Sunday Morning Greek Blog

February 23, 2025

Family Feud: Joseph Forgives His Brothers (Genesis 45)

Filed under: Faith, Faithfulness,forgiveness,Genesis,Luke Gospel of,Psalms,Spiritual Warfare — Scott Stocking @ 2:21 pm
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The Lord be with you.

I’m not looking for a show of hands here, but I want you to think about this for a moment: How many of you can say you have an enemy? Now for myself, I can’t imagine that anyone in this congregation has an enemy, but then, I don’t know everything about your lives or what struggles or challenges you all have overcome throughout your life on God’s green earth. If you have an enemy, do you remember how they became your enemy?

I have had enemies in my life. The usual way I’ve made an enemy is that I’ve spoken an uncomfortable truth to someone and they haven’t wanted to accept it. When I lived in Paxton, Illinois, a local businessman wanted to start what he called a “Raffle House.” We had had issues a few years prior to that with a native American tribe trying to reclaim some land outside the town for a casino. The community successfully rebuffed it, in part because they were able to demonstrate there was very little evidence that the tribe had legitimate historical claim to the area. Because of that opposition, I figured there was still some fire left in the community to oppose a gambling operation in our conservative little town.

To make a long story short (A Tale of Two Photos), I discovered he was essentially offering a Bingo game without a State license to play Bingo and in the process skirting the 5% tax on Bingo required by State law, so I tattled on him in a letter to the editor. The Raffle House only lasted about 8 months before it went belly-up. A few months later, I received a tip from the owner’s disgruntled ex wife (or so it seemed) about a similar operation one of his relatives was running in the large college town 25 miles down the road. I reported it to the police there, and they shut it down almost immediately. The Raffle House owner wound up getting me fired from the church I was serving at the time because he had given money to the church, which he never attended, and demanded I recant. I didn’t recant, so I quit.

I don’t think that guy ever forgave me for the grief I caused him. But I forgave him. In fact, the experience I gained in researching the laws and regulations regarding that story helped land me my first full-time job after I moved back to Omaha a few years later. Did I “love” my enemy by confronting him? I’d had no interaction or relationship with him prior to all this coming up, but I’d heard a lot of things about his character, and very little was positive. Was I doing good to him by warning him about the State laws he seemed to be violating?

The Bible speaks of many different kinds of enemies and different ways we can respond to them. Our enemies can come from anywhere and can range from those who don’t know us at all to members of our own family (Matthew 10:36). They can be people who hate or dislike you for any number of reasons, including your gender or your skin color. They could be people to whom we speak uncomfortable or challenging truths (Galatians 4:16).

The gospel writers love to cite Psalm 110:1:

“ ‘The Lord said to my Lord:

“Sit at my right hand

until I put your enemies

under your feet.” ’[1]

This of course is one of the more prominent messianic psalms about Jesus being victorious over his “enemies.” Many Jews in the time of Jesus saw that as a promise that the Messiah would overthrow Roman rule, but God had a different idea. The enemies God had in mind were the Jewish leaders who had imposed a bunch of legalistic requirements on the Jews that weren’t necessary for salvation.

Paul says in his discussion of the resurrection in 1 Corinthians 15 says that Christ “must reign until he has put all his enemies under his feet. 26 The last enemy to be destroyed is death.”[2] So we’ll never really be free of our ultimate enemy, death, until Christ is victorious at the consummation of history.

The New Testament speaks quite a bit about how to deal with our enemies. “Resist the devil and he will flee from you.” “Turn the other cheek,” which in that culture meant don’t give your enemy the opportunity to continue to pummel you unless he wants to disgrace himself. “Carry the soldier’s pack a second mile,” which would by default bring shame upon the soldier. “Lend without expecting anything back.”

I could say much more about what the Bible says about our enemies, but I think we could probably learn a little more dealing with enemies if we take a look at the story of man who had enemies within his own family as well as at the highest levels of the Egyptian government. I’m speaking, of course, about Joseph. Genesis 45:1–15 tells the story about Joseph reconciling with his brothers, and I want to read that first here. But I will go back and highlight some of the other events of his life that reveal how he responded to having and rediscovering his enemies.

Then Joseph could no longer control himself before all his attendants, and he cried out, “Have everyone leave my presence!” So there was no one with Joseph when he made himself known to his brothers. 2 And he wept so loudly that the Egyptians heard him, and Pharaoh’s household heard about it.

3 Joseph said to his brothers, “I am Joseph! Is my father still living?” But his brothers were not able to answer him, because they were terrified at his presence.

4 Then Joseph said to his brothers, “Come close to me.” When they had done so, he said, “I am your brother Joseph, the one you sold into Egypt! 5 And now, do not be distressed and do not be angry with yourselves for selling me here, because it was to save lives that God sent me ahead of you. 6 For two years now there has been famine in the land, and for the next five years there will be no plowing and reaping. 7 But God sent me ahead of you to preserve for you a remnant on earth and to save your lives by a great deliverance. w

8 “So then, it was not you who sent me here, but God. He made me father to Pharaoh, lord of his entire household and ruler of all Egypt. 9 Now hurry back to my father and say to him, ‘This is what your son Joseph says: God has made me lord of all Egypt. Come down to me; don’t delay. 10 You shall live in the region of Goshen and be near me—you, your children and grandchildren, your flocks and herds, and all you have. 11 I will provide for you there, because five years of famine are still to come. Otherwise you and your household and all who belong to you will become destitute.’

12 “You can see for yourselves, and so can my brother Benjamin, that it is really I who am speaking to you. 13 Tell my father about all the honor accorded me in Egypt and about everything you have seen. And bring my father down here quickly.”

14 Then he threw his arms around his brother Benjamin and wept, and Benjamin embraced him, weeping. 15 And he kissed all his brothers and wept over them. Afterward his brothers talked with him.[3]

Those of you who know the story of Joseph, or who have seen Andrew Lloyd Webber’s Joseph and the Amazing Technicolor Dreamcoat, know how Joseph, the first born of Jacob’s first love, Rachel, was his favorite son and had received “a coat of many colors,” or as more recent translations put it, a “richly ornamented” (NIV 1984) or “ornate” (NIV 2011) coat, or as the NRSV puts it, “a long robe with sleeves,” which doesn’t sound nearly as exciting as the other descriptions. The point is it was a special coat that made his brothers extremely jealous. As the apple of Jacob’s eye, Joseph (17 years old at the time) had earned the ire of all his brothers. Not a very good way to enter adulthood!

