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Goal Updates and Scheduling

First Published: 2024 December 10

Draft One:

I know that I literally made the goals less than a week ago, but I have already forgotten them. With that in mind, I think that it might be good to start going through the goals I’ve accomplished, and organizing the ones I have left so I have a reminder.

Having forgotten about most of these, stretching is really the only one I’ve been particularly good about doing. I did write a hymn harmonization on Sunday, though, which I suppose is a good thing! I think that now is a great time to begin putting explicit time markers on my life. I know that my schedule will change when I begin to teach again next semester, but the first of those is at 11 AM, so in theory I can schedule anything I like before then. It might be worth considering locales as well.

For those events which happen multiple times a week, that means setting aside multiple blocks of time. For writing the song, I think that one time on Sunday makes sense, since I’ll already be doing music, and the other maybe on Wednesday. Great, they’re in at 8AM those two days, and I’ll for now plan on doing them at home.

For pop science, I think that Friday mornings could be a good day, and it would be nice to do them in a coffee shop. That means I need to pick one out on Thursday and print it out, since I’d like to avoid having to use my computer.1 I’ve booked it an hour a week, starting at 8am this Friday.

When do I want to work on drawing? Realistically, whenever. I know that I want to do it at home, though, if only because it’s embarrassing to have others see my work. MTWR makes sense to me? I get a long weekend off of it, which would be cool. In at 7 50 am so that on Wednesdays it will not conflict with music time.

I have scheduled 3 to 5 pm on Sundays for reflecting on the Gospel and writing the hymn harmonization, and 4PM Saturday for prereading it.

That takes care of all the weekly events, so now it’s time to start scheduling the daily events! I recently got an app that asks me about my day at start and end, and I’m going to treat that as good enough for now. 715 to 725 will daily be guitar time. I haven’t quite figured out where musing is going to fit into my schedule, but I think that it might help to figure out what my days actually contain on a weekly basis first.

725 to 740 is booked each day for the first stretch, and the second will happen before bed. I don’t think that I want to do daily affirmations, and I’ll plan to walk to the pool daily at 1050 am, except for Wednesdays, when I’ll move it to 10 AM.2

Wow, it feels kind of nice to have the whole day scheduled out like that. I know that tomorrow we will not be able to follow the schedule exactly, because it takes me more than 20 minutes to get ready and to work, and I have to be at work at 850. Guess everything gets shifted back 15 minutes! I hope that I’ll find a way to make this routine both helpful to me and also maintainable.

  1. though I suppose the ipad might also be a good choice.↩

  2. and other days maybe, whenever I have an 11am meeting↩

A Few Happy Memories

First Published: 2024 December 9

Draft One:

As I mentioned in my last musing, I’ve run into the issue of trying to do highly emotionally charged musings at times and places where that is not necessarily conducive to finishing them. With that in mind, and keeping in mind the two desires that these musings result from: wanting to feel close to my mother still and wanting to muse more often, I thought that it might be good to just go through a few quick and happy memories I have of my mother while they’re as fresh as they’ll ever be again.

There is a slight issue in doing this, though, because so much of my relationship with her was about the constancy, so the many conversations we have blur into one cohesive sense of warmth. One memory that comes to mind right now, though, is from Hanukkah one of the years that I was in high school.

It was during one of the phases that either I or my father1 were in the space of connecting to our Jewish heritage, and so we were lighting the candles. On Wednesday, though, we2 had Religious Education, and for some reason my father was not available to watch the candles burn. So, she had me take the menorah to the church basement, and I lit them before class. It was shocking to me how many Catholics, especially confirmed ones, were so unaware of the Jewish roots of our faith.

I think that it ended up derailing the planned class discussion, because rather than talking about whatever the planned lesson was, we talked about Hanukkah and the Church’s relationship to Jewry.

