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Thesis Appendix: Rotational Spectroscopy Primer

First Published: 2024 January 15

Draft 2

b]

There are any number of texts which derive and define rotational spectroscopy from first principles.1 The goal of this work is not to produce a thorough and mathematically rigorous derivation of rotational energy and transitions, but instead to provide a high level overview of the concepts and ideas which underlie this thesis. Rotational spectroscopy probes the lowest energy of the quantized transitions in a molecule. Most texts which derive rotational spectroscopy begin with the simplest case: a diatomic2 molecule. These molecules have a simple and algebraic3 expression for both the energy of a given level and the energy of transitions between the levels. There are also fairly rigorous rules for what transitions are “allowed.”4 From there, the texts will move to the more difficult cases of a general linear molecule5 , a planar molecule6 , a spherical top, and then the two forms of a symmetric top: oblate and prolate. Only then will the texts get to the solution for the most common problems faced by spectroscopists: asymmetric tops.

One benefit of deriving spectroscopy in that manner is that certain assumptions and simplifications seem more sensible when presented in those orders. However, as mentioned, this is not a rigorous treatment, and so hand waves will be needed. First, what is a molecule?

A molecule, in rotational spectroscopy, at least, is something which meets two criteria: it is comprised of specific atoms7 arranged in a specific pattern.8 What can we do with that knowledge? First, we must assume that the molecule rotates completely rigidly. That is, the energy we apply to it does not change the structure at all, and rotational energy is completely separable from vibrational energy.10 Once we have done so, however, we can simplify the problem significantly.

A molecule can have any arbitrary number of atoms any arbitrary distance apart from one another.11 Since we would like our solution to be generally useful, rather than starting from the beginning for each molecule, we then define an axis through which we hit the greatest mass of nuclei.12 This axis is known as C. We then pick the axis orthogonal to this which contains the greatest mass of nuclei that we can still reach, B. At this point, there is a single axis remaining: A.

Once we have our molecule arranged in these axes, we reduce it to a three dimensional object by taking its reduced mass. That is, we look at the distance each atom has from each axis and multiply it by the mass of the atom, then sum over the entire molecule.13 We do the same with the expected position of the electrons, and this gives us the dipole in each direction.14 The dipoles are only relevant as a scaling factor for the expected magnitude of a rotational transition.

Having now reduced our molecule to three moments of inertia, we can define the rotational constants, which are simply the inverse of the moments of inertia.15 You may notice that A is definitionally smaller or equal to B and the same for C. When B is equal to A or C, we can treat the molecule as a symmetric top, which has a general analytic solution. If none of the constants are equal, however, we can only solve for the energy in matrix form.

What does it mean to solve for the energy of a molecule in matrix form? Tl;dr, there are three diagonals that we fill in, and the quantum numbers are only vaguely meaningful anymore.16 Along the main diagonal, the matrix adds a minus E. When setting the determinant to 0, you can solve for E. It turns out that every rotational level J has 2J+1 energy levels available.17 Because the matrix can be rearranged into a tridiagonal matrix, the solution is far faster.

In general, the rotational energies of a molecule are almost never solved for symbolically. There are a variety of reasons for this, most of which come down to the redundancy of doing so. Solving a numeric matrix is something that computers are famously optimized for, and A B and C can be at least roughly estimated given a molecule.

Of course, even slight errors in calculating A, B, or C will result in lines being shifted from their predicted locations. The goal of fitting a spectrum, then, takes a guess for A, B, and C and a known spectrum of the molecule, and forces the two together. In general, the constants can be predicted with fairly high accuracy using modern computational methods.

Of course, the earlier assumption about rigid rotors is not entirely accurate. Those familiar with vibrational spectroscopy may be aware of the harmonic approximation used in that spectroscopy. As most rotational transitions have been historically assigned within the ground vibrational state of molecules, quartic distortions, which account for the quadratic shape of the energy well, are often needed. In fact, as Gordy and Cook note18 , by solving for quartic distortion terms, the slope of the well can be found. As higher energy transitions and higher sensitivity instruments are used, corrections to the quadratic well can be added, though only on even powered terms.19 Add in a few selection rules, and tada you have rotational spectroscopy.

1 Bernath, Gordy and Cook, etc. etc. etc

2 and therefore inherently linear. There are so many ways to prove that any two points can be connected with a single line, and given the whole “this is not meant to be mathematically rigorous”, it is left as an exercise to the reader to prove that the molecule is linear

3 meaning you can write one expression once for all values that the energy can take

4 scare quotes because forbidden transitions still occur. In much of astrochemistry, the forbidden transitions are actually the most easily detected

5 there are an infinite number of ways you can construct a line from any number of atoms in a molecule

6 two dimensions! Spicy. Also yes, we will ignore the fact that these molecules are not infinitely thin, and so are never inherently linear or planar

7 the fungibility of atoms will not be discussed in detail here, but isotopes and other charge differences are actually relevant, which sometimes throws people off

8 that is, structural isomers9 or even different shapes of the same molecule will have different rotational spectra

9 molecules with the same atoms bonded differently together

10 that is an assumption we do correct for later, but note that it is a correction, rather than an actual solution

11 there is a question about how well rigid rotor approximation would work on like HeH+ infinitely far apart, but if you assume rigid rotor, it does work, I suppose

12 again, this is not rigorous, but trust that it works

13 it feels like a centered molecule should have 0, but it turns out that we do not end up with that, which is pretty dang cool. There might also be a square somewhere, distance rather than just displacement, but I’m not being rigorous at this point

14 wow look at that handwave. what do we mean by expected position of an electron and everyything else I said? ask ur chem prof bruh

15 give or take some scaling factors

16 this is way too handwavey, but it’s getting to be bed time and I want to just post this more than I want to get through this rigorously right now

17 oof i need to discuss that in way more detail later

18 double check that it’s actually them ofc

19 i think that this might be too handwavey. Should read again in the morning, even though I know that I probably wont

Draft 1

a] Rotational transitions are the lowest energy of the quantized ways that a molecule can absorb and emit energy. There is probably more to say about that, but I don’t have the energy to do so right now.

