A new sandpit for long side discussions, *idees fixes* and so on.

Skip to content
# John Quiggin

## Commentary on Australian and world events from a socialist and democratic viewpoint

# Sandpit

##
10 thoughts on “Sandpit”

### Leave a Reply

A new sandpit for long side discussions, *idees fixes* and so on.

%d bloggers like this:

This is a bit of wonkish post. It’s a copy of a post I put in Bill Mitchell’s blog. It’s to do with the relationship between models and reality and the reasons why good functioning models have dependable laws both internally and with respect to reality. It goes further and propounds the existence of System Meta-Laws and their uses which concept is explained in the body of the post. This post is not just about MMT or even primarily about MMT. It just uses MMT as an example. Considerable reference is made to game theory albeit at a higher conceptual level rather than at a technical detail level.

The Argument.

Argument about causes is not relevant in the case of first order MMT description. MMT at this level is an empirical project seeking to discover empirical facts and Laws of the system and not causes. In terms of the search for knowledge, it is vitally important to distinguish between the search for “Laws” and the search for causes. Taking the example of hard science, the Laws of Physics describe only the apparent invariable relationships between certain quantifiable phenomena. These relationships are discovered by the process of hypothesis-making and hypothesis-testing by experiment; in other words discovered from repeated and verifiable empirical observations and measurements. These apparent invariable relationships we call Laws. We do so once we are sufficiently confident they consistently hold true (within an acceptable range of error) under all observable and conceivable conditions or in a carefully defined range of conditions.

Thus, the famous equation e = mc2, for example, does not assert anything about causality. There is no way we can extract, from Einstein’s famous equation, any notion that matter “causes” energy nor that energy “causes” matter nor even that the interaction of mass and the speed of light “cause” energy. All these notions are nonsensical. The equation is of mass–energy equivalence (an identity) not of mass–energy conversion. Mass–energy equivalence does not in any way imply that mass is “converted” to energy as mass is always preserved. The three quantities are simply related in an identity statement. (It perhaps allows for matter to be converted to energy but this leads us into very difficult areas, physically and philosophically.)

Overall, ontological causality (what causes something to exist) is a non sequitur. Equations like e = mc2 (an identity) from relativity physics or Y = C + I + G + NX (an identity) from MMT do not suggest a temporal relation of before and after nor of progress from cause to effect. They simply assert a point-in-time or a non-temporal (unchanging across time) identity, empirically derived. Mathematically this is expressed in an equation where the equation is satisfied for all values of the involved variables.

So MMT critics are strictly correct in saying that the identity equations of MMT “say nothing about causality”. (I am not saying that other parts of MMT say nothing about causality.) In the same way, e=mc2 (an identity equation) also says absolutely nothing about causality. Laws of this kind never say anything about causality, in and of themselves, precisely because they are ontological and mathematical identities. This is not to say these laws are useless or meaningless for later considerations of causality. This is far from the case. Such Laws, once discovered, are profoundly important. They allow the next steps, which are our algorithmically or heuristically guided searches and actions seeking to cause changes in specific quantities over time (for example the quantity of unemployed persons in the economy).

If I might request the indulgence of readers of this blog, I believe I can answer the following crucial questions.

How can a seemingly arbitrary and formal human invented system (like the modern financial system) have dependable laws (like physics for example)? Surely, an arbitrary, invented system can take any form and be changed at will thus obviating any chance of its possessing dependable Laws?

Formal invented systems of the class known as models have dependable internal Laws. Good models even have Laws of relation to the real system being modelled. My particular path to the following discovery lay through game system theory and AI theory, particularly the theory of RTS (Real Time Strategy) games. In essence, the issue is to do with systems modelling where the formal system (an actual game or an actual financial economy) attempts to model, quantify and relate by dependable calculations (identities, laws and algorithms) some aspects of the real world.

To ensure we are clear what we are talking about we must note this. The extant financial economy models the real economy. Financial transactions of money units have to model real transactions of goods and services. If there were not some degree of congruency and approach to accuracy, the result would be chaos for the system of individual and national finances and real transfers of goods and services. The financial economy interacts with the real economy too, which is a second order concern and where analysis becomes more complicated. The financial economy even develops its own devices and imperatives and this becomes a third order concern for analysis.

