First Published: 2022 August 16
Like my last post on the topic, I missed writing and uploading a post last night because I was at an open mic. Unlike last time, though, I was performing at this one. A friend from my graduate program and I have played at this open mic twice now, and it was a great time.
The vibes are really nice at the place. The crowd is generally supportive but not hyperfocused on the music.1 The other performers were almost universally better than me, but incredibly supportive.2 So yeah! I’m excited to keep going.
First Published: 2022 August 14
Jeremiah 38:4 “Then the princes said to the king, ‘This man ought to be put to death. He is weakening the resolve of the soldiers left in this city and of all the people, by saying such things to them; he is not seeking the welfare of our people, but their ruin.’”
Again I start this reflection reflecting on the lack of cheer. All three readings point to a single common element today: the Peace we are promised is not temporal. That is, though living a Christian life will bring us peace, that does not mean we will live without conflict. Each reading points to a different way in which our struggles to live as Christ commands will be redoubled by the world.
In the first reading, we hear Jeremiah being condemned by the nobility in the city. In the context of today’s readings, this reminds us that to live a holy life is to be persecuted for righteousness. Now, this isn’t to say that people being mad at your choices means they’re holy, there are plenty of ways to be persecuted rightly. But, to truly live a life centered around the Lord’s will means going against the powers of the day.
The second reading reminds us that, though our spiritual struggles are painful, we are spared from the worst of it. Indeed, there is no way that we could redeem ourselves through merit alone. It is through the grace of our Lord alone that we have the strength to resist sin, and it is through His sacrifice that we are redeemed. This reading reminds us that, though we can always strive more, we should strive always to model Christ.
The final reading is in many regards the hardest. The Church has always had enemies with temporal power, and hopefully there’s no need to be reminded that Christ suffered for us. Instead, the Gospel today tells us that even the people we love most in this world may be at odds with us in following a holy life. There’s an expression I’ve heard, that all love on Earth is only good in so far as how it orients us to He who is Love, but having it expressed as Christ does showcases the pain. There is a more joyful reading though: the love a parent has for their child is nothing compared to the love that Love has for us.
First Published: 2022 August 10
This summer I joined a book club at my parish. The book the parish chose to read was C.S. Lewis’s1 The story is a retelling of Eros and Psyche focusing on one of Psyche’s sisters.
I really enjoyed the book, especially looking back on it. At the beginning, I found that there was a lot of anger and world-building that I couldn’t quite see the point of. Unlike most of the Lewis books I’ve read, there was no immediate didactic idea I could find.
I really don’t know how to write a review, but I did really enjoy the book. Lewis does a great job taking an unreliable narrator and using the unreliability in the text. Most of what is beautiful about the book to me entirely spoils the reveal of the book, so I’ll leave it there.
The general premise of the book is that in the kingdom of Glome, which is far from Ancient Greece, there lives a king and his three daughters. One of them is beautiful, one shrewd, and one doesn’t really matter.2 The first two3 are mentored by a Greek, who they lovingly refer to as the Fox.
Overall, I’d give the book a 4 out of 5. It was really captivating as it continued, and it has a lot of great places for me to see how I can improve as a person. However, the beginning was really slow for me.
First Published: 2022 August 9
Yesterday I claimed that I have the ability to freestyle a cogent narrative about tuning theory. To test1 that claim,2 I figured that I should do that here. Halfway through writing this, I already realize that I can speak on the theory, though not in a cogent way.
I hope that I don’t need to motivate what music is, at least informally. Pitch is fairly fundamental to most of Western Music3. The concept of pitch as inherent to a specific body is an ancient thought.
Pythagoras is reported to have begun his theories on tuning when he observed blacksmiths. Regardless of how hard the smith struck an anvil, each anvil rang at its own pitch.4 He then allegedly measured them, and found what it was about each anvil that made it produce its specific pitch.
Moving now from the story to reality, tuning theory is based primarily on the harmonic series. The harmonic series is produced5 by any resonating body. It’s really easy to visualize harmonic series now that Fourier transforms are easy to perform. Put simply6, it’s every7 integer multiplication of a base frequency. That is, if your fundamental pitch is at 100 Hz, the first harmonic occurs at 200 Hz, the second at 300, and so on.
The ratio between any two8 of these pitches in the series corresponds to a harmonic interval. A one to two ratio is an octave.9 A two to three ratio is a fifth. A three to four ratio is like a 2:3:4 ratio, and so therefore a fourth, since stacking a fifth over a fourth is an octave. A four to five ratio is a major third.
The human ear, of course, can’t perfectly hear intervals. If you have something close to a 2:3 ratio, instead of hearing 1999:3001, for instance, your ear is likely to hear a simple 2:3. The smaller the numbers in the ratio, the more likely it is that you will hear when it’s out of tune.
Pythagorean tuning is the earliest Western tuning we have. It’s based on the first three pitches of the harmonic series. To construct it, start with a base frequency, then stack fifths until you get back to your starting note, dropping octaves as needed.