There are any number of texts which derive and define the way that rotational spectroscopy works1 , and the goal of this work is not to go through a thorough and mathematically rigorous definition of a Hamiltonian, let alone a rotational Hamiltonian. Instead, the goal of this appendix2 is to provide a high level overview of how to conceptualize the contents necessary to understanding most of this text. So, we can begin by demystifying the opening sentence: “rotational transitions are the lowest energy of quantized ways that a molecule can absorb and emit energy”. What does that mean?

Rotational transitions are more or less what they sound like. A molecule is rotating at one speed, and then it starts rotating at another. Unlike a bike wheel, however, the speeds that a molecule can rotate at are not continuous. That is, a molecule can only be rotating at very specific energies (quantized).

It is the lowest energy of these quantized transitions, which implies the existence of other transitions. There are, indeed, other molecular transitions: vibrational and electronic. Electronic transitions will not be covered at all in this work, and vibrational transitions will only be covered as necessary to explain breakdowns in the standard rotational model. However, claiming that rotational transitions are the lowest energy of quantized ways, that implies that there is at least one way for a molecule to absorb and emit energy that is not quantized. And, indeed, we find that molecules3 can move at any arbitrary speed, using translational motion.

What do we mean by a molecule? Now, there are any number of ways to define a molecule. There is the classic reductionist view popular among physicists and physical chemists: a molecule is a collection of atoms bound together by different forces.4 There is the opposite view, from an observational perspective: a molecule is the smallest unit that a thing can have. That is, although molecules are made of atoms, breaking molecules fundamentally means changing the material you are working with. The specific placement, numbering, and kind of atoms in a molecule is essential to understanding the molecule itself. Both of these definitions will be necessary to understand rotational spectroscopy.

What does it mean to absorb and emit energy? Energy, as far as this text is concerned, takes two forms: potential and photon. That is, molecules can absorb energy, taking in photons and moving to less stable states. Or, molecules can relax, letting go of small packets of light.5 How? Without getting too deep into the weeds, light and matter interact only weakly.

Light, as is often said, functions as both a wave and a particle. What does that mean? Wait no I don’t want to get into that duality here. I’ll assume that I’ll cover light somewhere else in the thesis.

Why does rotating take specific amounts of energy? Only some molecules have rotational transitions. Those molecules have what is known as a dipole, or an uneven distribution of its electrons’ expected positions.6 Most works on rotational spectroscopy begin with a simple linear molecule, showing that the energy is both quantized and algebraic. That is, from just a few known pieces of information about the atoms in a linear molecule, you can predict7 exactly how much energy it will take to make the molecule rotate, or how much energy it will release when it stops rotating.

N.B. Coming back a few hours later, I think that I lost the thread a little bit. I’m going to restart and see if I cannot do better.

1 Bernath, Gordy and Cook, etc. N.B. When actually including this in your thesis, make sure to actually, you know, follow proper citationing

2 section? redefine as needed

3 or indeed, anything

4 I should find places that claim this, if only because it’s fun to cite many random books who say things the same ways

5 photons. I should probably start with that definition

6 oof that’s a bad definition of dipole, make sure to work on it

7 ignoring distortion effects and everything else, which I am going to do right now. Do I think that I get to use footnotes in my thesis? hard to say for certain. I certainly like them, but I understand that they are somewhat inherently informal. I’ll see. Probably more in the appendices and background information sections, since those are more likely to be skimmed over and what not

Beetlejuice Review

First Published: 2024 January 14 (because I forgot to post, not bc forgot to write.)

Draft 1

Hi!

You may have noticed that I’ve been gone for the past few days. Sorry about that, the beginning of a new year always comes with a lot of upheaval, and a new invigoration for the research I do does mean that my energies are focused there rather than on this blog. As a result, I not only have not been writing this blog, but I also have not been working on the Saturday musings that I wanted to do. So, today we’ll be going back to old school blog: reviewing a show I just saw.

I just got back from a matinee performance of the musical Beetlejuice. Unlike most musicals that I’ve been to , I went into the show today with absolutely no idea what to expect. What do I mean by that?

Most of the time, I have listened to the entire soundtrack of a musical almost ad nauseum before seeing it performed. It is always fascinating to listen to the difference between a cast recording and a different cast performing the same songs. More than that, though, most of the time I try to be familiar with the show that I am about to see. I read up on the show, and I try to get a sense of what is going to happen within it.

I think that I can name on one hand the things that I knew about this show going into it. It was based on a 20th century Tim Burton film. There’s a guy named Beetlejuice, and he wants a girl to say his name three times. Oh gosh that’s far less than one hand. Those two facts were both true, and they both remain true. The show, however, is so much more than that.

It opens at a funeral, where we meet our main protagonist: Lydia Deetz. She sings a ballad about how invisible it feels to be sad. As the song ends, the show begins in earnest, as Beetlejuice comes out to break the fourth wall and explain the premise of the musical. It is clear that the entire show is meant to be a parody of many things, the classic musical form amongst them.

And yet, the show treats everything it does with a shocking amount of love and care. The sets and scenery were absolutely stunning. Sorry, I’m going to take a step back from the plot to just gush about the technical aspects of the show.

As the show opens, an animation begins to play on the backdrop. I had never really thought about the options that using projected back sets could have, but it was mesmerizing watching the way that a clouded moon and trees could be drawn in, starting with what seemed like a single shaky hand. The technical mastery remained in full force throughout the rest of the show. Each room of the house is built with multiple forced perspectives, making the entire home feel disorienting. The lights were completely invisible, drawing no attention to themselves, only to suddenly spring out at the audience when the parody sections of the show came back. The blend between set and backdrop was also amazing. Anyways, that’s lighting and set, the two parts of technical theater that I care about.

The show is so obviously a parody, but one made in good faith. The classic Broadway musical solo where the lead woman gets to play the role of a classic prima donna is played up, and the actress playing Lydia shone in all of those moments. The show, for all that some of its jokes fell a little flat, never ceased acting earnest.

I’m sure there’s more I could say about the show, but anything else would really start falling into the realm of spoilers, which I don’t always love in my reviews. Anyways, I am so glad that my new research group mate told me about the show and that I ended up going today.

