The original Carolingian lowercase "l" from 1200 years ago had a small right hook at the inferior end, which made it easily distinguishable from other similar letters, like uppercase "I".
Unfortunately after the invention of printing there has been a bad fashion in serif typefaces that made lowercase "l' too similar with other letters, by replacing the traditional hook with a serif identical to the serifs of all letters that end on the baseline, so that the only difference from uppercase "I" remained in a triangular left serif added to the upper end.
Even worse, in the 19th century, after sans-serif typefaces became popular, most of them have simplified lowercase "l" even more, making it almost identical with uppercase "I".
Nevertheless, while many of the typefaces used today follow the bad styles of serif or sans-serif designs with hard to distinguish lowercase "l", there exists a decent number of typefaces which have returned to the original form of lowercase "l", with a right hook at the lower end, which is easy to differentiate from any other letters. I am using almost only this kind of typefaces. Examples are Palatino Sans and FF Meta, but there are many others. Also all recent monospace typefaces intended for programming have such lowerspace "l" (being a narrow letter, in monospace typefaces lowercase "l" also has a left slab serif at the upper end, to expand its width).
In handwriting, the best solution for lowercase "l" is not to make it cursive like suggested in the parent article, but to make it with a low right hook, like in its original ancient form.
> The original Carolingian lowercase "l" from 1200 years ago had a small right hook at the inferior end, which made it easily distinguishable from other similar letters, like uppercase "I".
It might help a little. "Easily distinguishable" is dramatically overselling things.
I, capital and lowercase, also has a serif hooking to the right at the bottom of the stroke. Look at the first line beginning with a big red I.
It says "Iterum autem pilatus locutus ẽ. ad illos volens".
The line above it says "Et homicidium missus In carcerem;".
How much difference do you see between the capital I in "In carcerem" and the lowercase L in "pilatus"?
It's easy to distinguish lowercase L from lowercase i because L is taller. Capital I is only slightly different.
(I should note that wikipedia's page on Carolingian minuscule also includes an image of a page of written Slovene. I couldn't really use that as an example, because without any knowledge of Slovene I can't reliably identify the letters. But I think that goes to show that the alphabet by itself doesn't reach the level of perfect unambiguity.)
I'm interested to see that all Ses look the same. At some point we got word-final "s", but this was clearly not that point.
Perhaps this is because I am used to it, but for me the lowercase "l"s from your example are impossible to confuse with any other letter. For me the hooks are very visible and clearly distinct from any other kind of stroke termination.
The serif at the lower end of capital "I" is bilateral symmetrical, besides having a flat termination, so it looks very different from the asymmetric and curved right hook on lowercase "l".
Also in my handwriting, I write lowercase "l" with a right hook and uppercase "I" with serifs, making them impossible to confuse.
It is true that unlike the capital "I" that starts the row immediately below, your "I" happens to have a shorter left serif, either because it has become erased due to the age of the manuscript or because it has been poorly written originally.
Despite this defect of this particular letter, which is not a frequently seen defect, I still cannot see how the right serif could be confused with a right hook. The letters would have to be much more degraded for the difference between an orthogonal serif and a curved hook to become invisible.
I agree that the differences between the 6 narrow alphanumeric characters "1IJijl" are small so they are more likely to disappear when the letters are partially erased, but when the letters are intact and they have been written with the right distinct shapes they can still be distinguished easily, in contrast with some typefaces (usually sans-serif typefaces) where they are intentionally made more similar than they were traditionally, which has been a very bad idea, so such typefaces (e.g. Helvetica or Arial) should be avoided.
While we're here, any suggestions on what works better for writing math to a digital whiteboard? Wacom type tablet with no display, or an ipad type tablet with pen?
I would imagine something where you can see the immediate results of what you're writing under your pen to be better, otherwise you'd have to be facing the board somehow and not the class
A display is much better for this. I recommend Samsung tablets, as the Wacom stylus they use can't awkwardly run out of battery on you in the middle of a class.
This is a very personal choice. A Surface-style tablet pc works best for me. The accuracy difference between an "active" Wacom pen and a glorified piece of plastic is noticeable. Display-less Wacoms have a much steeper learning curve before you produce good handwriting.
