Calculating logarithms?!

As I was culling my book collection, I came across three delightful books by Bob Miller, a CCNY math professor:  his Precalc Helper, Calc I Helper, and Calc II Helper, all published in 1991 by McGraw-Hill's Schaum division.  That was around the time I started taking calculus courses, though I do not recall using those books.  I may have acquired them shortly after I completed my year of calculus.

Regardless, as I was leafing through these books on this last day of 2014, nearly a quarter century after they were published, I was particularly struck by Miller's treatment of logarithms.  In the Precalc Helper, Chapter 12, "Modern Logarithms", begins with this paragraph (p. 75):

We will do a modern approach to logs.  Modern to a mathematician means not more than 50 years behind the times.  We will not do calculations with logs (calculations involving characteristics and mantissas).  This is no longer needed because we have calculators.  What is needed is a thorough understanding of the laws of logarithms and certain problems that can only be solved with logs.

If I ever did calculations with characteristics and mantissas, I certainly don't remember them now. It is likely that my high school had already abandoned coverage of that topic by the time I was a student.

Then on page 1 of the Calc II Helper, opening the first chapter, titled "Logarithms", we find the following passage.

Most of you, at this point in your mathematics, have not seen logs for at least a year, many a lot more.  The normal high school course emphasizes the wrong areas.  You spend most of the time doing endless calculations, none of which you need here.  By the year 2000, students will do almost no log calculations due to calculators.  In case you feel tortured, just remember that you only spent weeks on log calculations.  I spent months!!!

I suspect the future arrived a lot sooner than Miller thought it would.  When I was in high school in the late 1980s, we were using a then-new software program, Derive, to graph mathematical functions.  In college, we were using Mathematica.  When I was a teaching assistant in graduate school, graphing calculators were already pervasive, and my students were allowed to use them on exams.  (I have never owned one myself.)  Evidently graphing calculators are still in use, though equivalent apps have been available for smart phones for a few years now.  (I have never owned a smart phone either, but I suspect this will have to change one day.)

At this point I am too far out of touch with mathematics teaching and technology to know what is considered standard of practice.  Nonetheless I am grateful I never had to do endless logarithm calculations by hand.  Make no mistake, logarithms are essential for science, engineering, and medicine.  In fact, I worked with logarithms at work earlier today.  But I let the computer do the calculating.

Congratulations to arXiv

According to Nature, the arXiv preprint server has reached one million articles in its holdings.  DTLR congratulates arXiv.org, and its founder Paul Ginsparg, on this achievement.

A Review of Abrahm Lustgarten's "Run to Failure"

On April 20, 2010, the Deepwater Horizon oil drilling platform was completing the task of drilling a pipe into BP's Macondo well in the Gulf of Mexico.  The pipe experienced a blowout, and the blowout preventer failed, resulting in an explosion and eventual sinking of the platform.  Eleven workers were killed, and seventeen were seriously injured.  The rupture of the pipe resulted in a massive oil spill event that lasted 86 days.

The disaster was eminently preventable.  Investigation of its causes has focused on a number of technical and engineering issues; however the larger context was BP's corporate culture.  Understanding that culture requires a deeper study of BP's checkered history of operations management and industrial safety.  The book Run to Failure, by Abrahm Lustgarten (2012), provides just that.  Written in conjunction with the Frontline documentary, The Spill, it provides an in-depth examination of BP's history in North America, beginning in 1989 when John Browne was named head of worldwide exploration and production.  Browne would later become BP's chief executive, and on his watch there were major disasters at two of BP's legacy assets:  its Texas City refinery and its operations on Alaska's north slope, site of its Prudhoe Bay oil fields, as well as an extensive pipeline network.  These legacy assets were considered sources of revenue to be milked as much as possible, but they were not opportunities for growth, and thus infrastructure investments were minimized.

