Austrian economics and Flat Earth geography

The first sentence in your last paragraph is a mess.

SOUNDINGS IN NON-EUCLIDEAN ECONOMICS

The American Economic Review,Vol. 11, No. 1, Supplement, Papers and Proceedings of the Thirty-third Annual Meeting of the American Economic Association (Mar., 1921), pp. 132-143.

It is fairly obvious, if one stops to think of it, that there are systems of economics with axioms fully as far removed from each other as the geometrics of Euclid and the non-Euclideans; perhaps as far apart as the conventional physics and Einstein. Probably the foremost non-Euclidean economist is Professor Veblen, and his theory of invidious prestige might be called a theory of economic relativity.

Orthodox economics undertakes to interpret equilibrium: Veblen undertakes to interpret progressive change. And in the social world this is much the same as saying that orthodox economics studies the assumptions of contentment and Veblen the assumptions of discontent, both of which are undeniable facts. Since undeniable facts are difficult to ignore, the net result is very largely to call them by different names.

…

What do I mean by non-Euclidean economics in the present instance? The question can best be answered by taking six axioms which represent in a general way what might be called the orthodox position on a number of important points, and inverting them. …

The talk of mathematical formalism reminded me of an old joke in the vein of scientific disciplines ribbing each other:

There were two men taking a balloon ride, when fog came rolling in and the wind shifted. They soon had no idea where they were. The first man suggested they might be able to call out to the ground and someone could hear them.

They dropped their balloon as low as they felt safe too and then the first man called out into the mist “Where are we?” It echoed for a moment before a response came up from the ground. “You’re in a hot air balloon.”

The first man nodded and said “Well, at least we know there is a mathematician down there and we could try to reason where we are from that.”

The second man looked confused, “But how do you know he was a mathematician?”

The first man replied, “Because, he gave us an answer that was technically correct but totally useless.”

The six axioms that Clark presented and inverted were the following:

Proposition 1. Economics is the science of wealth, and wealth consists of things (a) useful, (b) limited in supply, (c) exchangeable, (d) appropriable.

Proposition 2. Consumption is the end of economic activity and production is a means to that end.

Proposition 3. The standard of economic service is the gratification of human wants through the increase of marketable goods and services.

Proposition 4. As a general rule, cost varies in proportion to output: “overhead costs” which are independent of output are the exception and arise in connection with large fixed capital only.

Proposition 5. The rational foresight of individuals is at the basis of individualistic economics.

Proposition 6. Capital, including machinery, consists of instruments of production utilized by human beings for the production of wealth.

“hasn’t lived up to expectations” = “paper mechanisms whereby armchair theorists can grind out misleading results”

While the analog to geometry makes an argument against formalism, I think invoking it considering economics is missing the point. Say what you want about Euclidean geometry, when you try to measure the sum of the angles of a triangle, it is 180 degrees every time. Euclidean geometry only start to lose it power when you started working on something truly spherical, say a triangle connecting New York, London and Madrid. The point being the faith behind the formalism is based on irrefutable evidence at the time. I see nothing like that in economics. Hide behind formalism when the evidence is against you is not science.

The point is that “the world is complicated” serves as an all purpose shield against the process in formalism that you describe where the world feeds back on the axioms. In fact, the process never happens in a way that changes the axioms. What happens, as a matter of practice, is that the economists claim that the world actually is the way their formal model predicts (there’s inflation if you know where to look) or there are ad hoc modifications to the model that aren’t, well, formal, that is, they are ad hoc.

Either way, a priori and real world never meet. And poor people die.

@JQ I hope you see the parallel on the minimum wage theory versus reality and the Euclidian non-Euclidian geography question. The data tells us we live in a non-Euclidian world. It says the same thing about a theory that predicts job losses due to minimum wage increases. But economists don’t see that because human interaction is infinitely complicated. Therefore, by definition, there will always be an unaccounted for variable that (it can be argued by Neoclassical Euclidian Economists), if we could measure it, would demonstrate that we were right, the globe is governed by Euclidian economics.

Right, my understanding is that that is more or less where we’re at on the minimum wage. Good for them for going after the data.

Digging deeper into the Euclidean/non-Euclidean metaphor in economic thought, Pigou had this to say in Economics of Welfare, published in 1920:

Wonder, Carlyle declared, is the beginning of philosophy. It is not wonder, but rather the social enthusiasm which revolts from the sordidness of mean streets and the joylessness of withered lives, that is the beginning of economic science. Here, if in no other field, Comte’s great phrase holds good: “It is for the heart to suggest our problems; it is for the intellect to solve them…, The only position for which the intellect is primarily adapted is to be the servant of the social sympathies.”