Oh! I was just about to say pulling back from the review, but that is one thing that I want to discuss. The fourth wall is a tenuous concept in art, and one of the biggest trends I’ve noticed in my life is the general dissolution of it in most media. One way that’s often manifested in musicals is through this idea that I can’t remember the name of that I encountered back when I studied music. The general idea, though, is that music in a show is either part of the world of the show, where the characters are aware that they’re singing and dancing, or something strictly for the audience.

In the early parts of the show, it is clear that the music coming from everyone exists in the real world, not in the world of the show. Beetlejuice is the only one to directly address the audience, or whose music even seems directed outward. As he is complaining about the people next to him, however, they mention that they can hear him. At that moment, the fourth wall, which I thought had been shattered, reasserts itself. We are once more separated from the antagonist, who is once again brought into the show.

As the show continues, the wall starts falling down more and more, and the classic scenes where groups come out and pose for the audience are numerous. When the curtain call comes, it is hard to know whether the event is taking place within the universe of the show or outside of it.

I also really liked that the show had likeable characters. I find that one issue I have with a lot of musicals lately is that we aren’t really supposed to root for anyone, and nobody really grows. Everyone in this cast, however, has a plausible and sympathetic goal, and everyone changes throughout the show to become someone more likeable. It was nice to be able to root for the main character, and even for the antagonist, to some extent.

Now pulling back from the telos for this specific post, and moving to the telos of posting generally, I have been more lax about writing my daily reflections on days that I do not blog. I wish that wasn’t true, but alas, it has been. With that in mind, though, I do think that my daily reflections are best saved for my private notes, which I have been keeping more regularly. If anyone is particularly interested in reading them, I could be easily convinced to bring them back.

3 recently meaning the past almost decade, now that I think about it. I still think of high school as a somewhat recent phenomenon, but it was almost half a life ago wow

8 I think? I’m assuming that she’s meant to be a teenager, both because of the climax song and the fact that the attitude is general “theatre idea of a teenager”

Thesis Appendix: Latin Hypercube

First Published: 2024 January 8

Draft 2: 8 January 2024

Ok so I missed a few days of posting there. However, I do want to make some progress on my thesis work tonight, even if it is only an appendix. So, let’s revise RebelFit Latin Hypercube.1

One of the fundamental algorithms in Rebelfit is Latin Hypercube Sampling/ It was initially described by () at () as a method for effectively sparsely sampling a space.

It is sometimes difficult to conceptualize sampling high dimensional spaces. For instance, if one wanted to take five samples in each dimension and do it as a grid, the number of samples grows exponentially as the number of dimensions increases. By the time that one reaches 8 dimensions (the number of variables in a Reduced Rotational Hamiltonian with Quartic Centrifugal Distortion), a grid five samples wide would require nearly four hundred thousand samples.

Another instinctual method for sampling a high dimensional space is to use a random sample. Or, at least, a pseudo-random sample (see appendix: randomness for more details). Latin Hypercube is demonstrably better at mapping a space than random sampling, though that improvement is reduced as dimensions and numbers of samples increase.2

The name Latin Hypercube comes from the concept of a Latin Square, which is inspired by the work of Leonhard Euler.3 It does include some aspects of randomness. In each of M dimensions, the sample space is cut into N slices, where N is the number of total samples desired. The slices can be defined in any arbitrary way, but the most common are even spacings and a Baysian distribution based on prior knowledge. Once each dimension is sliced, a point is randomly picked in each of the N wells in each dimension, and they are randomly correlated together. Unlike random sampling, this ensures that values are measured over the entire range of each variable. Without randomly correlating the dimensions, the trivial Latin Hypercube is constructed, where you sample along the hyperhypotenuse.

Draft 1: 31 December 2023

One of the fundamental algorithms in Rebelfit is the Latin Hypercube. It was initially described by () at () as a method of more effectively sparsely sampling a space.

Its name comes from the concept of a Latin Square, which is an arrangement of rooks on a grid such that none can take each other. As with all sampling methods that are better than random sampling, Latin Hypercube sampling becomes less better4 than random sampling as the number of samples or the number of dimensions increases.

In order to construct a Latin Hypercube, you need to define the number of dimensions (M) and the number of samples (N) that you will use. In the general form of the algorithm, each of the dimensions is then cut into N different wells, and a point within each well is randomly selected.5 Each dimension’s wells are then randomly assigned to each other, so that you don’t just sample around the n dimensional hyperhypotenuse.6

Latin Hypercube’s benefits are best demonstrated by comparison to other common sampling methods. If we compare to a Grid Search, where we want to sample 10 different points in each dimension, that requires a million data points by the time that we reach the 7th dimension. The N for samples is constant over any number of dimensions you ad,.


  1. n.b. the previous draft is probably not needed to be read because I’ve actually revised, rather than wholesale rewritten↩︎

  2. I forget where I read that, but it does seem to be common knowledge at this point↩︎

  3. cite wikipedia unless I can find a better source/read the original source↩︎

  4. oof that’s rough↩︎

  5. see the appendix on randomness↩︎

  6. I know that’s not the real word, but it feels appropriate↩︎

A Conclusion to Science as Mysticism

First Published: 2024 January 6

Draft 7: 6 January 2024

d]

The line between passion and obsession is the point where pleasure turns to pain. Amateur means unpracticed and unskilled, not because love means that you cannot improve, but because love is fundamentally healthy. To become virtuosic requires moving well beyond the point of love, growing obsessed with the very smallest minutiae in a subject. A mystic is more like a great musician or a groundbreaking scientist than any of their followers are like them.

Obsession and passion are also the difference between knowledge and truth.1 Knowledge is simple. Knowledge is facts and figures. When we read and respond to the writings of the great thinkers, or when we play the notation that some great musician laid down, we are confronted with knowledge. When we grasp in the darkness, gathering and creating, we work with knowledge.

Knowledge is comfortable. It is practicing scales for hours on end, until the instrument feels like an extension of your own hands. It is cutting pounds upon pounds of carrots identically, until it is easier to julienne one than do anything else. Why do we spend our lives working with on these small minutiae? We work with them because we must.

