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Somehow I immediately stopped writing this blog again for a week, and I’m sorry for that. Anyways, I have a talk in a little over two months that I’d really like to go well, so now feels like as good of a time as any to start planning it.

My general plan for the talk is to try connecting astronomy¹ and music/tuning theory generally.² In theory, I should be able to tie the two together fairly easily. In the early days of Western Music and Astronomy, the two concepts were seen as pretty much the same. Or, if not the same, at least both very related.

So, my goal here is to start fleshing out the ways that I could construct the talk. Currently, my plan is to go through a history of the way different philosophers thought of the two concepts, and then move from there into the way they might have experienced music. From there, I’ll just hard pivot to tuning theory.

So that’s 6 different works/authors I need to read in order to create a cogent narrative. Thankfully, I can kind of just do the whole musical section by memory, since I already know much of what I need there.⁴ Anyways, I should really start reading them and thinking of an actual talk title.

because the talk is being hosted by my University’s Astronomy Department’s Outreach Team↩︎
because I like that topic and am always sad that others don’t know about it.↩︎
i think↩︎
The issue with tuning is that 1:2 (octave) and 2:3 (fifth) never line up, so you can’t have both in tune (that gets a major asterisk but)↩︎

On Metaphor

Draft 1

This past Sunday I remarked,¹ about how the work I do is entirely within the ivory tower. In my eyes, at least, there is almost no chance that a hungry person will be fed or a homeless person housed as a result of my research. A new friend commented that my research should instead be thought of as evangelizing wonder. I like that.

Earlier in the conversation, I was explaining how an FTIR² works. One of the other people in the conversation commented on how I did a really good job explaining hard concepts, which I thought about for the rest of the day. I have a lot of issues with the way we teach chemistry, and I guess hearing that was the inspiration I needed to start writing about chemistry. As I mentioned yesterday, I really want to work on that. I figure my blog³ is as good of a place as any.

So, what does any of this have to do with the title of today’s musing “On Metaphors”?⁴ Something that commonly bothers me about upper level chemistry and chemists is their denigration of metaphors. “Electrons dont really orbit around nuclei,” they say, “so why would we teach it that way?”

Maybe it’s because I’m a Catholic, so I understand how metaphors, while fundamentally untrue, still have a lot of use in understanding difficult concepts.⁵ Maybe it’s because I’m a musician, working in a field where we have to make the fundamentally abstract⁶ tied to completely physical and arguably meaningless values.⁷ Or, maybe it’s just because I like metaphors.

I think a good example of how metaphors work well, despite being wrong as you extend, can be seen in a way to teach multiplication.⁸ Imagine trying to teach someone multiplication. In this metaphor, to teach the multiplication of two positive integers⁹, you could say that you make a row of blocks as long as the first number and a column as long as the second. If you fill in the rectangle and count how many blocks you used, you get the answer for their product.

That is, if you are trying to multiply 2 and 3¹⁰, you make a rectangle 2 long and 3 wide. You would end up with 6 blocks in this method.

At this point, I can see two objections. The first is from the anti-metaphor people “that’s not what multiplication means”. Trying to teach what multiplication actually is is far too obtuse, in my opinion at least, to teach a child to love math.

I’m not going to go too far on a tangent, but I think that a primary goal of education should be instilling a love for the subject taught. That, of course, needs to be balanced with teaching the subject correctly, but I feel that the balance should skew more towards love of subject the younger a student is. A PhD student in Mathematics, for instance, probably¹¹ doesn’t need to be motivated to love math. A second grader¹², on the other hand, really does, especially given the culture we have.

Anyways, the anti-metaphor people are¹³ going to be unconvinced by any argument for metaphor, so I’m going to move on to the other objection. “Is that not just what multiplication is?” might be the other side of the argument. There are a few reasons that placing blocks into rectangles doesn’t accurately describe multiplication, which I’ll go into below.

First, this only works in the case of, as mentioned above, positive integers. Sure, you can weasel your way through some fractions through a few methods. For instance, if you’re multiplying by something and a half, you could just place a block every other row. I hope you see where that’s inherently wrong. Or, you could make blocks that are a fractional width of the standard box. That immediately stops working when we get to irrational numbers. I would love to see any person who can make a box exactly pi wide. There’s also the issue where the child in question is no longer counting blocks, but rather making unit blocks.