§ 2, If this conception of the motive behind economic study is accepted, it follows that the type of science that the economist will endeavour to develop must be one adapted to form the basis of an art. It will not, indeed, itself be an art, or directly enunciate precepts of government. It is a positive science of what is and tends to be, not a normative science of what ought to be. Nor will it limit itself to those fields of positive scientific inquiry which have an obvious relevance to immediate practical problems. For this course would hamper thorough investigation, and shut out inquiries that might ultimately bear fruit. For, as has been well said, “in our most theoretical moods we may be nearest to our most practical applications.” But, though wholly independent in its tactics and its strategy, it will be guided in general direction by practical interest. This decides its choice of essential form. For there are two main types of positive science. On the one side are the sciences of Formal Logic and Pure Mathematics, whose function it is to discover implications. On the other side are the realistic sciences, such as physics, chemistry, and biology, which are concerned with actualities. The distinction is drawn out in Mr. Russell’s Principles of Mathematics. “Since the growth of non-Euclidean Geometry, it has appeared that pure mathematics has no concern with the question whether the axioms and propositions of Euclid hold of actual space or not: this is a question for realistic mathematics, to be decided, so far as any decision is possible, by experiment and observation. What pure mathematics asserts is merely that the Euclidean propositions follow from the Euclidean axioms, i.e. it asserts an implication: any space which has such and such properties has also such and such other properties. Thus, as dealt with in pure mathematics, the Euclidean and non-Euclidean Geometries are equally true: in each nothing is affirmed except implications. All propositions as to what actually exists, like the space we live in, belong to experimental or empirical science, not to mathematics.” This distinction is applicable to the field of economic investigation. It is open to us to construct an Economic Science either of the pure type represented by pure mathematics or of the realistic type represented by experimental physics. Pure economics in this sense — an unaccustomed sense, no doubt — would study equilibria and disturbances of equilibria among groups of persons actuated by any set of motives x. Under it, among innumerable other subdivisions, would be included, at once an Adam-Smithian Political Economy, in which X is given the value of the motives assigned to the economic man — or to the normal man — and a non-Adam-Smithian Political Economy, corresponding to the geometry of Lobatschewsky, under which x consists of love of work and hatred of earnings. For Pure Economics both these Political Economies would be equally true; it would not be relevant to inquire what the value of x is among the actual men who are living in the world now. Contrasted with this pure science stands Realistic Economics, the interest of which is concentrated upon the world known in experience, and in no wise extends to the commercial doings of a community of angels. Now, if our end is practice, it is obvious that a Political Economy that did so extend would be for us merely an amusing toy. Hence, it must be the realistic, and not the pure, type of science that constitutes the object of our search. We shall endeavour to elucidate, not any generalised system of possible worlds, but the actual world of men and women as they are found in experience to be.

Wesley Mitchell used the non-Euclidean metaphor even earlier, in a 1910 article, “The Rationality of Economic Activity.” Interestingly, Mitchell uses “non-Euclidean” to refer to rarified theoretical abstractions that have little to do with reality.

Addendum to my comment @8 above:

In subsequent reworking of his essay (in The Trend of Economics, edited by Rexford Tugwell 1924), Clark added two additional propositions to make the total eight .

The additional propositions were: “A bargain between two persons concerns primarily those two persons, and only incidentally, under special conditions, becomes ‘affected with a public interest.'” (inserted between props 3 and 4) and “Private enterprise is necessary and efficient because people will work and sacrifice for their individual ends where they reap the fruits themselves and will not work as well for a collective end.” (inserted between props 4 and 5).

“I hope that Keynes or anyone else’s work is not the equivalent of Einstein’s relativity work.”

Relax — it’s a metaphor.

ZM, I have never heard about a concept called “referent of spacetime” in GR. In what context did you encounter that term?

I think referent is just the word for the thing that a word refers to. So cat is the reverent of cat. I understand what space is and I understand what time is – but I cannot work out what Einstein is referring to when he writes spacetime…

A great post, but regarding this statement:

“Having written this piece, I did a better Google search and found, as usual, that much of it is not new and indeed goes back to Keynes”

Slight misunderstanding here: the blog post “A Red Herring on Praxeology: A Reply to Lord Keynes” is a reply to my post you cite above.

“Lord Keynes” is a pen name I use for my blog:
http://socialdemocracy21stcentury.blogspot.com/

regards

Let me add a bit to Lee A. Arnold’s comment. There are at least two notions of formalism. (1) As notions of pure logical syntax used to construct axiomatic theories of some subject. (2) As notions from proof theory used to evaluate existing axiomatic theories or to construct new systems of formal logic. Notion (1) was the standard approach to teaching logic, until ideas related to model theory and refutation trees became popular, around 1970, at least in the USA. I think you mean (1). As for (2), some of Husserl’s ideas have been used in the proof-theoretical intuitionism of Per Martin-Löf. I don’t know if he read ‘Experience and Judgement,’ (Erfahrung und Urteil), but some work of his combines Husserlian notions of evidence with a reasonably formalistic system of logical and mathematical rules of construction and deduction. Evidence is said to be
fundamental to these, as it is claimed to be the final source of conviction that his rules and
deductive principles are valid. His work all but replaced the looser intuitionism of
Brouwer and perhaps Bishop, with more tractable ideas. Gödelian and Husserlian intuition of mathematical items like numbers and some axioms becomes insight into basic applications of a rule. Per’s work is beautiful, as its basic principles can be seen as either logical or mathematical but are more fundamental than either.