Add to that his dreams that his whole family, including his father, would one day bow down to him, and it’s not hard to understand the intense jealousy toward him. Although it’s not biblical text, I think the line Joseph’s brothers sing in “Joseph’s Coat” from the musical captures their jealousy quite nicely: “Being told we’re also-rans/does not make us Joseph’s fans.” From that point on, they had it in for Joseph. So they did what any jealous brothers would do: they overpowered him, faked his death, and sold him to some nomadic Ishmaelites, who in turn sold him into slavery in Egypt. That haunted the brothers for the rest of story.

But Joseph, having escaped the enmity of his brothers, found himself as a favorite slave in the house of Potiphar, the captain of the Egyptian guard. However, even in that position, he had an “enemy” in Potiphar’s wife, who repeatedly attempted to seduce him. That eventually cost him his lofty position and landed him in jail. He probably could have been executed on the spot for such things, but I think Potiphar knew the character of his wife and needless to say, he didn’t think too highly of her. My guess is Potiphar knew Joseph hadn’t done anything wrong, but to save face publicly, he had to punish him.

Joseph found himself interpreting the dreams of two other officials of pharaoh, one being favorable and the other proving fatal, and the beneficiary of the favorable interpretation eventually remembered Joseph could interpret dreams and might be able to interpret a couple dreams pharaoh had dreamed. Joseph’s interpretation made sense to pharaoh, so pharaoh made him second in charge of Egypt. That essentially neutralized any of Joseph’s remaining enemies, if there were any left. Nine years later, two years into the famine, Joseph found himself with the perfect opportunity to get revenge on his brothers when they came to Egypt looking for food.

Most of you will remember that Joseph immediately recognized his brothers at this point, but they didn’t have a clue they were looking at their younger brother. So, like any good brother who’d been victimized by the rest of his brothers, he decided to play some head games with them to make them feel some pain. He had to be careful, though, because he was questioning his brothers closely about their intentions and accused them of being spies. They eventually “bought” some grain but had to leave one of their brothers in Joseph’s custody while they went back to Judah to get their youngest brother, Benjamin, whom Joseph may not have known.

The brothers went back to Judah to get Benjamin and discovered all their silver had been returned to them. Not sure how they missed THAT on the long trip. When they returned to Egypt a second time, Joseph kept at it with the mind games by seating his brothers from oldest to youngest and giving Benjamin five times the portions everyone else had.

That brings us to chapter 45. In spite of the fun Joseph must have been having playing these mind games with his brothers, he found he still loved all his brothers and broke down crying in a separate chamber. When he had composed himself, he returned to the dinner table and revealed himself to his brothers. Talk about being blindsided!!!

From this very real story then, what can we learn about dealing with anger or dealing with our enemies? [See also Psalm 37, which was read in the service before the message.] First, Joseph seemed to take much of this in stride. Never once do we read anything in the last fourth of Genesis about Joseph complaining about having been sold into slavery or wrongly accused of crimes against Potiphar’s wife. He knew what his own dreams meant and perhaps even when he was on the right path to fulfill those dreams, so he persevered through the worst conditions.

Second, and related to the first, Joseph never seemed to let anger get the best of him. When others in Joseph’s position found themselves faced with unfairness, they may not have endured with such patience and grace. His cool head landed him in the spot in Egypt, where his dreams finally came through: his father and brothers had to bow down to him to get the food they needed to survive. He trusted God to get him through to the fulfillment of those dreams.

Finally, he made a generous offer to his brothers and their now-large families: they could live in the land of Goshen during the famine so they wouldn’t have to make the longer trips from Judah. You and I may not have land-a-plenty to give away, but we can usually find a way to provide some small gift. There’s nothing wrong with a peace offering, especially if you know it would be accepted and there’s been a genuine attempt at reconciliation.

So what is the way to love your enemies? If you’re not a police officer arresting someone or a mama bear safeguarding her children, maybe you can try killing them with kindness. If God’s kindness leads us to repentance; if God can be kind to the ungrateful and wicked, then I think we can find a way to respond similarly when faced with the actions of our enemies. Kindness and love are always appropriate, and I learned even this past week just how important that is for maintaining peace. But that’s a story for later time. Grace and peace to you. Amen.

[1] The New International Version. 2011. Grand Rapids, MI: Zondervan.

[2] The New International Version. 2011. Grand Rapids, MI: Zondervan.

[3] The New International Version. 2011. Grand Rapids, MI: Zondervan.

March 16, 2024

8 ÷ 2(2 + 2) = 1, Part 2: A Defense of the Linguistic Argument

Filed under: Numbers (Cardinal & Ordinal),PEMDAS — Scott Stocking @ 12:30 pm
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(NOTE: This article was modified September 1, 2024, to include two new terms I recently coined: “functional monomial” and “operational monomial.” New material is in italics. When I say “PEMDAS” I’m implying Order of Operations (OOO) as well.

My original PEMDAS article has received quite a bit of traffic in the 11 months since I posted it. I’m well over 10,000 views at this point, which for the narrow appeal of my usual topics on this blog, is significant for me. It represented about one-third of the total views I had last year overall. The article has generated enough discussion that has allowed me to continue to fine-tune my arguments and further solidify my position that, bottom line, juxtaposed multiplication takes priority over any signed operations. I want to present a couple different views here, neither of which I feel has been adequately disputed by those who think showing me a page from a grade school math textbook is enough to convince me my arguments are faulty. I’ll start with an even stricter interpretation of PEMDAS then what the online PEMDASians apply, and then I’ll discuss the linguistic and syntactical arguments that has yet to be refuted by the paltry evidence the PEMDASians try to put forth.

A Stricter(!) Application of PEMDAS/OOO

(NOTE: This section is modified from post I made on Facebook to a different expression with similar issues.)

To refresh your memory, here is the expression in question:

8 ÷ 2(2 + 2)

Let’s start at the parentheses level of PEMDAS, shall we? The first step is simple enough. Add 2 + 2 to get 4, leaving us with:

8 ÷ 2(4)

Let’s set aside for a moment that this violates the distributive property to work what is inside the parentheses first, which would imply the expression becomes 8 ÷ (4 + 4} before solving what the parenthetical expression.

You’ll notice that we have parentheses around the 4, so we need to perform the function syntactically suggested by the parentheses, multiplication, to remove them. Notice I say “syntactically,” because math isn’t just about numbers, signs, and symbols; it’s about how those are arranged in an expression. This is the fatal error that the PEMDASians make: They fail to acknowledge the implicit relationships suggested by the presence of the parentheses.