Another issue is that there is no way to do a negative number, let alone an irrational number. You can’t have less than zero blocks.¹⁴

Finally, multiplication isn’t just a number, it can also have physical meaning. In the post linked above, he discusses how three bags of five apples per bag multiplies through to get fifteen apples. In order to teach that problem, you rely on students abstracting out the meaning. As I learned teaching general chemistry, students have a lot of trouble with dimensional analysis.¹⁵

That being said, I still think the block metaphor is a good place for students to start with multiplication. It teaches better than repeated addition, which is something I just really don’t like as a concept. Once students understand how the blocks move, they¹⁶ can abstract out the blocks and multiply in their heads.¹⁷ And, it’s fun. Kids like blocks.¹⁸

I mentioned above that I might tie to powers, and I still have steam so I’m going to. The first few powers come kind of well with this block metaphor.¹⁹ Three to the first power is a line three blocks long. Three to the second²⁰ is a square three by three. Three to the third²¹ is a cube of side length three.

Sure, this doesn’t expand into the fourth dimension by building blocks, but I honestly see that as more of a pro than a con. Thinking in dimensions that aren’t 0,1,2, or 3 is really vital to a lot of the work that even I, a non-mathematician do. The sooner students start seeing that as an option, the better off they’ll be, in my opinion.

Anyways, as I keep writing this, I keep thinking of more benefits of blocks²², but I’m going to stop here.

as I probably do too much↩
Fourier-Transform Infrared (Spectrometers)↩
I still don’t know whether the pedant in me should really be saying ’blog, but↩
I know that common practice has punctuation within quotes but I hate that practice↩
see: every explanation for the Trinity and its associated heresy↩
feeling and emotion↩
the exact frequency of pitches, also the relative frequencies.↩
also powers but we’ll get there later↩
which is where I, at least, started↩
I still don’t know if I’m going to get into what numbers really are↩
hopefully↩
google says when kids learn multiplication↩
as strawmen must be↩
Economics isn’t reflective of physical reality↩
multiplying units to cancel and change them.↩
I think, I really have no idea how children’s visualization skills are↩
or on a piece of paper once they learn their times tables (which I do see incredible value in)↩
in my experience↩
the rest do too if you really want to get students thinking in many dimensions↩
squared one might say...↩
cubed??↩
learning limits, approximating areas (kind of the same thing I guess), learning that (n+1)² = (n)²+2n+1↩

Monthly Reflection

Draft 1

Welp, another month has slipped through my life. It feels like it’s only been two or so weeks, but that’s all kinds of untrue. Major life updates are really just that I’ve given my first public talk.

maybe friends!↩︎

Reflections on Today’s Gospel

Psalm 90:14 “Fill us at daybreak with your mercy, that all our days we may sing for joy.”

Draft 1

Today’s readings are certainly less cheerful than the past few Sundays have been. We begin in Ecclesiastes, where we are told that “All things are vanity”¹ That statement stands in stark contrast to a lot of meditations that I use, at least. Rather than emphasizing the fact that everything which is good comes from He who is Goodness, and therefore can orient us to the eternal, the author of Ecclesiastes instead focuses on the fact that most of our daily interactions are not directly with the divine. As a result, they are inherently transitory and empty.

This cynicism is extended in the Gospel passage, where we are told to focus on growing rich in what matters to the Almighty. Interestingly to me, immediately after this passage in the Gospel, Jesus tells his followers not to worry about food or clothing. He uses the imagery of birds and flowers, who do not work yet are beautiful and fed.

This is also really clear in the second reading. The pieces of us which are earthly lead only to ruin and sorrow. If we exist focused on the secular, we will end up living lives of vanity. We are instead to take on Christ and focus our eyes towards heaven.

On Running

Draft 1

As I mentioned in my last monthly reflection, I wanted to be able to run a 5K this month. I claimed to have run a 5K at reunion, which is debatably true. I entered the race, and I was given a reward for finishing.

But, I didn’t run it continuously. Instead, I took lots of walking breaks. Today, in contrast, I ran a full three miles continuously.¹

As I was cooling down from the run, I thought a lot about why running a 5K straight felt so strange. More or less, I think it comes down to the fact that² I in many respects feel like I’m past my prime as an athlete. I know that I’ll never be able to dive as well as I did in college,³ I’ll likely never swim as fast as I did in high school,⁴ and I probably won’t ever get my maxes up to where they were last summer.⁵

So why does running 3 miles matter to me? As far as I can tell, I have never run that far in my life. All through high school, I ran at most a mile at a time.⁶ Throughout college, I had a very frequent goal of running a 5K, but I was never able to get there. There are all sorts of excuses that I can make as to why I never did, but they fundamentally boil down to the fact that I’ve always thought of myself exclusively as a sprint athlete. As any coach or modern self-help book can tell you, a fixed mindset where you believe you can’t do something will generally see you being correct.