I have some disagreements with your history of formalism, which doesn’t negate the main point at all. The basically Platonic conception of mathematics was not progressively undermined by non-Euclidean geometry, much of which can be understood as geometry on curved surfaces. It, and its associated notions about rationalism, were overthrown in an unexpected, violent, fairly quick revolution instigated by Frege’s Begriffsschrift, which suddenly threw the whole idea of timeless and eternal mathematical truths into chaos and replaced them with timeless and eternal logical truths. The effect was rather to create an even stronger kind of rationalism, one that was mixed up in complex notations and obscure language that rendered it inaccessible to most people, but even more able to force counter-intuitive and often genuinely false conclusions on people in the name of “reason.”

If I were telling the story, I would start with Gauss’ line about mathematics as the ‘queen of the sciences’ and ‘number theory’ (= arithmetic in Gauss’ era) as the queen of mathematics. (Die Mathematik ist die Königin der Wissenschaften und die Zahlentheorie ist die Königin der Mathematik in OV) Think of early 18th century and early 19th century math as a divine right monarchy that appears eternal and stable just as modernism begins to expose the cracks in its foundation when faced with the increasing use of calculus and algebra in geometry – the development of modern analysis – and the problems created by calculus. Each mathematician exposing the cracks in the edifice swears up and down they are really trying to fix it, to eliminate the little nagging problems and contradictions, right up through men like Gauss. I would put this in parallel to the notion of economics as a theory of morality and justice as a thread running from Aquinas, Ibn Khaldun and the School of Salamanca right through Smith, Locke, Say, Ricardo, and Mill.

Then Frege comes along and burns the entire damn thing down by giving the whole of arithmetic a basis in logic. The divinity of numbers, and the Platonic worldview, simply cannot recover from the revolution. You might put this in parallel with the second industrial revolution, the rise of the German Empire, and the entire rearrangement of economics around the needs of the state, and at the same time Frege’s contemporary Karl Marx, who seems to have been the first person to think the economy was about actually “production and reproduction of real life” (Engels’ words, so the analogy isn’t perfect) instead of moral sentiments. Bosanquet’s line about the “Empire of Logic” fits here.

The Empire reaches its peak in the Hilbertprogramm and smashes up on the rocks of the Gödel incompleteness theorems, just as Marxism and imperialism were wrecked by the two World Wars. It is replaced in some quarters with a postmodern cynicism about the whole project, in others with a kind of quasi-socialist bureaucratic centralism led by the Bourbaki group in France (“math for the working mathematician” was their line), and to some degree by the advance of category theories and universal algebras in other places as a kind of mathematics version of the “managerial capitalism” of the post-war era in the west.

This falls into a sort of Brezhnevite-stagflationary decadence by the 70s, when the computer appears on the scene and forces a kind of quasi-empiricist glasnost into mathematics. Today, as a result, math is dominated by a practical interest in getting rich quick, with the best minds and greatest talents going into quantitative finance, crypto, and Internet start-ups, and only a few altermondialists looking at building a kind of neofoundationalism out of algorithm theory – guys like Martin-Löf and Peter Grünwald representing its more respectable, intellectually coherent side, and a kinda of silly side represented by… someone I might need a job from someday and who knows how to Google.

All of this makes hyperformalist economics in the Arrow-Debreu tradition look faceplamingly retro, like science fiction from the 20s or 30s, and the Mises-wannabes look like they’re the economics equivalent of neo-Confederates, or those people who think the 16th amendment was never legally ratified so they shouldn’t have to pay their taxes: People who never got over the 19th century, much less the 20th.

The general point about the sterility of a priori reasoning is sound. Nearly everything of substance in math and science since the French revolution has come from abandoning it. You’re missing its appeal to the minds of college sophmores, who are just educated enough to see the beauty of simple formal logics, and not nearly educated enough to see their massive gaping flaws, and how very important that is to Austrian economics as a proselytizing faith. But I strongly encourage telling the history of mathematics and logic in strongly humanist terms: as a succession of crises and failures and recoveries that were doomed to fail from the outset – in short, math as politics. Doing that takes away its magic, and deprived of its magic power, it becomes a laughable basis for an economic theory.

@ZM

Leaving General Relativity aside for the moment, suppose that we live in a three dimensional Euclidean space. What is the referent for “three dimensional Euclidean space”?

