Physicists and astronomers honored on US postage stamps: another update.

I previously blogged (2021) about physicists and astronomers honored on U.S. postage stamps, with an update last year here.  It's time for another update, not because any new stamps of interest have been issued, but because I have learned of two other stamps that I should have mentioned in my original post, along with a few other notable finds.

First, in 1973, the 500th anniversary year of his birth, Polish astronomer Copernicus appeared on an 8 cent stamp.  He is a major figure in the history of science, and the only one of those mentioned in this series of posts that did not live in the United States at some point during their life.

Second, in 1988, aviation pioneer Samuel P. Langley (along with his Aerodrome #5) appeared on a 45 cent airmail stamp.  He was an astronomer, mathematician, and physicist.

While I find it odd that I couldn't think of a single chemist honored on a postage stamp (but see below), the American Chemical Society has twice been so honored:  in a 1951 three-cent stamp celebrating the ACS's diamond jubilee, and a 1976 thirteen-cent stamp celebrating their centenary.  Similarly, the American Society of Civil Engineers was honored on the centenary of its founding with a 3-cent stamp in 1952.  This was preceded by another 3-cent stamp in 1950 honoring the Railroad Engineers of America.  This stamp features "Casey" Jones, and was issued on the 50th anniversary of his death. 

"The Sciences" were honored on a 5-cent stamp in 1963, celebrating the centenary of the founding of the National Academy of Sciences, whose first president was a great-grandson of Benjamin Franklin.  In 1983, "Science and Industry" was honored on a 20-cent stamp, issued on the 50th anniversary of Chicago's Museum of Science and Industry.

In 2018, a set of four Forever stamps were issued in honor of STEM education.  They honored Science, Technology, Engineering, and Mathematics.

Since I've spent time in the pharmaceutical industry, I will also note that in 1956, a 3-cent stamp honoring the 50th anniversary of the Pure Food and Drug Act was issued, which features Harvey Washington Wiley, a major driving force in the passage of that law, and an official at the USDA agency that was a predecessor to the modern Food and Drug Administration.  So, I found at least one chemist after all!

At some point, I hope to find and scrutinize a history of every postage stamp issued by the United States Postal Service, to see if I can find any others of note.

Once again I'm grateful to the website of the Mystic Stamp Company.

Can't stop blogging about book reviews!

My last post commented further about book reviews in the physics community.  An announcement today that the Mathematical Association of America (MAA) has appointed a new editor for its MAA Reviews has reminded me that the mathematical community is doing relatively better on the book review front than the physics community is.  I don't read MAA Reviews regularly, but I see that it is a professional-society sponsored source of curated book reviews.  They also feature a Basic Library List, a downloadable spreadsheet which includes books they recommend for college and university libraries.  The list is annotated with a star system, with 3 stars for books considered essential, 2 stars for strongly recommended, 1 star for "recommended", and zero stars for "suggested".  I haven't examined the list in detail, but conceptually this seems to be a good idea, and quite useful for students and self-learners as well.

More broadly, I can't speak to the quality of MAA Reviews, as I'm not a regular reader, but the concept seems like exactly what I think is missing in the physics community.  As a bonus, all the content seems to be freely available online.  Unfortunately, using the search feature I was able to find only a single reviewed book in the field of fluid mechanics, and only 3 under physics.  Its coverage of statistics is not at all comprehensive, with only 6 books showing up in the search feature for statistics, 6 more for probability, with 3 more under probability theory, two under "Statistics and Probability", one more under Bayesian statistics, one each under classification and clustering, one more under data visualization, and one more under data analysis.

