The Half-Life of Facts

by Samuel Arbesman

  4. Harvey Lehman published a curious little paper: Lehman, Harvey C. “The Exponential Increase of Man’s Cultural Output.” Social Forces 25, no. 3 (March 1, 1947): 281–90.

  5. along with a few more recent areas examined: Enquist, M., et al. “Why Does Human Culture Increase Exponentially?” Theoretical Population Biology 74 (2008): 46–55.

  6. A group of researchers at Harvard Medical School: Lee, Kyungjoon, John S. Brownstein, Richard G. Mills, and Isaac S. Kohane. “Does Collocation Inform the Impact of Collaboration?” PLoS ONE 5, no. 12 (December 15, 2010): e14279.

  7. a group of researchers at Northwestern University: Wuchty, Stefan, et al. “The Increasing Dominance of Teams in Production of Knowledge.” Science 316, no. 5827 (May 18, 2007): 1036–39.

  8. It was created by Jorge Hirsch: Hirsch, Jorge E. “An Index to Quantify an Individual’s Scientific Research Output.” Proceedings of the National Academy of Sciences of the United States of America 102 , no. 46 (November 15, 2005): 16569–72.

  9. The National Science Foundation has examined how much money: Lehrer, Jonah. “Fleeting Youth, Fading Creativity.” Wall Street Journal, February 19, 2010.

  10. decided to study the scientific output of Nobel laureates: Zuckerman, Harriet. “Nobel Laureates in Science: Patterns of Productivity, Collaboration, and Authorship.” American Sociological Review 32, no. 3 (1967): 391–403.

  11. the distorted words we often have to read correctly: This is known as the reCAPTCHA project and can be found here: www.google.com/recaptcha.

  12. eurekometrics: Arbesman, Samuel, and Nicholas A. Christakis. “Eurekometrics: Analyzing the Nature of Discovery.” PLoS Computational Biology 7, no. 6 (June 2011): e1002072.

  13. “In the 1940s there are six such moments”: Cowen, Tyler. “The Great Stagnation in Medicine.” Marginal Revolution, 2011. www.marginalrevolution.com/marginalrevolution/2011/02/the-great-stagnation-in-medicine.html.

  14. a Swedish medical student named Ivar Sandström: Carney, J. Aidan. “The Glandulae Parathyroideae of Ivar Sandström: Contributions from Two Continents.” American Journal of Surgical Pathology 20, no. 9 (1996): 1123–44.

  15. if you uttered the statement: Price. Little Science, Big Science.

  CHAPTER 3: THE ASYMPTOTE OF TRUTH

  1. Marjorie Courtenay-Latimer, a young woman in South Africa: Goodall, Jane, Gail Hudson, and Thane Maynard. Hope for Animals and Their World: How Endangered Species Are Being Rescued from the Brink. New York: Grand Central Publishing, 2009.

  2. an example of what are known as Lazarus taxa: Intriguingly, since the discovery of living coelacanths, fossil coelacanths have been found from the past sixty-five million years. Personal communication with Brian Switek.

  3. two biologists at the University of Queensland in Australia: Fisher, Diana O., and Simon P. Blomberg. “Correlates of Rediscovery and the Detectability of Extinction in Mammals.” Proceedings of the Royal Society B: Biological Sciences (September 29, 2010).

  4. a team of scientists at a hospital in Paris: Poynard, Thierry, et al. “Truth Survival in Clinical Research: An Evidence-Based Requiem?” Annals of Internal Medicine 136, no. 12 (2002): 888–95.

  5. a clear decay in the number of papers that were still valid: This decay is a relatively smooth linear decline, so we might need many more years of data to fit it nicely to an exponential decay.

  6. towering well above other publications: Sometimes they become so important that they actually stop being cited. Newton’s work is foundational for physics to such a large degree that it has become unnecessary to cite his books.

  7. a study of all the papers in the Physical Review journals: Redner, Sidney. “Citation Statistics from More Than a Century of Physical Review” (2004). http://arxiv.org/abs/physics/0407137.

  8. Other researchers have even broken this down by subfield: Midorikawa, N. “Citation Analysis of Physics Journals: Comparison of Subfields of Physics.” Scientometrics 5, no. 6 (November 26, 1983): 361–74.

  9. In medicine: Tonta, Yasar, and Yurdagül Ünal. “Scatter of Journals and Literature Obsolescence Reflected in Document Delivery Requests.” Journal of the American Society for Information Science and Technology 56, no. 1 (2005): 84–94; doi:10.1002/asi.20114.

  10. Price himself examined journals from different fields: Price, Derek J. de Solla. “Citation Measures of Hard Science, Soft Science, Technology, and Nonscience.” In Communication Among Scientists and Engineers, eds. C. E. Nelson and D. K. Pollock. Lexington, MA: Heath, 1970. pp. 3–22.

