I was thinking about research hyperboles. We have already worked on problems that impact “billions” of dollars. Next, papers will claim to solve problems that impact “trillions” of dollars (applications to US govt)?
My own reaction was: well, of course I’m working on trillion dollar problems, and so is Muthu and so are most researchers. Almost all theoretical work in most branches of science is doing so too. If you take a fundamental problem and try to estimate its worth in dollars, any reasonable measure will give you trillions of $’s. (One may certainly doubt that such a monetary quantification exercise is useful or tasteful, but that’s another question.) Now of course, I’m not “solving” any trillion dollar problems, only making small steps, but if even a single paper out of the 100 that I write during my whole career makes even a 0.01% step towards the “solution”, then that will give an average value of a million dollars per paper — certainly much more than society is paying for it.
For the skeptics who worry about the numbers rather than laugh at the whole notion of quantification in $’s, let me justify the trillion dollars, at least for “algorithmic game theory” at large. (It is probably not hard to undergo a similar exercise for many other branches and sub-branches of science , although likely but not all of them.)
World GDP is over 60 Trillion dollars per year and rising fast. Computing the present value of all of future humanity’s GDP requires an assumption on future growth as well as a heroic choice of an an interest rate, but the answer will certainly be in the quadrillions (quadrillion = 1000 trillion). Is it hard to imagine the Internet affecting 10% of that GDP, and algorithmic game theory deserving 1% of the credit for this future Internet? Is it hard to imagine better theoretical understanding of economics making a 10% change in that GDP, and algorithmic game theory contributing 1% of that understanding? I would say that each of these four numbers is actually an under-estimate.
Turing's Invisible Hand 
Looks like a usual mistake of multiplying large numbers with not sufficiently small percentages. Usually as the large numbers become larger, the percentage impact on them decreases, e.g., small companies grow faster, large companies usually can’t.
All your numbers look quite generous. Suppose AGT understanding research gives some enlightenment. May be a similar enlightenment others could find by trial and error, since the activities involved are large. One should look at the difference. Also the enlightenment may both increase or decrease the GDP.
Suppose one can do the math the otherway round, counting the negative number. Suppose scientific research increases the economic gap among countries by 1%, and economics research has 1% contribution to it, and AGT has 1% of it, and suppose this increased gap among the countries increases the chance of a future nuclear war by another 1%, then with finite probability a researcher could be destroying the world. Sad but meaningless. Of course you could say that AGT techniques could actually cut the chance of a future war. Who knows what directions the effect of AGT goes in, likely positive, but the difference could be even smaller.
Also discussing research in $ terms is not only meaningless but could also be harmful. If people just discuss things in $ terms, then one could try to maximize it by biasing the research activities which improves the lives of rich people. Indeed, the effect could usually trickle down, such as even the not-so-rich people use cell phones these days. But not-so-rich people have problems of their own too, which the research community should try to tackle to make the world a better place to live.
I of course agree that these $-counting games can not be taken too seriously, and certainly not literally (e.g. GDP is at best a vague proxy to what we care about.) But I think that the general idea of science making very small steps towards very highly beneficial results, yielding high expected value to humanity is right. This is really just the basic tenet of enlightenment that reason will improve the human condition.
Never the less, I wouldn’t at all dismiss out of hand your own calculation either: “Suppose scientific research increases the economic gap among countries by 1%, and economics research has 1% contribution to it, and AGT has 1% of it, and suppose this increased gap among the countries increases the chance of a future nuclear war by another 1%, then with finite probability a researcher could be destroying the world.” Actually, I think that it’s quite reasonable that each of us may (indirectly) destroy the human race with probability 10^{-8} (give or take one or two orders of magnitude)
Incidentally, based on average productivity, average researcher salaries + overhead etc., I estimated the price the public pays per paper at about $50k.
Without quibbling over numbers, I agree with your general outlook: in many scientific disciplines, a successful researcher contributes vastly more to economic output than is reflected in their pay.
Many scientific innovations contribute as much to society over the years as any business does. With entrepreneurs, the great potential (as well as the variance) in creating value to society is reflected in the wealth that one has an opportunity to accumulate. With scientists, not so much. Because of this, it can be a little hard to intuitively appreciate the monetary value of research. I think the numbers do give us the right sense of scale, even if they sound too ridiculous to believe.
Of course, you have only discussed the absolute value of the contribution and not its sign.
many theories throughout history caused damages that are estimated in the trillions of $, or in human lives.
This includes theories in Medicine, Psychology and of course Economics, although I can’t think right now of any particularly malevolent theory in Computer Science.
“It is my wish that this book increases the interest of students in Quantum Mechanics. They should not forget that one fourth of USA´s GDP is obtained through technologies based on that science.”(my translation)
This is a quote from a book i was browsing recently. Both the comment (unusual in my country) and the figure (i ignore where it comes from and if its correct) surprised me. I can hardly imagine any of the 12 founding fathers of QM (PPSEEHDDbSBEB) worrying about the economic impact of its discoveries, a perfectly legitimate one in our days (even if its correct evaluation is hard: the most adequate methods are those used to evaluate patents for sale or licensing, which still are quite insatisfactory).
The wish to know the truth is perfectly compatible with the wish to impact economicaly and fundamental research must not be necesarily slow in outputing economic impacts. To accelerate the latter is precisely what this kind of laws (see the page you are linking to) is looking for and must not be necessarily harmfull to fundamental research. So i can not be sympathetic with some romantic reactions, unfortunately so usual in Europe. World (and science with it) is changing, don´t lament, just adapt !
I was a little silly, but not totally (people working in networking/sponsored search/software/graphics can claim impacting “billions” of dollar businesses, I was upping the ante and pointing to impacting the govt which is trillions of dollars business). Thanks for pointing out Leslie’s great page.
– Metoo
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