The other memory coming to me right now is when she said something which more and more I’ve come to realize is both absolutely fundamental to my own faith and also not incredibly common: all theology needs to be rooted entirely in love. That is, when speaking against something, love has to be central to the entire argument. Rather than using fear of damnation and hellfire, using the knowledge that the Lord is Love and that love is our highest calling is not just the key to good apologetics.

Honestly, the more I think about those words, the more that I find them benefiting my life. The more I can act and speak from a place of love, and the more that I try to ascribe good intentions to others, the better the world seems and the better my relationships become.

I also remember the first time that I crocheted a basic hat for my mother. She was bemoaning losing hair from her cancer treatments, and asked me to make her a hat. It took me a few hours of half attention, but I saw her wearing it so much afterwards. I know that it’s so trite to talk about how the smallest things we do can have the largest impacts, but I do truly find that to be the case.

In short, I miss you mom, but I wouldn’t trade my memories for anything.

  1. or quite possibly both of us↩

  2. I and my mother↩

Reflection

First Published: 2024 December 9

Draft One Written 7 December 2024

It’s been more than a day since my last post, which is not exactly what my goal was. Alas, the world is what it is, and I became far too optimistic about how much mental and emotional energy I had and would need to write the posts that I had been planning.1 Still, I do know myself well enough to know that daily musing does, in fact, make me feel generally better about life, and since I want to get back to writing my web serial2, this feels like the good and gently way to slowly edge back into it. With that in mind, I think that I’m going to treat this like I treat the beginning of most periods of my life, and go for some goal creation. Unlike most of my reflection posts, however, I’m not going to be looking back at old goals.3

Also unlike most of my reflections, I don’t think that I’m going to focus on deliverables as much.4 I know that there’s a lot of research talking about how goals are best when they’re actionable and etc., but the most important of the things that I want to accomplish in the next few months aren’t really the sort of thing that one can break down piece by piece. Anyways, with that disclaimer out of the way, time to stream of consciousness some goals, which I’ll then organize into time frames, etc.

Ok well that feels like a good enough list, if one that’s probably both too vague and too specific at the same time. I know that setting really optimistic goals for myself rarely works out, so I’m going to try to avoid that if at all possible. With this in mind, what’s a good way to break up the goals? There’s something to be said for timelines, there’s also something to be said for actionable versus overarching goals. Maybe I’ll just go through them all and think about how I can work on them before the year ends? That seems reasonable enough. Other than that, I’ll compile the list so that I have starting material for the future. So, without commentary, my goals for the foreseeable future right now are:12

So, since working on all these things at once would be, frankly, insane, let’s set come up with at least one way that I could work on each of them as a goal before the New Year, and then compile a list of what I’ll actually do.

Huh wow, that was far easier than I expected.

Given how many of these seem to be schedule based, scheduling my life is clearly a must. Since none of these are things that absolutely have to be done before the end of the year, I think that it might be best to focus on the bigger picture ones, like compiling lists. With that in mind, my goals for year end are:

Well, that’s honestly not the worst list I’ve ever made. I do love how many of them are list based, if I’m being totally honest. For now, however, I’m going to step away, if only because I don’t want to burn out too early.

  1. Thinking I had far more and it would take far less, respectively↩

  2. I’m terrified to see what comments have been left while I’ve been away↩

  3. for the triad of reasons: I don’t want to, I’m worried about what I’ll find, I don’t know how applicable they are to my day to day these days↩

  4. or, at least, I don’t intend to.↩

  5. I always hate ending sentences with an abbreviation that uses a period↩

  6. which, by words, I have done↩

  7. maybe one for the parish (pastorate?) day, or else one for the Church’s patron? Will consider, and probably ask my fellow choristers↩

  8. I know that that is a relatively sad goal, but it is what it is↩

  9. not that I do not still have any number of motivators, just that they aren’t the primary motivator↩

  10. if only nominally↩

  11. that is to say, find a way to make it so I can make food that nourishes my body, doesn’t leave me craving, and is doable with the life I live↩

  12. feels so weird to say that, as though there’s nothing else that I’m hoping to strive for, but it is kind of true↩

