The Year of Mathematics

I have just learned that 2026 has been declared "The Year of Mathematics"or YoM2026, by the Conference Board on Mathematical Societies.  Unlike previous celebrations noted on this blog, such as last year being the international quantum year, this YoM2026 designation seems to be restricted to the United States.  At time of writing, they have announced that a bipartisan Congressional resolution has been introduced in the U.S. Senate.

Why 2026?  Apparently this year the International Congress of Mathematicians will be meeting in Philadelphia, in the year of the United States' 250th anniversary. The quadrennial Congress was held in the U.S., according to Wikipedia, on only two previous occasions (1950 and 1986).  Otherwise, I am not aware of any particular anniversary being celebrated in 2026 in connection with mathematics.  In this respect the selection of the year seems as arbitrary as 2020-2021 as the International Year of Sound.  In contrast, I noted several epochal anniversaries being celebrated when 2015 was designated the International Year of Light and Light-based Technologies.  (Wikipedia tells us that in addition to the ones I noted in my post at the time, there were also 1865 and 1965, respectively, anniversaries of Maxwell's electromagnetic theory and the Penzias/Wilson cosmic microwave background discovery.)  Of course 2005 was the World Year of Physics to celebrate the centenary of Einstein's annus mirabilis.  Then 2011 was the International Year of Chemistry, celebrating the 100th anniversary of Marie Curie's Nobel Prize in Chemistry (um. she also won a Nobel in Physics in 1903) as well as the centenary of the International Association of Chemical Societies.

So, in contrast with these various physics-related celebration years, there is no specific anniversary being celebrated by YoM2026, nor is the celebration international.  Even the International Year of Statistics (2013) was a global event, though I am not aware of any particular statistics anniversary being celebrated that year.  Last year's quantum year celebrated, of course, the centenary of Heisenberg's matrix mechanics.

Perhaps the granddaddy of them all was the International Geophysical year in 1957-1957, which Wikipedia tells us traces its heritage the International Polar Years of 1882-1883 and 1932-1933.  However, unlike the more recent celebrations I noted above, the geophysical and polar years featured surges of actual research and international collaboration.  In comparison, the more recent celebratory "years" seem to be largely about outreach and propaganda.

 

Hydrodynamic Quantum Analogs and nonlocality

Last month's SIAM News featured a front-page, above-the-fold article by Prof. John Bush of MIT, "Shifting the Classical-Quantum Boundary:  Insights from Pilot-wave Hydrodynamics".  Among other things, the article challenges the conventional wisdom that quantum theory is inherently and demonstrably nonlocal.  It does so by championing Hydrodynamic Quantum Analogs (HQAs), which are classical analogs of quantum phenomena, using fluid mechanics.  The author uses HQAs to lend credence to the de Broglie-Bohm pilot wave formulation of quantum mechanics.

I have a passing interest in HQAs, regardless of whether they supports alternate interpretations of quantum mechanics, or challenge nonlocality.  I keep an open mind about Bush's assertions, but am neither a cheerleader nor dogmatic opponent of these ideas.  More importantly, I know almost nothing about the field, except what I've learned from Bush's article, and glimpses of other papers in the area (including his) that I've seen over the years.

However I do think Bush does his readers a disservice in the following passage.

The notion of nonlocality, or action at a distance, should be anathema to any rational scientist. Nevertheless, most physicists have made peace with it; they either remain agnostic on the subject or believe it to be an essential, inescapable feature of quantum physics. Because standard quantum theory describes probabilities but not particle dynamics, nonlocality is perceived to be everywhere — in wavefunction collapse, single-particle interference, the quantum mirage, and interaction-free measurement. Correlation at a distance is taken as evidence of action at a distance. HQAs have demonstrated that if we adopt de Broglie’s physical picture of quantum dynamics, we need not invoke nonlocality for any such effects. In short, HQAs suggest that quantum nonlocality is a misinference that is rooted in the incompleteness of quantum theory. While nonlocality is a feature of quantum theory, it need not be a feature of quantum physics.