The Prophet Jeremiah puts it in a striking way. “I say I will not mention him, I will no longer speak in his name. But then it is as if fire is burning in my heart, imprisoned in my bones; I grow weary holding back, I cannot!”2 That is to say, truth is not something you get to choose. Truth grasps you and forces you to share what you have learned. It is the difference between shining a light in a dark room and a bolt of lightning illuminating the entire space. One is active, and the other is passive.

It is here that the real difference between knowledge and truth comes. Knowledge is something we seek, something we can create or discover.3 Calculus today is knowledge. Nearly every college student for generations has been expected to understand it. Literacy today is knowledge.

Calculus in the time of Zeno, however, would have been truth. Without calculus, Zeno was able to formulate any number of real and unsolvable paradoxes. When Newton and Leibniz discovered calculus, they did something that no one before had been able to do.5

When a mystic sees a vision of the world, they feel compelled to share it. The reasons for their compulsions are as varied as the mysteries they reveal. However, if they do not share it, the truth dies with them. A scientific invention, unless shared, does no good to the world.

Truth becomes knowledge when it moves from the individual reception to the broader person. The mystic, the poet, the scientist, and the musician all are given a revelation. That revelation spreads, and the magic is gone.

1 wow I’m actually really loving this so far

2 Jeremiah 20:9

3 depending on your belief structure and what specific piece of knowledge we’re constructing. I think that as I’ve grown older I more and more believe that there are very few absolutes. Someone can create the most optimal implementation of an algorithm in a language on a machine, but there is an optimal way to sort in general that we have to find4

4 Or maybe we’ve already found it, I guess. I’m not particularly up to date on anything computer related. I doubt that we’ve found a proof for something generally optimized, but I refuse to look it up because I want to stay on track

5 I think that I remember reading that some non European also discovered calculus at some point, but that does kind of add to the point that I’m trying to build to, which is that truth only becomes knowledge once spread. I only realize now that my goal was to do that

Draft 6: 6 January 2024

The difference between science and Science is the difference between music and Music or religion and Religion. At its core, it is the difference between truth and Truth. It is the difference between passion and obsession. It is, in short, the difference between knowledge and revelation.

Knowledge is simple. It is facts and figures. We can express it in theorems and proofs. Calculus today is knowledge. Almost anyone can learn calculus today. Calculus was once revelation.

On the other side of experiential knowledge, the realm of virtuosity is constantly pushing forward. In one generation, we have Jimmy Hendrix, who is frequently called the best rock musician ever. Now that the music has been transcribed, however, anyone can learn and play it.

I feel like this is getting away from me again.

Draft 5: 6 January 2024

One of the hardest questions you can ask a musician is what makes something music. Like basically any definition, you cannot draw a boundary without cutting out something that is music or including something that is not. Everyone has their own definitions of music as well, and one person’s music is another’s noise.

Draft 4: 6 January 2024

c]

In the modern world, knowledge can be broken into any number of binaries. Most commonly, though, I see truths1 as broken into subjective and the objective. We have the objective truths we find in science, where the speed of light or the boiling point of water is constant. On the other side of this coin, we have knowledge which is only true for the individual. Think of the way that a song may remind one person of heartbreak and another of their first love. The objective and subjective may be a helpful distinction in many regards, but there are so many places that it is lacking.

No this is bad

1 truth and knowledge will be interchangeable in the rest of this musing

Draft 3: 6 January 2024

The core question behind any inquiry is what it means to gather new knowledge. Are we shining lights into a dark room, illuminating what is already there? Or, are we forcing a wave function to collapse, creating truth from the realm of possibilities? Whether knowledge is created or discovered, however, both of these approaches presume that new knowledge comes from an active source.

To be sure, there are any number of places where we do, in fact, gather knowledge in an active form. As a scientist, much of the work that I and every other scientist do is bean counting. As a musician, almost all of what I do is practicing scales and other rote learning. Artists need to practice drawing lines over and over in order to be able to transfer their thoughts onto the page.

However, when we speak of art or music or science, we are not speaking of these repetitive practices. While we need these small details in order to fully illuminate our space, but that is not what we care about. What we care about it the new rooms, rather than the note taking.

No no no this is bad.

I need to plot out what I want to say. What do I want to say here?

Conclusion needs to be “knowledge is passively received”. How do I get there, though?

Ok I can talk about the fact that we think of the two sides of learning as like science and art. The two sides are instead knowledge received and knowledge taken. Knowledge received is fundamentally deeper. Knowledge received can be shared and given away. That’s great. Maybe see something there? Like ideas once learned are able to be shared and seem almost obvious.

See if that works for the next draft?

Draft 2: 4 January 2024

b] Mysticism and science are interrelated through a weird network. Wait wait, I have an idea.

When mystics share their findings, we get religions and new philosophies. As the information spreads, it becomes less explosive and therefore more up to questioning. You cannot question a mystic about what they saw. What you can do, however, is ask someone three hundred years later about the consequences of what the interpretations of their experience has caused. That can be formalized into philosophy.

Mathematics, as we all know, is a form of philosophy.

On the other end, a scientist has a sudden inspiration for an experiment. Because science requires rigor, that idea is then formalized out into a proof or an experiment that’s actually run. When we continue to try to understand what’s happening, we get to mathematics?1

Let us try again.

I already have the framing, which is important. What I’ve struggled with, however, is the who cares, the takeaway. What does it mean or matter if there is an overlap between the two?

Looking at yesterday’s drafting, I think that I was going to try the framing of knowledge being discovered rather than created. Then there’s the question I have to ask myself, which is how to connect the two. Even though I do think that the Catholic Church is True, I don’t know if I want to explicitly make the musing Catholic. I don’t know why, but I have this gut instinct that it’s something like how I feel like it’s intellectually lazy to just go “ipso facto, Catholics are right”.

WAIT!

As I was writing there at the end yesterday I had the connection to eldritch knowledge. Knowledge spreads like a fire. Lies spread like a fire.

Flames illuminate, sending light further into the darkness, heating and illuminating more space for fire to spread.2

A common thread in science fiction is the idea of forbidden knowledge. More than that, though, nearly every society has had some variation on restriction of knowledge. No, I don’t think that leaning into the forbidden aspect is where I want to go.

