How the Manuscript Review Process Should Work

The review process provides a level of quality control that insures that published papers are correct and of interest to the scientific community.  Since reviewers are themselves scientists with busy schedules, and being a reviewer provides no compensation aside from the satisfaction of being a good citizen, editors often find it difficult to get the best people for the job.  This has led to an increase in desk rejects by the editor, which avoids wasting reviewers' time on manuscripts that will most likely not be accepted.  The review system is frustrating to all parties involved.

I've been involved on all sides.  As an editor, I took lots of grief from angry authors.  In one case, I got a phone call from an irate author whose paper I had rejected.  He lectured me that as an editor of a prestigious journal decades prior, he would use at least one of the reviewers that the author had recommended.  Why had I not done so?  Because the review process is anonymous, I could not tell him that I used two of the three physicists that he had suggested, and they both recommended that the paper be rejected.  As a compromise, I selected his third choice of reviewer, along with yet another one.  Again, they all rejected the paper.  I could have avoided the next phone call and the indigestion that followed if I would have disclosed the fact that I had chosen at least one of his recommendations.  But I could not.

On another occasion, one of my colleges refused to act as a reviewer on a paper for which he was perfectly suitable.  That same colleague had an issue with one of his papers (not to my journal) where he needed my help, so I used it as leverage to get him to act as a reviewer for me.  There are all sorts of behind-the-scenes dynamics that are not always obvious to authors or reviewers.  The bottom line is that the process is far from perfect, which brings disdain from authors who are unhappy with the results.

I am writing this post to describe an example of a rainbow amidst the storm.

The American Journal of Physics is one of the coolest Physics publications on earth, so I read every monthly issue cover-to-cover.  There are always a few articles in each issue that surprise and delight.  They often point out subtleties in topics that you might think mundane, and bring insights that have been missed by the research community.

Being an author of a couple papers in AJP over the last two years, I have found the review process to be excellent.  The reviewers are knowledgeable and seem to spend lots of time trying to understand the work.  The exchanges are a real learning experience, and all parties are flexible -- admitting mistakes and savoring the process.  Here I describe an example of my experience with a paper that will be appearing in December (here is a link to the preprint).

The editor notified me that my paper had mixed reviews:

"Attached you will find copies of the reviewers' reports on your manuscript "Length as a Paradigm for Understanding the Classical Limit." Though the reports differ in recommendation, it is the content of the reports that is more important than the recommendation per se, and all three reviewers seem to be focusing on the same (or almost the same) issue: The justifiability of your model for what you call length. It will be necessary for you to address this issue in a revision. There are additional detailed corrections and suggestions that should also be carefully in a revision.

If you wish to revise your manuscript along the lines indicated, we would continue its editorial consideration once it has been resubmitted using the procedure indicated on the AJP website. If you do resubmit, please indicate in a single cover letter how you have responded to the various comments of the reviewers. DO NOT send separate replies for each reviewer.

Thank you for your interest in the American Journal of Physics."

The first thing that caught my eye was the fact that this was not the usual form letter used by most journals.  The editor had carefully read the reviews and noticed some common criticisms.  I eagerly dove into my revisions, finding that the reviewers' questions and confusion were the result of deficits in my paper.  I knew what I was trying to say, but my obtuse presentation of the material was only made obvious by their comments.  Most importantly, responding to the reviewers forced me to think more clearly about the physics.  As a result, I gained insights into my own work when making the revisions, increasing substantially the quality of presentation.

Exchange With Reviewers 

Particle in a Box

I will focus here on the common complaint made by all the reviewers, which centered on my use of the particle-in-a-box model.  Here are their complaints:

REVIEWER #1

My only concern is the basic assumption used to model the ``quantum'' systems.  The author is assuming the quantum system is inside a box with hard walls (it uses the infinite well model to derive the wave-function of one electron, and then generalizes it to non-interacting particles).  While this is a simple an intuitive model to work with, it is not clear that the results would carry on with more realistic potentials that might have different boundary conditions. 