The Basic Library List has much better coverage, but no reviews are attached to the entries.  Looking at the fluid mechanics sections of the list, I count only 13 titles included, of which only two are rated at 3 stars (essential), both by James Lighthill:  his Waves in Fluids and Informal Introduction to Theoretical Fluid Mechanics.  Both are excellent choices that I would agree with.  There are no 2 star recommendations, but earning a single star are Acheson's Elementary Fluid Mechanics, Lamb's Hydrodynamics, Courant and Friedrichs' Supersonic Flow and Shock Waves, Stoker's Water Waves, and a book I'd not heard of until now, Gary Sod's Numerical Methods in Fluid Dynamics.  Aside from that last one, I would consider the rest as classics.  A 14th book, Batchelor's Introduction to Fluid Dynamics, also a classic, appears under "Mathematical Physics:  Fluid Mechanics".  However there are quite a few other classics that should have been included, many of which were written by physicists or engineers.  So, in execution the list might not live up to my expectations, but I suppose opinions about books are always subjective, so that no such list would make everyone happy.

In addition to MAA, I am a member of SIAM (the Society for Industrial and Applied Mathematics), and their SIAM Review (a journal sent to all members) maintains a healthy book review section.

Anyway, perhaps the physics community needs a source of free, online, curated book reviews in the spirit of MAA Reviews, to replace the fallen books section of Physics Today.  A professional society might be a good central place to host one.

 

 

 

 

 

 

 

Robert L. Devaney (1948-2025)

Today I learned that the Boston University mathematician and educator, Robert L. Devaney, died in November of last year.  He was especially known for his upper level textbook, An Introduction to Dynamical Systems, first published in 1986, back in the heyday of chaos theory, and whose third edition came out in 2022.  My first course in nonlinear dynamical systems was in 1994, where we used the first edition of his 1992 (much gentler) textbook, A First Course in Chaotic Dynamical Systems:  Theory and Experiment.  I believe it was the only math textbook (other than my first-year calculus textbook) with color illustrations.  The book also featured very brief biographical profiles of some of the pioneers of chaos theory, nearly all of whom were still alive at the time.  One of them was Devaney's Ph.D. advisor, Steven Smale, who outlives him.  A second edition was published in 2020.

At the time I took the course, I was preparing for a summer physics project in nonlinear dynamics, and I probably read James Gleick's Chaos around this time as well.  So the course was very timely, and in retrospect, the book I think was successful in at least introducing me to the field.  The book was probably a bit more mathematical and less "physical" than other books I encountered then and later, so I'm not sure I would use it today to teach a class on the subject, but I would certainly refer to it in developing my lectures, and possibly cite it as supplementary reading.

I'm not positive, but I believe I did see Devaney speak once, at a New Jersey section meeting of the Mathematical Association of America, sometime in the 2000s.  Unfortunately I failed to get a chance to ask him to sign my copy of his textbook, either because I forgot to bring it to the meeting, or I didn't get chance to have a one-on-one conversation.  I can't remember anymore.  I certainly regret the missed opportunity, but am grateful for his contributions to dynamical systems education over a distinguished career.

 

 

 

Mathematical fluid dynamics, revisited

In April I noted a piece in Scientific American about the work of 3 mathematicians on their work rigorously deriving the links among 3 levels of hierarchy involving the description of fluid dynamics.  Recently a really nice piece by Leila Sloman for Quanta magazine, on the same topic, has been making the rounds.  Again, it's worth checking out.

 

Physicists and astronomers honored on US postage stamps - Update!

Continuing the theme of my last post, let me call back a post from 2021, where I blogged about physicists and astronomers depicted on US postage stamps.  Back then I counted about a dozen such, and I conjectured about possible future honorees.  Top of my list among the latter was Nikola Tesla.  Well, this was an oversight on my part, as Tesla was indeed depicted on a 20 cent stamp in the American Inventors series, issued in 1983.  Also depicted on the same stamp is his induction motor.

I am grateful to this list for helping me identify Tesla's stamp. The list has a number of notable foreign stamps as well, but it is incomplete.  For example, according to the National Institute of Standards and Technology, American Nobel laureates in physics, David Wineland and Daniel Schechtman (both affiliated with NIST), are depicted on foreign postage stamps.