Many cultures have a version of a Promethean myth. Humanity was gifted fire.

No, I continue to circle this damned3 conclusion, unable to reach it. I feel as though the conclusion is staring at me from behind a stained glass window, just distorted enough that I cannot see more than its vaguest outlines. There’s a fun joke there here where I can do the whole “I would have a conclusion to share, but I haven’t gotten the revelation yet.”

What are things that we can take away? Truth versus a truth?

There’s the comment that the friend made to me, which went something like “we’re always told there’s only one right answer in math and science, but that’s not true.” It is true, though, but there are a lot of questions that are subtly different with vastly different answers. I tried to get to that for why and how.

In rubber ducking a friend,4 they had the idea of being able to refuse knowledge, but not revelation.5 We also came to the idea that the coins are not science and humanities, but revelation and busywork. I think that something about refusing knowledge is an idea for a takeaway. Another idea of a takeaway is that, if knowledge is something we experience, then great6 poets are not separated from great scientists by anything except for what revelation they were given.

Oh wait. Wait.

Wait.

Ok so if knowledge is something that we discover, rather than create, then how do we discover? Discover is the wrong word, I think. There we go. We don’t discover truth, truth is revealed to us.7 This feels really good, but I suppose we’ll see what rubber duck8 says. Update: approved! Great, so now we just have to write the musing.

1 Ugh that’s so dumb I don’t quite know what I’m trying to get at, but this certainly isn’t it

2 hmm, the metaphor is starting to lose its coherence, and I am getting far too into the poetic, rather than illuminating my goal.

3 interesting how I only feel as though I could put profanity in this blog when I fall into a poetic form

4 where you basically just talk to something inanimate to find an answer. In this case, I do it to a person, who often has great insights of their own

5 who then also required me to cite, because plagiarism is bad

6 or really any, but I feel like starting with great is a safer line of inquiry

7 Passive voice intentional here, because the point is that this type of knowledge is not obtained but received

8 there is an idea that we could have recurring people in my life show up as the same nickname over and over, but idk if we’ll do that

Draft 1: 3 January 2024

a] I recently mused about the fact that there is a shocking overlap between mysticism and science. Or, at least, I mused about the way that I consider the two fundamentally related. In a beautiful example of metacommentary1 , the next day’s posting was about the fact that I cannot find a way to write conclusions. I haven’t been satisfied with the way that the science and mysticism post turned out, and it’s been playing in the back of my mind on some level since.

Today, I met a friend for coffee, and we ended up talking a little bit about the theory of mathematics. One of the big questions in my view of theory of mathematics is whether mathematics is discovered or created. I then connected it quickly to an alleged early Irish musical claim, which is that all the Irish airs were given to humans by the Tuatha.

I don’t know if I can quite put the dots together right now, but there’s no place to try like here. So, I’ve always been one of the sort who believes that mathematics are discovered, rather than created. There’s the idea of shining a light into a dark room. We steadily see more of reality, even if mathematics is an orthogonal reality to the real real world.2

Ok so let’s see if we can’t do something with that. Mathematics is3 , in many regards, the intersection of science and religion, being as it is one of the purest forms of philosophy. No, that isn’t quite what I wanted to say.

The friend mentioned something about how artists are famous for working under altered states, often with drugs. Mathematicians, similarly, often describe their great discoveries as though they have been themselves under a trance like state. However, just as musicians can share their songs with us even after they’ve come down from a high, the truths revealed to us by science are equally shareable. There’s something about the whole “forbidden eldritch knowledge” that I’ve always thought about, especially 1 I really do need to reduce my usage of meta, for all that it remains an accurate representation of what I mean. It’s commentary without being explicit? Ok so there’s probably a better way of phrasing, but I don’t want to put the work in on it right now

2 I’m sure that there’s another way to describe this, and should revise it in a future revision, but for now I’m just trying to get ideas down onto the page

3 are? I never know how plural the word mathematics is

Flash Fiction Friday

First Published: 2024 January 5

Draft 1

a]

Another Friday, which means that it’s time for another musing on Flash Fiction Friday. This week’s prompt is a little late, in my opinion, but is “how it ends”. There is a lot that I can do with that prompt.

Given the album work I’m doing, something on the topic of star death or heat death of the universe is tempting. Of course, the idea of writing a villanelle inspired by do not go gentle into that good night remains something that I want to do. Villanelle remains a poetic form that I am in love with, if only because there’s something really inherently intense in the form. Something from the hollow men also seems tempting, though that is just because the text is so, so very into the public consciousness.

That being said1 , I do think that there’s something good about looking far smaller. Rather than taking the death of everything and animating it, it could be fun to turn the end of something small into a larger picture. Things that end include relationships, classes, friendships, lives.

I guess one immediate question is whether I want this to be poetry or prose. I haven’t been writing a lot of poetry lately,2 and I do want to get into song writing. Maybe trying to do something that’s more elevated prose?3

I could try doing a villanelle inspired piece of prose? No, I don’t think that would work. What makes a villanelle so compelling is the fact that it is only nineteen lines and full of repetition.

Having now come back about an hour later, I find that I’m inspired also by a song that my band4 played “Til Forever Falls Apart”5 That’s a song about some nebulous end, but I think that it’s about death? Or maybe the potential of death. The group also did “I Will Follow You Into the Dark” at the same time, and I get those two songs stuck in my head together.6 That song is more explicitly about a murder suicide pact, which is its own form of romance.

So, based on my musing so far, it does really seem as though my muse wants me to be writing poetry, probably about death and related to romance. Since I don’t think that the album will be about romance,7 I don’t have to worry about putting out this set of lyric. Since it’s going to be anything I want, I want a villanelle.

That’s AbA’, abA, abA’, abA, abA’, abAA’.

That is, even though the entire poem is nineteen lines long, I only have to generate 13 lines of rhyming meter, five in the b rhyme and seven in the a. I will have to break myself of the habit of wanting perfectly strict meter here, because villanelles sound way too sing songy when written in meter.8 Nothing left to do but try to write it, I suppose. Given that the flash fiction minimum is 100 words, I do need to have lines that average out to at least 5 words a piece, which is hardly a struggle usually.