REVIEWER #2

In the work, the focus lies on the electrons of a material and the nuclei are taken as a scaffolding for them, which is the usual approach for solid state physics. Yet, the wavefunction for the entire ruler will truly include the atoms as well. I would expect that the length of the ruler as calculated through this procedure will change when including these additional fermions, while I reality the length of the rod will remain the same. If this is so, it would jeopardize the numerical results in this work (although not its method)

REVIEWER #3

It is also strange the definition of the length of an object as the sum of the densities of the electrons confined in that potential, like the example of the particle in the box. The length of a real material should depend on the properties of the nuclei as well as of the electrons.

My Response:

Since all the reviewers brought up a similar point, I responded to them as a group.  Here is the verbatim response:

We interact with materials either by looking at them with our eyes (light scattering from electrons) or touching them (repulsion between electrons in the material and within us).  I believe that we all would agree that what we ``see" are the electrons, though their density does indeed depend on the presence of the nucleons.  So two materials with the same electron density but different nuclear positions would appear the same.  The mass, of course, is dominated by the nucleons, but we are viewing/touching the electrons when determining the length.  The length would be different if we did scattering experiments that are tuned to only probe the nucleons, but on the scale of human senses, we see only the electrons.  In either case, the lengths determined in these two ways would be similar for multi-atom quantum systems.

The positions of the nucleons are well represented by the Born-Oppenheimer Approximation, where the nuclear equilibrium positions are determined by the configuration with the lowest total energy.  Some of the electrons are involved in stabilizing the system -- which can be viewed as chemical bonds -- and in materials such as metals, the rest of the electrons are delocalized over the bulk material.  In the absence of defects, bulk metals appear smooth so each conduction electron moves approximately freely within the metal and encounters a large barrier at the edges.

This picture roughly holds for all materials and uniform electron densities are found is a variety of systems with delocalized electrons modeled by particles in a box.  These include small molecules such as the polyenes, as modeled by Kuhn in the 1940s, to metals as described in solid state textbooks, to nanoparticles that straddle the classical/quantum divide as recently reported by Scholl.

I would thus argue that the particle in a box is a good model that roughly holds well for many systems.  Much more sophistication is required to deal with the nuances.  I therefore believe that using the particle in a box model contains the correct physics that is assessable to a student.   Taking into account the reviewers' comments to explain this to the reader, I have added a third paragraph to Section III.A that reads:
 

"Models of materials with non-interacting electrons in a box roughly predict the electronic properties of small molecules such as the molecular class of polyenes,\cite{kuhn48.01} describe metals as found in solid state textbooks\cite{OpenStax20.01} and accurately portray the quantum to classical transition of nano-particles.\cite{schol12.01}  This shows that the effect of the nucleons on the electrons can be roughly taken into account with a box that confines the elections within.  We will thus model typical materials with uniform electron density as non-interacting electrons in a box.  The reader should keep in mind that this is a first step in modelling materials in which electrons are delocalized.  Later we treat materials made of such units that are ``pressed" together.  Then, the electrons are localized within domains rather than over the full material.  For simplicity, we will treat only one-dimensional systems.  Other potentials can be treated in the same way, but this exercise does not result in significant-enough insights about length itself  to make it worthwhile to treat in this paper."

The reviewers we satisfied with my response.  Here are excerpts from their second set of comments:

REVIEWER #2 - Second Response

I'm particularly satisfied with the argument to not include the
nucleons in the the total wavefunction. I've learned a new insight
here, using the Born-Oppenheimer approximation. Also, I think the
added paragraphs to section III add to the quality of the story.

REVIEWER #3 - Second Response

The author presented an improved manuscript that discusses the
difficult concept of quantum length. The language in the response
and the changes in the text greatly improved the manuscript.

Definition of Length

REVIEWER #3

This reviewer thought that my paper was wrong and should be rejected on the basis that I defined the length in a certain way that was arbitrary.  In the reviewer's own words:

It is my opinion that the manuscript is not technically correct as it starts with the definition of length of rod in terms of its uncertainty in the position.