Agreed. I did a pure math degree where most of my classes involved copying down 2-3 pages of axioms/proof per lecture, and I settled on mead letter size college ruled spiral notebooks, and yellow note pads for scratch work. Wide ruled led to too much wasted space, graph paper was visually busy and led to awkwardly spaced letters, dot paper just didn't really work. Smaller paper sizes didn't end up holding enough information per page, spiral binding was best for being able to rip out and toss pages, the perforation was nice for the occasional hand in sheet, and I had no need for a nicer quality paper.
Also I always kept Pentel Twist Erase III mechanical pencils with 0.5 mm lead, Hagoromo chalk, and a 4 color set of chunky expo markers in my bag.
I used plain for a few years but it has some problems. I now use faint lined paper. Usually Muji notebooks. I leave a blank line between each statement. The lines are handy if you want to make something readable and well aligned which is fairly important. Scans fine.
My kids were forced to use heavily marked blue squared paper. They had problems writing and reading. I pointed this out to their mathematics teacher and said that it may be detrimental and got a diatribe of “what do you know”. Such a bad attitude. I had an answer to this which was embarrassing to him.
I assume most middle school teachers specify how papers should be organized in binders and labeled with names, dates, etc; but below was my method I developed halfway through college:
Top Margin use: left - name, center - class, right - date
One binder per semester; a divider for each class; handouts, tests, etc were hole-punched and placed with my notes in chronological order.
If my notes didn't make sense as I was copying down what the professor did, I would rewrite my notes later that day while figuring the problem-solving process out and making the notes/arithmetic easier to follow.
This method also applied to non-math-related classes.
I love engineering paper too! My weapon of choice is this pad: https://www.rspaperproducts.com/products/95182/ I have not tried the Tops yet, I think because I saw somewhere it was thinner? I like the slightly thicker paper the buff pads come with, and it plays nice with my fountain pens.
Worth nothing you don't need squared for mathematics. Not even slightly. Most of the stuff is written in English with a few lines of other stuff between.
I don't think I needed squares for any of my notes. Graphes that I drew were just approximate. The squares are great for indentations, lists, tables, etc. My notes always looked sharper on engineering paper than regular ruled paper.
Grid or lined, placed underneath thinner blank paper (heavier paper won't let the lines or grid show through as easily, if at all). Keeps the final presentation neat while giving the structure you may need to keep things aligned.
Also, when I look at the prices on amazon.se it looks like they cost around 5-10c each, a bit hefty for a student.
Another note, it was actually surprisingly difficult even to get a hold of blank paper notepads in Sweden in the 90s. At least cheap enough. The cheap ones were all lines or squares.
Even today for students constrained financially, they can print out a dot grid on blank printer paper, perhaps in a faint blue or grey to recreate the effect.
You get a nice mix of benefits of blank paper and graph paper.
I switched to plain white when I was ca 20 years old and never looked back. I need to use plain white since then and I am so used to it that I find lines or grids slightly offensive to me and it throws me off from layouting. You can get used to anything.
that's right with mechanical pencils written on a proper writing surface with plenty of arm/elbow space with real erasers for completely removing noise from mistakes.
I was once taking a real analysis class and there was a very gifted student in my class. She pulled out her notebook one day at a study session and I noticed it was kind of unusual - the pages were very large, and made of a somewhat thicker material, with a slightly rougher texture. Ink also seems to set onto its surface slightly nicer, and it doesn't really bleed through onto the other side either.
She explained to me that it was actually a kind of notebook specifically for artists, and that she much preferred it to the normal plain paper notebooks you typically get.
I bought one myself, and I had to agree with her - it was a much 'nicer' experience to write on it - diagrams could be way less cramped, branch out without hitting the edges. The tactile feedback due to the thickness of the paper was also nice - in a way, it felt like the "mechanical keyboard" of paper notebooks.
Never switched back again after that, and many people I work with have found it curious and nice to work with too.