Having now written a draft and sent it to a fantastic and eloquent friend, the friend mentioned no small number of issues with the poem. Chief among them, I chose an incredibly trite refrain, and I did not think of any meter at all. Now almost two hours later, however, I have a completely different poem that is miles away better than where I started. All of the improvement is due to the fact that my friend patiently led me to water, then, when I was about to collapse from thirst, reminded me it was there.8

There’s really not much more for me to talk about, so that’s nice. Goodnight all!

1 for my reader who appreciates the turn of phrase

2 Ok as soon as I typed that I remembered that I did, in fact, write more than 20 sonnets last month. That was a whole year ago though, so it doesn’t really count, in my mind at least

3 Then again, the last time I was proud of the prose I wrote my least interacted with fiction ever, so maybe that isn’t the best idea

4 it always feels weird to say my band, but that is far fewer syllables than the band that I played with, back when we still did that

5 No, I will not be taking questions on why I capitalize song titles but not poem titles

6 Mashup potential?

7 Except maybe incidentally in like a single song. There’s always a chance that I am wrong, but it does really feel like that’s where my muse is pulling me

8 I’m sure that a better poet than I has managed to make it work, but I am not that poet right now

8 I think I might have lost the thread of the metaphor

What I Read and Wrote

First Published: 2024 January 5 (because I forgot to post, not bc forgot to write.

Draft 1

It’s been another week, which means that I get this week’s version of what I’ve been reading and writing. I’ve read basically nothing over the past week, which is a little sad. It is also Christmastide still, so I guess that it doesn’t surprise me that much, and it isn’t really that bad of a thing.

However, I did just start reading the extended Percy Jackson Universe book about Nico and Will, so we’ll see how fun that ends up being. Once I’ve finished that, it will probably be more or less time for me to go back to the actual reading goals that I have.

In terms of writing, I mused about the album that I’d like to write, and I’ve started thinking about the album’s content. I’ve also managed to continue with daily musings, filled a few pages in my lab notebook with notes, and I’ve written two chapters of my web novel.1 I think that’s everything!

Oh wait! I’ve also been working on some of my Saturday musings. That really is everything, which is a little bit disheartening, but I suppose doing this every week should hopefully keep me at least somewhat accountable for how much I’m reading and writing. Time to do another draft of one of the musings, I suppose.


  1. that is, I was well ahead by writing a chapter two days in a row, and then I haven’t really written since. I was worried about boom and bust, and it seems like that was a reasonable concern.↩︎

Album Update

First Published: 2024 January 5 (because I forgot to post, not bc forgot to write.

Draft 1

Today is the first Wednesday of the year. As a result, it is the first in my series1 of reflections on the album that I am going to have written, recorded, and released by my 26th birthday.3 I spent half an hour or so this morning unplugged and thinking about what I might want to have an album be about.

Some of my readers might know that I have really only written a few songs in recent years.4 The song that’s received the most praise is a song that I never really gave a title to. Its working title is5 “Starfall,” which prompted an idea for how I could arrange the album.

As my readers may also know, I have been6 giving talks on space. And so, like every scientist interested in art, I decided to mix the two. My album will be 11 songs based around the birth, formation, life, and death of a star. I’ve planned it to be the following songs:

  1. Emptiness I

  2. Diffuse Cloud

  3. Dense Cloud

  4. Pressure

  5. Ignition

  6. Emptiness II

  7. Planet Formation

  8. Homeostasis

  9. Pressure Redux

  10. Nova

  11. Emptiness III

Of course, all of these names are significantly less than finalized. My idea is to write it as a triptych, with the first four, second four, and final three songs as smaller acts within the piece. I’m hoping to have the Emptiness songs be in communication with each other.

There is, obviously, more to an album than what the album specifically is about. The way that messages are conveyed and the metameaning7 are just as important as the text and music of the songs themselves. I haven’t fully decided what I want the album to be about in that sense, though I do think that I want it to be about a journey.

I’ve visualized the first act as the period(s) of a life where you become aware of the influences that have brought you to where you are today. As Pressure breaks to Ignition, we reach the second act, where a person sees their own place in the world, distinct from those influences, though obviously still aware of their impact. Finally, as Homeostasis gives way down to Pressure again, we see the impacts that we have on the world around us.

A star is born from the ashes of a dead star. Its own ashes eventually become the cradle for another star to be born. Between those, it exists as a bright point of a light, plasma, and potentially life.

Of course, I haven’t really figured out to what extent I want the pieces themselves to be about stars and star formation. I think that, on some level, at least, I want to reference the stages of the star’s life in each song. However, much like Starfall uses the idea of gravity to discuss a failed relationship, I think that the astronomical concepts may end up better used as framing metaphors for the individual songs. A part of me wants there to be a binary star, which could work for the relationship aspect.

A healthy partnership, after all, is nothing like a planet orbiting a star. There are probably relationships that I can think of to make the idea of planets around a star a metaphor for something, but I’m not sure what just yet.

So, now that I have the framework, I need to start working on the music. I think that I’ll work on the set points of the album: Emptiness, and see if that helps me with the goals? That could be something good.

Anyways, I realize that I have also not been doing my daily reflections for the month. Might as well do that here.8 Goals for January:

That means that my daily reflection should be:

I feel like most of the goals are best worked on after I return from my familial home. That being said, my minimal exercise has been going well, I’ve been blogging, and today is the first day in a while that I have not written an entire chapter of the Jeb. As demonstrated, I have made some progress on the Album9 , and tomorrow I plan to do more of the actual research work. Reading needs to be more of a priority for me, but I don’t quite know how to make it one.

1 to be2

2 hopefully, at least, but I suppose that we’ll see

3 which wow now that I’ve written it out like that, it really sounds like a lot

4 I keep wanting to say that I’ve only written a few songs, and then I remember that I’ve written at least a dozen or so songs for solo voice. It’s just that many of them reflect the fact that I am constantly learning and growing in my ability to create. In order to be where I am now, then, I needed to have written worse music.