  13. I think that I forgot to give this its own bullet point↩

  14. this one is new as I compiled the list, but I really hate the way that my life is a mess (physically speaking, if not metaphorically).↩

  15. I think that I forgot to give this its own bullet point↩

  16. that is, figure out what occasion I could write a song for that would actually get performed↩

  17. in general, I do want to get better at composition and music, and I think that writing the song was my way of saying that↩

  18. i hate that I’m not allowed to end a sentence with abbreviated I have↩

  19. lol↩

  20. That didn’t work super well last time, but maybe this time↩

  21. as two footnotes above↩

  22. I’m not putting any further details here, because I um don’t want to incriminate myself further/make it something problematic (not that I have any ill intentions, just writing something semi publicly makes anything seem more nefarious↩

  23. I know this one is new even here, but it is something I’ve always wanted to be able to do, and it’s something that I can absolutely do systematically↩

On Music Memories

First Published: 2024 November 12

Draft Three

My mother died between my last posting of this blog and now. Looking at the calendar, there were a solid two months between when I stopped and when we learned that her death was imminent. However, as I find myself avoiding both this blog and thinking about her, I find that I’m spending far too much mental energy that can no longer be used for anything I want to spend time on. So, today I want to use my musing to put down in writing some key memories I have with my mother in relation to music.

The first memory that keeps coming to my mind happened sometime while I was in high school or college. We were in her truck, driving to Williamsburg.1 We started listening to some music on my phone through the car speakers, and ended up on a Johnny Cash album. Eventually we got to his Christmas album, where my mom and I joked about the fact that he didn’t really sing so much as speak while a gospel choir behind him sang. What sticks out to me, though, is her discussing recording technology.

She claimed2 that, before mono and stereo had gained supremacy, there was a period of time that music was recorded to be played through four locations at once. Apparently a lot of Johnny Cash was recorded in that form, and the sound was somehow fundamentally off for only being stereo.

Although not a single event, there was a recurring conversation through my life. I would be listening to Harry Chapin, my mother would express how much she loved his music, and my dad would make some comment about how it was too saccharine or not actually folk.3 The music I find myself listening to when I want to just listen to music is so inherently shaped by the music she4 introduced me to.

Some of it5 may not have been the most developmentally appropriate music for children.6 Right now I can’t remember any specific instances of her singing along with the music, but given how much my brothers and I do, it feels like she must have, at least while we were younger.

Less a memory of her and music in particular, I do recall conversations we had starting in high school, where I really began to realize how close my family was. After one of my concerts7, she mentioned that another parent was shocked at how her children were always at their siblings events. My mother made some retort along the lines of “I don’t make that an option.” That framing doesn’t convey what she meant though.

To my mother, family was something that deserved our complete support. It wasn’t a question that we would be at each other’s events because it wasn’t a question that we would support each other. As she was in her final days, that was something that we returned to. Despite the fact that she was incredibly busy with her work8, she made herculean efforts to make it to every one of our9 events. It was this unequivocal and unconditional love and support that gave me the confidence to be who I am.

Returning to the subject of music, my mother would often have her coworkers over for holiday parties when we were younger. Once my brother and I were at an age where we were competent at music, she would ask us if we wanted to play for the events. We, being the attention seekers that we were10, took her up on the offer.

Honestly, the last two reflections do a lot to clarify to me why I have so much difficulty coming up with single instances of memory. The way she raised me11 was so full of love that any individual event falls into the general haze of positive love. I do remember her mentioning her mother’s love of bagpipes when I took them up, and that helped me feel connected to my family.

She played guitar when I was younger, though stopped as we grew older and she became busier. In her last months, she wanted to return to guitar, but I don’t think managed to do so. She’s the reason that I took up guitar.

Much as I miss my mother, I wouldn’t trade any of my memories of her for another day with her. Tears are starting to well in my eyes right now, though, which feels like a good reason to stop musing here.