The presence of the parentheses represents two issues: First, the juxtaposition itself implies parentheses around BOTH juxtaposed numbers as a single unit of value. We see this with mixed numbers, where the horizontal juxtaposition of a whole number and a fraction IMPLY addition, yet we treat the mixed number as one value. You’d be hard pressed to find a textbook that always puts parentheses around a mixed number in any expression. We also see this with fractions. Keep in mind that a fraction is not always intended to be a division problem. The figure 3/4 (diagonally juxtaposed with a solidus; or its display equivalent with vertical juxtaposition separated by a fraction bar or vinculum) would typically be pronounced “three-fourths.” The expression “3 ÷ 4” would be pronounced “3 divided by 4.” There is a qualitative difference between the two expressions, and we cannot assume that one substitutes for the other. It would be rare, but not unheard of, to see such a fraction with parentheses around it in an expression, because the fraction, like the mixed number, represents a single value.

The logical conclusion from this line of reasoning is this: If a juxtaposed mixed number is considered a single value and a juxtaposed fraction is a single value, then juxtaposed cofactors that use parentheses around one or more of the numbers to distinguish the values of the cofactors (i.e., “2(4),” “(2)(4),” and “(2)4”) all represent a single value of “twice four” as opposed to “24,” which represents “twenty-four” with no intervening parentheses. The lack of an operational sign (remember, the vinculum and solidus in in-line texts are grouping symbols first and foremost, NOT operational signs; only the obelus is an actual operational sign) in these three formats (implied multiplication, mixed number, display fraction) suggests that these forms do NOT fall with the last four steps of the “order of operations”/PEMDAS and instead should be given a higher priority. I would consider these “functional monomials,” because the function they perform is not explicitly stated by the use of operational signs but by the syntax of the format. This priority is heightened by the fact that when you have to divide by a mixed number or a fraction, you have to manipulate the fraction and the extant operational sign to properly work the expression.

Because “functional monomials” do not use explicit operational signs outside of their use in parentheses, they belong in the first two steps of PEMDAS/OOO where we find other functional monomials that reflect implied operations: powers (e.g., 33) and roots, factorials (e.g., 5!), and trig and log functions (e.g., 2 cos2 x; log10 423), among others. They are calculated before any other operational signs acting upon them and are not disturbed or separated by preceding operational signs. (See below for the discussion of “operational monomials” in contrast to “functional monomials.”

If you accept my first point above, then, this second point is moot, but I’ll address it anyway. We can’t get rid of the parentheses (remember, we’re still in the parentheses step) until we perform the function inherent in the parentheses. The PEMDAS/OOO charts get it wrong when they interpret “inside the parentheses” as only what is in-between the parentheses. “Inside” also means “inherent in the nature of,” so the function of the parentheses must be performed as well in the absence of any extant sign. The parentheses are still present, so we’re still in the parentheses step of PEMDAS. It’s at this point that the PEMDASians want to just simply replace the parentheses with a multiplication sign. But where in the parentheses step does it allow that kind of substitution? You have a syntactical relationship between the 2 and the (4) that simply disappears if one makes such a substitution. That substitution is not a valid or necessary math function when evaluating the written expression! Yes, you must use the multiplication key on a calculator if you really need to use one for this type of problem, but that is a matter of technology and not of math theory. The only way to address the parentheses at this point in the process and finish the parentheses step in PEMDAS is to perform the implicit multiplication first, because the juxtaposition creates an implied set of parentheses around the 2(4). Only then are we done with the parentheses step and are left with the simplified expression:

8 ÷ 8

Which of course equals 1.

Still not convinced that substituting the multiplication sign for the parentheses isn’t valid (except when you’re entering it into a calculator, but we’re not using a calculator here), then consider this. The relationship between the two 8’s is that of a dividend to a divisor only. We wouldn’t look at the way that is written and say 8 is the numerator and the other 8 is the denominator. It’s not written that way. We could only do that if we used a vinculum or fraction bar. As such, then, the vinculum, which is a juxtapositional symbol implying division, creates a unique relationship between the two numbers not implied by the obelus. As such, it’s not a valid substitution! With the vinculum, the numbers represent a part of a whole or the whole divided into parts. (I work in a field that requires a significant amount of government reporting on data, and they are always speaking of the populations in terms of which set is the numerator and which set is the denominator.) If the vinculum is such a juxtapositional tool that it creates or represents a unique relationship between the two numbers, then the parentheses serves the same purpose for multiplication. The 2(4) can’t be reduced to a simple multiplication. Depending on the context in which such an expression might arise, it may refer to a single quantity, like a bundle of 2 packages of golf balls with 4 balls in each package (8 golf balls).

Therefore, the only way one can claim that 8 ÷ 2 is somehow the term multiplied by what is in parentheses is to unequivocally declare it so by putting it in parentheses or constructing it as a block fraction using a vinculum vertically centered on the (2 + 2). As I said above, an expression using the obelus is NOT syntactically or linguistically equivalent to a fraction using the same numbers. Since the PEMDASians have failed to clarify the function of 8 ÷ 2 by enclosing it in parentheses, they do not have any solid ground to stand on to insist the answer is 16. This is where my other new term applies, “operational monomial.” If the problem had been written 8 ÷ 2 x (2 + 2), then those who believe the answer is 16 would have a point, because PEMDAS/OOO rules tell us division comes first, so they would then be correct to say the 8 ÷ 2 is the “term” as they define it that serves as the coefficient to the parenthetical expression. Since the expression uses an extant operational sign, it falls in the last four steps of PEMDAS/OOO, after the first two steps that represent “functional monomials.”

Explaining the Linguistic and Syntactical Arguments

(NOTE: This is copied from a response I made on the original article, with a few minor edits.) When I say there is a “linguistic” or “syntactical” component to the given expression, what I’m talking about is how Merriam-Webster defines the term: “The study of human speech including the units, nature, structure, and modification of language.” I take “speech” to mean the written word as well as the spoken word, especially since as a preacher I’ve gotten into the habit of writing out my sermons so I can make more intentional use of my language as opposed to speaking extemporaneously. And in the context of this article, I don’t just mean words alone, but any symbols or figures that we use to communicate, calculate, or cantillate (how’s THAT for an alliteration!): numbers, punctuation, “character” words (e.g., ampersand, &), mathematical and scientific symbols, proofreading symbols, and even music notation.

All of these elements of language, and linguistics more broadly, have their place in their appropriate contexts, and they are subject to their own respective set of rules for putting them together in a coherent form that communicates the message and meaning we intend subject to the rules and conventions of their respective contexts. When someone composes a musical score, the main melody or tune is subject to certain patterns that follow the chords that underlie the melody. If the tune doesn’t match the chords, it sounds, well, discordant. The notes of the melody, harmony, or even a descant are not strictly random. They typically have some relationship with the chord, and often playing a note that doesn’t exactly fit the chord prefigures a change in the chord or even a change in the key signature. Intentional discordancy is not without significance either, as it can communicate chaos or irrationality.