Of course, the mathematically inclined among you may notice that this doesn’t mathematically work. Other than the trivial case of n = m = 0, there is no m and n that satisfies: $$\frac{1}{2^n} = \frac{2^m}{3^n}$$ If you plot how close these numbers are, you will see that the closeness of fifths is optimized at 12 and 24.10
To balance having few pitches with good octave and fifths, they chose 12. The final fifth is just incredibly out of tune, and called a wolf fifth, because it “sounds like a barking wolf”. Thirds are also somewhat out of tune. That’s because a harmonically tuned major third is a 4:5 ratio, as mentioned above. In Pythagorean tuning, each step is well tuned, being a 8:9 ratio. However, two steps then becomes a 64:81 ratio, which is slightly different than 4:5. That’s not horribly out of tune. A minor third in harmonic tuning is a 5:6 ratio. A minor third in Pythagorean tuning is a a 32:27 ratio, which is different than 5:6.
As a result, as harmonies in the medieval time period started becoming based more around the third than the fourth and fifth, new tuning systems were derived. Among these is quarter comma meantone, where you take the difference between 12 fifths and an octave, the comma, and distribute it to make four intervals slightly worse. Other tuning systems come too, such as the well temperment of Bach fame. One commonality among these systems is that each key sounds different, because the intervals are slightly different.
Now we come to the modern tuning systems of equal temper and stretched octave equal temper. Why have intervals based on simple ratios, when you can instead say only the octave matters? In equal temper, each half step is the twelfth root of two larger than the note below. To discuss the difference between different temperments’ interval size, we use the term “cents”. One hundred cents are an equal tempered half step. Stretch octaves is what pianos are tuned to. Scientists have found that octaves slightly larger than 1200 cents sound more like an octave than a real octave does, so piano intervals are even different. Before this turns into a rant on pianos, I’ll move on.
In retrospect, maybe I should start with the explanation of equal temper so that I can say what the difference between intervals in tuning systems is. Anyways, this is at least some text that I can11 clean up and throw onto a slide deck. I think I cover most of what I want to cover here, though maybe I should tie it into the astronomy? That ties with Kepler well. We’ll see I guess.
Yesterday I claimed that I have the ability to freestyle a cogent narrative about tuning theory. To test12 that claim,13 I figured that I should do that here. Halfway through, I already realize that
I hope that I don’t need to motivate what music is, at least informally. Pitch is fairly fundamental to most of Western Music14. The concept of pitch as inherent to a specific body is an ancient thought.
Pythagoras is reported to have begun his theories on tuning when he observed blacksmiths. Regardless of how hard the smith struck an anvil, each anvil rang at its own pitch.15 He then allegedly measured them, and found what it was about each anvil that made it produce its specific pitch.
Moving now from the story to reality, tuning theory is based primarily on the harmonic series. The harmonic series is produced16 by any resonating body. It’s really easy to visualize harmonic series now that Fourier transforms are easy to perform. Put simply17, it’s every18 integer multiplication of a base frequency. That is, if your fundamental pitch is at 100 Hz, the first harmonic occurs at 200 Hz, the second at 300, and so on.
The ratio between any two19 of these pitches in the series corresponds to a harmonic interval. A one to two ratio is an octave.20 A two to three ratio is a fifth. A three to four ratio is like a 2:3:4 ratio, and so therefore a fourth, since stacking a fifth over a fourth is an octave. A four to five ratio is a major third.
The human ear, of course, can’t perfectly hear intervals. If you have something close to a 2:3 ratio, instead of hearing 1999:3001, for instance, your ear is likely to hear a simple 2:3. The smaller the numbers in the ratio, the more likely it is that you will hear when it’s out of tune.
Pythagorean tuning is the earliest Western tuning we have. It’s based on the first three pitches of the harmonic series. To construct it, start with a base frequency, then stack fifths until you get back to your starting note, dropping octaves as needed.
Of course, the mathematically inclined among you may notice that this doesn’t mathematically work. Other than the trivial case of n = m = 0, there is no m and n that satisfies: $$\frac{1}{2^n} = \frac{2^m}{3^n}$$ If you plot how close these numbers are, you will see that the closeness of fifths is optimized at 12 and 24.21
To balance having few pitches with good octave and fifths, they chose 12. The final fifth is just incredibly out of tune, and called a wolf fifth, because it “sounds like a barking wolf”. Thirds are also somewhat out of tune. That’s because a harmonically tuned major third is a 4:5 ratio, as mentioned above. In Pythagorean tuning, each step is well tuned, being a 8:9 ratio. However, two steps then becomes a 64:81 ratio, which is slightly different than 4:5. That’s not horribly out of tune. A minor third in harmonic tuning is a 5:6 ratio. A minor third in Pythagorean tuning is a a 32:27 ratio, which is different than 5:6.
As a result, as harmonies in the medieval time period started becoming based more around the third than the fourth and fifth, new tuning systems were derived. Among these is quarter comma meantone, where you take the difference between 12 fifths and an octave, the comma, and distribute it to make four intervals slightly worse. Other tuning systems come too, such as the well temperment of Bach fame. One commonality among these systems is that each key sounds different, because the intervals are slightly different.