Draft Two

I find myself realizing that I don’t recall ever truly spending time to reflect on my relationship to ordered sound.12 Right now, I find myself incredibly reflective on a lot of things, even as I find it incredibly difficult to think at all. There are any number of reasons for this, but the most crucial of these is the fact that my mother died a month and four days ago.

I know the last time that I said goodbye to her, the last time I said goodbye to her body, and the last time I said goodbye to the idea of her as a physical part of my life. What I cannot recall with anywhere as much clarity, however, is the last thing that she said to me, when she last said it, or the last time I saw her awake. My little brother and I both realized at her wake that, for all that we had done our best as a family to prepare for her death, we had forgotten to get her to record a short voicemail that simply said she loved us.

Rather than dwell on that,13 I will instead focus on something that she instilled in me from a very young age: a love for music.14 She often expressed shock that all three of her sons ended up as musical as we did, which never made sense to me.15 From a young age, she encouraged all of us to do a lot of music, especially vocal music.

However, my musing today is not meant to focus on my relationship to performing music.16 Instead, I want to focus on my relationship to listening to music, and what music means to me. I might also spend some time thinking about some memories I hold deeply with my mother, if only so that there’s a record of that. Actually, that sounds like a much better choice.

I’ll save the general musing for another day. Today we will muse on

Draft One

For some reason, I am convinced that I’ve written a musing on music and my own relationship to it before. However, a quick search does not bring anything up, other than a very short one which mostly discusses my own relationship with music. So, my goal here, in addition to restarting the blog again17, is to spend some time really thinking about my relationship to sound in general, and music in particular.

When I was younger, I used to have a constant soundtrack following me while I was at home. There were any number of reasons for this, but one that I had not realized until I found myself in the boundary waters, unable to fill my life with constant sound, was that it kept me from dwelling on negative thoughts.

Now, writing that brings me to something that’s been keeping me from writing here for the past month or so. Especially since returning to America and restarting this blog, I’ve tried my best to avoid identifying others, or even really to put too much of my own personal life in this blog. However, I don’t know if that really serves me. Without writing it here, I have seen over the past month that I just don’t write at all.

A month and four days ago18, my mother died. The soundtrack which followed me in middle school kept me from thinking about the death of my grandmothers. The constant sound I use right now doesn’t really feel like it serves the same purpose.

In part, I think that might have something to do with the way that my own relationship to sound has changed. Mr. Tanner, a song which once occupied the entirety of my mind, no longer stops me from wearing deeper ruts in my unhealthy mental spirals. Studying music for a degree has given me new ways to abstract myself from what my ears experience. And, I think as importantly, I am twice as old as I was then. My relationship to my mind and body is fundamentally different.

Still, though, I do and have generally filled my time and ears with constant noise for a while, even predating my loss. For a while, that took the form of any number of audiobooks, especially while I was traveling places or otherwise engaged in activities that did not require my full focus.19 I cannot listen to audiobooks when needing to read, write, or otherwise focus my mind, however, and so I have thought a lot about the music I can use to work, if only because people are distracting and I work in a shared office space.

Music with words shares many of the same problems that an audiobook brings, though to a lesser extent.20 I find myself listening to the words more than to what I’m writing.21

Classical music makes me remember my days as a student, and I find myself trying to follow the flow of counterpoint. Soundtracks, another popular option, never catch my interest enough to have playing for a while. I’ve always had an interest in minimalist music,22 and that helped for a little bit.

Music for Airports, in particular, gave me an incredibly productive little while to work. However, more and more, I find myself realizing that the music I truly prefer is process music. As I have written this musing so far, I’ve been listening to “Piano Phase” by Steve Reich.

It’s a really interesting exploration of what happens when two pianos play the same simple motif at slightly different tempi. It explores the phase space of each note lying in relation to each other, and has a real sense of tension and release, despite being so few notes. However, it is repetitive enough that there it lets me continue to focus on my work.