Part of me feels that there may be more than just a gimmick to this. In the way that it's been shown that pen and paper help for understanding versus typing, I wonder if "the niceness of the pen and paper experience" would have an additional tangible positive effect, too
This is famously how Maryam Mirzakhani worked as well. Huge thick A2 sheets where she doodled and did computations; she said she disliked the cramped style of normal notebooks.
Squares are pointless unless you're drawing graphs, but lines are very handy to have. Without lines my writing moves on an angle and the size of everything becomes inconsistent and usually too large.
I like squares because they allow me to align things vertically.
This is especially useful when maintaining two margins to write in as well as for indenting, blockauotes, or sometimes maintaining parallel lists or columns.
nice writeup, I always like taking extra care to view the actual motions a professor uses when writing the symbols on the board as it can sometimes be non-obvious the order or direction to start in.
would also love tips on making right curly brackets not be the bane of my existence. I don't get it, I write a right one basically for every left and yet they feel so different!
Crossing the Z is a good one. I cross 0 but understand the point with phi. Something that’s not mentioned is y (lowercase) and how they can look like a 4
I never used to cross my zeros until I was spending some time writing a lot of diagrams that had both O (for oxygen) and 0 (for the numeric label). It got very confusing!
I never took a real chem or bio class, but more than half my degree involved classes where 0 and ∅ were extremely frequently used. Thankfully no math or CS professor is stupid enough to use the letter o as a symbol or variable name.
I started crossing Z, 7, 0 and generally writing in as unambiguous a manner as possible in my math homework because I was afraid of the teacher reading it wrong and taking points off.
I always cross my zs in maths to distinguish them from 2s, but in some countries they cross the 2s to distinguish them from zs, so the ambiguities remain.
I started crossing the Z in college because I was tired of messing things up because I confused a Z for a 2. I only crossed the 0 when Os showed up and it could be confusing. Similarly my 1s would get the hat and feet if I felt like it wasn't clear what it was.
I can't say I ever had trouble with y and 4 looking the same. I use the open 4 but the y has one less angle and it sits lower. If anything a y is more likely to look like a v if you can't see the descender clearly
There are two other phis with the (non-mathematical) Greek letters earlier, but unfortunately fonts vary in which one they display as \phi or \varphi: φ (U+03CD), ϕ (U+03DC).
In my experience it would not be typical to use a wedge to represent a cross product. Typically a wedge is used to refer to the outer/exterior product, which in three dimensions would correspond to a bivector as opposed to the vector you get from a cross product.
Wikipedia says it’s more common in physics, and we mostly used it in that context (e.g. fluid mechanics) rather than pure math. It was pronounced “veck”, IIRC.
\times denotes the cartesian product (to my knowledge) universally.
If 3rd-semester calculus is when you introduce a general definition of continuity (I am not from the US, wouldn't know how the programs usually work there) on either metric or topological spaces, the cartesian product starts to appear quite a lot I guess ?
Typically in the US, the calculus sequence is one semester differentiation, one semester integration, and a third semester of three dimensional and vector calculus. The × symbol is used a lot for vector cross products in the third semester. Typically these courses don't involve proofs. Serious students frequently take a portion of this sequence +/- matrix algebra in high school as AP courses or dual enrollment where the school cooperates with a local college to share their exams and get official credit. They are technically considered to be college level courses in the US. I think a lot of the content in them is covered in A level further maths or IB HL math or whatever your local equivalent is.
This sequence is followed by differential equations courses for the physicists, engineers, and most mathematics majors. Then every college has a mechanism to generate mathematical maturity in their first or second year pure math majors - sometimes it's a proof focused version of linear algebra, sometimes it's a specific Introduction to Proofs course, sometimes it's a discrete math/set theory course, sometimes it's groups/rings or real analysis but slowed down a bit at first. This gates the upper level pure mathematics courses, where most programs require one semester each of algebra and analysis and some number of elective courses.
A general definition of continuity typically doesn't arise until a topology course or a second semester real analysis course. It is entirely possible to graduate from most mathematics bachelor's programs in the US without taking either of those courses.
I used to work in a field that used \Sigma for covariance matrices, and pervasively needed discrete summations which also use \Sigma (and often with an understood index set, so the \Sigma appears without clarifying adornment).
