Lessig

I did some quick calculations and based on his assumptions I think this means that 75 years _would_ qualify as "limited." Interesting stuff.

three blind mice commented thus (Feb 23, 3:16 AM):

even if the constitution said perpetuity, the actual duration of this could still be argued from cantor’s rigorous proof that one can derive different finite values for infinity from different infinite constructions.

Everyone makes mistakes, but I think that it is reasonable to ask if posting a comment like the above is ethical, because the poster plainly has no clue as to what s/he is talking about.

I'm sorry, but this calculation doesn't make much sense. It's completely unrealistic to model the cash flow from a successful publication as a constant income over many decades. Ultimately the reason we are able to sustain positive interest rates is because the economy is growing over time. Given the existence of economic growth, a successful publication can expect its sales to increase with time. In a future world which is far wealthier and more prosperous than the present, it's incredibly valuable to an author to have his creation still be earning money in that time of great wealth. This growth potential shows that the model in Keenan's article simply doesn't work.

Keenan's piece is rhetorically nice, but fundamentally it's a play on words.

The notion of the 'duration' of a bond was introduced, and named, by Frederick Macaulay in 1938. His formula yields a number expressed in units of time. A very slight modification of Macaulay's formula -- dividing by 1 + yield to maturity (for a bond with an annual coupon) -- gives a dimensionless number that is truly useful in finance: 'modified duration', as it is called when given its full name, is the elasticity of the bond's price with respect to the market interest rate, i.e. the sensitivity of the value of a bond portfolio to a change in the interest rate.

Taken in this sense,'duration' can be defined for virtually any tradable asset -- and for some, it can even be *negative*. A negative value is hard to accept for a notion that purports to relate to a span of time, and indeed, mention of the original association with time duration is now a historical digression in finance textbooks.

If the name Macaulay chose had not stuck, his concept might have come to be known as, say, "Macaulay's w" (by analogy with "Tobin's q") . . . and Keenan's rhetorical turn would not have been possible.

The issue here isn't interest-rate sensitivity. There is no need to invoke 'duration' to make the showing that, under realistic assumptions, the present value of cash flows beyond 95 years to infinity is a tiny percentage of the total.

As far as the mice go...

One Seeing's original response was perhaps a bit brusque. While harshly critical, it failed to elucidate any specific concerns. Now I can only guess, but perhaps One shares my concern, as below.

I have studied the history of infinite sets, and I'm not worried by Three's analysis, merely with its relevance to Constitutional interpretation. Perhaps if Three had evidence to show that the founders were students of Set Theory as we are.

There might be something to be said for sticking very strictly to the letter and not reading in terms of intent, but I'm not sure that's all everyone's concerned with here. That's probably the source of the confusion, and the subject of lively debate in another forum.

There are others who've worked this angle from the context of behavioral law and economics:

Avishalom Tor and Dotan Oliar, INCENTIVES TO CREATE UNDER A "LIFETIME-PLUS-YEARS" COPYRIGHT DURATION: LESSONS FROM A BEHAVIORAL ECONOMIC ANALYSIS FOR ELDRED V. ASHCROFT 36 Loy. L.A. L. Rev. 437, 2002.

Essentially they argued that creators rarely make the decision to create based on the length of their copyright term, and when they do, they rarely get the net present value calculation correct because of cognitive biases and heuristics.

Wendy Gordon also makes a similar argument about the expected economic benefit to authors from term extension in AUTHORS, PUBLISHERS, AND PUBLIC GOODS: TRADING GOLD FOR DROSS 36 Loy. L.A. L. Rev. 159, 2002.

The key here is that all three of these arguments nicely refute the economic justifications for term extension, but none of them really rise to the level of a Constitutional attack on term extension without some convoluted semantic acrobatics. Term extension is neither perpetual, nor is it not a limited time (sorry Professor Lessig), nor is it conclusively detrimental to the progress of arts and sciences to such a degree that it permits a successful Constitutional attack. I think the bottom line is that term reduction will have to happen via the congress, and that as organizational costs decline (thanks to the internet), the public choice problem that the Bono Act so nicely illustrates can be solved.