Billikin,
I think that is a compound referent – the referent of three being the abstract quantity three + the referent of dimensional being dimension plus al making it an adjective qualifying the object to follow + the referent of Euclidean being the long dead fellow Euclid plus ean making it an adjective (likely about his geometry work rather than his bodily person) qualifying the object just ahead + the referent of space being space which is the object of the fragment and the object of Euclid’s work in geometry.

I cannot unpack spacetime in this sort off way and have been told it cannot be simply summed up to me but that I would have to spend four years to study the matter before understanding what the word is meant to refer to :(

ZM, 4 years of study sounds way too much. The need for a combined “spacetime” concept is already clear in special relativity, and SR is really not that hard. At least, not “4 years of study” hard. It’s typically a single course for new physics students in their first year.

ZM: “I cannot unpack spacetime in this sort off way and have been told it cannot be simply summed up to me but that I would have to spend four years to study the matter before understanding what the word is meant to refer to :(”

Well, whoever said that to you thought that you meant something different. As a matter of fact, you can unpack spacetime in exactly the same way that you did Euclidean three space. Before the theory of general relativity, it was thought that there were three dimensions of space and one dimension of time, which could be graphed as though it were another dimension of space. You see such graphs all the time, where time is one dimension with years or minutes equally spaced on the time axis, for instance. Einstein showed that that view of things did not hold up. Time was not just like another spatial dimension. However, it was soon discovered that you could view time as just another dimension, but not a space-like dimension. It has different properties. Distance in space-time with three spatial dimensions is not like distance with four spatial dimensions. Also, the idea of a straight line in spacetime is not the same as that of a straight line in Euclidean space.

So if you want to understand spacetime, it can take years. But if you only want to refer to spacetime, then you can do it as you refer to Euclidean space, with time as one of the dimensions. Whoever told you what they did was thinking about how long it would take you to understand spacetime, which is difficult, not about refering to spacetime, which is easy. :)

Billikin,
Sorry, I didn’t explain the context. I was not at all interested in concepts of space – I can only remember geometry from high school and if I have misrepresented Euclid I am sorry – I didn’t know his work had a truth claim that space itself was 3 dimensional – I thought he just found a helpful way of representing bodies in space on paper. understanding Euclid’s conception of space was not what I was trying to learn about.

I was interested in changing concepts of time, historically and culturally, as related to social groups’ environmental sustainability and unsustainability.

So I was interested in different conceptions of time – and why Einstein put space and time together and referred to this as spacetime – and what spacetime as a concept meant. I was also interested in how Newton understood there to be real absolute unmeasurable time and representational measurable relative time – but Einstein said there was no real absolute time at all, not even relative time by itself, but only relative spacetime. Also I wanted to know how if spacetime was made up of empirical equations it was able to do away with unmeasurable absolute time which shouldn’t really be affected by empirical equations since it is unmeasurable.

To understand this the professor said I would need years of physics study, so I still don’t know what spacetime refers to as a 20th century concept of (some sort of version of) time.

J Thomas,
Thank you for trying to explain, but I think I would need to improve my understanding before I can understand your explanation. Maybe this is why it would take me 4 years but Zamfir could learn it quickly.

Thanks, ZM. Now I have a better idea of what you want.

You talk about Euclidean space as a way of “representing bodies in space on paper”. That’s what I thought you meant, and said that spacetime was a way of representing positions in space and time. At least, that’s what I was trying to get at.

But you want to understand different concepts of space and time and spacetime. I don’t think that you need a lot of physics for that. Philosophy and anthropology have a lot to say about those concepts. Before Einsteinian relativity there was Galilean relativity, which Newton understood quite well, OC. IIRC, Newton believed in absolute space, anyway, even though you had a choice where to put the origin of any coordinate system, and a choice of the directions of your dimensions. But there were other natural philosophers who thought that space did not exist, only distance. Leibniz? I am not sure.

As for the idea that time is unmeasurable, I don’t know what you mean by that. Galileo certainly measured time. Without doing so he could not have made all of his discoveries.

I don’t know about Einstein’s original idea of spacetime in general relativity, because it was quickly superceded by Minkowski spacetime, which J Thomas explained briefly.

Anyway, it sounds like you have been frustrated by the idea of taking four years of physics to understand spacetime. You may find philosophy and anthropology more relevant to your interests and more satisfying.

Scott Martens. Apologies for the typo.

“Doesn’t all of this thread, excellent though it has been, tend toward the ineffable? By which I mean, aren’t consequences always, inevitably, richer than the putative mechanisms which produce them?”

Yes. C.S. Lewis used the analogy of looking AT the telescope and looking THROUGH. The telescope. Looking at the telescope is a good thing, because it allows us to make the telescope better. But looking through the telescope is ultimately the point of building telescopes. A lot of social science gets so bogged down in looking at the telescope that it actively inhibits looking through it.