After the prologue, which describes the Deepwater Horizon accident and introduces the book, the next fourteen chapters are dedicated to events prior to that accident.  We observe a corporate culture where site managers were frequently rotated, while being pressured to produce financial results.  This produced a short term mentality, perpetual cost cutting, and an avoidance of investing in infrastructure maintenance, even where safety and the environment were at risk.  Safety management focued on the less expensive "slips and trips" rather than the vastly more expensive process safety.  Workers who raised concerns were ignored, and whistleblowers were blacklisted.  An attitude of "run to failure" pervaded at BP's legacy assets.  However, even BP's preferred areas for investment, such as the Gulf of Mexico, provided an example of corner-cutting in the rush to start making money.  The near sinking of BP's Thunder Horse platform during Hurricane Dennis in 2005 was caused by the mistakenly backward installation of several check valves in the platform's pontoons.

BP's poor safety record is compared unfavorably with those of other major oil companies, particularly Exxon, which seems to have taken to heart the lessons of the notorious Exxon Valdez oil spill.  The rate of spills and other process accidents for BP was usually several times higher than that of its competitors.

The last two chapters, and the epilogue, return to the Macondo well and the Deepwater Horizon accident.  The exposition of events reveals a series of poor decisions as well as equipment failures that all point to a culture of corner cutting in the rush to get results.  It provides a case study of engineering and business decision analysis and ethics.  The book ends with evidence that BP hasn't really changed its corporate culture, and implies that the company's next disaster will occur on Alaska's north slope.  A post from earlier this year in the Columbia Journalism Review, by Alexis Sobel Fitts, shows that BP is even now aggressively trying to influence public perception of the Deepwater Horizon disaster.

One issue that arises is the role of federal and state government regulators.  The author discusses this issue, including a number of agencies, though the primary emphasis is on the Environmental Protection Agency.  This is perhaps due to his access to very candid sources from that agency.  There is relatively little discussion of the US Department of Interior's Minerals Management Service (MMS); fortunately you can read more about the role of this obscure agency in a May, 2010, Rolling Stone article by Tim Dickinson.  I wish that Lustgarten had incorporated more discussion of other regulators, including Dickinson's findings.

Run to Failure has been reviewed in a number of scientific journals such as Nature (Mascarelli, 2012).  The most useful reviews in my view are those by Peter Dykstra at Enivonmental Health News (here), and Matthew T. Huber (2013) in Contemporary Sociology.  I strongly recommend this book for those interested in engineering and business ethics, corporate culture, and the energy industry.

References

Matthew T. Huber, 2013:  Review of Lustgarten (2012).  Contemporary Sociology, 42:  400-401.

Abrahm Lustgarten, 2012:   Run to Failure:  BP and the Making of the Deepwater Horizon Disaster (W. W. Norton, New York).

Amanda Mascarelli, 2012:  Plumbing the depths.  Nature, 483:  154-155.

Congratulations to the Royal Society

The Royal Society of London is celebrating the 350th anniversary of its Philosophical Transactions, the world's oldest scientific journal. The journal has pioneered many of the features that we associate with scientific journal publishing, such as peer review, establishing priority, archiving, and dissemination.  The journal evidently was founded in 1665 by the Society's secretary, Henry Oldenburg.

This Royal Society blog post by Julie McDougall-Waters provides some context to the celebration.  DTLR joins in congratulating the Royal Society in celebrating this anniversary.

Journals unite for reproducibility: DTLR is pleased!

Today Nature and Science posted joint editorials (here and here) endorsing a Proposed Principles and Guidelines for Reporting Preclinical Research, posted at the U.S. National Institutes of Health.  It is the product of a June, 2014, workshop sponsored by NIH and the two journals, and endorsed by over 30 other biomedical journals.  It provides a bare minimum list of criteria for good reporting practices of animal experiments in biomedical research.  The list is less detailed than one given by Landis et al. (2012) which they cite.

DTLR joins in endorsing the proposed principles and congratulates all the participants for taking a major step forward in promoting reproducible research.  It reflects a discipline-wide concern about the metastasis of non reproducible research across the spectrum of journals, as abundant evidence has made clear in recent years.  The proposed principles emphasize study design issues such as randomization, blinding, sample size, and appropriate replication.  Appropriately, such issues receive more space than analysis.  (The use of the term "inclusion/exclusion criteria" is a little confusing here - in clinical research, this refers to patient enrolment criteria; but the authors here seem to use it to refer to selective reporting and data omission, certainly an important issue, but one I would have found other language to describe.)  The sharing of data sets and the full disclosure of biological reagents are also welcome features.  In general, materials and methods sections of papers really should be expanded such that an independent laboratory could reproduce the experiment and expect to obtain similar results.