When we write a sentence, we generally expect a subject and verb to be close together and to arrange direct and indirect objects appropriately with any modifiers or prepositions, and so forth. For example, consider the difference between the three sentences, which have the exact same words.

  1. I eat fish only on Friday.
  2. I eat only fish on Friday.
  3. I only eat fish on Friday.

Sentence is truly ambiguous, because the placement of “only” can be taken either way. Is it “Fish is the only thing I eat on Friday” (akin to Sentence ) or “Friday is the only day I eat fish” (akin to Sentence )? Does that sound familiar in the context of this post? More on that in a bit.

In the original article, I make reference to the relationship between the definite article, noun, and adjective in a Greek adjectival phrase. The position of (or absence of) the definite article impacts how the phrase can be interpreted. I’ll use transliterated words to demonstrate.

  1. kalos logos [beautiful word]
  2. ho kalos logos OR logos ho kalos [the beautiful word]
  3. ho logos kalos OR kalos ho logos [the word is beautiful]

In Greek, Phrase , which has no definite article (the indefinite article “a” can fairly be implied absent other contextual clues), would be considered ambiguous by itself. We would need contextual clues to know whether it means “a beautiful word” or “a word is beautiful.” (Greeks do not have to use a form of the copulative verb “to be” if that is the only verb in the sentence.) In Phrase , the definite article precedes the adjective, which means the adjective is attributive, that is, it directly modifies the noun (“The beautiful word”). It doesn’t matter if the noun is first or last; it’s attributive either way. Phrase has a predicate construction. This means that the noun is the subject of a sentence, and the adjective would come after the verb in that sentence. In this case, it doesn’t matter where the adjective is, although there may be a nuanced implication one way or the other. Either way, the translation is still “The word is beautiful,” so no difference there.

Given those three examples (music, English adverb placement, and Greek definite article placement), I think anyone who’s reading this is starting to see the bigger picture of how linguistics (in this case, specifically syntax) influences mathematics as well, especially in the context of the expression at hand. So let me use the expression in the same way I used the sample phrases above:

  1. 8 ÷ 2(2 + 2) = 1 (in my worldview and the worldview of those who are of the same mind) OR 16 (in the competing worldview)
  2. (8 ÷ 2)(2 + 2) = 16 (in both worldviews; NOTE: if the expression had been written with (8 ÷ 2) as a block fraction with a vinculum centered vertically on the (2 + 2), there would be no argument that it equals 16; see text for my critique of that, however.)
  3. 8 ÷ (2(2 + 2)) = 1 (in both worldviews)

Expression A seems unambiguous from the perspective of one’s worldview then. But are both worldviews equally valid? We can make arguments from our respective worldviews to try to convince the other side, but it is very difficult to convince one to change their worldview without a powerful defining event that shakes their worldview to the core. Otherwise, we’re comfortable with our ways. I happen to think that several of the arguments I’ve made to support my worldview are quite devastating to the competing worldview, but alas! there has been very little evidence of any change of heart among their hardliners.

Just like the position of adverbs and definite articles, so then is the generous use of parentheses needed to clearly avoid the ambiguity of the given expression. But let me make yet another appeal here for the case that the given expression, in light of my demonstration here, is not really ambiguous at all. The juxtaposition of the 2 to (2 + 2) is akin to Phrase in my Greek examples above. The attachment between the two places them in an attributive relationship (the 2 is the definite article; the (2 + 2) is the adjective). The 2 directly modifies the (2 + 2) by telling us how many of that quantity we need to divide by and keeps the monomial on one side of obelus without an extant multiplication sign. In other words, it isn’t separated from its cofactor by the “action” of the obelus. There is no need for the extant multiplication sign because the relationship is clearly defined. If one were to place a multiplication sign between the 2 and (2 + 2), that would emphasize that the 2 and (2 + 2) are not cofactors and sever the relationship between them. This would make the expression like Greek Phrase above, where the modifier is divorced from what it modifies modified and dragged kicking and screaming all alone into the action of the obelus. That which appeared to modify the (2 + 2) now modifies the 8. The implications of the expression change by substituting the multiplication sign. Additionally, in the case of Greek Phrase , if we would add the implied copulative verb where it is not technically needed, that would also place emphasis on the verb and suggest a more nuanced meaning.

Greek verbs demonstrate a similar phenomenon; most Greek verb forms have an ending that tells you what “person” [1st, 2nd, 3rd, or I/we; you/you; he, she, it/they] is the subject of the verb. If there is no explicit subject accompanying the verb, the corresponding pronoun is implied [“He eats”]. If a Greek pronoun is used as the subject, that implies emphasis [“He himself eats”]; so an extant multiplication sign emphasizes the function of the sign over the relationship between the two cofactors when the multiplication is implied by parentheses. The bottom line for the Greek phrases, then, is when you add a word that isn’t necessary for the base form of what you’re communicating, you alter the meaning of what you’re communicating. You also alter the meaning when you add a multiplication sign that isn’t necessary for the basic calculation of the given expression.

This may seem kind of heady to some, but I hope I’ve made my position a little easier to understand. My worldview and what I consider the strength of my arguments here and elsewhere, along with a ton of historical evidence, do convince me that the given expression is unambiguous and has no need for extra parentheses to understand the answer to be 1. For those who think writing ambiguous expressions is somehow educational and instructive when you know there are those who think otherwise, I declare that you have met your match in me. Game over. Checkmate!

Pastor Scott Stocking, M.Div.

My opinions are my own.

May 29, 2023

Toward an “Active” PEMDAS: Strengthening Its Theoretical Foundation

Filed under: Numbers (Cardinal & Ordinal),PEMDAS — Scott Stocking @ 11:56 pm
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If you like this article, you may also like 8 ÷ 2(2 + 2) = 1: Why PEMDAS Alone Is Not Enough or 8 ÷ 2(2 + 2) = 1, Part 2: A Defense of the Linguistic Argument.

I’ve gotten caught up in the PEMDAS/Order of Operations (Parentheses/Brackets, etc.; Exponents; Multiplication & Division [left-to-right]; Addition & Subtraction [left-to-right]) discussions on social media. I must admit it is frustrating to see how religiously some people cling to an imperfect and almost thoughtless understanding of PEMDAS. It is a convention that, as currently practiced, has no theoretical soundness and is clearly NOT intuitive. In linguistic terms, I would describe the current application of PEMDAS as passive, that is, it doesn’t seek to recognize certain theoretical and intuitive constructs in mathematics, and even undermines them, and as such represents a primitive view of mathematics.