 

The reviewer continues with technical details.  This comment led me to see that I was unclear in my presentation.  I responded with:

Your major criticism of this manuscript is with the ``definition of the length" and your argument against this definition is based on the fact that the coefficient $\sqrt{12}$ would change if the material were not uniform.  The original version treated only the uniform classical rod as the length element.  In the revised manuscript, an appendix describes how a non-uniform classical rod is treated, and is referred to in the main text.  Your argument is analogous to stating that the Pythagorean theorem can't be right because the expression would depend on the shape of the curve along the hypotenuse.  As with Pythagoras, where the length of the curve is obtained by dividing it into infinitesimal straight sections, so too the classical length is computed as the sum over uniform segments.  In retrospect, the original manuscript did a horrible job by neglecting this description.  I believe that using an appendix eliminates confusion yet maintains the flow of the narrative.

I have also added a couple paragraphs, as described above in the general section, which argues for the ansatz for the quantum length, a regime where it is no longer possible to subdivide a material without changing its properties.  I hope that these two major revisions remove confusion and makes you comfortable with the length expression that results from applying translational invariance and classical correspondence.

 

In response to my revisions, the reviewer adds: 

 

The added appendix lets the reader know that there are other
definitions that would converge to the proper classical limit. I
would like to see incorporated in the beginning of manuscript the
statement that the author made about how theories are developed.
This would be very helpful for the readership to explain how one
should approach making comparisons between new theories and their
classical limits. Incorporating these ideas on someone’s teaching
can help students navigate phenomena they are seeing for the first
time while relating them to things they are familiar with. These
ideas are incorporated in the Lessons Learned section, however,
helping the reader have this framework at the beginning of the
manuscript can guide the reader on understanding the assumptions
made, the development of the concepts, and finally understanding
the conclusions in the end.


It is my opinion that the manuscript might be published in the
present form, but it can still be improved by incorporating the
four points on theory developed in the introduction:


1. Setting the physical constraints. Here the length is required to
be translationally invariant and to give the correct classical
result.

2. Choosing the simplest ansatz that meets the constraints. The
uncertainty happens to meet the translational invariance criteria
but the length is NOT ad hoc defined as the uncertainty.

3. Demanding that the quantum theory in the classical limit gives
the classical result. Here, the quantum length and classical length
converge in the many-particle limit and for one particle in the
limit of it occupying the highest-energy state.

4. Investigating the Consequences. Here we apply the ansatz to
rulers and measurement.

In addition to being satisfied with my revisions, my comments to the reviewer led them to conclude that the response I had directed at the reviewer in my rebuttal was so useful that it should be added to the paper.  This was a great idea, and an example of what I was thinking when I was writing the paper, but something that I had not verbalized. This gave me the opportunity to carefully craft  what I think is an important takeaway message of my paper.

Conclusion

There are many other useful exchanges with the reviewers that would take too much time to summarize here and would add too much length to this post.  So instead, I have uploaded all the files with the reviewers' comments and my responses, to which I provide links below.  The end result is that I got great advice, which led to a much better paper not only in the presentation style, but in substantive additions to the content.  More importantly, I feel a deep kinship with these reviewers, who bared their minds to me in a frank dialog that gave me a more nuanced understanding of the topic.  I am indebted to these individuals who sacrificed their valuable time without compensation, other than to savor the satisfaction of learning about and understanding the subtleties of our world.

• Link to the reviewers' comments, my reply and their final comments.  Click here for the folder.
• Here is a link to the final version of the paper, which is scheduled to appear in December.

Quantity, quality and language

I write more for myself than for an audience. The act of writing flushes out ideas and provides a record of what I was thinking so that I do not spend time reinventing the wheel (by wheel, I mean my personal wheel, not new ideas to the world, which I am sure are few). Sadly, I often get hot about an idea, start writing about it, and then get too busy with other things to finish. As a result, my ideas are lost.

I spend a few minutes every few months erasing incomplete posts. Today, while I was clearing several such posts, I pondered about the wasted effort of the process and the added entropy to the universe each time I hit "delete." So, I decided to share this one with myself and anyone else who cares to read it.

To place the state of my mind in perspective, I was writing this post in the first half of August, 2011, just before the start of the semester, when I was slated to teach Classical Mechanics. I recall being excited about my insights on the topic, but sadly, I no longer recall the punchline. Perhaps one of you can help me out.

Here it is:

Language is often inadequate to describe what we are feeling. A far greater problem is that language permits imprecision and inconstancy. As a result, we are falsely lulled into a sense of meaning when there is none.