 

Peter Lax, 1926-2025

As I noted just last month, DTLR does not dwell on mathematics very much, but a second exception seems just as warranted as my earlier post last month.  Today we learn of the passing of Abel Prize laureate Peter D. Lax (1926-2025), a retired professor at the Courant Institute at NYU, last Friday.  He was a highly accomplished pure and applied mathematician, who worked in the field of partial differential equations, and on numerical methods for their solution.  Much of this work has direct relevance to applied physics and engineering, including fluid dynamics.

Prof. Lax is also the only Abel Prize winner I have ever met in person.  It was just a brief meeting during a visit I made to the Courant Institute in the late 2000's on other business.  We did not exchange many words, but I was honored to meet him.

I've attended lectures by at least two other Abel Prize winners, S.R.S. Varadhan and the late John Nash, but did not meet them face to face.

I'll take this chance to mention my encounters with winners of the other major international prizes in mathematics.  As far as I know, I have neither met nor attended lectures by any of the Fields Medalists, except for Shing-Tung Yau.  As for the Wolf Prize in Mathematics, both Lax and Yau are the only ones I've personally encountered as noted.  Well, it must be evident that I don't attend math conferences or math lectures very often.

Mathematical fluid dynamics

I don't often write about mathematics here on DTLR, but this piece by Jack Murtagh in Scientific American is a worthy exception, as it pertains to fluid dynamics.  Namely it reports on the work of 3 mathematicians who claim to have found a way to derive the hierarchy of methods for 3 levels of describing fluid motion, the individual particle level, the statistical description of particle behavior of Maxwell and Boltzmann, and the continuum level of the Euler and Navier-Stokes equations.  The mathematicians posted their work to arXiv, so let the peer review proceed.

 

 

 

The 2023 Abel Prize

Additional news this week includes the awarding of this year's Abel Prize in Mathematics to Luis A. Caffarelli, for his work in nonlinear partial differential equations.  Of interest to DTLR is his 1982 work, with Robert Kohn and 2015 Abel Laureate Louis Nirenberg, on singularities in the Navier-Stokes equations, work directly relevant to the topic of the (still unsolved) Clay Millenium Prize problem related to the Navier-Stokes equations.

The Abel Prize was begun a few years after I left graduate school, so I consider it a recent phenomenon.  It is intended to be considered the equivalent of the Nobel Prize for mathematics.  In reading the list of past laureates, I realized that I've attended lectures by several.  I attended a lecture by 2015 laureate John Nash at New York University, likely in 2008 or 2009.  Unfortunately Dr. Nash and his wife were killed while traveling home from the Abel Prize ceremony.  Also around the same era (Dec. 2008), I attended the 100th Statistical Mechanics conference of Rutgers University.  There were many notable speakers there, and as I reread the speaker list, I am amazed.  The 2007 Abel laureate, Srinivasa S. R. Varadhan, and future 2014 Abel laureate Yakov G. Sinai, both spoke there.  I honestly can't recall watching their lectures, nor those of many other luminaries on the list (including names I did not come to fully appreciate until over a decade later).  I do recollect sitting next to Juan Maldacena at the conference dinner, where I couldn't resist bringing up Lee Smolin's argument against string theory (see Smolin's book, The Trouble with Physics).  Dr. Maldacena's response (I'm paraphrasing) was that many smart people work on string theory, and they wouldn't be doing that if it were as hopeless as Smolin seems to think.

I have only met one Abel laureate in person, and only briefly, Peter D. Lax (2005), during a visit to the Courant Institute in the mid-2000s. Similarly, while I have attended lectures by dozens of Nobel laureates (too many to attempt to list here), I only met one in person, and again only briefly:  the late Paul C. Lauterbur, 2003 laureate in physiology or medicine.  I met him at a book signing of his at the San Francisco IEEE EMBS annual meeting in 2004.

A tribute to Academic Press' Mathematics in Science and Engineering series

Almost a year ago, I wrote about Academic Press' acclaimed International Geophysics book series, which published a total of 104 volumes, the last one in 2014.  Though many volumes remain in print, it is unclear if any new volumes are anticipated.