Seems to me the thinking that characterizes economics is neither inductive nor deductive but procrustean. People endlessly argue about whether economics is a science or a prescience, but didn’t the subject actually grow out of a very different set of activities—business practices like accounting and what they call cameralistics in Europe, i.e. techniques that rationalize important aspects of human affairs by force or agreement? Doesn’t economics belong to Herrschaft rather than Wissenschaft?

ZM, have you tried Feynman’s essay on relativity? (http://www.amazon.com/Six-Not-So-Easy-Pieces-Einstein%C2%92s-Relativity/dp/0465025269) I think it conveys well the meaning of spacetime. It turns out that transformations in 3-space and 1-time, which in Newtonian physics are treated as independent of each other, cannot really be independent – transformations affect both space and time (which leads to empirically observed phenomena such as time dilation). Spacetime is the mathematical structure that provides the (theoretically and empirically) correct transformation groups.

#52

Thank you for trying to explain, but I think I would need to improve my understanding before I can understand your explanation. Maybe this is why it would take me 4 years but Zamfir could learn it quickly.

I want to try one more time.

People generally feel like they understand something when they have a picture that fits it. But a physicist understand relativity when he can do the homework problems and get the right answer. This is a very different thing.

So as a simple example, it’s easy to think of us as living on the surface of a giant sphere, the earth. But if you change the math around just a little bit, you could have us living on the *inside* surface of a giant sphere. All of the outside universe shrinks inside of that sphere, distances shrink more and more, until at the center there is a point missing which is perhaps infinitely far away. The sun is little ball of energy that revolves around the inside of the sphere, and since light does not travel in straight lines, when the sun gets too far away from our part of the sphere surface its light is lost to us.

All the math can work out to do that, and get the same results we get assuming we are on the outside of the sphere. We don’t do it that way because it’s more intuitive for us to do it the way we do, but the two are equivalent. They are basicly the same theory and the same picture, but they don’t seem the same.

Similarly, there are various ways to look at special relativity. Some of them make more sense than others. Physicists settled on one that doesn’t make much sense and is hard to wrap your mind around. I speculate that they did it because they enjoyed mystification and it made them look special to understand things that appeared to make no sense.

General relativity has much harder homework problems because it solves harder problems. But the fundamental ideas are not much more complicated than SR. I will look at SR.

They wanted to think of time as another dimension. To do that, it helps if you can measure all the dimensions in the same units. And you can. You can measure time as the time it takes light to go a unit distance. Then time is a distance. Or you can measure distance as the distance that light travels in a unit time. Choose one.

Once you do that, you can use the pythagorean theorem. Total distance squared is the sum of the distances in different right-angle dimensions, squared. But right away there was a problem because they had minkowski distance instead of euclidean distance.

T^2 = x^2 + y^2 + z^2 – t^2

They said that no matter how the x,y,z,t changed, T would be constant. Here’s what it means:

Say you make a flash of light and 3 seconds later you make another flash of light. Somebody 1000 feet away who knows precisely the time and the distance can subtract the time^2 for the second flash from the distance^2 and they will get 9 = 3^2. No matter how long the distance and the time, the time difference between the two flashes will be the same! That is the minkowski distance.

Well, but we can do it in a more intuitive way.

t^2 = x^2 + y^2 + z^2 + T^2

The total distance the light has traveled from our origin, is the square root of the space distance squared plus the proper time distance squared. Now it’s all euclidean. It’s the same formula, just rearranged.

Similarly with momentum.

4-momentum = [energy, momentum-x, momentum-y, momentum-z]

and -mass^2 = -energy^2 + momentum-x^2 + momentum-y^2 + momentum-y^2

And when you adjust the momentum and energy because your own velocity is different, the mass^2 term is constant! What a surprise! And you can graph it as a hyperbolic rotation.

But switch the terms around.

energy^2 = mass^2 + momentum-x^2 + momentum-y^2 + momentum-y^2

Now it’s all pythagorean. There’s nothing mysterious going on at all. The rest mass (rest energy) is of course constant, and when you change your estimate of velocity you change the momentum and the energy, and there’s no rotation at all much less a hyperbolic one.

If you do the homework problems you’ll get the same result either way. One way it is very hard to grock, and the other way it’s easy. But for physics it doesn’t matter whether you have a clear picture how it works provided you can get the right answers. Right answers are easy for SR and hard for GR. But if you want to “understand” it, you could easily take four years to do that the minkowski way.

Bad Jim #27:

Flat-earth thinking is not confined to religious believers. Most of us rational, scientifically-trained westerners still refer to sunrise and sunset, despite knowing for half a millennium that it is the earth doing the relative setting and rising respectively, not the sun.