The classic example of self contradiction is the sentence: "This sentence is false." We can reject this construction for obvious reasons. However, consider the statement, "His action was immoral." The first three words are well defined, but the last is not.

At issue is the fact that many concepts in language are based on subjective feelings, that when assigned a word, may be imprecise or nonsensical yet carry an absolute sense of its existence. When analyzed dispassionately, we can surmise that the sense of morality is an inbred feeling that was shaped by evolution, and helped the survival of our species. Thus, when someone cheats, our sense of distaste stems from our collective disapproval of behaviors that weaken the group.

However, our gut assigns to the concept of morality a sense of absoluteness of "right" and "wrong" of actions - two additional words of the same ilk. Morality is thus elevated to an absolute standard that cannot be questioned. It is wrong for women to vote. Why? Because it is an absolute, and absolutes cannot be questioned. Thus, the sense of morality can lead to concepts such as women being mere property to serve at the pleasure of men, homosexuality as an evil, drawing a cartoon of certain individuals an objectionable action deserving of death, etc.

One may argue that without an absolute morality, humans would be lost and unable to decide what is right. Humans have been making the "right" decisions for ages without religion; but, this is not the point of this post. Instead, I want to speak about a different kind of language that does not suffer through the same pitfalls; but ironically, is responsible for the development of imprecise language; and that is, mathematics.

One of the earliest incarnations of mathematics was counting. Shepherds wanted to make sure that all their flock was accounted for by the end of the day. The simple act of counting may seem trivial and lack meaning. As it turns out, it is the basis for everything.

Mathematics became more sophisticated with the introduction of multiplication, which is the act of counting groups of groups of things. Three families of four make twelve people. Division is then the inverse of multiplication as is subtraction to addition. Aside from keeping track of cattle and assigning value to property, mathematics in this guise appears devoid of any deep meaning.

But, mathematics progressed. Variables were introduced to assign unknown quantities, functions to describe relationships between variables, etc. The growth of mathematical structure grew hand in hand with applications. Exponential functions could be used to describe the growth of livestock, the degree of hotness was associated with temperature, etc.

Then operations on functions were introduced. Derivatives gave slopes of curves and integration, the reverse of a derivative, yields the area under the curve. It was a stroke of intense insight when someone recognized that numbers associated with various physical quantities behaved in correspondence with what the operations predicted. This is a subtle point that deserves more - later.

Then came abstract mathematics that deals with groups theory, linear algebra, differential geometry. Even these seemingly non-practical concepts describe things such as the curvature of space-time, that governs the the motion of spacecraft and makes the GPS system possible, and predicts the groupings of elementary particles.

All of this leads to the obvious conclusion that there is no dichotomy between quantity and quality. Quality is in fact described in terms of quantity.

For example, we may say that gold has the qualities of being soft, yellowish, and shiny. Silver, on the other hand, is harder, greyish or some would say colorless, is shiny and half as dense as gold. As it turns out, the difference between the two atoms is in the numbers of protons, neutrons and electrons. Silver has 47 protons in a tiny nucleus and 47 orbiting electrons Gold, on the other hand, has 79 protons and 79 electrons (we ignore the neutrons since they don't affect an atom's chemical properties). It is the number of electrons and protons that determines the quality of the material. Thus quantity determines quality.

The numbers of various atoms in a molecule determine its properties. As we go up the later and make complex molecules, cells, organs, people, communities, and the universe, the properties of each object is determined by numbers that quantify the underlying things.

I have failed to mention forces, which determine how matter "sticks" together. The forces, which behave according to simple laws, determine the structures of molecules, galaxies, and nuclei. The simple laws that describe forces are formulated in terms of equations that represent numbers. So there are numbers everywhere that determine the quality of things.

However, the macroscopic universe is so complex, that it is difficult on human scales to express its properties in terms of the numbers that quantify the smallest units. This is where it is easier to think in terms of quality. You would prefer to think of your winter coat as warm and cozy rather than describe it in terms of the thermal conductivity of its parts, the chemical reactions in your body that create heat, etc.