Today I'd like to pay tribute to another Academic Press book series, Mathematics in Science and Engineering.  Academic Press is now part of Elsevier, and the latter's website shows that this series, apparently launched in 1961, is still going strong, with the latest volume published earlier this year.  Volume 1 was titled Concepts from Tensor Analysis and Differential Geometry, by Tracy Y. Thomas.  Sixty years later, the series published Luigi Berselli's Three-Dimensional Navier-Stokes Equations for Turbulence.  The website seems to suggest that the last numbered volume was #213, published in 2010, and at least 7 volumes have been published since then.  The longevity of a 60-year old series is truly impressive.

Scanning the list of titles and authors, there are indeed some impressive contributions.  Remarkably, I only own one of these volumes, Morton Gurtin's An Introduction to Continuum Mechanics (1981), volume 158 of the series.

Physicists and astronomers honored on US postage stamps

Today I received an order of US postage stamps, including a sheet of the new Forever stamp honoring Chinese-American nuclear physicist Chien-Shiung Wu.  Adrian Cho wrote about this stamp last month in Science.  The stamp was issued on the International Day of Women and Girls in Science.  As far as I know, Dr. Wu is the third woman physicist honored on a US postage stamp, and the first Chinese-American one.  The end of Cho's article talks about other physicists honored on US postage stamps -- there are many fewer of these than American Nobel Physics Laureates!  Cho mentions several, including some aerospace scientists, though he says the US Postal Service doesn't actually track how many there are.

This got me thinking about that very question.  How many physicists and astronomers are honored on US postage stamps?  There are just over a dozen, by my count. The overlap with mathematicians is considerable (since there are far fewer of those), so I'll include them too in this post.

The most honored American physicist on our nation's postage stamps is, of course, Benjamin Franklin.  It may be no coincidence that Franklin was also the nation's first Postmaster General.  I haven't even tried to count how many US stamps have honored Franklin.

At a distant second place is Albert Einstein, honored on two stamps:  an 8 cent stamp in the Prominent Americans series in 1966, and a 15 cent stamp in 1979 issued on the centenary of his birth. All other physicists on US stamps have a single stamp in their honor.  These include Robert Millikan, on a 37 cent stamp issued in 1982 as part of the Great Americans series, and Enrico Fermi on a 34 cent stamp issued in 2001.

The American Scientists series, which began in 2005, was a boon for physicists.  Josiah Willard Gibbs (a polymath claimed equally by mathematicians and chemists) and Richard P. Feynman were included in the first round (37 cents), while John Bardeen and astronomer Edwin Hubble appear in the 2008 second round (41 cents).  Maria Goeppert Mayer was honored in the third round (2011) with a Forever stamp.  Unfortunately, the series appears to have been discontinued after the third set.  (Did they just not sell well?)  The first round in 2005 also included mathematician John von Neumann, who made colossal contributions to physics, computer science, and meteorology, among other fields.  

The new stamp honoring C.-S. Wu is the second to honor a physicist in the decade since the last set of American Scientists was issued.  It follows the 2018 issue of a Forever stamp honoring Sally K. Ride, astronaut, physicist, and stamp collector.  Of the honored physicists mentioned, Einstein, Millikan, Feynman, and Mayer were Nobel laureates, with Bardeen being a double Nobel laureate in physics.  (Cho's article disucsses that many feel that Wu should have received a Nobel as well.)

Also worthy of note is Benjamin Bannker, honored in 1980 with a 15 cent stamp in the Black Heritage series.  Banneker was a surveyor, mathematician, and astronomer, who like Franklin, published his own almanacs.  A math teacher, Jaime Escalante, was honored with a Forever stamp in 2016.  Along with Wu, Banneker and Escalante are the only non-whites honored by stamps among those discussed in this post.