  11. Rong Tang looked at scholarly books in different fields: Tang, Rong. “Citation Characteristics and Intellectual Acceptance of Scholarly Monographs.” College Research Libraries 69, no. 4 (2008): 356–69.

  12. three scientists working at the Thermophysical Research Properties Center at Purdue University: Ho, C. Y., R. W. Powell, and P. E. Liley. “Thermal Conductivity of the Elements.” Journal of Physical and Chemical Reference Data 1, no. 2 (April 1972): 279–421.

  13. Isaac Asimov, in a wonderful essay: Asimov, Isaac. “The Relativity of Wrong.” The Skeptical Inquirer 14, no. 1 (1989): 35–44.

  14. Sean Carroll . . . wrote a wonderful series on his blog: Carroll, Sean. “The Laws Underlying the Physics of Everyday Life Are Completely Understood.” Cosmic Variance, 2010; http://blogs.discovermagazine.com/cosmicvariance/2010/09/23/the-laws-underlying-the-physics-of-everyday-life-are-completely-understood.

  15. Carroll even lays down, in a single equation: This is known as the Dirac equation. Carroll, Sean. “Physics and the Immortality of the Soul.” Cosmic Variance, 2010; http://blogs.discover magazine.com/cosmicvariance/2011/05/23/physics-and-the-immortality-of-the-soul/.

  16. A quote from Science Daily: Census of Marine Life. “Giant Undersea Microbial Mat Among Discoveries Revealed by Marine Life Census.” Science Daily, April 18, 2010.

  17. Kevin Kelly refers to this sort of distribution: Kelly, Kevin. “The Long Tail of Life.” The Technium, 2010; http://www.kk.org/thetechnium/archives/2010/04/the_long_tail_o.php.

  CHAPTER 4: MOORE’S LAW OF EVERYTHING

  1. The @ symbol has been on keyboards: Rawsthorn, Alice. “Why @ Is Held in Such High Design Esteem.” International Herald Tribune, March 22, 2010.

  2. Moore wrote a short paper in the journal Electronics: Moore, Gordon E. “Cramming More Components Onto Integrated Circuits” (Reprinted from Electronics, pg 114–17, April 19, 1965). Proceedings of the IEEE 86, no. 1 (1998): 82–85.

  3. number of pixels that digital cameras can process: Myhrvold, Nathan. “Moore’s Law Corollary: Pixel Power.” New York Times, June 7, 2006.

  4. Magee, along with a postdoctoral fellow Heebyung Koh: Koh, Heebyung, and Christopher L. Magee. “A Functional Approach for Studying Technological Progress: Application to Information Technology.” Technological Forecasting and Social Change 73, no. 9 (2006): 1061–83; Koh, Heebyung, and Christopher L. Magee. “A Functional Approach for Studying Technological Progress: Extension to Energy Technology.” Technological Forecasting and Social Change 75, no. 6 (2008): 735–58.

  5. They begin to run out of space: This growth pattern assumes a continuous food supply.

  6. Clayton Christensen, a professor at Harvard Business School: Christensen, Clayton M. “Exploring the Limits of the Technology S-Curve. Part I: Component Technologies.” Production and Operations Management 1, no. 4 (1992): 334–57.

  7. they found mathematical regularities: More recent research has debated whether these are truly exponential or other fast-growing functions, such as power laws or double exponentials. The upshot is the same: There are regularities. See McNerney, James, et al. “Role of Design Complexity in Technology Improvement.” Proceedings of the National Academy of Sciences 108, no. 22 (May 31, 2011): 9008–13; Nagy, Béla, et al. “Superexponential Long-term Trends in Information Technology.” Technological Forecasting and Social Change 78,
no. 8 (October 2011): 1356–64. For more curves, see the performance curve database: http://pcdb.santafe.edu.

  8. has even been found in robots: Powell, Corey S. “The Rise of the Machines Is Not Going as We Expected.” Discover (May 2010).

  9. Kevin Kelly, in his book What Technology Wants: Kelly, Kevin. What Technology Wants. New York: Viking, 2010.

  10. If you plot prefix sizes against the years: Personal research. Underlying data from Bureau International des Poids et Mesures. The International System of Units, 2006.

  11. cost of genome sequencing is dropping rapidly: MacArthur, Daniel. “The Plummeting Cost of Genome Sequencing.” Wired Science, 2011. http://www.wired.com/wiredscience/2011/02/illustrating-the-plummeting-cost-of-genome-sequencing.

  12. These technological doublings in the realm of science: Mathematics also has such doublings. For example, the number of digits of the largest known prime number has increased exponentially, due to growth in computing power that allows for the discovery of larger and larger primes. Further information available here: http://primes.utm.edu/notes/by_year.html

  13. Moore’s Law of proteomics: Cox, Jürgen, and Matthias Mann. “Is Proteomics the New Genomics?” Cell. Cell Press, August 10, 2007. http://linkinghub.elsevier.com/retrieve/pii/S0092867407009701.