I ended up writing my discrete summation \Sigma's with a little serif on the bottom, and ordinary \Sigma's as in OP, with 4 quick back-and-forth strokes.
chuckle I'm teaching high school math, and I have students who are jedi knights of making ambiguous mathematical signs. They make their "1"'s with a long top serif, which make it look like it could be either a "1" or a "7". A "4" written with a curly hook on the bottom can be mistaken for an "8", etc etc.
Not to mention a glyph which is maximally ambiguous between "T" and "F" so that when grading true/false questions, could stand in for either :-)
If the students would put half as much effort into learning the material as they do in trying to trick teachers they would get straight A's ;-)
I'm probably too much of a stickler for high school. If I had students try to trick me with T/F confusion I'd immediately announce a "round towards the wrong answer" policy and watch 'em tidy up right quick.
Some european students threw me when I started grading in university though. Their 1s look like my 7s as you describe, but they cross their 7s to disambiguate.
It's incredible to realize how many of the habits mentioned in this post that I've unintentionally picked up while studying applied math. Even after graduation, I still follow a lot of these 'conventions'.
Most important to me was something not mentioned here: to make i/j les ambiguous, I but effort into explicitly add the right swoop at the bottom of the i, which allowed for the j to be a straight longish line dotted at the top.
There’s an old joke about “mathematical maturity” meaning being able to write a lowercase zeta, but I took enough classes from professors that would confuse xi and zeta that it probably doesn’t matter that much.
Mostly unrelated, but I wish the field of math would step away from greek letter notatation and just make variable and function names readable as programmers do. I know there are historic reasons, and I'm sure that mathematicians' time is so valuable that they can't be bothered to write more than 1 character, but it's a real barrier to entry in my opinion.
the vast majority of mathematical equations/terms would become completely unreadable if you replaced single symbols with descriptive terms. You are going to have to internalize what the symbols refer to anyways to understand the formula, and once that is accomplished any additional description is a waste of space and cognitive bandwidth.
We did try it. We tried it for a couple of millenia. It was much harder to understand and our collective mathematical output as a human species was much slower than it is now.
You know when you go to a foreign country, ask for a particular thing in a restaurant proudly in their language that you picked up on Duolingo the week before and the waiter starts talking to you quickly in their language and you lose it completely.
We are just that waiter. You didn't learn the language or get the prerequisite skills. So do that or don't bother. It's not easy and there are no shortcuts.
Even if i agreed with you that full words/phrases were easier to parse, any gains made here are easily offset by how much harder and laborious it is to manipulate them on paper
The use of the Greek alphabet is mostly driven by convention. You get used to it. They aren't just sprayed around randomly wherever you look.
As for your code, urgh. A mathematician would carefully define what the function and operands are and the domain of each. More, and I'm vasty simplifying here as I don't have LaTeX available. I don't know what your code does so I've invented some words.
Let f(x,y) represent the rate of change of doodads where x is the number of doodads and y is the amount of doodads per gronk.
The code is unclear because it has single-letter variables instead of names, exacerbated by being in Greek, which mathematicians reached for because they were using single-letter variables, and ran out of them, and weren't bold or imaginative enough to break from convention. Then they used up the best of the Greek letters too and moved on to things like Gothic. This is stupid.
No they didn't use them because they ran out. You know nothing about mathematics clearly. There are conventions to keep it concise. Some definitions of simple things would be unreadable if you used longer names. Consider the quotient rule:
It's only a small part of the barrier to entry, though. I could write Einstein's equations out in words, and most people still wouldn't be able to do GR.
Grep is from an ed editor command: global (g) to apply a command to all lines that match a regular expression, a regex surrounded by slashes (/), and print (p) to display those lines. Or g/re/p for short. This proved a useful enough operation that they made it a separate command in the early days of Unix.
> they can't be bothered to write more than 1 character
You try handwriting all of your code and let's see how long until you start abbreviating everything.