5 was? will forever be because I’m not including it on the album

6 have and will likely continue, which I guess means that present perfect is the right tense? I think

7 wow I should make sure that I stop relying on the prefix meta so much

8 I.e. I will be doing it here

9 henceforth written with a capital A on this blog

Footnote Frenzy Continued

First Published: 2024 January 2

Draft 1

a] At the beginning of the ’blog, I mentioned that one of my great inspirations for writing this was my father.1

One of the2 most striking pieces of his blog is the use of footnotes. That is, in addition to using footnotes,5 he also uses end notes which are called from other end notes.6 Now, like many people exploring a medium, he has done any number of interesting things with these end notes.8

As someone trying to emulate a lot of his blog,10 I also wanted nested footnotes. It turns out that, while I am not unique in this request, I am close to it. There appears to be a single reason that style guides believe that footnotes or end notes11 can be reasonably nested. As we know12 , there are only a few circumstances that most style guides will accept footnotes.

Obviously, citations can go there in some style guides, but there is absolutely no reason that you would need a footnote from a citation.13 Otherwise, asides are sometimes welcome in the footnote, though, of course, it is bad for bonus thoughts to have their own bonus thoughts in most formal writing. Finally, translator’s notes or editorial comments on editorial or translated editions, counterrespectively,14 are allowed end or footnotes. I’m sure that some of you have pieced together where the nested footnote is allowed. A translator’s note on a translated editorial piece may need to reference an aside as an aside.

These tend to be ranked, however. They are nested, so there is a clear sense of ownership between first level and second level footnotes. I don’t like that. To me, there are three levels of importance in the words within a text: main text, footnote, and not included.15 I want footnotes referenced in other footnotes to be on the same level.

Unfortunately, as I’ve mentioned a few times on here, this ’blog17 is written in LaTeX which is then compiled into HTML. LaTeX generally does not have issues with nesting of footnotes, but pandoc does not support it natively. For a while, I thought that I might need to switch to Markdown. Thankfully, I am related to people who are not just infinitely better at their domains than I am, but are also incredibly skilled in those domains on an objective level. My father was willing and able over break to figure out how to let nested end notes be a thing in my writings without forcing me to change from LaTeX. It does require a little bit of change, but that isn’t too much.18 One benefit will definitely be that the text will stay cleaner, because the bonus thoughts will keep being nested somewhere else.19

For other examples of endnotes used in creative ways, I have been told the book20 “House of Leaves” does a wonderful job exploring the limits of the written page.

1 That remains true, but I did say it then

2 arguably3 the most

3 arguably implies that there are people on both side of the argument. Given that I’m making my own private echo chamber here, I don’t need to do that

4 he calls them end notes. Given that it’s an infinite scroll page, the two do feel interchangeable. Then again, when you scroll multiple musings at once, they do appear at the end of each musing, so end note might be more accurate

5 Like this

6 Like this7

7 An end note which was called by another

8 such as having multiple references to the same end note, programming his system to automatically skip the number of a baker’s dozen9, I think once even having end notes referenced back to the main text, though I don’t recall that in particular

9 the integer between 12 and 14, for those keeping track at home

10 and as someone who has lots of bonus thoughts attached to every thought

11 For some reason my dictionary thinks that endnote isn’t a word. I’ll respect it, for now

12 or, at least, as I know now and have vague senses of having known before

13 I mean I can think of plenty of reasons, but those mostly boil down to like “I do not condone this author’s viewpoints, etc.,” which should probably go in the main text

14 I love counterrespectively, even though I know it’s poor form to use it. It reminds me of how the Majors of Chemistry, Biochemistry, and Biology at my undergraduate were sometimes referred to as Bio Bio Chem Chem

15 Which I suppose should be implicit, given that every work is finite, and there are infinite combinations of words16

16 I suppose that there is also an infinite amount of nonsense, but that’s its own issue, I suppose

17 I’m using apostrophe because I’m copying my father more closely in this musing

18 Mostly I just have to use endnotemark and endnotetext instead of just footnote

19 Of course, that comes with its own bags of worms, one of which being that needing to type endnotemark, a number, endnotetext, a number, and then my footnotes means that I have a much easier time losing the thread of whatever I’m discussing

20 Book may or may not be the right word. Experience?

Yearly Reflection

First Published: 2024 January 1

Draft 2

Happy New Year! It has been basically a year to the day since my last yearly reflection. Last year I did five things that I was excited for and five things that I was excited to have done in the previous year. So, five things that I am excited for in the upcoming year:

Five things not on last year’s list that I’m glad I did,

Last year I also had five items that I was excited for!

I had a number of goals for last year, and I generally did not do a great job with them.3

This upcoming year, as with every year, I have any number of goals, however (un)reasonable they may be.

That’s far more than I think might be reasonable, and so I will hope that I can make it through everything, increasing in productivity constantly.

Let’s move on to the other portion of the reflection, which is the monthly reflection. I think that monthly goals remain useful for constructing my month in the way that I would like to live it.

Goals for the upcoming month:

Anyways, goals for the upcoming month, which should hopefully reflect my goals for the upcoming year.

Draft 1

So, it’s been a year.6 I’m planning to work on this in a few drafts, so let’s take a page from last year’s yearly reflection and do five things I was grateful for last year and five things I’m excited for this year.

Last year I thought that I would be excited for:

All of those tasks that I did accomplish were things that I am glad I did. Other highlights from the year,10

That is all very exciting! What am I looking forward to in 2024?

Ok cool, that also includes some of my goals for 2024. Turns out I did set goals for 2023, I just put them in a separate document. My goals last year were to:

Last year I wanted to make an effort to learn species counterpoint better. I don’t think that this is a goal that I am going to take with me to 2024. I’ve briefly talked about it before, but to recap: I do want to compose, but mostly for my own solo performance, rather than traditional choral composition. I don’t think that there are enough hours in the day, days in the week, or weeks in the year for me to explore everything that I want, so I need to prioritize.

What else are things that I want to work on or do this year?

I said in my 25 for 25 post that I want to learn how to weave, swim a mile, take an improv class, learn a polka on the accordion, and spin yarn. Those all remain things that I think that I want to do. Let’s see what I think that I would need to accomplish each of the tasks:

What else do I want to accomplish?

Wow that’s a lot of things that I want to do. I guess that I should either reduce the goals or increase my productivity. Those both sound like a lot of work, so we’ll see what ends up happening. For now, time to look away from this and do work for the day, rather than looking months into the future.