Now we come to the modern tuning systems of equal temper and stretched octave equal temper. Why have intervals based on simple ratios, when you can instead say only the octave matters? In equal temper, each half step is the twelfth root of two larger than the note below. To discuss the difference between different temperments’ interval size, we use the term “cents”. One hundred cents are an equal tempered half step. Stretch octaves is what pianos are tuned to. Scientists have found that octaves slightly larger than 1200 cents sound more like an octave than a real octave does, so piano intervals are even different. Before this turns into a rant on pianos, I’ll move on.
In retrospect, maybe I should start with the explanation of equal temper so that I can say what the difference between intervals in tuning systems is. Anyways, this is at least some text that I can22 clean up and throw onto a slide deck. I think I cover most of what I want to cover here, though maybe I should tie it into the astronomy? That ties with Kepler well. We’ll see I guess.
prove?↩︎
and because I have no desire to actually do research on the topics I don’t know today↩︎
and other music, but I’m only doing Western thoughts here↩︎
there are connections I see to the photoelectric effect, but that’s too much of a tangent (for now)↩︎
in theory↩︎
I think?↩︎
positive?↩︎
sequential usually↩︎
I might use the piano in the room for these demonstrations↩︎
and so on and so forth↩︎
should↩︎
prove?↩︎
and because I have no desire to actually do research on the topics I don’t know today↩︎
and other music, but I’m only doing Western thoughts here↩︎
there are connections I see to the photoelectric effect, but that’s too much of a tangent (for now)↩︎
in theory↩︎
I think?↩︎
positive?↩︎
sequential usually↩︎
I might use the piano in the room for these demonstrations↩︎
and so on and so forth↩︎
should↩︎
First Published: 2022 August 8
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.
The general chronology, as far as I can find on Wikipedia, goes:
Pythagoras, who allegedly ties the two together. Of course, we have no surviving writings from him3, so I’ll look at Pliny the Elder’s Natural History, which apparently recounts the story.
Plato, who apparently discusses how we are formed to experience astronomy and music in the same ways with different senses in his Republic. Ideally I’d find more about his views on either, but we’ll see.
Aristotle, who apparently writes about it in his book “On the Heavens”, which sure feels like the sort of book I’d expect to see takes like this in.
From there we skip a while and move to Boethius. Boethius wrote “De Musica”, which again, feels like it will have good takes.
Kepler comes next. He apparently really wanted the universe to be musical. Even better, he’s still respected in astronomy stuff today.
Kinda ends there, except for the whole orbital resonance thing, which I don’t know if I want to get into.
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)↩︎
First Published: 2022 August 2
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↩︎
First Published: 2022 August 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.
My goals were:
Blog daily
Stretch daily
Be able to run a 5k
Listen to BiaY more
Practice guitar every day
Practice accordion at least 2x a week
Write a short story every day
Maybe finish the book?
Finish either of the two songs I’m writing. I started working on a choral setting of Stabat Mater Dolorosa, and I finally put some words and a melody to a chord loop I really like. It would be nice to finish a project
Welp, lets go through them in order:
I blogged 10 times. Welp, I could do better there.
I stretched less than ten times I think
I did it!
I set up a reading plan with a friend and got through three books!
I think I practiced guitar most days at least, and I’m certainly getting better
I practiced at least 10 times which is certainly an average of 2x a week.
I wrote 10. Wild that I got as many of each, because I really had no idea which I did more.
I cut the remaining plot points that I had been planning on writing, so as a result I am now done!
Well... I started writing a new song, more or less restarted Stabat, and dropped the other song after working on it a bit. I did also add chords to a song that a friend was working on.
In August I will try to:
Blog daily! As with last month, I prefer having a record of my times. I also have an idea for a chemistry book/curriculum I’d like to work on, so may post notes there.
Stretch daily. I really do feel better when I stretch more
Be able to run 5.49 miles. As I mentioned, I need to be able to, so might as well try.
Keep up with my reading buddy for BiaY. That feels self-explanatory to me
Practice guitar daily. I’m doing open mics with a friend1 and I’d like to not hold them back.
Practice accordion at least 3x a week. The above friends mentioned wanting some accordion on a song, so I’d better get better.
Revise the book I wrote? I don’t know if this is a good goal, but I would sure like it to be. I have certainly become a better writer since I started the book and I’d sure like to demonstrate that to myself.
Write 20000 words of a new story? I have an idea for an urban fantasy novel. Well. I have a few things I’d like to explore at least. At worst I can probably just write the sequel to the above book.
Decide what I want to write my Research Proposal on. That’s the next exam in my life, so I should work on that.
maybe friends!↩︎
First Published: 2022 July 31
Psalm 90:14 “Fill us at daybreak with your mercy, that all our days we may sing for joy.”
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.
Ecc. 1:2↩︎
First Published: 2022 July 29
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 5.3989 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↩︎
First Published: 2022 July 24
Genesis 18:27 “Abraham spoke up again: ‘See how I am presuming to speak to my Lord, though I am only dust and ashes!’”
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.
I’m going to stop here before I ramble too much more.