sentence, instead of quoting a paragraph or 3 of Mises and then spending 10 posts arguing about what it really meant…
I will say that if I read a passage by Rothbard on Action and a passage by Mises on Action, I can see the congruence, but the wording will be very different. I’ve seen others get into odd arguments about apparently contradictory statements (in English) by Mises. They may in fact have an underlying form that is expressible in a formal manner. Now we agree that they are in fact identical and logical and true (I think that’s what you are meaning by formal logic above), but I don’t think this is the same thing as I mean, which is having a formal semantics and grammar for expressing the statements, givens, and deductions in mathematical forms. I guess it might be interesting to look to see if such things have been done.
Hi David, I just want to let you know that much of what you’ve said above resonates with me and I am currently trying to in my own feeble way, to do some of it.
I’m currently working on a slightly history of thought based price theory dissertation at a neoclassical school and am looking to demonstrate Bohm Bawerk’s theory of value and price, as a logically consistent, sounder and algorithmic price theory that can then be used to analyse via a computational model built from sound praxeological rules it inputs, allowing the tracing of movements in price and capital structures which then yield many nontrivial consequences missed by mainstream macro and micro frameworks. If I it ends up half decent, I’d be happy to send it to you when I finially finish it. (I have till the end of September)
I think this is a naive view regarding the costliness of ideas and information as well as the pressing nature of hedonic wants. Curiosity is an end like any other and satisfying it can lead to satisfaction in the general sense but your curiosity will never displace your food appetite in priority. I think history is instructive in this regard. A wealthy man (usually a king or noble) with a taste for scientific speculation may decide to patronize an scholar that he is particularly fond of and, thus, free that scholar to do “pure research.” Today, we simply take this kind of thing for granted and imagine that it’s just in the ordinary course of things that there should be lots of people who do nothing but sit around all day and speculate on things that literally have no conceivable application. But this is actually extremely costly (think of all the things that are consumed by the speculative class as a group) and we only have such a large population of such people because of tax subsidy, which is a pretty horrid reason in my opinion.
If you can convince someone to pay you to engage in useless speculation then more power to you. But my guess is that - outside of tax-funded grants - you’re not going to find very much demand for such “services.”
I don’t think these arguments hold up to scrutiny. If you discard the intentional stance (i.e. the concept of action/purposeful behavior as an axiomatic category in its own right), then there really is no distinction between the mugger holding a gun in your back and the greedy businessman who won’t sell you a glass of water at a price you can afford when you are dying of thirst, or even the candy-shop owner who won’t sell you a lollipop for less than a dollar because, well, it’s his lollipop. All these people are impeding you from getting what you want so, in the purely materialistic view of things, they’re all the same to you. Obstacles to your desired state.
This is the whole reason why Mises’s idea of human action is so profoundly unpopular. It is simply not allowed to reason about humans as frankly purposeful beings.
You seem to equate formalism with material reductionism. If you want material reductionism, then yes, you’re going to be disappointed with Austrian methodology. But Austrian economics is formal. It’s just not reductionist.
It’s not informal.
Then what the hell is the point? I have two programs on my computer that simulate the motions of the heavens (Stellarium and Celestia). I have no interest or use nor does anyone have a use for a program that simulates “something like” the motions of the heavens “but not actually” the motions of the heavens. What possible use could that be???
But we already know that’s impossible. Please see my post above regarding the difference between input-output functions and causal systems.
Modern computers are abysmally stupid. NB: I’m a computer engineer.
Please read this. You have an extremely naive view of the issues.
I recommend you try to get a deeper appreciation of what already exists in the toolbox before trying to reinvent the wheel. I’m all for extending the toolbox but what I’m seeing so far from you looks counter-productive.
Clayton -