Chris @43 “Hence Jerry Cohen’s well-known essay `Marxism and Contemporary Political Philosophy, or: Why Nozick Exercises some Marxists more than he does any Egalitarian Liberals`.” That sounds interesting, I thought, so I tried to find an online copy but they all seem to be behind a pay wall, then I looked at books by Cohen in Amazon, but (1) most did not show the contents, so I have no idea if the essay was included, and (2) cost US$100 or so (above my touch). (I do note Cohen wrote a book called ‘If you are an egalitarian, why are you rich?’. Now I know.)

Is there a way to read the essay without access to a University library or spending a lot of money?

John Quiggin: ” Rights aren’t a side constraint for Nozick”.

Nozick: “In contrast to incorporating rights into the end state to be achieved, one might place them as side constraints upon the actions to be done: don’t violate constraints C”.

“The side-constraint view forbids you to violate these moral constraints in the pursuit of your goals”

And so on. This is central to Nozick’s view, not something I just made up.

This is just the wrong way to attack Nozick, unless you want to take issue with deontology (which, incidentally, is fine with me). Someone who believes in rights thinks that rights trump other considerations. That’s what deontology is. Your beef is probably with the rights that Nozick defines, not the existence of rights. At least, that’s the right way to understand the dispute between liberal deontologists like Rawls and someone like Nozick. Your options are (a) say that Nozick has misidentified what rights we have or (b) reject the notion of rights (perhaps just economic rights).

Here’s an example from Nozick where he has consequences doing the heavy lifting. Animals, he says, don’t have a right not to be tortured. But we shouldn’t torture them, because the consequences – making ourselves inured to cruelty – would be bad.

The Crisis of Democratic Theory: Scientific Naturalism and the Problem of Value
Edward A. Purcell, Jr.
Publication Year: 2014
Chapter 4: Non-Euclideanism: Logic & Metaphor

Neil Levy: “Here’s an example from Nozick where he has consequences doing the heavy lifting. Animals, he says, don’t have a right not to be tortured. But we shouldn’t torture them, because the consequences – making ourselves inured to cruelty – would be bad.”

So I guess it’s all right for a sadistic sociopath to torture animals, because he is already inured to cruelty?

J Thomas, and TM
Thank you for help with understanding the concept of spacetime.
Billikin,
“spacetime was a way of representing positions in space and time”
I think of it as likely being representational (like I do with Euclid’s geometry) – but as I understand it the physicists’ shared cosmology holds it to have a truth value about the real nature of time – which is that there is no time only spacetime (which I still can’t work out the meaning of).

“Newton believed in absolute space. . . other natural philosophers who thought that space did not exist, only distance” “As for the idea that time is unmeasurable, I don’t know what you mean by that.”
Newton distinguished between absolute real time which is unmeasurable (I presume because it is transient) and human relative time which is measured through space-based devices such as sun-dials and clocks and so forth. With Einstein absolute time is no longer in the physicists’ cosmology and relative time becomes spacetime.

J Thomas,
“They wanted to think of time as another dimension. To do that, it helps if you can measure all the dimensions in the same units. And you can. You can measure time as the time it takes light to go a unit distance. Then time is a distance”
I did ask the Professor this – if I could just say space-time referred not to space or time but just to movement of bodies and distance measured between them – he said I wouldn’t be giving an accurate representation of the concept of spacetime if I did that.
Thank you for your sums, I will copy them down to try to read one day when I have more time.

TM,
Thanks for the reference, I hadn’t heard of that one.

Neil Levy
“Here’s an example from Nozick where he has consequences doing the heavy lifting. Animals, he says, don’t have a right not to be tortured.”
Well I don’t think you can claim there is not a moral absolute against torturing poor animals. Anyhow, it is certainly not the case in all legal systems. In Scandinavia animals, for example the beaver, had rights. Under the laws of Haco, foster-son of Athelstane, the beavers right to a home and rights as an inhabitant were important – and if anyone killed a beaver they would be fined. Bears and wolves were named as outlaws, but even bears had a right to a trial if they did anyone wrong, and it was thought bears had a fair enough understanding of Danish for this to work. Civil tribunals would also make decrees telling rats and mice and insects what they were meant to do in the land.
Palgrave 1832 p. cxlii

I think you’re using side-constraints in a different way to Nozick. For him, it’s equivalent to what Dworkin calls ‘trumps’.

Is this right? I thought Nozick’s (‘side-constraints’) was stronger- no right can be disregarded (except to prevent moral armageddon)- whereas the ‘trumps’ metaphor allows one right (a low card) to be over-ridden be a another one higher up the food chain (a picture card). But I’m very rusty on this…

@ZM

J Thomas can correct me, but by the time that we get to the concept of Minkowski spacetime, time is another dimension in addition to the dimensions of space, except that it is in units of the square root of -1 (imaginary units). Perhaps that was the difference that the professor was referring to. Distance in spacetime is quite different from spatial distance. Spacetime is not like space with an additional space-like dimension called time, even though you can draw graphs like that for some purposes. I don’t think that you can get much of an idea from the physics prof saying, “That’s not it,” and “That’s not it, either.” I am pretty sure that what the prof thought that you said and what J Thomas said are not the same thing.