-- This is where my post ends, with typos and incomplete thoughts. Perhaps someone can figure out what I had in mind. If so, please send me a note.

The amazing world of numbers

The other day, I was trying to get straight the words for the numbers in Italian. While our counting system maintains a strict pattern, the words representing them are irregular. The exceptions to the regularity got me thinking about how number systems developed from primitive times. As a good scientist, I will first propose my hypothesis without looking at the history books, though I admit having some knowledge on the topic.

Consider the necessity of counting to the Shepard while letting his flock out into the field and needing to know if any are missing at the end of the day. The Sheppard added a stone to a pile for each sheep going out into the field and then removed a stone for each returning one. If a stone remained, the Shepard knew that a sheep had gone missing. In addition to being a practical counting technique, this procedure established the one-two-one correspondence between two sets of objects with the same number of elements. From a physicists point of view, one could say that this also established the principle of conservation of stones and conservation of sheep. Their numbers did not change, they just moved about from one location to another.

To solve the issue with proliferating sheep and shortages of stones, the Shepard recognized that he could use a different type of stone to represent, let's say 10, sheep. Thus, after the ninth stone was placed on the pile, the tenth sheep would be represented by the single 10-sheep stone while removing the previous nine. An extra stone would again represent each additional sheep until the 20th, at which point the next 10-sheep stone was used. Later, it became apparent that one need not use a special stone representing 10 sheep. Rather, one could place a stone in a different spot. Thus evolved the base 10 system, with separate symbols, or numerals representing one to ten, with these same numerals representing tens when placed in the tens spot, etc.

The "base" 10 number system most likely originated because of the ready availability of 10 fingers. I find it interesting that the word for finger and number shares the word "digit."

Other bases are also possible. When we were in Italy, I was at first puzzled at the system of Roman numerals engraved into the ancient buildings, which differ from what we commonly refer to as roman numerals today. For example, the modern form IV was represented as IIII and what we would recognizes as IX was written as VIIII. This even carried over to larger numbers, such as CD which they wrote as CCCC. Clearly, the original form of the Roman numeral system seemed to suggest base 5, as one would expect from counting on the fingers of one hand.

Now back to Italian. The pattern from zero to nine is as one would expect for base ten, with unique names corresponding to each numeral. Above dieci (ten), the system becomes schizophrenic. Undici (for eleven) seems to be saying one and ten, but quindici (for fifteen) is irregular in the sense that it is not a compound form of dieci and cinque (five). After Sedici (sixteen), the pattern reverses to diciassette, diciotto, diciannove, etc. Interestingly, the naming pattern for 20 and above continues along a strict convention without exception. Happily, 50 is cinquanta not quinquanta as I would have expected given the expression for 15. This pattern suggests an original base 16, or perhaps 15 with origins in the Roman base 5 system, which later got fixed to be consistent with base 10 convention. Whatever the case, the words hint at a mixture of systems.

Words and grammar can carry secret messages from the past. Ideas that were once imbedded in peoples' minds crept into language and became firmly rooted once it was formalized into written form. Thus, what remains today in any language language provides a snapshot of common usage from the past, which reflects the understanding of those times.

I was excited the morning that these ideas raced through my mind. I then thought about numbers in different languages. The words for the numbers in English are distinct until thirteen, which takes the form of three and ten, etc. Could this show the remnant of a base 12?. This seemed plausible, given the fact that some units of time (12 hours representing half a day and 12 months making a year) seem to have a preference for 12. And don't forget 12 inches to a foot.

I then rattled off the numbers in Ukrainian. It was purely base ten. I had taken French in high school and some in college, but my French got totally erased when I started to learn Italian (except for the time that French got mixed in with my Italian when I said to a French colleague while in Italy "qualchechosa," a hybrid of "qualcosa" (Italian) and "quelque chose" (French)). So, I asked my wife to remind me of how to count to twenty, and the pattern turns out to be the same as in Italian!

Stones may correspond to sheep, but how does one deal with fluids? This is an important quantity when bartering in liquids (as in ordering a beer). At some point, humans must have recognized that liquids are conserved. In other words, they can be moved around and split into smaller amounts, but when recombined, the quantity fills the original container in the same amount.