Mathematical notation is all abbreviations. We used to write mathematics without abbreviations. It was absolutely horrid. Try reading some 13th century mathematics, translated to your language (e.g. Fibonacci https://archive.org/details/laurence-sigler-fibonaccis-liber... ), and see how much of it you understand without the benefit of symbolic notation. We would even write aaa instead of a^3.
The point with mathematical notation is that it can all be sounded out and it's extremely general and abstract. Generally, x is not a measurement, a quantity with a unit, a meaningful anything. It's just a number, and x is a better name than front_server_count or whatever thing you're programming about.
A massive amount of day to day pure mathematics work is still done by hand, on paper, whiteboard, or even chalkboard (and there's a preferred brand of chalk). Of course it will all be typeset before sharing, but mathematicians typically think by writing by hand, not think by typing.
I came up with similar rules over decades (I still write sometimes mathematical symbols), and I have to only take care of my "u" vs "n" and "r" vs "v", and write these pairs especially slowly because in my handwriting (especially u and n) look the same.
But for all the others I’ve developed similar disambiguations.
The blog writer has particularly bad handwriting, and maybe that's why he needs these tricks. I've seen a lot of math handwriting, and seriously his is among the worst. Maybe he was drawing the letters with a mouse.
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[ 3.3 ms ] story [ 211 ms ] threadThis barely matters at all; context will tell you what symbol is being used, just like it does in prose, and most material is typeset.
It really is a very bad idea to use lowercase Ls, though.
Unfortunately after the invention of printing there has been a bad fashion in serif typefaces that made lowercase "l' too similar with other letters, by replacing the traditional hook with a serif identical to the serifs of all letters that end on the baseline, so that the only difference from uppercase "I" remained in a triangular left serif added to the upper end.
Even worse, in the 19th century, after sans-serif typefaces became popular, most of them have simplified lowercase "l" even more, making it almost identical with uppercase "I".
Nevertheless, while many of the typefaces used today follow the bad styles of serif or sans-serif designs with hard to distinguish lowercase "l", there exists a decent number of typefaces which have returned to the original form of lowercase "l", with a right hook at the lower end, which is easy to differentiate from any other letters. I am using almost only this kind of typefaces. Examples are Palatino Sans and FF Meta, but there are many others. Also all recent monospace typefaces intended for programming have such lowerspace "l" (being a narrow letter, in monospace typefaces lowercase "l" also has a left slab serif at the upper end, to expand its width).
In handwriting, the best solution for lowercase "l" is not to make it cursive like suggested in the parent article, but to make it with a low right hook, like in its original ancient form.
It might help a little. "Easily distinguishable" is dramatically overselling things.
https://upload.wikimedia.org/wikipedia/commons/b/bd/Minuscul...
I, capital and lowercase, also has a serif hooking to the right at the bottom of the stroke. Look at the first line beginning with a big red I.
It says "Iterum autem pilatus locutus ẽ. ad illos volens".
The line above it says "Et homicidium missus In carcerem;".
How much difference do you see between the capital I in "In carcerem" and the lowercase L in "pilatus"?
It's easy to distinguish lowercase L from lowercase i because L is taller. Capital I is only slightly different.
(I should note that wikipedia's page on Carolingian minuscule also includes an image of a page of written Slovene. I couldn't really use that as an example, because without any knowledge of Slovene I can't reliably identify the letters. But I think that goes to show that the alphabet by itself doesn't reach the level of perfect unambiguity.)
I'm interested to see that all Ses look the same. At some point we got word-final "s", but this was clearly not that point.
The serif at the lower end of capital "I" is bilateral symmetrical, besides having a flat termination, so it looks very different from the asymmetric and curved right hook on lowercase "l".
Also in my handwriting, I write lowercase "l" with a right hook and uppercase "I" with serifs, making them impossible to confuse.
No, look at the capital "I" that I indicated in my comment. It has neither of those qualities.
Despite this defect of this particular letter, which is not a frequently seen defect, I still cannot see how the right serif could be confused with a right hook. The letters would have to be much more degraded for the difference between an orthogonal serif and a curved hook to become invisible.