DTLR does not believe that the proposed principles go far enough, however.  For instance, the section on statistics requires a disclosure of "the statistical test used"; the fact that the emphasis here is on a statistical test rather than an estimation procedure is a serious oversight, in my view.  The reporting of confidence intervals instead of tests provides a sense of magnitude and direction that is lacking in a p-value, allowing evaluation of both clinical and statistical significance.  A statistical test outcome only communicates statistical significance. A confidence interval implicitly reports a test result when the confidence limits are compared with zero (for a conventional null hypothesis test).  Other types of estimation (tolerance intervals, prediction intervals) may be more appropriate in some situations.

DTLR is glad to see a growing consensus in the scientific community that nonreproducible research is corrosive and must be reduced.  This is a terrific step forward, but just one step.  Now, individual laboratories must take these guidelines to heart and use them to improve the design, execution, analysis, and reporting of their studies. 

References

Nature, vol. 515, p. 7 (2014).

Science, vol. 346, p. 679 (2014).

S. C. Landis, et al., 2012:  A call for transparent reporting to optimize the predictive value of preclinical research.  Nature, 490:  187-191.

Evolution of airplanes: a follow-up

I thank Prof. Bejan for graciously replying to my critique of his work in a previous post.  Permit me to follow up briefly here.

Bejan is correct that his earlier publications have cited Tennekes and the others.  He is also right that the earlier writers did not include land and aquatic locomotion in their analyses.  I was aware of Bejan's 2006 paper with Marden (which cites Tennekes only as a data source, not for analysis) but have not seen his 2000 book published by Cambridge U.P.  I thank Prof. Bejan for clarifying these points, although my original post did make many of them already.

Nonetheless, Bejan's 2014 paper makes a specific point about the Concorde case, which Tennekes has discussed at length, as I showed.  A citation in Bejan's 2014 paper in the context of the Concorde discussion would have been pertinent for readers.  As it stands, the 2014 paper makes it seem that the 'outlying' nature of the Concorde on the diagram is a new finding, when it is not.

Bejan's comment also offers a very important distinction, one that I strongly affirm.  A purely empirical analysis of observational data is a wholly different activity to first-principles modeling of such data, especially when the latter is then validated by empirical data.  Many scientists indeed fail to appreciate this distinction.  However, the quantitative predictive modeling in Bejan's 2014 paper seems to be based on basic aerodynamic scaling arguments.  The link with evolution seems at best a metaphor; it is not clear to me that the evolutionary component of Bejan's work is predictive in any quantitative sense.  I stand by my previous comments on interpreting data, particularly the pteranadon case.  Being an outlier on the graph does not prevent the pteranadon for being fit for its ecological niche in its day.  This would seem to limit the scope of the evolutionary metaphor when linked to specific aerodynamic scaling arguments.   My methodological criticisms of correlation analysis also remain valid.

The "evolution" of airplanes: DTLR is not impressed

About three weeks ago, the Journal of Applied Physics published a paper by Adrian Bejan and collaborators, “The evolution of airplanes” (Bejan et al., 2014).  Bejan is a named professor of mechanical engineering and materials science at Duke University, and author of well-known textbooks on heat transfer and thermodynamics.  His co-authors are a Boeing engineer and Duke alum, Jordan Charles, and a French civil engineering professor, Sylvie Lorente, who is also an adjunct Duke professor.  The publisher and Bejan’s university both issued news releases about the paper, and Bejan wrote about his work at The Conversation.  Indeed, the paper has received a lot of online press coverage.  The publisher’s own Inside Science news organ did include some critical comments in its coverage; additional critical comments were also posted at The Conversation in response to Bejan’s post.  The criticisms focus on the overall logic and philosophy of the paper.  I strongly sympathize with these criticisms.  Here, however, I will provide an additional perspective beyond those aired by others thus far.