By “primitive,” I mean that some of the proponents of a strict PEMDAS are childlike in its defense, resorting to emotion and circular arguments based on their assumptions. No one has offered any proof that what they believe about its inner workings is in fact how people have historically interpreted some of these expressions. Nor have they offered anything to counter the various arguments and peer-reviewed documentation I have offered except by returning to their assumption and repeatedly showing us how they think the target expression should be worked even as we question their premise. PEMDAS pays too much attention to the individual signs and symbols, but it lacks the sophistication to understand the “syntax” or intention of certain conventions of expression we have developed over the centuries.

PEMDAS as practiced today is like reading the synoptic gospels of the New Testament without reading the gospel of John, or like reading the New Testament without also reading the Old Testament to understand its foundations. If you’re not biblically minded, it’s like reading Shakespeare without a 16th century dictionary at hand. I aim to fill that void here and make PEMDAS something so theoretically reliable that we won’t need to have wasteful discussions in social media about who’s right and who needs to go back to elementary school. My purpose is to propose such a theoretical structure whereby we can agree on one rule to address the issue of these viral problems.

Properties

I want to begin with a discussion about the basic mathematical properties we all had to learn at the beginning of the semester in Algebra. Properties are demonstrable principles in mathematics that will help lay the foundation for what some have begun categorizing as “grouping.” But more on that later.

Associative and commutative properties are intuitive. By that I mean that it’s obvious to most that if we have the expression

a * b * c

it does not matter how we “group” the terms, that is, how we “associate” them within parentheses or how we “commute” terms in the order of presentation, we get the same result. Every permutation of the variables multiplied together yields the same result. They’re all cofactors of the product, after all, so you get the same result every time. As such the following expressions are ALL literal identities of each other.

(a * b) * c ≡ (a * b)c ≡ (ab)c ≡ a * (b * c) ≡ a(b * c) ≡ a(bc) ≡ c * (a * b) ≡ c(a * b) ≡ c(ab) ≡ b * (c * a) ≡ b(c * a) ≡ b(ca), etc.

Distributive property is intuitive as well because it’s the undoing of factoring:

a(b+c) ≡ (ab+ac)

That expression represents implied (or implicit) multiplication, and the result demonstrates that the distributive property is a form of grouping equivalent to putting parentheses or brackets around the entire expression. As a type of grouping, then, it belongs to the P in PEMDAS. In addition, I would argue that even when there is an explicit multiplication sign used for the distributive property:

a * (b+c) ≡ (ab + ac)

this does NOT negate or override the application of the distributive property, and the expression thus written is also considered grouped and should be treated as if it has parentheses or brackets around it. Why? Because we know that if two expressions are equal or identical to a third expression, the other two expressions are identical as well:

a(b+c) ≡ a * (b+c).

Since both expressions are identical, it is necessary to consider both as grouped, as implied multiplication by the action of the distributive property at least, and in the case of the first one, by the syntax of implied multiplication. As such, my first proposal to strengthen PEMDAS and place it on a sounder theoretical ground is this:

Proposition 1: Mathematical properties should be considered at the same level of grouping as parentheses in PEMDAS, and when so recognized, the human person working such expressions has both the responsibility and authority, by virtue of any applicable mathematical properties, to place such expressions within the appropriate form of brackets to indicate priority given to the calculation. In doing so, the human person working the expression should ensure that any units of measurement or counting associated with the expression are not affected by so organizing.

The Trouble With Computers and Calculators. Most calculators do not recognize grouping characterized by this implicit syntax (I know syntax is primarily a linguistic concept, but for math, it refers to the arrangement of the signs and symbols, including the numbers, of an expression and how those influence the interpretation of the expression). You typically must apply the parentheses or brackets around the expression to force it to do so. Without parentheses, calculators assume all else in the syntax of an expression is explicit.

Implicit Multiplication Generally

Having trouble accepting implied multiplication is a form of grouping? What is a number with an exponent if not implied multiplication? The term 33, or in calculator language, 3^3 is 3 * 3 * 3, but we don’t undo the exponent notation if a division sign comes before it. Why? Because we’ve given this form of implied multiplication priority over signed multiplication in PEMDAS. The implied multiplication is grouped into the simple expression, algebraically speaking, of an. If you do deconstruct the implicit multiplication of an exponent, you’ve obviously taken PEMDAS to an unacceptable extreme.

PEMDAS does not address what to do with a factorial expression.

4! = 4 * 3 * 2 * 1

Algebraically, this is expressed as

n! = nPr =n(n – 1)(n – 2)…(n – r + 1])

where nPr is the number of permutations (P) of n things taken r at a time and n = r.

The factorial is also considered a form of implied multiplication, then. However, since PEMDAS doesn’t explicitly deal with factorials in the order of operations, how should we treat it? Algebraically, the first term in the grouping doesn’t have parentheses around it, so if we come across a ÷ n!, are we going to treat that as (a/n) * (n – 1)! then? Absolutely not! I’ve already hinted at why. It’s considered a grouping of factors implicitly multiplied. Because it’s a grouping, then, we would also treat it as if it were either an exponent or within parentheses. If these two types of implicit multiplication (powers and factorials) are generally treated at the E level in PEMDAS, why shouldn’t the implicitly multiplied expressions a(b + c) or even ab for that matter, or any variation thereof as described above, be treated at least at the E level, if not the P level of PEMDAS?

This leads me to my second proposition and a subsequent corollary to strengthen PEMDAS and place it on a more solid theoretical ground:

Proposition 2: In the absence of properties, any terms or expressions using implied multiplication should be considered at the grouping level of Parentheses in PEMDAS, and when so recognized, the human person working such expressions has both the responsibility and authority, by virtue of the implied multiplication, to place such expressions within the appropriate form of brackets to indicate priority given to the calculation. In doing so, the human person working the expression should ensure that any units of measurement or counting associated with the expression are not affected by so organizing. [Added 7/6/23] Within the grouping level, exponents and factorials should be processed first, then any implied multiplication would follow. So 3x^2 (without parentheses) should be evaluated as 3(x^2) and NOT (3x)^2.

Corollary 1: Any expression using explicit or implicit grouping markers (parentheses, brackets, juxtaposition, etc.) should NOT be rearranged in such a way as to undo the intention of the syntax or to fit certain elements into the framework of a property. For example, an expression in the form a/(bc) (explicit grouping) or a/bc (implicit grouping) should not be undone and reworked to become (a/b) * c or (ac)/b. NOTE: Some on social media tried to say the distributive property worked as follows:

b ÷ a(x+y+z) = [b * (x+y+z)]/a.