I agree that the differences between the 6 narrow alphanumeric characters "1IJijl" are small so they are more likely to disappear when the letters are partially erased, but when the letters are intact and they have been written with the right distinct shapes they can still be distinguished easily, in contrast with some typefaces (usually sans-serif typefaces) where they are intentionally made more similar than they were traditionally, which has been a very bad idea, so such typefaces (e.g. Helvetica or Arial) should be avoided.
https://en.wikipedia.org/wiki/Minim_(palaeography)
I guess blackletter script was an obstacle to mathematics (and reading).
In Sweden you were expected to use paper with squares but it adds a lot of clutter.
Blank paper is too... Blank! And I'm more prone to write big and messy and waste pages (even though it's all digital)...
Also I always kept Pentel Twist Erase III mechanical pencils with 0.5 mm lead, Hagoromo chalk, and a 4 color set of chunky expo markers in my bag.
My kids were forced to use heavily marked blue squared paper. They had problems writing and reading. I pointed this out to their mathematics teacher and said that it may be detrimental and got a diatribe of “what do you know”. Such a bad attitude. I had an answer to this which was embarrassing to him.
https://www.amazon.com/Tops-Engineering-Computation-Punched-...
I assume most middle school teachers specify how papers should be organized in binders and labeled with names, dates, etc; but below was my method I developed halfway through college:
Top Margin use: left - name, center - class, right - date
One binder per semester; a divider for each class; handouts, tests, etc were hole-punched and placed with my notes in chronological order.
If my notes didn't make sense as I was copying down what the professor did, I would rewrite my notes later that day while figuring the problem-solving process out and making the notes/arithmetic easier to follow.
This method also applied to non-math-related classes.
Grid or lined, placed underneath thinner blank paper (heavier paper won't let the lines or grid show through as easily, if at all). Keeps the final presentation neat while giving the structure you may need to keep things aligned.
Another note, it was actually surprisingly difficult even to get a hold of blank paper notepads in Sweden in the 90s. At least cheap enough. The cheap ones were all lines or squares.
You get a nice mix of benefits of blank paper and graph paper.
She explained to me that it was actually a kind of notebook specifically for artists, and that she much preferred it to the normal plain paper notebooks you typically get.
I bought one myself, and I had to agree with her - it was a much 'nicer' experience to write on it - diagrams could be way less cramped, branch out without hitting the edges. The tactile feedback due to the thickness of the paper was also nice - in a way, it felt like the "mechanical keyboard" of paper notebooks.
Never switched back again after that, and many people I work with have found it curious and nice to work with too.
Part of me feels that there may be more than just a gimmick to this. In the way that it's been shown that pen and paper help for understanding versus typing, I wonder if "the niceness of the pen and paper experience" would have an additional tangible positive effect, too
This is especially useful when maintaining two margins to write in as well as for indenting, blockauotes, or sometimes maintaining parallel lists or columns.
But if you just slightly misalign your lines it will look even uglier.
You'll just have to learn to draw straight lines. Or trade one benefit for the other.
Here is an example, 4 different dot sizes:
http://trondal.com/p1.pdf http://trondal.com/p2.pdf http://trondal.com/p3.pdf http://trondal.com/p4.pdf
You need to print them to see which one is suitable.
would also love tips on making right curly brackets not be the bane of my existence. I don't get it, I write a right one basically for every left and yet they feel so different!
As a computer science student, I have to juggle O, o, 0, and ∅. (capital/lowercase letter, zero, empty set. Fun!
I can't say I ever had trouble with y and 4 looking the same. I use the open 4 but the y has one less angle and it sits lower. If anything a y is more likely to look like a v if you can't see the descender clearly
Tips for Mathematical Handwriting (2007) - https://news.ycombinator.com/item?id=32665846 - Aug 2022 (2 comments)
Tips for Mathematical Handwriting (2007) - https://news.ycombinator.com/item?id=22983274 - April 2020 (76 comments)
And I write every Latin letter in its capital form, however actual capitals twice as large. Put a dot in zero.
That way everything looks distinct
Or make it \varrho (ϱ).
> Keep the slash in the phi vertical; keep the slash in the empty-set symbol slanted.