  14. the number of neurons that can be: Stevenson, Ian H., and Konrad P. Kording. “How Advances in Neural Recording Affect Data Analysis.” Nature Neuroscience 14, no. 2 (February 2011): 139–42.

  15. “Science and technology are closely related”: Cole, Jonathan R. The Great American University: Its Rise to Preeminence, Its Indispensable National Role, Why It Must Be Protected. New York: Public Affairs, 2009.

  16. Henry Petroski, a professor of engineering and history: Petroski, Henry. “Engineering Is Not Science.” IEEE Spectrum 9 December 2010.

  17. In 1928, the engineer Trygve Dewey Yensen: Yensen, T. D. “What Is the Magnetic Permeability of Iron?” Journal of the Franklin Institute 206, no. 4 (1928): 503–10.

  18. game after game has become: Cirasella, J. and D. Kopec. “The History of Computer Games.” Exhibit at Dartmouth Artificial Intelligence Conference: The Next Fifty Years (AI@50). Conferences, Seminars and Symposiums: Conference Presentation. Dartmouth College, Hanover, NH, July 13–15, 2006.

  19. polio is now generally regarded: Unfortunately, polio’s eradication in the developed world is one of our more slippery mesofacts. Polio still exists in developing countries, and due to our globalized world, it still has the potential of spreading to developed countries where it has been eliminated.

  20. while aluminum used to be the most valuable: Kotler, Steven, and Peter H. Diamandis. Abundance: The Future Is Better Than You Think. New York: Free Press, 2012.

  21. have added about 0.4 years: Wolfram|Alpha. “Life Expectancy, United States”; http://www.wolframalpha.com/input/?i=life+expectancy+United+States, 2011.

  22. actuarial escape velocity: Grey, Aubrey D. N. J. de. “Escape Velocity: Why the Prospect of Extreme Human Life Extension Matters Now.” PLoS Biol 2, no. 6 (June 15, 2004): e187. Further reading: Finch, Caleb E., and Eileen M. Crimmins. “Inflammatory Exposure and Historical Changes in Human Life-Spans.” Science 305, no. 5691 (September 17, 2004): 1736–39.

  23. The physicist Tom Murphy has shown: Murphy, Tom. “Galactic-Scale Energy.” Do the Math, 2011. http://physics.ucsd.edu/do-the-math/2011/07/galactic-scale-energy.

  24. self-fulfilling propositions: Kelly. What Technology Wants.

  25. The Hawthorne effect was defined: McCarney, Rob, et al. “The Hawthorne Effect: A Randomised, Controlled Trial.” BMC Medical Research Methodology 7, no. 1 (2007): 30.

  26. The tiny population of Tasmania: Henrich, Joseph. “Demography and Cultural Evolution: How Adaptive Cultural Processes Can Produce Maladaptive Losses: The Tasmanian Case.” American Antiquity 69, no. 2 (April 1, 2004): 197–214.

  27. “The more populous periods”: Caplan, Bryan. http://econlog.econlib.org/archives/2011/05/replies_to_crit.html. 2011.

  28. A classic paper by economist Michael Kremer: Kremer, Michael. “Population Growth and Technological Change: One Million B.C. to 1990.” The Quarterly Journal of Economics 108, no. 3 (August 1, 1993): 681–716.

  29. More recent research: Bettencourt, L. M. A., J. Lobo, D. Helbing, C. Kuhnert, and G. B. West. “Growth, Innovation, Scaling, and the Pace of Life in Cities.” Proceedings of the National Academy of Sciences of the United States of America 104, no. 17 (2007): 7301–06.

  30. Using these two assumptions: Kremer. “Population Growth.”

  31. first-order model: The very simplest model is a zeroth-order model, but here we have at least the relationship between population and technological progress.

  32. higher population densities in certain regions: Ashraf, Quamrul, and Oded Galor. “Dynamics and Stagnation in the Malthusian Epoch.” National Bureau of Economic Research Working Paper Series no. 17037 (2011).

  33. the concerns of the English people: Merton, Robert K. “Science, Technology and Society in Seventeenth-Century England.” Osiris 4 (January 1, 1938): 360–632.

  34. decided in 1989 to make a special sort of map: Cliff, Andrew, and Peter Haggett. “Time, Travel and Infection.” British Medical Bulletin 69 (January 2004): 87–99.

  35. these other modes of transportation: Ibid.; Grübler, Arnulf. Technology and Global Change. Cambridge, UK: Cambridge University Press. 2003.

  36. examined the city of Berlin: Marchetti, Cesare. “Anthropological Invariants in Travel Behavior.” Technological Forecasting and Social Change 47, no. 1 (September 1994): 75–88.