I thought John’s originals complaint was that Nozick doesn’t consider the consequences of his theory (eg, as Brian Barry has pointed out, letting the needy starve to death, etc), not that consequences play no role within it (they do, as Neil says). Actually, iirc Nozick did sort of do the first- in the chapter where he claims libertarianism is a ‘framework for utopia’ – but it was rather pathetic iimho (albeit marvelously well-written).

I would like to know what spacetime means for physicists’ cosmology

Relativity was probably the first point at which physicists decided that it didn’t have to make sense. If you can get the right answer then that’s all that’s really important. And yet they did try hard to make sense of it.

The old way, you had completely separate space and time. You could measure space. You chose some interval of unit length, and it was arbitrary what your unit was. Yards or meters, it didn’t really matter, choose one. And then you had three “axes”, and you could arbitrarily choose any three provided they were all perpendicular to each other. Suppose you chose one set and somebody else chose another. You could transform measurements from one to the other easily when you knew how, it would amount to a rotation about some axis. You could rotate in two dimensions by considering one axis to be the “real” one and the other to be “imaginary” with square root of minus one. Easy mathematical rules to do the rotation. When you rotate the length stays the same, but how that length is distributed between the two axes changes.

The easy and good way to rotate in three dimensions is with quaternions. You get a special fourth dimension which is not like the first three. It becomes the “real” one and the three space dimensions turn into three “imaginary” ones you can label i j k. Again the total length does not change, but the distribution among the three space dimensions does change. Usually you would set the fourth dimension to zero at the start and finish.

So it’s arbitrary what you choose for your three axes, you get equivalent results whatever you choose, and you can translate back and forth among whatever choices seem useful.

In the old way, time was independent of all that. Time proceeded forward inexorably, at the same rate for everybody everywhere, completely independent of space.

They believed in something that was later called “galilean relativity”. It’s arbitrary what unit distance you choose. It’s arbitrary which axes you choose to measure by. It’s arbitrary where you set the origin. And it’s arbitrary how fast you have the origin move, provided the speed and direction of movement are constant. If you have two ways to measure, and with one of them the origin is moving relative to the other, all your physics experiments will get the same results with both. If there is a difference it will be because of some outside force which affects them different because of the movement.

What changed all that was electromagnetism. Here’s the key history:

1. Michael Faraday was self-educated and he didn’t care much about math. He thought in pictures. He studied electricity and magnetism and he drew what he saw.

2. Various people tried to put Faraday’s insights into mathematical form. They kind of succeeded. Maxwell combined Faraday’s work with other things to get a consistent system which appeared to describe everything about electricity and magnetism traveling through empty space. He predicted that they travel at a constant speed, which turned out to be lightspeed. By his theory it made sense that light was the result of a vibrating electric charge, and it traveled at lightspeed.

3. Maxwell originally assumed that electricity and magnetism had their effects instantaneously everywhere. The math was simpler that way, his results are still widely taught that way, and usually the results are tolerably accurate. But he deduced that there was a delay. When you try to account for the delay the math gets messy and peculiar, and it’s easier to ignore the problems. And Maxwell’s equations are not consistent with galilean relativity. Faraday did all his work relative to his lab bench, he didn’t care about galilean relativity. Maxwell used Faraday’s results. Electromagnetism as defined by Maxwell works fine for one coordinate system traveling at one velocity. If you try to transform the results into a different system with a different velocity they turn weird. Maxwell assumed that light has a constant speed, and that speed is the same constant for everybody no matter how fast they are moving. If you measure the speed of a light beam, and somebody else measures the speed of the same light beam and they are traveling at half lightspeed, they will measure the same velocity that you do.

4. The Michaelson-Morley experiment appeared to show that Maxwell’s equations were true. They measured the same light when the earth was traveling in opposite directions, and they got the same lightspeed. It looked like arithmetic was broken.

5. The new approach said that time was not completely independent of space. It was another dimension, kind of like the other dimensions but different. When you measure things with an origin that has a velocity relative to another coordinate system, you are doing a kind of rotation between the space dimensions and the time dimension. Time and space will be distorted, just enough so that both ways the same light can be measured and get the same lightspeed. If you perform the simple lorentz transform between two coordinate systems, it all works. You will get the right answer on homework problems. And as usual, no one coordinate system is the *right* one, they are all equivalent and we can convert from one to another and get the right answers. To make that work we have to give up some ideas. Time is not something that just happens to everybody at the same rate. Various things can happen that look like paradoxes. But they aren’t paradoxes, they just happen. They only conflict with our previous assumptions.