I have studied the history of infinite sets, and I’m not worried by Three’s analysis, merely with its relevance to Constitutional interpretation. Perhaps if Three had evidence to show that the founders were students of Set Theory as we are.

thomas thank you. the point we were trying to make (before being subjected to the usual attacks from our opponents) is that keenan’s mathematical analysis of “limited times” (which was the subject of this thread) is meaningless to the constitutional construction. if reasonable people can – and do - argue over the size of infinity, then reasonable people can - and will - argue over the length of “limited times.” it simply cannot be resolved mathematically as keenan attempted to do.

He proved that there exist at least two sizes of infinity; he did not prove anything about “deriv[ing] different finite values for infinity” because that statement is pure, unadulterated nonsense. Both infinities, not to put too fine a point on it, are infinite.

jeremy bowers, you are correct. it was a misstatement. what we should have said is that both infinte values are infinite. derive is correct. thanks for pointing out our typo, but you could have done it without a lot less arrogance and nastiness. your reply proves, once again, that arguments advanced on the tip of a spear are rarely strong ones.

again, the point is that when even something so elementary as infinity is subject to more than one definition trying to create a universal mathematical expression to define an ambiguous term such as “limited times,” as keenan as attempted to do, is a stretch of credibility – it is advancing self-serving rhetoric disguised as mathematics.

face it, keenan’s paper is only interesting in that it supports the predominate political agenda advanced here. had keenan’s analysis shown 200 years was a “limited time” it probably never would have been mentioned, because - in this blog - any mathematical/legal/rhetorical construction that gets in the way of all that free downloading is met with howls of disapproval, and often erudite ones at that.

that’s why it’s so much fun to debate here - despite killjoys like jeremy bowers.

I'm the author of the Note under discussion. Following are some brief responses to the comments posted above.

•  seth says that under the assumptions in my Note, 75-year copyrights are time-limited. This is correct.

•  three blind mice disagrees with the second half of the following statement from my Note:

... the constitution give Congress the authority to grant a copyright.... The purpose of this is clear from the context: economic benefits.

That is my common-sense reading of the constitution. Also, there was a lot of economics-based reasoning in the Eldred v. Ashcroft trial. But, I do not have legal training (my relevant background is doing mathematical research on Wall Street). So discussing this argument might be better left to others with more relevant skills.

three blind mice then goes on to talk about definitions of infinity (also in later comments). This is seriously confused (and might be a troll). Going into details is inappropriate for this forum. As other commenters have suggested, three blind mice should consult a mathematician before posting. (tbm: me, if you like.)

•  Timothy Phillips proposes an argument related to the one in my Note, based on present values of cash flows. The problem here is that the argument is purely economic and the constitution does not impose any economic limits. Although my Note relies on economics (as well as other things), its argument is not primarily economic, but rather chronological--and this is crucial, because the constitution does time-limit copyrights (though of course without specifying what the limit is).

Timothy Phillips also suggests two other formulae, which he himself acknowledges to be arbitrary.

•  An anonymous commenter claims that it's "completely unrealistic to model the cash flow ... as a constant". Here I defer to Eldred's Amici Curiae (by Akerlof et al.), which argues that a constant model is extremely conservative.

•  Karl-Friedrich Lenz asks if there is anything new in my Note. He cites note 16 of the majority opinion on Eldred, which in turn is based on the dissent of Justice Breyer. The argument presented there is related, but it is purely economic. I agree with the majority in holding that a purely-economic argument does not have a constitutional basis (though such an argument might be appropriate for consideration by Congress). The point of my Note is to make an argument that is based on time (as above).

•  Bob Killingsworth questions the definition of "duration". The definition (average maturity of the cash flows) is natural and obvious, which is why it was first put forth long ago. (The commenter's points about modified duration, etc., are neither relevant nor correct, but I won't go into the financial math here.)

•  Tim Cullen's comment cites some interesting behavioural studies. These would not affect the underlying arguments of my Note.

•  John Goodwin comments on my Note's definition of "significance". The definition of "significance" is the one debatable point in my Note, of which I am aware (this is explicitly stated). The comment of John Goodwin, though, does not seem to be based on considering the relevant points that were discussed in my Note.

•  David Douglas raises a point about people not living longer than 95 years. This is relevant for personal copyrights. My Note, however, is about copyrights for corporations--whose lifetimes are in principle limitless (there are corporations that have existed for longer than their home countries).