Counting to 41,044,208,702,632,496,804 and beyond...

Counting is a rather simple thing. You increment a given number by one just like in the journey of one thousand miles you take a step and repeat. Trouble is knowing when to stop. Ultra runners might not stop until they get to 100 miles (about 180,00 steps), but few will be able to tell you exactly how many steps they took. It's just too annoying to keep the count up and enjoy the view. Regardless, this gives us a good estimate of how high a person might be able to count in a day (if they count really fast). To get to the number in the title, it would take such a person over 600 billion years...

Now consider how long it would take to count the number of possible distinct non-recrossing paths following the edges of a square between the opposing corners along a diagonal. That's two, and it takes you less than a second. Suppose that you make it a two by two square. The number of possible distinct non-recrossing paths now comes up to 12. You might then ask about a 3 by 3 square or larger. Or maybe not as that might seem a little too mathematical. Dr. Minato and his colleagues followed this train of thought and made a YouTube video to illustrate how quickly the count grows. It's in Japanese with English subtitles and already has well over a million page views!

While this is a very fundamental question, it's useful to recognize that knowing how to count paths (particularly using Minato's clever algorithms) on an arbitrary network has lots of cool applications. Among these could be the determination of the sum of chemical pathways between reactants and products. That's the problem that I'm interested in, but it's a little harder because each path has a different weight (or cost.) The cost isn't necessarily the same for each of Minato's subsets and consequently it isn't trivial to reuse his existing algorithms. But here lies a challenge to a possible advance in the field of chemical physics.

Check out "The Art of 10^64 -Understanding Vastness-Time with class! Let's count!" on YouTube.

6. The blurring of physical chemistry and chemical physics

In 1980, Mostafa El-Sayed took over the Journal of Physical Chemistry. Because of the mistakes of his early predecessors in confining the physical chemistry they published to thermodynamics, the Journal of Physical Chemistry had been regulated to a second tier status. Mostafa quickly turned this around by simply asking all his friends to submit articles to the Journal. It helped that he had a lot of smart friends, and that they were spread through the entirety of the interdisciplinary space between chemistry and physics. That is, physical chemistry as codified by the eponymous ACS journal was finally redefined to include all physics, not just thermodynamics. Mostafa's drive to resuscitate the Journal of Physical Chemistry was also helped by the fact that the Journal of Chemical Physics had also ignored a critical part of the field. In the latter's drive to be increasingly rigorous, there was little room for phenomenological papers in which nature was not fully understood. Putting this together over the 24 years that Mostafa was at the helm (which also included his move from UCLA to Georgia Tech!), he succeeded in raising the Journal of Physical Chemistry to the top tier status it enjoys today.

The road between chemistry and physics has two lanes. One of these heads from chemistry to physics. Call it physical chemistry. The other lane heads from physics to chemistry. Call it chemical physics. But the road is the same road. As such, there truly is little difference between the names. However, there is a subtle difference due to the fact that each is pointing in a different direction. Chemistry has historically been an empirical science over which principles are constructed. Physics has historically been driven by axiomatic principles that give rise to the nature that we see. In likewise fashion, the Journal of Physical Chemistry has always tended to publish a slightly greater portion of phenomenonolgical results, that in turn have practical implications in advancing the field. Meanwhile the Journal of Chemical Physics tends to publish a slightly greater proportion of theoretical results and precise measurements, that in turn have implications on advancing fundamental principles. But both are moving towards the middle. As such, even these subtle differences should soon be lost (if they haven't already).

A different journal run by the Royal Society of Chemistry replaced the Faraday Transactions and formalized the blurring between the two names by simply naming itself as Physical Chemistry Chemical Physics (PCCP) in 1999. There is evidently plenty of room for us to publish our work. More importantly, the true meaning of physical chemistry and chemical physics is fundamentally the same and truly lies on a one-lane road between chemistry and physics.


(This is the sixth and last post in a series starting with the first one on interdisciplinary sciences.
Click here for the previous post.)

5. Chemical Physics: The rise of quantum mechanics

In the 1920's, along came an entirely new physics, quantum mechanics. It's clearly not classical and it takes some effort to connect it to thermodynamics. Nevertheless there were chemists who saw the potential of this new physics in describing chemical processes. The trouble was that such papers couldn't be published in the Journal of Physical Chemistry. The editor of the time, Wilder Bancroft, limited physical chemistry to only that which used thermodynamics. This mistake would unfortunately last until roughly 1980. In the meantime, the community found a different solution in the founding of the American Institute of Physics (AIP) Journal of Chemical Physics in 1933. Thus was defined the new interdiscplinary field of chemical physics as that science which utilizes physics—the more rigorously the better—to chemical processes.