A macroeconomic model (like MMT) seeks to understand the formal features of the first order financial model of the economy and then seeks to further analyse second order concerns (feedback interactions) and third order concerns, which we might call term endogenous financial artifices, expedients and imperatives. In summary, the extant financial economy is a model of the real economy. MMT, or any macroeconomic theory, is a both a model where it models the real economy and a meta-model (a model of a model) where it models the extant financial economy’s model of the real economy.

All models abstract, simplify and distort real world phenomena. That is the essence of what a model does in execution of the modelling project. It is important to include consideration of the various phenomena of distortion in the analysis. Sometimes, making a model work requires specific intentional distortions (of relativities, values etc) as well as abstraction and simplification. Abstraction and simplification, in and of themselves, imply a degree of unavoidable distortion. By “abstraction” I mean abstracting a discrete quantifiable modelling value from a real world phenomenon which is complex and often at least partly qualitative. Assigning a money value to a real world item or value (a process we undertake ubiquitously and repeatedly in running a money economy) is “abstracting”.

What I have found from my own investigations of game system modelling and AI theory is that all internally consistent model systems have Laws as well as rules. Rules are “the rules of the game”. For example chess has rules; rules that govern the size of the board (a two dimensional delimited of array 8×8), the moves of the pieces and the rights and obligations of players and bystanders. Though these are formally called the Laws of Chess it is better for our purposes to call them the Rules of Chess. The word “Laws” must be reserved for a another, clearly defined use. Chess is part of a genre of games which we might call turn based array games. Chess, draughts, noughts-and-crosses, tic-tac-toe (3 dimensional noughts-and-crosses) and 3 dimensional chess are all examples of this genre. What we find is that games of this genre exhibit consistent and dependable laws which are unaffected by rule changes or parameter changes provided the fundamental nature of the genre (games of dimensioned, delimited arrays, with alternate turns and movement by discrete quanta) remains intact. An example of such a Law is that any piece with any kind of omni-directional move or influence “controls” more array elements (squares in chess) from the centre of the array than it does from a side or corner of the array. This would not be true for a “wrap-around array” game which thus by definition would belong to a different genre.

What MMT theorists have done in essence (from my point of view) is take a model with relatively consistent and delineable rules, the Modern Monetary System, and first enumerate the rules and parameters of the genre (MMS mixed economy capitalism) and then second, derive the consistent Laws of this genre of models.

In game theory, it is clear that each genre of game models partakes of the same essential law-bound nature as the real physical world, though genre does so in its own particular way. There are clear reasons for this. The physical (and even biological) Laws of the real world impose both “hard” and “elastic” constraints on the game world; on the model world in other words. The Laws of the real world (some of them) ineluctably push into and impose themselves on the models. A very central example is dimensionality. We are familiar with the notion that we live in a world of four obvious dimensions. These are height, width and depth (the x, y and z axes of 3D space) plus time. A game with a geometric basis, like chess as mentioned above, need not model all the space dimensions but it must model some (two in the case of chess). A chess board models two space dimensions and is a finite two-dimensional array (8 x 8). Thus, the internal Laws of chess consistently reflect some aspects of the physical dimension-conditioned Laws of the real world.

An example of an in-game “Law” in chess, given above, is that a piece will “control” more squares from the centre of the board than it does from the corner of the board. This is mathematically and geometrically axiomatic. This “control” is a movement potential dependent on the movement rules of chess and on obstacles imposed by other pieces on the board and the board’s array limits. This Law has its direct physical analogue in the real world where, for example, I can sweep more horizontal area with my arms while standing in the centre of the room than I can while standing in a corner of the room. The crucial thing about all such in-model Laws, where the model models the real world in some way, is that they are mathematically/geometrically axiomatic in-model and their direct analogues are also empirically true in the real world.