In general, I find that right now I’m incredibly interested in the way that art can become obsessive. Villanelles, which are often seen as an inherently obsessive poetic form, are the only kind of poetry that my fingers seem willing to type.23 I’m sure that I could psychoanalyze that desire, and how it relates to the loss that I’ve experienced, but we’ve already left the initial topic of this essay so much that it hardly seems worth continuing this draft.24

  1. why we were driving there, whether we stopped there, any other details about the event I cannot recall at this point.↩︎

  2. and I unquestioningly believed, and have to this day never really bothered to confirm↩︎

  3. because apparently if you have a full orchestra and gospel choir you can’t call yourself a folk artist↩︎

  4. and my father, who actually purchased the music generally↩︎

  5. the Bad Examples, Dr. Hook and the Medicine Show, among others↩︎

  6. Arguably Bat out of Hell, even if I didn’t really pick up on the sexual supertext (I don’t know what to call something that is more blatant than outright stating) until recently↩︎

  7. more accurately, a concert in which I was a member of the ensemble↩︎

  8. which her wake would have us think meant constantly causing formative positive experiences in everyone she interacted with↩︎

  9. objectively excessively many↩︎

  10. are↩︎

  11. not speaking for my brothers, though I am almost positive they feel the same way↩︎

  12. or disordered sound, but music is a much more interesting thing to talk about than just “I am easily over stimulated”↩︎

  13. Tears formed in my eyes, and it immediately became hard to breathe. While that is absolutely a sign that I should spend time reflecting on this more, now doesn’t feel like the time↩︎

  14. of course, she was not unique in this. My father, brother, extended family, schooling, and so much more did the same, but, potentially for the emotionally charged reasons, the most emotive memories I have of music are with her↩︎

  15. That isn’t entirely true. She had been told often that she couldn’t sing well, and as I think about it, she didn’t tend to sing as far as I can remember. That’s sad, though for other reasons.↩︎

  16. Small’s “Musicking” aside, I do still think that there’s a difference to me in being the consumer or producer of music.↩︎

  17. For a variety of reasons, not least of which is that I want to be writing a lot more words↩︎

  18. as of the day of writing this↩︎

  19. playing video games, knitting, embroidery, and so on. Unfortunately practicing scales never became something I could do that for. Stretching, on the other hand, has always been a great way for me to feel great about listening to a book.↩︎

  20. of course, the fact that I do not listen to music at three times speed might have something to do with that↩︎

  21. for all that I don’t think I have a mental voice when I read, I know that I do when I write↩︎

  22. maybe not always, but for as long as I can easily remember, at least↩︎

  23. outside of a few needlessly dark songs, but that’s neither here nor there.↩︎

  24. wow meta↩︎

On Writer’s Slumps

First Published: 2024 July 2

Draft 1

I’ve written at least a few times about writer’s block. Today, however, a friend asked me to write about being in a writer’s slump. Despite not being within the friend’s own lived experience, I do feel like I have at least a vague idea of what was being referred to.

Writer’s slump, as I see it, at least, is at least apparently different than writer’s block. In writer’s block, the motivation to write is there, even if the ability feels as though it is not. In a writer’s slump, however, the motivation to write has vanished.

Most of the time, what manifests as writer’s block is itself a form of writer’s slump, at least for me. That is, most of the time that I feel as though I cannot think of anything to write, I am really just in a position where I don’t want to write, for whatever reason. As such, I hope that my methods for dealing with writer’s block can be at least a little helpful for an acute writer’s slump. Given that the friend is in more of a chronic writer’s slump, however, I don’t know if the advice is as helpful.

Of course, the first question I find myself asking when a hobby that once brought me joy no longer does is whether I have an interest in anything. My desire to do any particular hobby often ebbs and flows due to life situations and my own experience with the hobby. Sometimes it isn’t the season of my life to be doing any given hobby, and I find that being intentional about setting it aside1 does a lot to inspire me to pick the hobby back up when the season is correct again. If, for whatever reason,2 nothing seems like a hobby I want, then I address that instead.