The paper presents a number of simple analyses including basic aerodynamic scaling arguments, compared favorably with empirical data about aircraft geometry and performance.  A particularly vivid graph in the paper shows empirical data comparing the body mass and velocity of airplanes with those of running, flying, and swimming animals.  The diagram (the paper’s Fig. 2) is reproduced below.

The Ref. 1 in the caption is Bejan and Marden (2006).  The authors make the point that the Concorde is an outlier in this diagram, and further comment as follows.

Looking at the graphs of this paper, we see that there is an outlier, the Concorde, which was perhaps the most radical departure from the traditional swept wing commercial airplane.  The Concorde’s primary goal was to fly fast.  In chasing an “off the charts” speed rating the Concorde deviated from the evolutionary path traced by successful airplanes that preceded it.  It was small, had limited passenger capacity, long fuselage, short wingspan, massive engines, and poor fuel economy relative to the airplanes that preceded it.  Even when it was in service, the Concorde did not sell, and only 20 units were ever produced (whereas successful Boeing and Airbus models were produced by the thousands).  Eventually, due to lack of demand and safety concerns, the Concorde was retired in 2003.  (Bejan, et al., 2014, p. 6.)

Except for the remark about the "evolutionary path", all of this is factual.  However, many of these observations are not original.  In a book published originally in Dutch in 1992, Henk Tennekes (2009) presents the following graph (his Fig. 2) comparing cruise speed and body weight; in the graph he tacitly ties cruise speed to wing loading (weight divided by wing surface area).  Although it does not include running and swimming animals, the graph is otherwise similar in spirit to Bejan et al.’s graph.

Tennekes attributes this sort of analysis to the former DuPont company head, Crawford H. Greenewalt, and later scholars, including Colin J. Pennycuick.  Greenewalt’s original analysis was published in 1962; see Tennekes (2009) for citations and sources of data.  Tennekes also derives a simple scaling formula relating wing loading to cruise speed.  The equation 2 referred to in the caption is a version of this scaling formula.

What does Tennekes have to say about the Concorde?  In Chapter 1, he writes the following.

Wasn’t it supposed to fly at about 1,300 miles per hour?  How come it didn’t have higher wing loading and therefore smaller wings?  The answer is that the Concorde suffered from conflicting design specifications.  Small wings suffice at high speeds, but large wings are needed for taking off and landing at speeds comparable to those of other airliners.  If it could not match the landing speed of other airliners, the Concorde would have needed special, longer runways.  The plane’s predicament was that it has to drag oversize wings along when cruising in the stratosphere at twice the speed of sound.  It could compensate somewhat for that handicap by flying extremely high, at 58,000 feet.  Still, its fuel consumption was outrageous.  (Tennekes, p. 18)

And in the preface, Tennekes writes:

The Concorde went out with a bang.  A fiery crash near Paris on July 25, 2000, signaled the end of its career….In retrospect, the Concorde was a fluke, more so that anyone could have anticipated.  From an evolutionary perspective it was a mutant.  It was a very elegant mutant, but it was only marginally functional.  The fate of the Concorde inspired me to draw parallels between biological evolution and its technological counterpart wherever appropriate.  (Tennekes, p. xii)

Tennekes has more extensive comments on the Concorde in Chapter 6.  At his doctoral thesis defense, he argued “that supersonic airliners would be a step backward in the history of aviation” (p. 165).  He explains that with supersonic flight, the aircraft would have to generate shock waves in the air, which requires “a lot of energy” (p. 166).  On the same page,

Although Concorde passengers didn’t notice anything as their plane penetrated the sound barrier, the economic barrier was real enough.  If you want to exceed March 1, it will cost you 3 times as much as staying below the speed of sound.  For the aircraft industry, supersonic flight was indeed a step in the wrong direction.  Time and again, before aeronautical engineers started dabbling with supersonic flight, they had managed to reach higher speeds and lower costs.  The Concorde broke that trend.