Thus, asserting (for example) that all models of a game genre like RTS have the same reliable basic internal Laws is really asserting no more than the following. RTS games are all of a structure which models the three space dimensions plus time as the arena of action and then models and places simulacra of materials, energies and units (machine or human representations) within that 3D, time-dependent world. All these features can be, and indeed must be, quantified. They are governed by mathematical-geometric Laws analogous to the classical Laws of physics of the real world. These laws are explicitly analogous in those modern games which use Newtonian physics engines.

To sum up we can state;

• Laws describe the invariable relationships in a system. Hence Laws (correctly derived) are unchallengeable.

• RTS computer games are mathematically, geometrically and algorithmically governed systems models of the real world and as such they have invariable relationships both internally and with regard to the real world which they model. These relationships can be described by Laws.

We then find, for example, that simplistic Euclidean laws like “the shortest distance between two points is a straight line” are true in the real world and in the game world provided the (local) geometry is of a precisely or closely approximate Euclidean nature in both cases. At a slightly more complex level, we then find that the military law of strategic attenuation (it gets harder to project military power over greater distances) applies equally in the real world and in the modelled world of the game (provided the model is accurate in its essentials).

Where this theory gets really interesting and could cross over into good macroeconomic modelling, in my opinion, is when we discover that each genre model, be it a game model of the real world or an economic model of the real world, begins to demonstrate what I call System Meta-Laws (SMLs). The idea of using this word for this new concept is suggested by the term “metadata”. Simplistically, “metadata” means data about data but it can also mean the discipline of creating structures for data. The structural metadata field is concerned with the design and specification of data structures.

Similarly, System Meta-Law (SML) is concerned with the design, specification, building and use of complex mathematic-geometric-algorithmic (MGA) systems. RTS (Real Time Strategy) is such a system. The Modern Monetary System (MMS) is such a system. Each discrete, though complex, MGA system will have its own unique set of System Meta-Laws and these must be derived from the Laws of the particular MGA system under consideration. System Meta-Laws will allow us to;

• Guide goal-seeking design of a complex MGA system from concept design onwards.

• Guide goal-seeking construction (or amendment) of a complex MGA system.

• Guide the fit of the complex MGA system to desires, needs and abilities of human users.

• Guide goal-seeking execution of tasks in the completed complex MGA system itself.

To reiterate, System Meta-Laws (SMLs) must be derived from the intrinsic laws of the mathematical-geometrical-algorithmic (MGA) system in question. Thus deriving SMLs is a two stage process. First the intrinsic Laws of the MGA system must be discovered and proven logically and mathematically. Second, the SMLs must be derived and expressed in a form which I describe as a “Firm Heuristic” (as opposed to a rough or loose heuristic). A firm heuristic is a firm and dependable goal-seeking guide. What we are saying when we derive a firm heuristic from MGA System Laws is this. The MGA Laws of this system (provable in mathematical terms) comprehensively suggest this Meta-Law heuristic to us and further suggest that it is substantially correct, to the point where we can deduce that it too (the SML) would be provable mathematically if it were not for the exponential problems of combinatorial mathematics and/or the sometimes necessary inclusion of qualitative terms and goals. In summary, each MGA system genre (including RTS or the MMS) has intrinsic Laws and thus design, re-design and execution (game-play or economic activity) must have System Meta-laws or what could also be called Structure-Conditioned Meta-Laws.

Now obviously I have not done MMT work nor have I done the work of formally proving that the MMS (the Modern Monetary System or actual money and financial system) as a first order model of the real economy is a model with internal invariable laws and certain invariable relations (also laws) with the real economy. Nor have I enumerated the MMS’s comprehensive and relatively consistent internal rule set nor the empirical reasons for MMS having not these only internal laws but also (some) laws of invariable relation with the real world. Yet I am confident that these laws exist and are discoverable. One clear law of relation between the extant financial system (which I call the MMS model) and the real world economy of real materials, energies, agents, goods, processes and services is that both exhibit time dependency. This point is fundamental, not trivial. There will be inflexible laws of time dependency linking the two. Accounting would not be possible if this were not so.