I've quoted the whole paragraph to ensure that context is provided, but the main problem I have is with the very first sentence of this paragraph.  Should "action at a distance" be "anathema to any rational scientist"?  I am reminded of Bohr's response to Einstein, who said "God does not play dice."  Bohr replied, "Don't tell God what to do."

Newton's original formulation of his gravitational law was manifestly an action-at-a-distance phenomenon.  Yes, it has been superseded by a local field theory, Einstein's general relativity. But is it fair to accuse Newton of not being a "rational scientist"?  (Perhaps so given his interest in alchemy and biblical chronology, but surely not because of his gravity theory!)  What about the 19th century action-at-a-distance rivals to Maxwell's theory (such as Weber's electrodynamics).  Note how Coulomb's law resembles Newton's.  Again, the rival theories were essentially cast aside as incomplete or even wrong once Maxwell's local field theory was fully understood and accepted, but does that make Coulomb, the Webers, and others failures as rational scientists?

Bush gives no citation nor even an argument as to why action at a distance is unworthy of a "rational scientist".  This is because it is nothing more than an opinion, a preference of the author.  He is just offended by the notion of nonlocality in nature.  Offended!

It's okay to be offended.  Such attitudes drive research on the foundations of quantum theory, in defiance of the "shut up and calculate" mentality.  Such research has led to quantum information science, quantum computing, etc.  This is all good stuff!

All I'm saying is that Bush's dictum, that nonlocality should be anathema to rational scientists, is the least persuasive sentence in this article.  The sentence is itself irrational, as it is based on neither reason nor evidence - it is a purely emotional expression as it stands.  And yes I am also making an emotional expression when I condemn it.  

Perhaps there is a good reason that nonlocality should not be considered rational science, and I'm sure other physicists and philosophers have advanced such reasons.  But Bush fails to do so in this article, nor did he cite those who do.  It's nothing but a cheap shot.  In this, he has not served his readers well.

Finally, I realize that it's quite funny that I wrote an entire blog post about one pesky sentence in an otherwise intriguing and informative article :-)

 

"The Grand Design" by Hawking and Mlodinow

I have just finished reading The Grand Design, by Stephen Hawking and Leonard Mlodinow (New York:  Random House).  The book was originally published in 2010, and I acquired a glossy-paged edition in 2013, but it sat on my shelf unread, until a few months ago.  I have been meaning to read it for a long time.  Hawking died in 2018, so this book belongs to the final decade of his career, and I regret not getting to it until long after his passing.

Sadly, since the book was published, both authors (as well as many, many top physicists) have been associated with Jeffrey Epstein.  However as far as can be determined at this time, any allegations of improper or illegal conduct by either Hawking or Mlodinow have not been substantiated.  

On to the book itself.  Much of it is science popularization, and though I am conversant in the more familiar parts of physics exposited, the book did clarify a couple things for me, which I appreciated.  For example, I have often been confused by the use of the term "effective theory" in physics, and the book explained it in layman's terms.

The important point made by the book is a strong endorsement of supersymmetry and M-theory.  On the final page, the authors write that "M-theory is the only candidate for a complete theory of the universe"(italics original).  They also advocate the multiverse concept, and the strong anthropic principle.  Along with these, they present a metaphysical principle, "model-dependent realism", which superficially appears to be a hybrid of instrumentalism and realism.  However, I'm not sure if you can really eat your cake and have it too.  The principle appears to be crafted specifically to accommodate M-theory, which is actually an infinite number of theories, each with its own domain of applicability, though where the domains overlap, the theories make the same predictions.  I don't see what is realist about "model-dependent realism"; it appears to me to be a variant of instrumentalism.