  1. this was something from last year, but it remains true↩︎

  2. well, at least I think that I improved in terms of quality↩︎

  3. feel free to read the last draft if you’d like more details↩︎

  4. with the disclaimer that I may not post the ones I don’t like↩︎

  5. I would ideally like that to happen, for all that I don’t really expect it to work↩︎

  6. since the last year, I guess. It’s been more than a year since a lot of things have occurred and far less than a year since others have happened↩︎

  7. total chapter views divided by chapters↩︎

  8. given the opportunity to? Kind of both↩︎

  9. arguably good for me, especially if they dislike the parts of me that I personally like↩︎

  10. because it feels kind of wrong to double count↩︎

  11. slightly different, but it felt so different, because it was a completely wild experience where I just got peppered with questions about literally anything (in retrospect, introducing the idea of quantum uncertainty may have been a mistake)↩︎

  12. well, at least I think that I improved in terms of quality↩︎

  13. ideally, at least. I think that I’m close, and it should be very doable↩︎

  14. This is something I said last year, but it remains true this year↩︎

  15. I think that they call themselves a university, at least. Wow I need to start working on that talk↩︎

  16. he really is the brains of the family↩︎

  17. I remembered recently (read: my family reminded me) that many people expect an album to tell a story over the course of its songs. I should probably try to have mine do that, but of course, that is a goal that I am willing to give up on if it becomes untenable↩︎

  18. not going to confirm that right now↩︎

  19. also, 2023 lasted just forever, and I can’t recall what things I did then and what things I didn’t do since 2022↩︎

  20. not to be confused with all right↩︎

  21. or will have given me, as the case may be (don’t ask)↩︎

Reflections on Today’s Gospel

First Published: 2023 December 31

Draft 2

Today is the Feast of the Holy Family. There are a number of optional readings today, which means that there is no way that I would be able to discuss every variation on the readings. Instead, I am going to reflect on the readings that were read at the Mass I went to today.

Year B’s version of the first and second readings focus on Abram turned Abraham. We see his conversation with the Lord, where he bemoans the fact that all of his blessings will fall to his servant, rather than one of his descendants. This conversation is striking to me for a variety of reasons.

First, the G-d of the Old Testament, for all that we talk about the anger, is also a kind and loving Father. I could never imagine a Greek myth where someone complains to Zeus about the way that they have not been blessed the way that they wanted to be. Of course, the Greek gods are gods in a very different sense than the Almighty. I don’t need to go into that, but it is something that I thought about as I started redrafting this musing.

Second, the Lord assures Abraham that his children will be as countless as the stars. As a child, that felt interesting to me, because it seemed like we should be able to count the stars. Or, at least, there is a way to count all the stars that the naked eye can see in the night sky.1 Similarly, there is, in theory, a way to measure all of the biological descendants of Abraham. We could genetically sequence the world and find all of his living children, at least.

However, the stars in the sky are far more than the stars that we can count. One of the biggest discoveries of Hubble was that there is no such thing as empty space. For those who don’t know, one of Hubble’s projects was staring into a dark void, previously thought to be empty space. What it found was more and more dimmer and darker stars. Similarly, as the priest reminded us during his homily today, all Christians are adopted children of Abraham.

The second reading reminds us of the many ways that the Old Testament prefigures the new. Abraham is willing to trust his son, his only child with Sarah his wife,2 to the Lord. When the Lord says that the is to kill his son, Abraham trusts that he could bring his son back from the dead. Thankfully, however, the Lord does not require Abraham to go through with the sacrifice. In the New Testament, however, the Lord does give up his only son.

I’ve seen discussions of the Binding of Issac which point out that Abraham was ancient when he was asked to kill his child. There was no way, the commenters claim, for Abraham to overpower his child. That is, his child went to the sacrifice willingly. That doesn’t directly relate to the Gospel today, but it feels at least somewhat relevant.

Anyways, time to move to the Gospel. This passage, like one of the readings from Luke a few weeks ago, contains one of the Canticles that we use frequently. We have the Canticle of Simeon. The Canticle of Simeon, like the Canticle of Mary, is a song of praise to the Lord. Today’s reading notes that Simeon is full of the Holy Spirit as he says the words.

It is also important to note that Christ is introduced to the Jewish people according to custom. For all that modern Catholicism tends to overlook a lot of the way that Christ existed as a Jew in the Second Temple Era, it was a vital part of the early Christian theology. Christ was brought into the Temple, the same way that every other Jewish boy child would have been.

However, this entry to the Temple is not entirely filled with joy. A prophetess of the Lord sees Mary and tells her that a sword shall pierce her heart.

Sometimes I think about the song “Mary did you Know?” It’s often unpopular among the theologically inclined, because the answers to most of the questions are yes. For all that these complaints are valid, I do think that there’s something really powerful in knowing that Mary spent 33 years with her son, knowing the entire time that he would be murdered before she would die. It is often said that the worst fear a parent has is outliving their child. I cannot even imagine what it would be like to not only outlive your child, but to watch him grow and develop knowing, the same way that you know the Lord is G-d, that he will die before you. Anyways, I think that’s as far as I can get in understanding the readings right now. I’ve still got some hours until the New Year3, so there’s always a chance that I’ll be inspired to write more in the upcoming time. If not, I’m pretty ok with where I’ve gotten.

Draft 1, Realized there’s some critical framing errors

I found out today that there are optional first and second readings for Years B and C for today’s readings.4 In the Year B readings, we focus on Abram5 and the promise the Lord gave him, that he would have descendants as countless as the stars. As a person tangential to astronomy, that’s an interesting thought to me. Every time we look in what should be a dark region, we see more stars, fainter and further away.

The Second Reading comes from St. Paul, who reminds us of the first reading. Abraham is gifted children countless beyond any number because of his trust in the Lord.


  1. zero, if you live in many places↩︎

  2. not his only child, one might note↩︎

  3. well, one of the new years, at least↩︎

  4. revise this sentence please↩︎

  5. Abraham? I never know how we’re supposed to refer to the biblical characters who get renamed when we discuss their actions before being renamed↩︎