In the case of liquids and weights, there appears to be a preference for base 2, which makes sense given the ease with which we can split liquids in half over and over again. There are 2 cups to a pint, 2 pints to a quart, 2 quarts to a half gallon, and two half gallons to the gallon. Also, there are 8 ounces to a cup and a pint is 16 ounces (base 16!). And don't forget 16 ounces to a pound. The relationship between weight (or more precisely mass) and volume is clear. 16 ounces of water or beer weighs 16 ounces, or one pint weighs a pound. No wonder!

The birth of the decimal Metric System (base ten) coincided with the French Revolution, when two platinum standards representing the meter and the kilogram were deposited in the Archives de la République in Paris, on 22 June 1799. This was the first step in the development of the present International System of Units, in which the basic units of distance, mass, time and current are the meter, kilogram, second and ampere, respectively.

For convenience, modern day computers use binary, or base two: ones and zeros are easily representable with the gate of a transistor being on (1) or off (0). For programing convenience, the bits (binary digits) are combined into groups of 4 leading to a hexadecimal representation (base 16), where two hexadecimal "digits" can represent the numbers 0 through 255. As such, pairs of hexadecimal numerals are used to describe the alphabet (upper and lower case) the ten base 10 numerals, as well a bunch of special symbols.

The simple act of counting eventually led to the transformation of primitive society into one that can understand the mysteries of nature, which since antiquity had been thought incomprehensible in the absence of deities. Our language, on the other hand, provides clues of the thought processes that went into the development of counting, which forms the basis of mathematics, physics, the sciences, engineering and technology - historically following approximately that order.

After writing this post, I searched Wikipedia for additional information on various bases used by various civilizations in various eras. In the third millennium BCE, the Summarians used a base 60 numeral system, called the sexagesimal system. The symbols used are shown to the right. Incidentally, our system of 60 seconds to the minute and sixty minutes are -- you got it, base 60! But so are angular measurements. There are 60 arc minutes in a degree, and sixty arc seconds in an arc minute. This connection makes sense given that the timing of the sun's apparent motion in the sky is measured as a change in angle over a change in time period.

It is obvious how the base 5, 10, and 20 systems follow from counting with fingers and toes. Thus while the sexagesimal system is base 60, the symbols follow a base 10 pattern. However, an advantage of base 60 is that 60 has a large number of factors (1,2,3,4,5,... you can determine the rest) so that fractions are easier to represent.

According to the Wikipedia article on base 10, peoples using other bases are as follows:

• Pre-Columbian Mesoamerican cultures such as the Maya used a base-20 system (using all twenty fingers and toes).
• The Babylonians used a combination of decimal with base 60.
• Many or all of the Chumashan languages originally used a base-4 counting system, in which the names for numbers were structured according to multiples of 4 and 16.
• Many languages use quinary number systems, including Gumatj, NunggubuyuKuurn Kopan Noot and Saraveca. Of these, Gumatj is the only true 5–25 language known, in which 25 is the higher group of 5.
• Some Nigerians use base-12 systems
• The Huli language of Papua New Guinea is reported to have base-15 numbers. Ngui means 15, ngui ki means 15×2 = 30, and ngui ngui means 15×15 = 225.
• Umbu-Ungu, also known as Kakoli, is reported to have base-24 numbers. Tokapu means 24, tokapu talu means 24×2 = 48, and tokapu tokapu means 24×24 = 576.
• Ngiti is reported to have a base-32 number system with base-4 cycles.

So, what became an innocent language lesson on the numbers led to a train of thought that occupied my mind for a morning and gave me the satisfaction of understanding something that was new to me. The fact that I had not learned something new to the world did not bother me a bit.

With all this numerology and talk of ancient number systems, am I worried about 2012? What do you think?

I am finishing this post after our traditional zillion-course Ukrainian Christmas dinner, followed by a glass of eggnog and countless chocolate-covered pretzels, so errors in my logic are undoubtedly plentiful. No apologies!

I wish all of you the best that the holiday season has to offer. Given the international nature of my handful of regular readers, I would be interested in hearing about how you form the words for the numbers in your native languages, and at what point if any, they are irregular. In the meantime, I will be sipping on another eggnog. Good night!