Since Cho's article mentions aerospace scientists and inventors, let's look at them too.  The Wright Brothers and their achievements were honored on the 25th, 46th, 75th, and 100th anniversaries of their first powered flight.  The first stamp (2 cents) was issued as one of a pair honoring of the 1928 International Civil Aeronautics Conference, in that year.  It featured the Wright Flyer.  Three airmail stamps honored both the Wrights and their aircraft, in 1949 (6 cents) and two in 1978 (31 cents).  Finally on the centenary of their first flight, another stamp featuring the Wright Flyer was issued in 2003 (37 cents).  Other aerospace pioneers include Robert Goddard (1964, 8 cents), Igor Sikorsky (1988, 36 cents airmail), and Theodore von Karman (1992, 29 cents).  As far as I know, von Karman is the only fluid dynamicist honored on a US postage stamp! 

Unfortunately, I cannot think of another American fluid dynamicist who should next be honored with a US postage stamp, for reasons similar to those I wrote about in an earlier post. But what about other American physicists, astronomers, and mathematicians?  Who would you nominate next?

I surmise that those known among the general public would have the best chance of being honored on a stamp, compared to those best known just within the physics community.  So, Nikola Tesla seems an obvious choice.  You can guarantee that such a stamp would sell well.  Perhaps W. Edwards Deming, though he is best known for his work in statistics and management consulting, or J. Robert Oppenheimer.  However, I am delighted that less publicly celebrated figures like Gibbs, Millikan, Fermi, Mayer, Bardeen, and Wu have been honored.  There are thus many worthy choices for the next postage stamp.  If only the American Scientists series could be revived!

Among astronomers, I'm surprised that Carl Sagan hasn't already been so honored.  Among mathematicians, perhaps Benoit Mandelbrot (the maestro of fractals), John Nash (Nobel in economics, subject of A Beautiful Mind), and Katherine Johnson (of Hidden Figures fame) might be considered.

I am grateful to the website of the Mystic Stamp Company, and Wikipedia, sources of the information I have provided above.

A physicist attends JMM

The Joint Mathematics Meetings (JMM) are advertised as the world's largest mathematics conference. This year's meeting was held in San Diego, CA, last week. DTLR attended despite his mild allergy to pure mathematics. This was my first time attending JMM, and I chose the sessions I attended with great care, and learned a lot. Some highlights are discussed below.

San Diego Convention Center, site of JMM 2018.

Physics

The best talk given by a mathematician was a physics talk, “Toy models,” by Stanford professor Tadashi Tokieda. He used a series of toys exhibiting unexpected, puzzling, and surprising behavior to illustrate ideas in physics, using almost no mathematics at all. Rather, he relied on qualitative reasoning and dimensional analysis rather than direct computation. After I returned home I discovered that many of his examples, and others, can be found in his Youtube videos, some of which are collected here. He was an exceedingly entertaining speaker – I was not bored for even one second. I would rate this as the best talk of the conference.

Computer scientist Dana Randall (Georgia Tech) gave a presentation on statistical physics, “Emergent phenomena in random structures and algorithms.” She discussed phase transitions in lattice gases, randomized algorithms, and swarm robotics, among other topics. (Phase transitions were also one of the topics addressed by Tokieda.)

Fluid Dynamics

Edriss S. Titi (Texas A&M and Weizmann Institute) provided a review of mathematical results on existence, uniqueness, and regularity of solutions for the incompressible Euler and Navier-Stokes equations under various conditions, such as 2D vs. 3D flows, and types of initial conditions. This is of course the subject of one of the million dollar prizes offered by the Clay Mathematics Institute. Rayleigh-Benard convection was given as an example. 