It’s ridiculous to think that a coefficient (or cofactor) should become a divisor in this situation.[1]

Let me also add here a call to return to standards. If the ISO standards don’t recognize the obelus anymore, then let’s just stop using it altogether. We can retain references to it for historical purposes, but in formal education (including textbooks), edit it out. People have tried saying the obelus is different from the vinculum, but again, I’ve never seen any formal explanation as to why this is, because the obelus isn’t a standard! I’m using it in this article because that’s how the expressions appear in the social media threads.

Excursus on Implicit Functions—Added 08/29/23 (from a post I made on Facebook), and lightly edited on 04/01/24.

Exponential terms don’t require a standard operator sign (+-x÷/) but rely on juxtaposition of the exponent.

Roots do not require a standard operator sign but the juxtaposition of the superscripted power and value in relation to the radical or of a fractional exponent. In some settings, the radical is NOT fully evaluated unless the answer can be expressed as a rational number. If the not-fully-evaluated radical is in the denominator of a fraction, the fraction must be rewritten so the radical is only in the numerator.

Factorials don’t require a standard operator sign but rely on the juxtaposition of a punctuation mark.

Cosine, sine, tangent, etc. don’t require a standard operator sign, but rely on the position of the measurement next to an abbreviated form of the word, and in the case of inverse trig functions, the juxtaposition of a -1 “exponent.”

Logarithms don’t require a standard operator sign but rely on the juxtaposition of a subscripted base (as needed) next to the abbreviated form of the word and the position of the value after the word/base combination.

Absolute value does not require a standard operator sign but juxtaposes, or brackets, the value between two pipes.

A fraction written with a vinculum does not require a standard operator sign that typically disappears when the operation is performed. The vinculum typically only disappears when the fraction can be represented as a whole number (mixed numbers, which consist of a juxtaposed whole number and fraction [implicit addition!!], typically have to be converted to an improper fraction when working them in an expression) or when, during the evaluation of the expression, the denominator divides evenly into the numerator. The fraction is a vertical juxtaposition of the two values with the vinculum indicating the grouping in the denominator and the relationship with the numerator. This is implicit division without actually dividing the two values to create a decimal. A fraction is considered a single value and NOT necessarily a division problem in the context of an expression. [This paragraph expanded from original on 04/01/24.]

Now while some of these functions do require parentheses to group the values being evaluated, NONE of them have a standard operator sign extant outside of any values in parentheses. These are all implicit functions, that is, they essentially have an implied set of brackets (or parentheses or some other grouping symbol) around them so they’re taken as a unit, or operand if you will. We don’t break out the implied multiplication of the exponent or factorial and supply the signs when evaluating the expression. Neither do we break out the implied addition when dividing by a mixed number, except in the manipulation of the mixed number to an improper fraction. In my opinion, that belongs in the P (parentheses) step of PEMDAS.

In the same way, an expression such as 2(2+2) is an implicit notation (no operational sign outside of the parentheses), so it belongs in the category of implicit functions. Operator signs break up an expression into operands. All this talk about “terms” that some have promulgated in the social media pages is meaningless, especially since the given expression above is technically one term by their own definition. We can debunk the contention 8 ÷ 2 should be treated as a fractional coefficient to what’s in parentheses. The obelus indicates we have two operands: 8 and 2(2+2). As an implicit function, with presumed parentheses around it, the 2(2+2) stands alone as the divisor in the expression. It should NOT be separated.

By the way, here’s how Wolfram defines “operand”: “A mathematical object upon which an operator acts. For example, in the expression 1×2, the multiplication operator acts upon the operands 1 and 2.” Implicit functions should have priority over explicitly signed operations and would need to have its own priority in PEMDAS for the functions included in that category.

End excursus.

Creating the Theoretical Foundation for PEMDAS.

Are you following me so far? Because I’m about to make it even more interesting. PEMDAS is neither intuitive nor theoretical (at least as applied) because there’s no proof to show why any one operation should be given preference over another. It is a convention that has rather haphazardly come into being historically without, as far as I can tell, any serious discussion about its theoretical or practical validity. As such, it does NOT mathematically or logically carry the same weight as properties.

The “intuitive” thing for a person to do just seeing a complex expression for the first time would be to simply work left-to-right through the symbols because we learn to read left-to-right in most languages. So such a person would treat the following as if it were in a series of brackets:

2 * 3 + 4 ÷ 5 – 6 = –4

becomes

{[(2 * 3) + 4] ÷ 5} – 6 = –4.

We used to play a game like that in 5th & 6th grade math class, where the teacher would give a string of numbers and operators (occasionally they’d put some operation in parentheses to see if we were paying attention) and we’d have to keep up with the math by taking the total as each new operator-number combination was announced and perform that operation on the running total. There was no going back through the string and figuring out PEMDAS or whether the distributive property applied. Whoever spit out the correct answer first got to advance toward the front of the class.

When we’re talking about PEMDAS, then, we’re talking about pedagogical construct that, historically speaking, seems to have been formulated rather hastily and loosely without much theoretical forethought. First, PEMDAS doesn’t account for everything that could be happening in an expression. I used the example of the factorial expression above. I’ve never seen anything in any explanation of PEMDAS that suggests where such an expression would fall. The factorial is important, for example, for calculating permutations. Treating a factorial in the wrong level of PEMDAS can potentially create false expectations about the probability of some event, like drawing winning lottery numbers. Exponents seems to be the most logical place because the factorial is a form of grouping by implied multiplication just like exponents are.

Second, in practice, PEMDAS is decidedly passive. It leaves too much room for interpretation, especially when historically, people have considered terms with implied multiplication to be grouped, bound, and inseparable. The PEMDAS absolutists in the social media threads on such problems have no respect for that historical reality. They suggest that the older generation’s understanding of PEMDAS is outdated when the real problem is their methodology and lack of critical thinking skills. This lack of critical thinking is becoming increasingly prevalent in American education today. Instead of a passive PEMDAS, we need an active, robust PEMDAS that focuses more on intentional grouping and a more sophisticated definition of grouping based on the assumptions made in the syntax of algebra.

Third, strict PEMDAS, at least as practiced by the absolutists, is no better than a calculator, because it fails to consider the implications of implicit multiplication. A calculator may be able to perform calculations quickly, but it doesn’t have a “mind” like you and I do to analyze the syntax and context of an expression.