Finally, I am no expert on MMT, but Bill Mitchell’s derivation of this fact – that a capitalist economy of the MMS mixed economy variety will exhibit ineluctably either a requirement for unemployment buffer stocks or employment buffer stocks of the form defined and implemented by a job guarantee – is indeed a System Meta-Law. That is to say, the MGA (mathematic-geometric-algorithmic) Laws of the system (provable in mathematical terms) comprehensively suggest this Meta-Law firm heuristic to us and further suggest that it is very substantially correct, to the point where we can deduce that it too (the System Meta-Law) would be provable mathematically were it not for the exponential problems of combinatorial mathematics and/or the sometimes necessary inclusion of qualitative terms and goals.

@Ikonoclast

You are on your way to become a (non-verbal) theorist in economics! Roughly speaking, your outline of the methodology corresponds to that used in axiomatic economic theory, both, general equilibrium and game theory models. Did you find Ben Kinmore’s book ‘Fun and Games’ useful?

@Ernestine Gross

I haven’t read Ben Kinmore’s book “Fun and Games”. In fact, I was not even aware of its existence. Essentially, I have done no reading or study on any game theory other than reading, many years ago, a book by Raymond Keene and David Levy about Chess Programming. Neither have I done any reading on economic methodologies per se. (Which I know is just asking for people to say, “It shows.”)

I have played a wide set of RTS (Real Time Strategy) computer games over the last 12 years… very badly… and gotten myself soundly beaten many, many times by younger players. I am 58 now and my slow mental reaction and physical reaction times tell against me. Even my volatile temperament is wrong for real time games which require cool, clear thinking on the spot and under pressure.

Against younger players, usually younger by several decades, I achieve 30 percentile to 70 percentile mediocrity depending on the game in question. However, I found I was much better at analysing the theory of RTS games, including theory for high level concept design, than actually playing them. This is in my own estimation which could be awry.

My development of RTS concept design theory has been done from scratch using my wide praxis as a base. In terms of developing a theory of these game models (or a wider theory of all formal models), I started to notice that these games and indeed all formal models have laws as well rules. I investigated how;

1. these laws had internal consistency (essentially because they were embedded in the formal mathematic-geometric-algorithmic models – my clumsy term – and thus were axiomatic);

2. these laws had a consistency and persistence which was remarkably independent of rule changes which tweaked parameters or even changed significant sub-elements of the game but which did not change the fundamental nature of the game (its genre);

3. these laws (at least some of them) are analagous or even equivalent to real world hard science laws both because the real world (a) ineluctably imposes elements of itself on the dynamic model world (time is a prime example) and (b) because the discipline of making a consistent working model forces the creator(s) of the model to embed mathematic, geometric or algorithmic representations of real world laws;

4. the existence of these consistent laws in model genres, then allows us to go to a higher conceptual level, the level of discovering system-conditioned meta-laws which can then function as aids to enable us to redesign our systems; and

5. as a by product you will notice I have found a quantitative way to judge and draw genre boundaries between game models or any set of system models including economic models. Laws hold within genre boundaries but not between genres.

When I talk about the Modern Monetary System (MMS), I am not particularly referring to Modern Monetary Theory (MMT). I am simply referring to the current national and international system of money and finance (unwieldy as such a disparate and conglomerate system is). We are not so lucky with economics as we are with games. Economics must be several orders of magntude more complicated at least. Thus I see this entire money and finance accounting system and all attendant national and international legal laws (not physical laws here) of global late stage capitalism (including China’s mix of market and state capitalism) as in itself a model, a model of the real economy.

As I said in my post, this model must perforce contain some congruence and accuracy with respect to the real physical economy otherwise all finances personal, national and international and all real economy movements would degenerate into chaos. This might appear a debateable assertion but I think it holds water to a strong degree.

So the first step or one of the first steps of any economics is to invetigate this model, what I call the extant model of the economy, namely the formal and official accounting which is accepted by virutally all participating parties. However, it’s clearly not the only zone to investigate. There are zones below and above. The zone below is the real economy of real materials, energy, agents, processes, goods and services. The zone(s) above include endogenous finance behaviour. Then there is also the issue of feedbacks between the zones. I do get frustrated with MMT because they rarely seem to want to analyse in depth the real economy of real materials, energy, agents, processes, goods and services.