Isabelle Gallagher (University of Paris Diderot) presented a review of mathematical results connecting the Newton hard-sphere gas model to the Boltzmann transport equation from the kinetic theory of gases, and to the Navier-Stokes equations for a continuum fluid. One of the puzzles is how does a fundamentally reversible system – Newton's laws applied to a gas of hard spheres – result in irreversible behavior characterized by the second law of thermodynamics (reflected in both the Boltzmann and Navier-Stokes models). Her answer to this is the Ehrenfest experiment, where such a gas begins in one chamber, and at a certain time the portal to a second chamber is opened. Eventually an equilibrium is reached where both chambers have approximately the same number of particles. The key is the number of particles. If there are just two particles, nothing remarkable is observed. However, when there are many particles, the most likely states of the system are those near the equilibrium state. Thus, the statistical properties of a completely deterministic system are consistent with the second law of thermodynamics. We might think of this as an emergent behavior, not unlike those discussed in Dana Randall's talk.

Data Analysis

Topologist Gunnar Carlson (Stanford) discussed “Topological Modeling of Complex Data”. Here the “model” is not a statistical model, but rather a network model that attempts to capture the shape of data. The idea is to apply overlapping bins to the data along some of the predictor variables, and cluster the data along these axes into nodes. Nodes with overlapping data are connected, forming a network graph.

Applied mathematician Tamara G. Kolda (Sandia National Labs) spoke about tensor decompositions, particularly a decomposition known as CP (canonical polyadic). These tensor decompositions are not  orthogonal, but the idea is to essentially project high dimensional data onto what I will call basis tensors. Randomization plays a key role in the algorithm.

Neither of these presentations is by a statistician, and neither addresses statistical inference, rightly so in my view. Rather, they belong to exploratory data analysis (EDA), a field that Carlson reminds us was invented by (topologist) John Tukey.

Computer Science

Harvard computer scientist Cynthia Dwork (joint appointment with Microsoft) presented a talk on differential privacy. Algorithms that exhibit differential privacy are randomized algorithms that respond to a query to a data base, and provide the following guarantee. A specific person's decision to be included (or not) in the data base should not affect the outputs of the algorithm. Let two data sets differ by a single individual's record (she is present in one data set, and a different randomly sampled person from the population replaces her in the second). Any outcome output from the algorithm run on either data set will be almost equally likely. Algorithms with the differential privacy property are also inherently robust in the statistical sense, and can be used for adaptive/exploratory reuse of the data for statistical modeling.

A theme is evident: the talks by Randall, Kolda, and Dwork all involve randomized algorithms in computer science, not a topic that I thought about when I was a student 20 or so years ago.

What about Math?

I did attempt to attend some actual pure math talks: Alissa Crans (Loyola Marymount University) on “Quintessential quandle queries” and Craig Huneke (Virginia) on “How complicated are polynomials in many variables”. I had not heard of quandles before; the speaker related them to both groups and knots. An application to cryptography was mentioned but not dwelled on. She did at least bring a prop (a giant tetrahedron) that she used for illustration. No applications were mentioned at all in the polynomial talk, which focused on something called Stillman's conjecture. I also attended a talk by a distinguished historian of mathematics, Joseph Dauben (CUNY), on the history of Chinese math (actually, the history of Chinese historians of mathematics).

A slide from Alissa Crans' lecture on quandles, showing the definition and the mathematician who coined the term.

I also attended a panel session on careers in business, industry, and government, which probably could have run longer than it did. I was pleased to see a high level of interest in this session, but sad that many math students aren't sure how or even whether to pursue such careers. It's a good thing that they came to this session, but their home departments should be doing more to stimulate interest and provide practical resources for such career development. There was also a talk by applied mathematician Stephen Hobbs (Space and Naval Warfare Systems Center) on a simple model for deploying aircraft-carrier based resources in a humanitarian aid scenario. Finally I attended a few sessions on statistical education, including one on developing a data science program within a mathematics department.

The exhibit hall was a delight, with many book and software vendors offering their wares.  The National Security Agency had a recruiting booth which featured an original Enigma encryption device, which attendees were invited to interact with (unlike museum pieces that remain behind glass).

An original ENIGMA device at the NSA booth.

Of course, San Diego is a nice spot to go in the winter, with many extracurricular delights.

Beef empanadas at a Spanish restaurant, Cafe Sevilla, in the Gaslamp District of San Diego.

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.