6. If space-time was a system where you could do rotations and keep the total distance constant, it would fit quaternion math. Time would be the fourth quaternion dimension. But it doesn’t work that way. Total distance is not conserved with the rotations people chose to use. They looked for a way to make the lorentz transform to be a rotation, and they found it fit Minkowski space which is weird and hard to understand. The pictures are hard to follow. Some of the math is not easy, it turns out that when you change velocity (particularly when you change direction) you get peculiar results that take somewhat-complicated math. Velocity is not a simple obvious concept with special relativity, it kind of goes against the grain of the system. It isn’t easy to follow the details. It isn’t intuitive. It isn’t that hard to do the homework, but getting a clear picture of it is very hard because it does not map well to how our brains work.

7. Nearly a hundred years after relativity was announced, people found an easier way to think about it. The new way is sometimes called “euclidean relativity” but there’s a lot of weird stuff that gets the same name so that isn’t an adequate search phrase. The new way, you start with a different way to measure velocity. When time was completely independent of space, it made sense to measure velocity as distance divided by time. But when time is just another dimension, it makes more sense for velocity to be space-distance divided by total distance. With a few other changes, you get a system which gives you the same answers to the homework problems but which is much easier to follow. Probably within 80 to 100 years it will be mostly taught this way.

Thanks, I didn’t know that ‘side constraint’ was a term in decision theory. I’ve only ever heard it used by Nozick (who as others have said, just means by it a constraint, a non-overidable limitation on what agents can do). Come to think of it, I’ve no idea why he uses that term- perhaps others do? (This is, as I’m sure you realise, at best an argument against his choice of terminology rather than his view of justice.)

Sorry, looking back I think I misunderstood your original point. I thought you were objecting to the term ‘side constraints’ being used for hard rather than a soft boundaries on a choice-set whereas I understand now you are objecting to it being used for a condition-set that fully determines the choice.

But in this case I don’t really understand your objection. Nozick doesn’t think that rights fully determine what an agent must do in a given situation [normally] and he expects them to leave room for consideration of consequences by the agent. It seems to me Nozick’s usage of the term is parallel to your ‘obey all relevant traffic laws’ rather than the example you gave above it.

Using terms like “side constraint” or “trump” suggests that his theory of justice is concerned with consequences

But they’re not ‘side constraints’ on justice, they’re side constraints on action. Agents are free to consider consequences in deciding what to do (rights constrain the choices they have).

That would be fine if he wrote two separate books. As it is, he wants to defend kitten/human-torture as a right, while pretending that his argument has a way of stopping this happening.

You’re right, Nozick doesn’t think, for example, that it’s good or okay for poor people to be left to starve in the streets, but he thinks that if society left them to do so, they wouldn’t have suffered any injustice. Demanding assistance from others who were unwilling to provide it would be treating those others as slaves. As I recall he does say libertarianish things in ASU (philanthrophy, etc) about why this shouldn’t happen, so he didn’t need to write two books, but whether it’s attractive or convincing is another matter (I didn’t think it was).

I’m not sure the problem you’ve raised is unique to Nozick though. A liberal might agree for example, that it’s a bad thing for someone to be without companionship, say, but forcing anyone to provide it to her as a matter of right would not be permissible. Instead, liberals would probably focus on creating conditions which would minimise the chances of this situation occurring (they’d argue).

J Thomas @92

Great explanation. Thanks very much.

Correction. Too early in the morning, I guess. The “light V” constructed with negative time is not anything like the light cone. Only the line with t >= 0 is concerned with the light cone when we add more space dimensions. Not that we can’t think of light going backward in time, but that’s another matter.

The liberal example is a genuine case of side constraints. Liberals would like to promote [X] and can do so by funding programs… but they are constrained to respect freedom of association.

It sounds like your stipulating that a genuine ‘side constraint’ must be a constraint on policy or law perhaps, rather than on agents’ freedom of action (which is how Nozick means it) So the US constitution is constraint on law perhaps, but the law itself is not a constraint on what citizens may do. I don’t think that’s persuasive, even as terminological quibble.

@ George Berger #38 — I think you are right. Perhaps there are also two notions of related words: “judgment” seems to have its oldest meaning from outside statements, outside logic, but then over there it becomes a type of statement among many other types of statements, and afterward it (judgment) is more like the status (position?) of “true” or “false” in a proposition. Just reading Crisis of the European Sciences right now, and it is interesting how much he was able to follow the change in the meaning of prescientific ideas. The discussion of how Galileo must have felt and grasped his own method, as opposed to how we see Galileo’s method now, is precise and practical, though written in 1936. Needs an addendum describing the even odder idealization of the lifeworld by the continuing mathematization of method, even to simulations of choosing/choice, in the era of the electronic computational revolution.