That’s enough for now other than to say I am following for the moment a naive, autodidact path of investigation where I hope ignorance of established paths and some natural facility might enable me to have an original thought. It’s probably highly unlikely. More likely I will laboriously reinvent some tiny part of existing theory, doing it much more than half wrong and couching it in opaque and idiosyncratic terminology.

Note: I have found that the book Ernestine refers to is by Ken Binmore. Yes, I too find the spoonerism “Ben Kinmore” a more plausible name. 🙂

@Ikonoclast

Good one.

Ken Binmore it should be. My sincere apologies to Prof. Binmore in his absence.

“I do get frustrated with MMT because they rarely seem to want to analyse in depth the real economy of real materials, energy, agents, processes, goods and services.” So we concur once again.

Hopefully you are sympathetic with me being all encouraging in your endeavours and you don’t mind if I do provide a concept which may interest you. A ‘commodity’ is defined by its physical characteristics, time of availability and location of availability. Isn’t this concept so much more useful than the term ‘goods’ for the purpose of empirical investigation and communication with natural scientists?

I hadn’t come across this more detailed or specified definition of a commodity as opposed to a good (which always sound kinda silly in the attempted singular). It sounds more useful for sure as you outline. It’s worth a sentence to note that a lot of non-technical sources simply use the word commodities as a synonym for goods (which is not good enough of course).

The more proper definition reminds me of the distinction made between energy and “energy available for useful work” (exergy) in thermodynamics. Similarly, there is clearly a difference between goods and “goods available for immediate purchase.” Though I am certain that I coild not think through the economic theory ramifications unaided.

My technical and mathematical knowledge of economics is minute. My mathematical ability these days is sadly decayed and it was very limited to start with (a reasonable to good result in High School Senior mathematics but never studied maths after that). LOL! However, I understand programming (in now essentially defunct languages), algorithmic procedures in general and certain tree-searching routines along with goal-seeking heuristically directed algorithms.

My crude mathematical exposition of lower bound complexity in RTS (Real Time Strategy) Game systems would no doubt make a real mathematician cringe. But it is probably enough to make the high level conceptual point I was attempting to make. Mathematicians who read this bog please feel free to pillory me.

The Example.

Complexity, understood as possible data points (corners) in a lattice system, goes up by the power of the dimensions. A one dimensional Euclidean line may be described by data for two points (for example to draw a line in a vector drawing system). Two dimensions square the possible data points, three dimensions cube the possible data points and four dimensions raise the possible data points to the 4th power.

We can provisionally treat time as a 4th Euclidian dimension in a digital time system. In one unit of digital time, the cube’s corner data points can cumulatively describe a departure position and an arrival position, thus increasing the points from 8 to 16, indicating the 4th power. Treating the 4th dimension, time, as another Euclidean dimension is not correct in any real space-time sense. True space-time is not a Euclidean space but this objection need not concern us here. We are simply looking for an estimate of the lower bound of the complexity of the system.

Complexity in a lattice could also be understood as the total number of unique directional vectors which can be drawn from all points to all other points as follows;

• Line (2 vectors) (forward and back)

• Square (12 vectors) (all lines forward and back including the diagonals)

• Cube (n vectors where n is a getting to be quite a large number)

Even this consideration (a first step in attempting genuine combinatorial mathematics) is enough to illustrate we can consider that describing the complexity of RTS in a real time digital system as going up by a function of x^4 simply describes the lower bound of complexity.

Therefore;

RTS Complexity > x^4

I think I should have written the final formula as:

RTS Complexity(x) > x^4

meaning RTS Complexity as a function of x is greater than x to the fourth power.

I have just found on Wikipedia that;

“Upper and lower bounds are usually stated using the big O notation, which hides constant factors and smaller terms. This makes the bounds independent of the specific details of the computational model used. For instance, if T(n) = 7n2 + 15n + 40, in big O notation one would write T(n) = O(n2).”