So in the mid twentieth century, we had a subtle distinction between physical chemistry and chemical physics. It was made concrete according to which of the two American journals you chose to publish your work. Physical chemists who wanted to go beyond the confines of thermodynamics had to turn to the physics community. The amount of chemistry that physical chemists needed to learn and teach made it difficult for them to fulfill the complete physics undergraduate curriculum or pursue doctoral degrees in physics. So where was a physical chemist/chemical physicist to teach? In practice, the answer was chemistry departments in the States, but often physics departments in Europe or other parts of the world. This gave root to yet another distinction between the names. To put it simply, you did physical chemistry in chemistry departments and chemical physics in physics departments. (Students went to both.) Of course, the distinction was in name only because most of the practitioners could easily transfer their appointments between the respective departments. Indeed, several of the editors of the Journal of Chemical Physics have held appointments in chemistry departments. The irony here is that physical chemistry become a core component of chemistry curricula when the subject is interpreted to have the scope of chemical physics.


(This is the fifth post in a series starting with the first one on interdisciplinary sciences.
Click here for the previous post.)

2. What's in a name? At the crossroads between chemistry and physics

In the 1700's, a dramatic paradigm shift was brewing in the chemical sciences. Until then, chemistry had been part art and part taxonomy. The question was whether one could make sense of it all based on fundamental principles about the substances themselves. (We didn't quite yet know that substances were made of tiny building blocks, namely atoms.) Or to put it bluntly, is there an underlying physics to chemistry? Thus physical chemistry (or is it chemical physics?) was born as an interdisciplinary science. It's now a part of the core of the discipline of chemistry. It is also a popular node in the web science in which the interdisciplinary sciences act as the links.

The interdisciplinary field lying between chemistry and physics took hold in the late 19th century. Ostwald recognized the power of the new physics of the day—thermodynamics—to help make sense of the energetics or molecular motions and reactions. Thus was born the field of physical chemistry, and the eponymous journal within the American Chemical Society. The trouble is that when new physics—such as quantum mechanics—came along, the editor of the Journal of Physical Chemistry at the time wasn't ready to accept it. This led to the rather odd definition of physical chemistry as being limited to the thermodynamics of chemical processes. This, in turn, necessitated the definition of a new interdisciplinary field, chemical physics, which included the use of all physics (even thermodynamics) to understand chemical processes. As the corresponding eponymous journal was subsumed under the umbrella of the American Institute of Physics, some chemists (though not most) did not make the jump to chemical physics. This, in turn, led the Journal of Physical Chemistry to focus on topics in the middle of the 20th century with decreasing relevance. (Fortunately this misdirection did not persist, and the happy ending is coming soon!) Meanwhile, the name confusion continues to recur as students routinely ask me what exactly is the difference between chemical physics and physical chemistry today. My answer to the question follows in the posts to come!

(Note that this is the second post in a series. Click here for the previous post.)

1. Interdisciplinarity is a buzzword in science, but how modern is it?

Everywhere you look, it seems that we are talking about new paradigms in science. Among the various disruptive forces, "interdisciplinarity" (or perhaps we should call it multidisciplinarity?) appears to be ever present. It certainly seems modern to be thinking about the breaking down of disciplines. Presumably, our students must learn new tools from each of the disciplines and thereby advance science in ways that the current dogma cannot. But would you be surprised if I were to bring up such a movement from the 1800's? How modern would that be?! Or perhaps, the current movements are actually post-modern in the sense that interdisciplinary sciences are a return to the beginning when science was but a single unified whole?

In the (post)modern science at the turn of the 21st century, the fundamental problems confronting us appear to require a new breed of scientist: interdisciplinary scientists who act as connectors between distant fields. Examples include so-called energy scientists, environmental scientists and data scientists. It has also driven the construction of institutes or buildings, such as the Molecular Sciences and Engineering Building where I work at Georgia Tech, that collocates students and practitioners in order to advance interdisciplinary research. The story of the development of physical chemistry coined around 1752 by Mikhail Lomonosov and taking root in the late 19th century doesn't diminish the value of these recent interdisciplinary threads in science. Rather, it is but one of the many examples in which the development of ties between existing disciplines—chemistry and physics in the case of physical chemistry—has led to major advances in the sciences. Thus interdisciplinary sciences are not a modern fad. History tells us that their growth has been a critical part of the practice of advancing science all along. In a short series of posts, I plan to summarize how the development of this emergent field had dramatic impacts on the practice of its science.