  37. The Black Death spread: Noble, J. V. “Geographic and Temporal Development of Plagues.” Nature 250, no. 5469 (August 30, 1974): 726–29.

  CHAPTER 5: THE SPREAD OF FACTS

  1. a group of telephone interviewers: Schwartz, David A. “How Fast Does News Travel?” The Public Opinion Quarterly 37, no. 4 (December 1, 1973): 625–27.

  2. Consider the case of Mary Tai: Tai, Mary M. “A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves.” Diabetes Care 17, no. 2 (February 1, 1994): 152–54.

  3. how certain cities were affected: Dittmar, Jeremiah E. “Information Technology and Economic Change: The Impact of the Printing Press.” The Quarterly Journal of Economics 126, no. 3 (August 1, 2011): 1133–72.

  4. Gutenberg combined and extended a whole host of technologies: I recommend going to the Gutenberg Museum in Mainz, which goes into all of this in astonishing depth.

  5. we have measured the average number of close social connections: Christakis, Nicholas A., and James H. Fowler. Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives. New York: Little Brown, 2009.

  6. We understand how social groups are distributed: Onnela, Jukka-Pekka, et al. “Geographic Constraints on Social Network Groups.” PLoS ONE 6, no. 4 (April 5, 2011): e16939.

  7. work done by him and his longtime collaborator James Fowler: Christakis and Fowler. Connected. The methodology in this research has been critiqued more recently. For details, see the following papers: VanderWeele, T. J. “Sensitivity Analysis for Contagion Effects in Social Networks.” Sociological Methods and Research 40 (2011): 240–55; Christakis, Nicholas A., and James H. Fowler. “Social Contagion Theory: Examining Dynamic Social Networks.” Statistics in Medicine, forthcoming.

  8. “[c]onclusions based on such work”: Gould, Stephen Jay. Bully for Brontosaurus: Reflections in Natural History. New York: W. W. Norton, 1992.

  9. the error was so widespread: Hamblin, T. J. “Fake!” British Medical Journal 283 (1981): 19–26. The persistence of incorrect facts in the literature over time was explored further in Tatsioni, Athina, Nikolaos G. Bonitsis, and John P. A. Ioannidis. “Persistence of Contradicted Claims in the Literature.” JAMA: The Journal of the American Medical Ass
ociation 298, no. 21 (December 5, 2007): 2517–26.

  10. While working on his book: Mauboussin, Michael J. Think Twice: Harnessing the Power of Counterintuition. Harvard Business School Press, 2009; See For Yourself: The Importance of Checking Claims, Legg Mason Global Asset Management, 2009.

  11. author Randall Munroe wishes for a world: Munroe, Randall. “Misconceptions.” xkcd. https://www.xkcd.com/843/.

  12. I have found instances of it: For these and more, search for the phrase contrary to popular belief in Google Books.

  13. “Dynamics of an asteroid”: Bothamley, Jennifer, ed. Dictionary of Theories. Farmington Hills, MI: Gale Research International Ltd., 1993.

  14. the article referenced in New Scientist: Bowers, John F. “James Moriarty: A Forgotten Mathematician.” New Scientist (December 23–30, 1989).

  15. But the citations to Moriarty’s work: Kennaway, K. D. “String Theory and the Vacuum Structure of Confining Gauge Theories.” PhD dissertation. University of Southern California, 2004.

  16. These errors “will live on and on”: Mauboussin, See For Yourself.

  17. I was taken to task soon after by James Fallows: Fallows, James. “Boiled Frog Does a Surreal Meta-Backflip.” The Atlantic, March 2, 2010. http://www.theatlantic.com/technology/archive/2010/03/boiled-frog-does-a-surreal-meta-backflip/36934/.

  18. research that quantitatively studied the differences: Barbrook, Adrian C. et al. “The Phylogeny of The Canterbury Tales.” Nature 394, no. 6696 (August 27, 1998): 839.

  19. actually measured: Among others, here are a couple of their papers: Simkin, M. V., and V. P. Roychowdhury. “Stochastic Modeling of Citation Slips.” Scientometrics 62 (2005): 367–84; “Read Before You Cite!” arXiv:cond-mat/0212043 (December 2002).

  20. From their paper: Liben-Nowell, David, and Jon Kleinberg. “Tracing Information Flow on a Global Scale Using Internet Chain-letter Data.” Proceedings of the National Academy of Sciences 105, no. 12 (March 25, 2008): 4633–38.

  21. it is often the case that credible information or news spreads faster: Castillo, Carlos, Marcelo Mendoza, and Barbara Poblete. “Information Credibility on Twitter.” In Proceedings of the 20th International Conference on World Wide Web. New York: Association for Computing Machinery, 2011. 675–84