A key passage is this (p. 58):

Regarding the laws that govern the universe, what we can say is this:  There seems to be no single mathematical model or theory that can describe every aspect of the universe.  Instead...there seems to be the network of theories called M-theory.  Each theory in the M-theory network is good at describing phenomena within a certain range.  Wherever their ranges overlap, the various theories in the network agree, so they can all be said to be parts of the same theory.  But no single theory within the network can describe every aspect of the universe--all the forces of nature, the particles that feel those forces, and the framework of space and time in which it all plays out.  Though this situation does not fulfill the traditional physicist's dream of a single unified theory, it is acceptable within the framework of model-dependent realism.

Later, they write (p. 143):  "We seem to be at a critical point in the history of science, in which we must alter our conception of goals and of what makes a physical theory acceptable". 

I am glad that I read this book after I read Jim Baggott's Farewell to Reality, which was published in 2013 (by Pegasus Books), and which I acquired less than a year after acquiring The Grand Design.  I read it within a year, and reviewed it on this blog in 2014.  In the decade since, I think it is fair to say that empirical evidence for supersymmetry has not yet been found, though back then, expectations were high that such evidence would be found within a decade.  This has weakened the case for The Grand Design and strengthened the critique given by Baggott.  Indeed, Baggott uses the phrase "Grand Delusion", which sounds like direct mockery of The Grand Design.  

On balance, reading The Grand Design was not a waste of my time.  It was important for me to know the views of one of the greatest physicists of my lifetime, and I did learn a few things.  However I am doubtful about its main conclusions, though I have a benefit of hindsight -- 15 years of physics progress since the book was published -- to reinforce my doubts.  If you're interested, don't let me stop you from reading The Grand Design, but if you do, do yourself the favor of also reading Baggott's Farewell to Reality in conjunction, to get a more balanced perspective.

 

 

 

The worst year in U.S. science since this blog began

Today I will depart from my usual avoidance of political matters, because of the extraordinary shift in the relationship between the U.S. government and its nation's scientific community this year.  I alluded to certain aspects of it in an earlier post, and I won't give a thorough discussion of the topic here.  Others more eloquent than me have done so elsewhere.  However DTLR cannot end the year without at least acknowledging the shift, for it has affected nearly every corner of the scientific community in the United States.

This blog began in July, 2013; now we are 12.5 years later in a completely different world.  In that time, incredible scientific tragedies were witnessed, such as the global COVID-19 pandemic, and two outbreaks of Highly Pathogenic Avian Influenza (the second, currently ongoing) in North America.  However, thus far, 2025, has been the worst year of all for science, since this blog began.  For we have witnessed the conscious, deliberate choice by the nation's leaders to cripple itself in many ways, including by crippling its scientific community.   Many scientists (including me) have been left in a prolonged state of under- or un-employment as a result.  Others have fled the United States, and many, many talented scientists have chosen not to even come to this country to learn or to work. At the same time, the People's Republic of China has been expanding its investment in science and in scientists, and could not have wished for a better boost for its scientific community than what the United States has voluntarily done to itself.  Investments in science, engineering, technology, and medicine are massive stimuli for a nation's economy, public health, and national security.  In this enterprise, the United States has used 2025 to build up China (including its ruling Communist Party) and weaken itself.  

In the big picture, this is not simply the fault of one particular homegrown party or group of politicians.  Collective blame should be shared with their domestic predecessors/opponents, whose multidimensional failures paved the way for the current regime's election.  Much of the damage will thus be irreversible.  Future leaders of any party will politicize and weaponize elements of "science" at their convenience, and use scientific funding to reward and punish.  The nonpartisan civil service, including its scientists,will never fully recover, and even if someday allowed to pursue its work without interference, will never be trusted by the taxpaying public again.

DTLR does not approve.  

 

 

The women cited in Lamb's Hydrodynamics

I was skimming through the index of the sixth (and final) edition of Horace Lamb's Hydrodynamics (Cambridge University Press,1932), when I stumbled upon the name of "Miss Fawcett".  Later was a "Miss Swain".  And I also found Sophie Kowalewski, a famous female mathematician (better known as Sofya Kovalevskaya, 1850-1891).  These were the only obviously female names I could find in the index.