I think about a poster which hung⁷ somewhere in high school. It read “Whether you believe you can or you can’t, you’re probably right.” I never saw myself as a person who could run 3 miles, and I was right. Now I know that I can.

Now that I’m done inflating my ego, it’s time to self-correct. Despite the fact that I wasn’t walking for any portion of it, my mile pace was less than 50 seconds faster per mile. I also apparently worked far harder, because my average heart rate was more than 30 points higher. I took an extra nine steps every minute, which is kind of funny. The part that’s wildest to me is that the peak of my heart rate during my first 5K was about the lowest that my heart rate was at during my run.

Anyways, the next goal is being ready for the “degree dash” that I signed up for, which apparently involves a 5.39⁸ ⁹ mile run. It’s weird that despite being a bigger difference in how far I can run than I was at, it feels much more doable of a run. Anyways, enough rambling from me.

which I am aware is not a 5K, but it’s close enough that I’m counting it↩︎
regardless of the truthfulness of it↩︎
mostly because I don’t have pool access↩︎
which I acknowledge is an unfair comparison because I tapered and shaved for it↩︎
if only because I don’t love lifting↩︎
or I snuck walks in in the middle of longer runs↩︎
hanged? I can’t remember which is which. Let’s see: cool hanged is people, hung is literally anything else. Posters are not people (allegedly) so we’re good↩︎
the average number of years it takes to complete a PhD↩︎
hmm, one source says 5.39, one says 5.41. That’s a big difference↩︎

Reflections on Today’s Gospel

Genesis 18:27 “Abraham spoke up again: ‘See how I am presuming to speak to my Lord, though I am only dust and ashes!’”

Draft 1

As with my last reflection, part of this is stolen from the homily I listened to today. In today’s Gospel, our Lord teaches his disciples how to pray.

Now, I always took that as just “say the Our Father,” but the homily I listened to pointed out something very different. The prayer that Christ teaches his disciples has the elements that our prayer should include. It begins with the familiar¹ relationship that we have with the Lord, beginning with “Our Father”. Our prayer should then turn towards blessing the Lord for His Goodness.² We move then into thanking the Lord for what He’s done in our lives.³ From there, we move to intercessory prayer.⁴ Then, we finish with praying for others.

The part that struck me most is the difference between how we are called to speak to the Almighty and how Abraham does in the first reading. Throughout the reading, Abraham reiterates his fundamental unworthiness to speak to the Lord, something which⁵ is missing from the prayer Christ teaches. I also see this reflected somewhat in the difference between how Jewish prayers⁶ and Christian prayers are structured.

More or less every Jewish prayer I’ve been taught begins with the formula “Blessed are you Lord our G-d, King of the Universe”, while most of the Christian prayers I can think of emphasize the fatherhood of the Almighty.⁷ There are a lot of reasons for this difference, but the most fundamental to me is Baptism. Under the Mosaic Covenant, Israel becomes the Lord’s people. In Baptism, we become His children. I’m struggling to really articulate the difference, but I think it can be seen somewhat in the line I highlighted.

We are as dust and ash because of our sinful natures. But we are washed clean in the blood of the Lamb through the Sacraments, and so can address the Lord more familiarly. The concept of ritual also comes in here.

Under the Mosaic Covenant, communicating with the Lord happens in very ritualistic manners. There are prescribed sins and remediations for the sin. Blessings are ritualized and rote, which is something Modern Judaism keeps.⁸ In a quick scroll, there are formalized prayers for many of life’s beauties, such as seeing rainbows or smelling flowers.

In contrast, the New Covenant places the emphasis of the law on our hearts. Gone are individual sacrifices for individual sins. Gone too is the concept of the priestly caste as wholly separate. We are all called to be Priest, Prophet, and King in our Baptism.

or familial↩︎
Hallowed be thy name...↩︎
Give us this day our daily bread↩︎
Ibid?↩︎
at least in my reading↩︎
that I’m familiar with↩︎
when prayer is focused on the Father of the Trinity.↩︎
such as the list here ↩︎

Whoops

Draft 1

How has it been almost two weeks since my last post? Intellectually it makes sense, but wow the passage of time is hard.

