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I’m trying hard to understand your points here. I am not against mathematical notation as that would be crazy. I am against using it to explain what something is the first time when there is an easier way. Bear with me because I am not a math major, but I am pretty sure “a linear equation is an equation that draws a straight line when you graph it” is a good enough explanation for someone to understand the basic concept.
To me, it seems like “ A(cx) = cA(x) and A(x+y) = A(x) + A(y)” is only the technical definition because they are the only two properties that every linear equation imaginable absolutely has to have in common for certain. However, suppose I didn’t know that, and I wanted to be able to tell if an equation is linear. Easy. Just graph it, and if the graph makes a single straight line, it’s a linear equation. Suppose I didn’t want to or couldn’t graph it. I can still tell whether it is linear or not by whether or not the slope is constant using y=mx/b, or I could just simply look to see if the variables are all to the power of one and only multiplied by scalar constants. Either of those things can help me identify a linear equation, so why is it that we are stuck with A(cx) = cA(x) and A(x+y) = A(x) + A(y) as the definition? Give me some linear equations and I can solve them and graph them all day without knowing that. I know that for a fact because though I am certain that definition was in some of my math textbooks in college, I never read the textbooks and if my professors ever put that on the board, I didn’t remember it, and I certainly never used it for anything even though I’ve multiplied and divided matrices before and still didn’t need it then either. I only got A’s in those classes.
That’s why I am having trouble understanding why that definition is so important how it is too wordy to say “a function or equation with a constant slope that draws a single straight line on a graph” The only reason I can think of is there must be some rare exception that has those same properties but is not a linear equation. Even so, I am fairly certain that homogeneity and additivity could be summed up as “one output per input” and “the distributive property of multiplication is true for the equation/function”. That’s still not that wordy. Let’s pretend for a second that a math professor instead of using words to do the lecture read the symbols phonetically and explained everything in short hand on the board. Would more or fewer people passing the class in your opinion?
I am also wondering what your definition of jargon is. Jargon has 2 required elements:
The key elements of jargon are:
Specific to a particular context: Jargon is used within a specific industry, profession, or group and may not be easily understood by those outside of that context.
Involves technical terms, acronyms, or phrases that are not part of everyday language.
Straight Line Property doesn’t qualify for the second element which is why I like it. That said, linear isn’t the best example of jargon because it has the word “line” in it which at least gives the reader a clue what it means. I’m not trying to redefine words, I’m merely trying to rewrite them so that they use common language words that give a clue to what they mean because I am certain that leads to better memory retention for the layperson hearing it for the first time and is also less jarring to readers with poor vocabulary skills. This should apply equally to all jargon by the definition I gave. However, giving a clue may be very challenging for some jargon words that describe very abstract and arcane concepts that don’t map well to normal words which is what I initially thought your point was.
The only downside I see to providing an option to automatically replace useful jargon on demand is that it might lead to a more permanent replacement of the words over time which would irritate people already familiar with the jargon. If your point is that it is not useful, then I would like to hear your counterargument to the point I made about memory retention and the jarring cognitive effect on people with poor vocabulary skills. The jarring effect is easily observable and it’s hard for me to imagine that word familiarity and embedded clues don’t help memory retention of vocabulary, but I am open to counter arguments.