Let's start with Kovalevskaya.  I knew she had worked in mathematical physics, primarily because of her work on rigid body dynamics and the "Kovalevskaya top", well discussed in Roger Cooke's book about her mathematics (Springer, 1984, Ch. 7).  However Cooke also discusses (Ch. 4) her reformulation of Laplace's model of the rings of Saturn, a self-gravitating liquid annulus.  It is this 1885 paper that Lamb cites in his Art. 376.  It was published in the Astronomische Nachrichten, 111 (3):  38-48.  The first page is reproduced here:

  

Now, who are Miss Fawcett and Miss Swain?  Both were British mathematicians.

Philippa Garrett Fawcett  (1868-1948) was the first woman to achieve the top score at Cambridge University's Mathematical Tripos examinations.  In 1893 she published "Note on the motion of solids in a liquid" in the Quarterly Journal of Pure and Applied Mathematics, 26:  231-258.  Here is the first page:

 

This is the paper cited by Lamb in his Art. 130.

Finally Lorna Mary Swain (1891-1936) is another Cambridge grad, who has two papers cited in Lamb's Hydrodynamics.  The first is a 1915  joint paper with Lamb himself, "On a tidal problem", The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, series 6, 29 (174):  737-744.  (Lamb did not insert his own name into his book's name index.)  Here is the first page of the Lamb and Swain paper:

 

The second is a 1923 paper with Arthur Berry, "On the steady motion of a cylinder through infinite viscous fluid", Proceedings of the Royal Society of London, Series A,102 (719):  776-778.  Lamb cites this in his Art. 339.  Here is what the first page looks like.

 

I find it interesting that both Miss Fawcett and Miss Swain are referred to as such in both the journal articles themselves, and Lamb's book.  

Lamb's monograph is probably the oldest of the "classic" fluid mechanics texts that can still be found on researchers' bookshelves today, thanks to a Cambridge Mathematical Library reprint edition. So it is notable that at least 4 papers by at least 3 female authors/coauthors were cited even in the venerable Lamb.  I also found Ben Franklin in the index as well!

 

 

 

What ails science

DTLR rarely tackles political matters related to current events.  Unfortunately recent years have seen the erosion of public support and trust for science and especially scientists, and this blog cannot completely ignore these trends.

Earlier this month in Science, Megan Ranney (Dean of the School of Public Health at Yale) reviewed a new book by Michael Mann and Peter Hotez, Science Under Siege.  I have not read this book and am not closely familiar with the work of either author, though I did meet Prof. Mann once at a book signing of his.  Since I haven't read the book I won't comment on it.  Instead I'd like to highlight some passages from Dean Ranney's review that I completely agree with.  Among her criticisms of the book, we find this:

It could also have done more to highlight the ways in which science has been undermined from within, such as the rise of poor-quality open-access journals or the publish-or-perish ethos that drives some scientists to unethical behavior.  If we are to restore trust, we must confront the problems within our ranks alongside the far more powerful external threats.   

Not only is the above passage sound in my opinion, the situation is even worse.  Many conventional practices in the sciences that are considered ethical and "normal" are actually traditions of methodological sloppiness.  Examples include HARKing, the winner's curse, the file drawer problem, and the "garden of forking paths" (Gelman and Loken). This has been well documented in Science, Nature, and this blog over its lifetime; for an introduction, see Richard Harris' book, Rigor Mortis.  Scientists need to fix their own house and earn each others' trust before we can expect the general public to support and trust what we are doing.

Moreover, Dean Ranney goes on to say "the book misses the fact that many people are rightfully fed up with the state of the world and that many lump scientists (and science) in with all the other structures that they feel have failed them."  She continues:

People's distrust of science is certainly being fed by bad actors and a vitriolic online culture. But it is also seeded by individuals' and communities' own experience with broken systems.  Think of the opioid epidemic, which resulted from a confluence of not just many of the same factors that Mann and Hotez identify but also the well-meaning recommendations of scientists and doctors; or the need for organizations such as ACT UP...to force access to trials and medications in the early days of the AIDS epidemic.  Populism has always been a strain in American society, and it gets stronger when people feel abandoned.  We will not make progress on antiscience sentiment until we collectively fix the underlying structural issues, for the sake of all.  Nor will we make progress without creating space for everyone to be part of the solution.