It seems to me that in my own naive attempt at finding a mathematical expression for the lower bound of RTS “complexity” (an admittedly ill defined “quantity of something” in my argument), I actually managed to derive an expression that somewhat mimics big O notation with the O expression “understood”.

I dunno, maybe that should give me some confidence I am stumbling in the right direction.

Its great to see sanity prevailing with the resumption of on-shore processing of asylum seekers. The GREENs, since the departure of Howard, have certainly exceeded my expectations in the department of counter-productive moral posturing. Its great to see the whole parliament publicly rebuffing their foolish and failed efforts at doing good.

If there is any honesty amongst Left-liberals they must now acknowledge that they were wrong on this issue. Otherwise they are no better than the denialists they castigate on the other side of politics.

I suggest Pr Q put up a post acknowledging that on this issue he was wrong and apologising to all those on the other side of the debate whom he castigated as “miserable bastards” who deserve to “freeze in hell” for their callous “racism”, “dog-whistling” etc . This would be appropriate act of contrition given the human cost of following the pernicious Left-liberal line on this issue. It turns out that those “racist..miserable bastards” saved lives whereas those oozing the milk of human kindness did the exact opposite.

So, lets look at the scorecard regarding the Left-liberal nineties cultural trifecta of Republic, Reconciliation and Refugees. We now have a constitutionally confirmed Monarchy, martial law more or less proclaimed with the Intervention on remote indigenous communities and the draw-bridge raised on people smugglers. In short, Howard’s Rules.

To the Wets, I call that three strikes and your out.

@Jack Strocchi

Strong words Jack but then I suppose from your point of view you are replying to strong words. However, when you say “resumption of on-shore processing” do you not mean resumption of off-shore processing”?

I am not sure your overall (implicit) logic holds up. Your implied logic seems to be that off-shore processing saves lives. The two key questions are in what way and compared to what other policies?

How could offshore processing save lives? The first argument advanced is that of deterrence. There is poor evidence that deterrence effects occur with regard to boat refugees. Do they read Australian media? Do they get the message in any other way such as the Indonesian media or the internet? Do they understand the nuances, legal and practical ramifications of off-shore processing even if they know it exists?

The second argument is that quick turnaround of spotted boats (or pickups of passengers) and straight transfers to the off-shore processing centres mean it is less likely that boats will have time to sink. Sinkings might occur during wrangles and stand-offs with Indonesia about turning back boats. This argument fails to the facts that quick direct transfer to Australia should also pre-empt sinking deaths.

The moral loophole and the logical loophole in your central argument is easily exposed. What is the basis of your (and Howard’s) opposition to rapid and comprehensive on-shore processing? Clearly your central fear is that “too many” refugees will be found to be genuine refugees. That is the only current basis for your fear of being swamped. If you were confident that few would be found to be genuine refugees then you would not fear rapid on-shore processing and rapid deportations in all appropriate cases. For it is also clear, to those who understand the relative costs involved, that rapid, expedited, legally appropriate on-shore processing is the lowest cost as well as the most human option. Thus, since you fear too many refugees are genuine, you wish to erect extra barriers of artifice, obstruction and distancing.

The real politicks of the situation are that we should follow U.N. refugee conventions, which we are signatory to, to the letter whilst rapid, legal on-shore processing continues to suffice. Should this model fail, it would only fail due to major global or regional crises which increased refugee flow to Australia by a factors of 10, 100 or a 1000. In this case, it would be clear the world had entered a new historical phase (global or wide-regional war or global or wide-regional starvation for example). The real politick response at that stage would national mobilisations of armies, civil defences and the closure of most national borders around the world.

I notice the Parliamentary refugee stats refer to “Boat Arrivals in Australia” without ever defining what this phrase means. The phrase needs definition as;

1. Certain locations were exempted from Australia’s migration zone. Are boat refugees taken directly there still referred to and counted as “Boat Arrivals in Australia”?; and

2. Pacific solution locations are not Australia under any definition. Are boat refugees intercepted and taken directly there still referred to and counted as “Boat Arrivals in Australia”?

Correlation is not necessarily causation in any case. The alleged drop in refugees (see my questions above) in the Pacific Solution years ignores push factors and many other factors.