The Priority of Operational Signs. Now that we have addressed the grouping issue and the weak nature of PEMDAS as currently practiced (if the absolutists are to be believed, anyway), it’s time to address the basic functions of mathematics: multiplication and addition. Since multiplication and addition are the primary operations mathematics, division and subtraction are respectively subordinate to them. We all can agree, I suppose, that division is multiplication by the inverse of the divisor, and subtraction is addition performed on a negative number. So while we’re beefing up the order of operations with a more active and robust use of parentheses to ensure any expression is solved the way its creator intended, let’s get rid of the obelus and the slash (solidus) as well and make everything about multiplication and addition. After all, isn’t that what we do when we divide by a fraction? We manipulate the expression (invert and multiply) to perform multiplication first, so wouldn’t that argue for the priority of multiplication in that instance? Let’s use only the vinculum to indicate “division,” and let’s put parentheses around a fraction with a vinculum so there’s no question that the vinculum is grouped. Fractions are, after all, more accurate than decimals if the decimal equivalent is not finite.

Let’s change all subtraction expressions to adding negative numbers expressions. Let’s keep all expressions with radicals as exponent expressions as much as possible. Let’s focus more on ensuring the proper ORDER of operations using parentheses and brackets rather than assuming everyone treats every expression in a uniform way. Obviously, that’s not happening right now. We can’t have a system of math where people are coming up with two (or more) answers to the same expression because they’ve been taught different things about it or work from a different set of assumptions. We need to firm up PEMDAS so we can have a uniform understanding of what fits where and restore uniformity. Without that, we’re wasting precious time arguing about ambiguities. It’s time someone cleared those ambiguities up. That’s why I’m stepping forward here to offer a theoretical solution.

One more question: If multiplication and addition are the primary operations of mathematics with division and subtraction respectively subservient to them, what is the theoretical reason then that multiplication and division are treated equally left-to-right? Why wouldn’t multiplication and addition be given priority over division and subtraction? I’ve never seen an explanation for this. After all, there are some out there who have a multiplication-first view of PEMDAS. I’m not sure I can fault that view given that multiplication has formal properties associated with it while division does not.

Conclusion

This whole process of “thinking out loud” in the social media posts has been, in my mind, anyway, a helpful discussion. In the process, I have more firmly codified my own beliefs about PEMDAS, as I’ve done here, and have continued to do so over the past year. I am even more firmly convinced that those who haven’t gotten the same answer as me on the more popular manifestations of this PEMDAS debate have a lack of theoretical understanding that should be corrected. I hope that I have filled that gap and that I have convinced at least some of you that the answer is 1, not the square of the numbers in parentheses (see Demonstration Proofs 1 & 2 below). I offer my proofs below of the three most popular expressions as a demonstration of application to my principles.

I do think PEMDAS is a valuable pedagogical tool, when properly understood with solid theoretical underpinnings. Professor Oliver Knill has repeatedly said the only way to ensure a problem is worked the way one means to is to overuse, if necessary, parentheses and other groupings.[2] Otherwise, ambiguous problems remain open to interpretation, and we’ll never get any kind of uniformity. My attempt here is to promote a uniformity of understanding so that we only get one answer for each unique expression.

Demonstration Proofs.

Proof

Given

36 ÷ 6(2 + 2 + 2)

Grouping by distributive property and implied multiplication

36 ÷ [6(2 + 2 + 2)]

Multiplication by inverse and grouping under vinculum

36×16(2+2+2)36 \times \frac{1}{6(2 + 2 + 2)}

Application of distributive property

36×16(2)+6(2)+6(2)36 \times \frac{1}{6(2) + 6(2) + 6(2)}

 Multiply terms in brackets

 

36×112+12+1236 \times \frac{1}{12 + 12 + 12}

Add terms in brackets

 

36×13636 \times \frac{1}{36}

Cancel common factors and simplify

1

QED

Proof

Given

8 ÷ 2(2 + 2)

Grouping by distributive property and implied multiplication

8 ÷ [2(2 + 2)]

Multiplication by inverse and grouping under vinculum

8×12(2+2)8 \times \frac{1}{2(2 + 2)}

Application of distributive property

36×12(2)+2(2)36 \times \frac{1}{2(2) + 2(2)}

Multiply within brackets

36×14+436 \times \frac{1}{4 + 4}

Add terms in brackets

36×1836 \times \frac{1}{8}

Cancel common factors and simplify

1

QED

Proof (From Professor Oliver Knill’s “Ambiguous PEMDAS” Web page. When presented with this problem, 58 of his 60 calculus students got the following result indicated in the proof. The other two treated (3y – 1) as the expression under the vinculum. NONE got the answer promoted by the PEMDAS absolutists.)[3]

Given

2x/3y – 1; x = 9, y = 2

Group by implicit multiplication and vinculum

2x3y−1\frac{2x}{3y} – 1

Substitute

2(9)3(2)−1\frac{2(9)}{3(2)} – 1

Multiply in brackets

186−1\frac{18}{6} – 1

Simplify

3 – 1

Subtract

2

[1] Professor Oliver Knill from Harvard (Ambiguous PEMDAS (harvard.edu)) cites Lennes, 1917. [No title given]: “When a mode of expression has become wide-spread, one may not change it at will. It is the business of the lexicographer and grammarian to record, not what he may think an expression should mean but what it is actually understood to mean by those who use it. The language of algebra contains certain idioms and in formulating the grammar of the language we must note them. For example that 9a2 ÷ 3a is understood to mean 3a and not 3a3 is such an idiom. The matter is not logical but historical” (emphasis in original). In scans from Lennes printed article, these statements appear: “A series of operations involving multiplication and division alone shall be performed in the order in which they occur from left to right.” However, the subheading in the very next paragraph says: “The Above Rule Contrary to Actual Usage,” and the author goes on to say: “It would, however, follow from this rule for carrying out multiplications and divisions in order from left to right, that

9a2 ÷ 3a = (9a2 ÷ 3) × a = 3a3.

But I have not been able to find a single instance where this is so interpreted. The fact is that the rule requiring the operations of multiplication and division to be carried out from left to right in all cases, is not followed by anyone. For example, in case an indicated product follows the sign ÷ the whole product is always used as divisor, except in the theoretical statement of the case” (emphasis in original).

The following section of the text has the subheading “The Established Usage” reconfirms that the obelus indeed means the entire product after it is intended to be the divisor, and not just the first term. (Who says the obelus has no grouping power!) He also goes on to say “All multiplications are to be performed first and the divisions next.”

I’ve also found similar analysis in a 1935 textbook Second-Year Algebra by Hawkes, Luby, & Touton, p. 19. That’s how I understood it the late 70s and early 80s in high school and college and in the early 2000s when I taught JH & HS math and algebra. I seriously doubt nearly 100 years of history (at least) of this understanding has changed in the past ten years or so.