Anyways, I did finish the blanket which is exciting, and I’m again coming to the realization that when I stop exercising I also stop being productive. I haven’t been running or stretching really, which really puts a damper on my monthly goals. But, inspired by a friend making a book review blog, I think I might start reviewing books here.

Why, you¹ might ask, would I do that? At worst, I have a record of books I read and how I felt at the time. At best, I have a way to fill up days that I have nothing to write about. It should also help hold me accountable for not reading books that I don’t want to review.² Then again, I may not actually review everything I read.

my hypothetical reader/future self↩︎
because they lack any merit, no other reason↩︎

Finishing a Blanket

Draft 1

I was at a craft circle when I started a bag that I made last week. Apparently my¹ ability to crochet got people’s attention, because one of the other members asked if I could help crochet one of their projects shut.

Another, later, messaged me to ask if I would be willing to finish a blanket that a dead friend of theirs started. I still don’t know how to respond to messages like that, but I went with “Yeah! I’d be happy to.” which may be too chipper in retrospect.

But, as it turns out, all the crocheting is done on the blanket. The person who asked knew that the pieces were all done and just needed to be assembled, but thought that also required crochet. Not so. It requires stitching, whip stitches to be exact.

Finishing a join that the friend² had started was terrifying at the end, because the strip I joined was longer than the one I joined it too. When I finished my second join and found that it was even longer I will admit to a slight panic. But, I realized it’s not totally my fault.

Of the five remaining panels to join³, each is a different length, with up to 6 inches difference. Anyways, I’m having fun practicing my whip stitch and getting better at it!

incredibly meager↩
presumably↩
six already being joined↩

Reflections on Today’s Gospel

Deuteronomy 30:10 “If only you would heed the voice of the LORD, your God, and keep his commandments and statutes that are written in this book of the law, when you return to the LORD, your God, with all your heart and all your soul,”

Draft 1

Being totally honest, the homily I listened to was absolutely stunning and I’m just going to steal from it. In the Gospel today, Jesus is confronted by a scholar who asks what the greatest commandment is and how he can follow it.

The priest pointed out that the scribe wants to have neighbor be as restrictive a category as possible. After all, if we have to love everyone like ourselves, where can we keep room in our hearts for hatred? But, Love is not satisfied with restrictions. Love is overwhelming and seeks to exceed.

In such a way, our neighbor is the whole of humanity. We are called to love the Lord with all of ourselves, heart, mind, body, strength and being. It may be incorrect, but I always saw the two parts of this commandment as a what and how. How do we love the Lord? We love the Lord in part by receiving sacraments and praying, obviously. But, we also love the Lord by loving our neighbor.

Anyways, that’s something I’ll have to think about and focus on for the next week. How do I avoid prioritizing my own self-interest above others?

Dungeons and Dragons Again

Draft 1

I just reread my ¹ last reflection on DnD and it’s funny. Apparently the last I wrote about Dnd was also a one shot hosted by one of my friends.² This was a much smaller group, only the three of us.

As before, we claimed we would end at 9, but really ended at 9:30ish. It was one of the group’s first time playing which is always really interesting. The way that people who aren’t super familair with the mechanics of the game approach it is far different from the way I³ do, often in really positive ways.

We three people met in the City of Arches, where we were hired by a Celf⁴ to find a chest of his and destroy it. Due to various shenanigans,⁵ we only got to a reasonable clue for where the chest was likely to be before we ran out of time.

I played a half-elf sorcerer with the gold-dragon sorcerous bloodline. It was funny because the other two PC’s were a high elf and a gold dragonborn, so in a way we were a fun little spectrum. I really enjoyed the session, and I think it’s more likely we continue this into a multi-shot, if only because there are fewer of us.

I think↩
the same one, coincidentally.↩
admittedly inherently metagaming↩
Cow Elf, from the Haywilds. Yes I love my DM↩
both in and out of character↩

Musings

I'm just copying my father

Home

Talk Planning

Draft 1

On Metaphor

Draft 1

Monthly Reflection

Draft 1

Reflections on Today’s Gospel

Draft 1

On Running

Draft 1

Reflections on Today’s Gospel

Draft 1

Whoops

Draft 1

Finishing a Blanket

Draft 1

Reflections on Today’s Gospel

Draft 1

Dungeons and Dragons Again

Draft 1