In my view, these comments by Dean Ranney deserve to be circulated more widely than in its current form as part of a book review.  Sadly I suspect the wisdom reflected in these words could be ignored by the vast majority of the scientific community, due to lack of awareness. Hence I highlight them here.

Environmental physics in the undergraduate physics curriculum

Earlier this week, the U.K.'s Physics World featured an excellent op-ed by Peter Hughes about environmental physics education.  He noted the importance of the topic, its practical value, and its incredibly wide disciplinary scope.  His definition, for example, is as follows.

Environmental physics is defined as the response of living organisms to their environment within the framework of the physics principles and processes. It examines the interactions within and between the biosphere, the hydrosphere, the cryosphere, the lithosphere, the geosphere and the atmosphere. Stretching from geophysics, meteorology and climate change to renewable energy and remote sensing, it also covers soils and vegetation, the urban and built environment, and the survival of humans and animals in extreme environments. 

He writes mainly from the perspective of the British university system.  One of his conclusions is "I believe a module on environmental physics should be a component of every undergraduate degree as a minimum, ideally having the same weight as quantum or statistical physics or optics."

While the thought is commendable, let's consider some reasons why it might not fly very far in the United States.

First, at many universities there already exist a robust academic ecosystem in the Earth and environmental sciences, with departments spanning soil physics in the school of agriculture, to atmospheric and oceanic sciences, geosciences, hydrology, civil and environmental engineering, and so on.  I live near a university where most of these disciplines have their own departments.  A physics student interested in this topic would be well advised to pick one of these disciplines as a minor or double major.  I personally find the multidiscplinary aspect of these fields to be quite exciting, but the key is to get out of the physics department and work directly with people who are well trained and active in one or more of these fields.

This leads to my second concern, which is that most physics faculty in the United States are ill equipped to teach or do research in any of these fields, with the possible exception of energy-related technologies.  I claim that within academia, environmental physics is primarily carried out by non-physicists (unless geophysicists are included - however, mostly they are found outside academic physics departments). Let's take a basic subject like fluid mechanics, which is essential for meteorology, climatology, and physical oceanography.  Most physicists have never taken a full class in this subject, and would hardly be qualified to teach one, given the outrageous things they teach about fluids in introductory physics classes.  A crowning example of this is the still often taught "explanation" of aerodynamic lift using Bernoulli's equation.  Granted, some physicists do work with fluid mechanics on a daily basis - plasma physicists, some astrophysicists, some condensed matter physicists, for example - but their focus is not necessarily on the aspects of fluids (like rotating frames of reference) relevant to environmental issues.

Third, it is difficult for me to imagine what, from this incredibly wide field of Earth and environmental physics, could be stuffed into a single undergraduate class.  It would end up being highly dependent on the individual professor teaching it.  I don't know if the Brits have managed to create a standardized curriculum for environmental physics.  

I see there are a few U.S. universities that involve their physics departments in environmental physics, but this is still rare here.  Kudos to them.  For the rest, the fastest way to get a program up and running is to partner with the other departments at the university that have been doing environmental physics from their birth.  In the longer run, physics departments would have to start hiring faculty explicitly in environmental physics.  It could take a decade or so to build a strong program, and not all departments would be well positioned to do so, especially given the hostile funding situation for academia currently prevalent in this country.

While I don't foresee environmental physics being on part with quantum physics, statistical physics, and optics, perhaps eventually it could be on par with solid state physics, astrophysics, or other elective physics courses in the undergraduate program.  However it would take a level of effort and commitment that may not be available in this time of shrinking enrollments and disappearing funding.