[2] Ambiguous PEMDAS (harvard.edu); see also https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html

[3] Knill, Oliver. “Ambiguous PEMDAS.” Ambiguous PEMDAS (harvard.edu), retrieved May 29, 2023.

January 2, 2022

2021 Reflection and Summary

Filed under: 1 Corinthians,Biblical Studies,Courage,Diagrams,Greek,Hebrew,Hebrews,Mark Gospel of,Matthew Gospel of,New Testament,Prophet,Soteriology,Textual Criticism,Tongues — Scott Stocking @ 6:37 am
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I wanted to take a moment and thank the readers of Sunday Morning Greek Blog (SMGB) for tripling the number of views from 2019 to 2021! I went from 2,856 views in 2019 to 9,130 views (across 130 countries) in 2021. The theme of my blog has always been “Dig deeper, read smarter, draw closer.” I hope that whichever one of those goals brought you to my site will continue to be something I am able to meet for you. And, if you ever have a request or a question about a biblical topic, I would be happy to research it for you. I’m always excited to dig deeper into God’s Word to help others understand it better.

Having said that, the blog was also a blessing to me as well this year. As 2021 kicked off and more churches started to resume in-person services, I was called to preach at a couple smaller churches that lost pastors during the pandemic through attrition (thankfully not to COVID). One is the (now) inner-city church I grew up in and which some of my family still attend, and the other is a rural country church in Iowa. For me, the blog turned out to be (way-in-advance) sermon prep! This blog was helpful in that I still have been working my full-time day job, so it was nice not to have to a lot of new research for sermons. What sermons I did write this past year wound up as new blog posts.

Top 5 Posts

My top post for 2021 surprised me, because it was a little more academically technical than my typical posts, but it must have struck a chord with some. I had written “Indignant Jesus: The Variant Reading of Mark 1:41” in January 2019 in part because I wanted to know for myself why the NIV translators had changed the translation from “compassion” to “indignant” The other reason is that I wanted to provide an example of how translators use internal and external clues to determine the quality or genuineness of a textual variant. I figured with all the NIV readers out there, many of them would be curious about an “indignant Jesus,” so I wanted to provide what I hope was an explanation of the thought process in layman’s terms.

“Indignant Jesus” had 86 views that year. In 2020, it saw a 360% increase to 310 views. In 2021, it nearly had another 360% increase to 1,106 views! That was over 12% of total blog post views for 2021. Judging from the access peaks, I’d say it wound up on a few recommended reading lists for college syllabi. If you happen to know who used it on a syllabus, I’d love to thank them. I don’t want any royalties; I’d just like to know what they found redeeming about it, or even if they thought it needed some work.

The second most popular post was “Seer” in the Old Testament. This has been a perennial favorite, having been the number one article for at least 6 years through 2018, again, most likely because it appeared on someone’s college syllabus. Obviously, it’s not a Greek word study, but a Hebrew word study, and it was one I had sent out in an e-mail thread long before blogs were a thing. I never expected much from it on the blog, primarily because I had been looking for something different to post and pulled that one out of the archives. I’m both surprised and pleased that it continues to generate great interest.

My third most popular post (just 23 views behind ) was 2020’s top post: “Take Heart!” That had slowly been growing in popularity, but it really caught hold in 2020, most likely due to the pandemic. I got one comment from a reader who said they had shared it with several health care workers at the time. They of all people had and continue to have a need for encouragement and endurance in the face of COVID and (if I may) the current lack of gratitude and sympathy from those at the highest levels of government for those hardworking heroes.

Number 4 is one that has steadily grown in popularity, but really began to take off in 2019, having three times the views in 2017. “Falling Away” tackles the difficult section of Hebrews 6 that at first glance seems to address the concept of losing your salvation. But a closer look at the text, grammar, and sentence structure (yes, there’s a classic sentence diagram attached; also an epilog post) shows the passage has quite a different meaning that isn’t so harsh theologically. Monthly views jumped dramatically in beginning in mid 2020, which makes me think the article also wound up on someone’s syllabus. I recently had a lively exchange with one reader who was asking for some clarification on a couple points, which also helped me sharpen my thinking and conclusions on the passage.

The fifth one was a total shocker to me. “Speaking in Tongues” averaged 49 views per year in the first 10 years it was online. In 2021, the post had 691 views, averaging over 57 views per month! Again, I’m not sure what sparked the sudden interest, but as with the other posts, the only thing I can think of is someone put it on their syllabus or perhaps cited it in a widely read paper.

Looking Forward

For 2022, I anticipate preaching about once every month, so I’ll continue to post sermon texts to the blog. I’d also like to break into the podcast sphere and start posting some videos or audios that can generate some ad revenue for me. I’m not really set up for that yet, and I’ll have to seek out some technical help most likely, but I’m pretty sure that won’t be a difficult learning curve.

I also have a blog called “Sustainable America,” which is my outlet for the intersection of politics, ethics, and faith in my life. That has never really taken off, although it has seen some modest growth. I’ve had just over 100 views the last two years, and 2020’s views (106) were a little more than double 2019’s views. Although it hasn’t really had many views, I do find it personally therapeutic as an outlet for what I’m thinking and feeling on such subjects. The founding fathers didn’t put “separation of Church and State” in the Constitution because they understood instinctively people’s politics derive from their religious and moral convictions (or lack thereof). The purpose of Sustainable America, however, is to analyze cultural and political issues and apply Scripture to them, while SMGB is all about analyzing the biblical text and discerning how it should affect and inform our lives all around, not just in the political or cultural spheres.

My most-viewed post on Sustainable America was “Why I’d Rather Not Work from Home Full Time.” After having spent much of my early career either working from home or working in a ministry setting where I was the only staff member, I found it quite enjoyable to transition to working in an office setting with lots of interesting people around. When the pandemic hit, all of that was defenestrated. I do miss working around other people. Somewhere along the way, I lost my introversion.

As such, one final goal for me for 2022 is to get back into the adjunct professor space, or full-time college instruction nearby, if someone wants to take a chance on my M.Div. degree with OT & NT concentrations. I found it ironic that, in 2020, the third-party supplier through whom I had been teaching Biblical Studies courses at St. Louis Christian College was bought out, and the acquiring company dropped the online adjunct service at a time when everything was moving online. Teaching Biblical Studies is really my first love, but it’s been tough landing positions without a Ph.D.

I wish you, my readers and blog followers, a happy and prosperous new year. Thank you for continuing to read, interact with, and spread the word about Sunday Morning Greek Blog!

Pastor Scott Stocking, M.Div.

My opinions are my own.

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