However, that answer doesn’t always work. As someone who has made a commitment to publishing a large amount of content, for example, I do not always have the luxury of setting it aside. More than that, sometimes writing in particular is something that needs to be done completely independent of my motivation. So, how do I keep up with a hobby when I don’t want to, especially one like writing?

One of the best things I’ve found is simply journaling a little bit, especially since my writing is usually done on the computer. Writing the date and then simply listing what I want to write and why often helps inspire me to writing. When that fails to inspire me, I often find that typing a motivational phrase3 helps me to remember why I’m writing. That leads to the best piece of advice that I have, which is to figure out why I want to write whatever I claim to want to write. If the goal is simply to write for the sake of writing, then I often swap between writing vaguely related to my thesis, the book I’m writing, inspiration for other books I’d like to write, and this blog depending on which feels best. When the goal is to write something in particular, however, I try to find a motivation that remains resonant to myself.

If all this fails, of course, I rely on external motivation in the forms of bribes and threats.

  1. often literally. If I have a physical project that works, I will move it a few feet away into a place where, although still visible (because anything I cannot see doesn’t exist), I have actively chosen not to engage with it↩︎

  2. cough cough, burnout, other things that aren’t going on the blog↩︎

  3. I’m partial to “the only way out is through, the only way through is forward, and the only way forward is going” myself, but that is because the phrase has taken an almost ritual meaning to me↩︎

Semi-Yearly Reflection

First Published: 2024 July 1

Draft 1

Well, it’s been half of a year! Despite the fact that I haven’t really blogged at all1, I do still want to keep making progress on all of my goals. Since it’s the first of a month, and the first of the quarter and half of the year, it seems like a good idea to potentially look through all of my goals and see where they’re at. My monthly goals2 were:

Moving to the yearly goals, I am somewhat curious about whether they still feel resonant and whether I’ve made adequate progress on them.4

Well then, with all this in mind, what are my goals for the month?

With this in mind, the daily reflections will be:

Given that the day isn’t quite halfway done right now, I’m debating between publishing this now and then adding a new draft later, and just waiting to post it until closer to bedtime. I’m leaning towards the latter, as it will give me more time to get items on the list finished.

Having now gotten to the end of the day:

  1. including after my post claiming that I would restart, whoops↩︎

  2. admittedly in January↩︎

  3. and I kind of want to plot out every chapter until the end of the arc↩︎

  4. Given that we’re halfway through the year, being halfway to the goal seems like something reasonable↩︎

  5. on? like it’s in works↩︎

  6. and I think that I lost another of them, though I have no clue where it could have gone (which I suppose is evidence for its being lost)↩︎

  7. technically still remains, because I do really need to drive up there sometime soon↩︎

  8. well a new to me one.↩︎

  9. meaning like decide that there’s nothing in the content that I need↩︎

Restarting (Again (again again again))

First Published: 2024 June 25

Draft 1

At some point I should really stop just appending a new again to the end of the title. Of course, at some point I should really either stop giving up on the blog or give up on it forever.1 That being said, neither of those are happening now.

I’ve started to get the familiar summer itch2 to restart the blog, and so here we are. Very few updates since last time, though of course, if you’re interested, they’re mostly available on my yearly goal tracker. In general, I think that I’ve been doing fairly well, which is nice to be able to say.

Anyways, I’ve now basically given up on the post for the day, so I’m going to post this. Hopefully tomorrow I’ll be up to the rest of the reflecting I should do.

  1. hmm actually no I do really think that there’re points in my lives wherein the blog is better or worse for me. That being said, I do generally feel like the majority of points in my life are at least not worsened by the presence of a daily blog post, and it does help me to remain more reflective↩︎

  2. ok so scrolling through the calendar of my posts, it doesn’t really seem like there’s a rhythm or rhyme based on the pseudo solar calendar we all know and love↩︎

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.

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↩︎

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