I think it is unfortunate that both Bejan and Tennekes are tempted by the evolutionary metaphor; the critical comments I alluded to in my opening paragraph zero in precisely on this aspect of the work, as well as Bejan’s “constructal law” which he also purports to be at work here.  (I won’t bother to discuss that aspect further.)  Nonetheless the authors are correct that the empirical data and aerodynamic scaling relationships are consistent with each other, and possibly of limited use and interest.  They should not, however, be used to narrow one’s thinking.  For instance, in Tennekes’ plot, a number of animals show up as more severe ‘outliers’ than the Concorde.   Tennekes states that deviations from the trend line may be justified.  The pteranadon, for instance, was a soaring animal.  In prehistoric times there were no polar ice caps, reducing the atmospheric temperature gradient between the poles and equator, compared to today.  As a result there was less wind back then.  He presents other examples, including aircraft.  More generally, just because the bulk of the data fall along a trend line or curve, data away from that trend should not necessarily be deprecated.  Furthermore, correlation should not be confused with causation.  Bejan et al. (2014) offer no such nuances or caveats in their discussion.  Consequently they exaggerate the importance and implications of their findings.

It is also of great concern that Bejan et al. (2014) do not cite, either in the main paper or their supplemental information, Tennekes' work, particularly in the context of the Concorde discussion.  This is unusually poor scholarship.  (Bejan does cite Greenewalt and Pennycuik in an earlier paper, Bejan and Marden, 2006.)  Bejan et al. (2014) also make pointless, tautologous statements such as “Small or large, airplanes are evolving such that they look more and more like airplanes, not like birds” and then in the next paragraph, “Small or large, airplanes are evolving such that they look the same.”  Their abstract ends with the non-sequitur, “The view that emerges is that the evolution phenomenon is broader than biological evolution.  The evolution of technology, river basins, and animal design is one phenomenon, and it belongs in physics.”  Such statements are unjustified, unhelpful, and provide heat rather than light to the discussion.

A technical point should also be made:  at one point, Bejan et al. (2014) comment on their data analysis that “the correlation is statistically meaningful because its P-value is 0.0001, and it is less than 0.05 so that the null hypothesis can be rejected”.  This is a fairly naive and unimpressive statement.  The 0.05 threshold is conventional but totally arbitrary; moreover, the null hypothesis is one of no correlation at all, which is an incredibly low bar to establish a “meaningful” relationship between two variables.  Statistical significance does not necessarily convey practical significance.  For instance, it is possible to make a relationship with a negligibly small slope "statistically significant" if the sample size is large enough.  Reporting any kind of statistical inference (the p-value) on observational, non-randomly sampled data is itself questionable.  Moreover, as Loh (1987) noted, the correlation coefficient does not actually measure the closeness of the data to the best fit line.  The fitted equation and coefficient of determination, which the authors do provide, are more meaningful measures of the strength of the relationship between two variables.  The great statistician John Tukey (1954) stated that "most correlation coefficients should never be calculated."

To conclude, the publication of Bejan et al. (2014) in the Journal of Applied Physics is questionable.  The work should instead have been submitted for review at an aerodynamics or aerospace engineering journal.  I suspect it might not have impressed reviewers in that community.  Moreover, the authors should have cited Tennekes (2009) who provides a more detailed and nuanced discussion of the Concorde case, and they should increase the care with which they interpret correlations in empirical data.  I think the rhetoric about evolution is superfluous and distracting from the authors' primary technical findings, and should have been dispensed with.  Other critics have focused their views on this last point, so I've not dwelt on it here.

References

A. Bejan and J. H. Marden, 2006:  Unifying constructal theory for scale effects in running, swimming, and flying.  Journal of Experimental Biology, 209:  238-248.

A. Bejan, J. D. Charles, and S. Lorente, 2014:  The evolution of airplanes.  Journal of Applied Physics, 116:  044901 (6 pages).

Wei-Yin Loh, 1987:  Does the correlation coefficient really measure the degree of clustering around a line?  Journal of Educational Statistics, 12:  235-239.

Henk Tennekes, 2009:  The Simple Science of Flight:  From Insects to Jumbo Jets.  Revised and expanded edition.  MIT Press (Cambridge, MA).  

John Tukey, 1954:   Causation, regression, and path analysis.  In Statistics and Mathematics in Biology, edited by O. Kempthorne, T. A. Bancroft, J. W. Gowen, and J. L. Lush.  Iowa State College Press (Ames), 35-66.