Again, \varphi (U+1D711 which HN doesn’t seem to like) is easier to distinguish.
The author silently chose \varepsilon in their TeX, but chose to ignore the rest of the variants.
My grammar school math teacher used a very large ascender for the alpha, almost into serif-£-sign-without-the-line-through territory.
I wonder if he's talking about the cross product.
https://en.wikipedia.org/wiki/Wedge_(symbol)
This sequence is followed by differential equations courses for the physicists, engineers, and most mathematics majors. Then every college has a mechanism to generate mathematical maturity in their first or second year pure math majors - sometimes it's a proof focused version of linear algebra, sometimes it's a specific Introduction to Proofs course, sometimes it's a discrete math/set theory course, sometimes it's groups/rings or real analysis but slowed down a bit at first. This gates the upper level pure mathematics courses, where most programs require one semester each of algebra and analysis and some number of elective courses.
A general definition of continuity typically doesn't arise until a topology course or a second semester real analysis course. It is entirely possible to graduate from most mathematics bachelor's programs in the US without taking either of those courses.
I ended up writing my discrete summation \Sigma's with a little serif on the bottom, and ordinary \Sigma's as in OP, with 4 quick back-and-forth strokes.
Not to mention a glyph which is maximally ambiguous between "T" and "F" so that when grading true/false questions, could stand in for either :-)
If the students would put half as much effort into learning the material as they do in trying to trick teachers they would get straight A's ;-)
Some european students threw me when I started grading in university though. Their 1s look like my 7s as you describe, but they cross their 7s to disambiguate.
There’s an old joke about “mathematical maturity” meaning being able to write a lowercase zeta, but I took enough classes from professors that would confuse xi and zeta that it probably doesn’t matter that much.
The real problem is, everybody else will complain, because its unconventional. Then you look foolish.
Shorthand is better.
You know when you go to a foreign country, ask for a particular thing in a restaurant proudly in their language that you picked up on Duolingo the week before and the waiter starts talking to you quickly in their language and you lose it completely.
We are just that waiter. You didn't learn the language or get the prerequisite skills. So do that or don't bother. It's not easy and there are no shortcuts.
So much more readable! /s
As for your code, urgh. A mathematician would carefully define what the function and operands are and the domain of each. More, and I'm vasty simplifying here as I don't have LaTeX available. I don't know what your code does so I've invented some words.
Let f(x,y) represent the rate of change of doodads where x is the number of doodads and y is the amount of doodads per gronk.
That's pretty tight and clearer than the code is.The code is unclear because it has single-letter variables instead of names, exacerbated by being in Greek, which mathematicians reached for because they were using single-letter variables, and ran out of them, and weren't bold or imaginative enough to break from convention. Then they used up the best of the Greek letters too and moved on to things like Gothic. This is stupid.
Surprisingly I've just gone through the last 30 pages of mathematical work I've done and there's a couple of π in ∫ there and that's it.
To have it his way, you'd right:
(derivative(right_expression))(expression)
and so on.
Clear as mud!
Perhaps he's a LISP programmer and has some spare brackets floating around :-)
ls, man, wc, ps, grep, …
instead of
list, manual, word count, process(es?), <actually, what the hell does that stand for again>, ….
You get used to it, and then it’s much quicker. And being able to write things down quickly is very important when you’re in flow.
Set theory has aleph א and beth ℶ which are refreshingly not Greek but Hebrew letters.
You try handwriting all of your code and let's see how long until you start abbreviating everything.
Mathematical notation is all abbreviations. We used to write mathematics without abbreviations. It was absolutely horrid. Try reading some 13th century mathematics, translated to your language (e.g. Fibonacci https://archive.org/details/laurence-sigler-fibonaccis-liber... ), and see how much of it you understand without the benefit of symbolic notation. We would even write aaa instead of a^3.
The point with mathematical notation is that it can all be sounded out and it's extremely general and abstract. Generally, x is not a measurement, a quantity with a unit, a meaningful anything. It's just a number, and x is a better name than front_server_count or whatever thing you're programming about.
But for all the others I’ve developed similar disambiguations.
thanks for the insight