Commenter Archive

Comments by Hartmut*

On “The law of the letter

Here's a post from Keith Devlin working through some thoughts about the tension between calculation and mathematical thinking.
https://devlinsangle.blogspot.com/2018/05/calculation-was-price-we-used-to-have.html
For any mathematician alive today, mathematics is a subject that studies formally-defined concepts, with a focus on the establishment of truth (based on accepted axioms), with various forms of calculation (numerical, algebraic, set-theoretic, logical, etc.) being tools developed and used in the pursuit of those goals. That’s the only kind of mathematics we have known.
Except, that is, when we were at school. By and large, the 19th Century revolution in mathematics did not permeate the world’s school systems, which remained firmly in the “mathematics is about calculation” mindset. The one attempt to bring the school system into the modern age (in the US, the UK, and a few other countries), was the 1960s “New Math”. Though well-intentioned, its rollout was disastrous, in large part because very few teachers understood what it was about – and hence could not teach it well. The confusion caused to parents (other than mathematician parents) was nicely encapsulated by the satirical songwriter and singer Tom Lehrer (who taught mathematics at Harvard, and did understand New Math), in his hilarious, and pointedly accurate, song New Math.
As a result of the initial chaos, the initiative was quickly dropped, and school math remained largely unchanged while real-world uses of mathematics kept steadily changing, leaving the schools increasingly separated from the way people did math in their jobs. Eventually, the separation blew up into a full-fledged divorce. That occurred in the late 1980s. The divorce was finalized on June 23, 1988. That was the date when Steve Wolfram released his mammoth software package Mathematica.[...]

Devlin is really good on matters pedagogical, and always worth the read.
I do tend to think, though, that students will have a very hard time with understanding math (or written communication) if they have not had enough experience with doing the work, and not seen enough examples to get an idea of the possible range of approaches to doing the work, etc.. Early in my teaching I tended not to give enough examples, figuring that teaching the conceptual side would lead students to sort through their own database of examples to see the underlying principles. I've since learned that most students come in having seen and understood too few examples, and having no idea of more than one approach to the tasks they have been called upon to do.
I do a lot more modeling of approaches, and evaluation of those approaches, now that I'm finally starting to figure out this whole teaching thing.

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I suppose I can see how, if everybody who knows how to read** has a phone/computer in their hip pocket, knowing basic arithmetic might be less critical than it once was. I'm not convinced, mind, but I can see that it might be.
** At the rate software is improving, I suppose computers will be able to read to us, and write down what we say as well. The reactionaries will no doubt be delighted if illiteracy once again becomes the norm. /snark

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I was taught using the School Mathematics Project, which seemed OK to me. But I may not be one of the "normal people".
I suggest that being able to divide accurately with pen and paper is now almost useless, whereas being able to divide approximately in one's head is useful for avoiding fat-finger errors. That is, the underpinnings have turned out to be more important than the algorithms.

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New Math was the same sort of thing. It pushed a much broader view of what math was than just the algorithms. Look, long division is done the way it is because hundreds of years of experience informs us that it's the best way to get the right answers when you have to do a hundred division problems a day, day after day. New Math failed when the teachers pushed the broader view but didn't teach the mechanics.
The trouble with New Math was that it was (apparently) designed by mathematicians. Mathematicians who had forgotten that a) you have to build the foundations (mechanics, as Michael says) first. And that b) normal people are not mathematicians -- and that's 99.99% (or more) of the population. They neither care nor need to know the theoretical underpinnings. They just need to know how to do basic arithmetic reliably.

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Camel notation* from computer programming would possibly be better: InternalCompustionEngine.
It is interesting that it is widely used in domain names, e.g. KaiserPermanente.org Clearly the sales and marketing folks think it will be easier to parse that way.

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Charles, I gotta ask, don’t you wonder about quoting an LLM that can call itself ‘MechaHitler’?
https://www.pbs.org/newshour/politics/why-does-the-ai-powered-chatbot-grok-post-false-offensive-things-on-x

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Charles, I gotta ask, don’t you wonder about quoting an LLM that can call itself ‘MechaHitler’?
https://www.pbs.org/newshour/politics/why-does-the-ai-powered-chatbot-grok-post-false-offensive-things-on-x

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I'm not sure if I'd be so harsh on the Roman alphabet. You don't want a system that encodes everything.
Something that floors my students is when I teach them about an abcedary, which is a chart that represents the letters by giving them a word that has the sound (A is for apple, etc) Because Japanese kana are the sound they represent, there is no need to create one.
About Michael's question, I think it would work in romanized Japanese because it is essentially creating an anglicized version of Japanese and the consonants plus the context can give enough clues to read them. However, Japanese don't process near as much text in roman letters, so that would be an issue.

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Michael, the scrambling thing is called Typoglycemia. In German it's Buchstabensalat (letter salad) and at a pedagocic course I had to suffer through at university as Badewanneneffekt (bathtub effect, no idea why).
https://en.wikipedia.org/wiki/Transposed_letter_effect#Internet_meme
With long words with completely random letter scrambling it's rubbish even if first and last letter are retained.

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Is this just an English thing?
According to Grok:
Scrambled Words Across Languages

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"Whole language" may have been a wrong turn if it really resulted in ignoring phonetics (I doubt that it really did in practice), but the fact is that proficient reading requires recognition of whole words.
To paraphrase a friend, "No one can get a PhD dissertation out of pushing phonics. You have to claim that something else is better." Or at least that something else is as/more valuable than recognizing the words early on. The new things are all well and good, but memorizing a few hundred words-as-a-chunk is still necessary. You can't sound out "bat" and "cat" forever; at some point it has to be automatic.
There are assorted postings -- the internet has made them more common -- that ask whether you can read "Aoccdrnig to rscheearch at Cmabrigde Uinervtisy, it deosn’t mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae." Is this just an English thing? Does Romanized Japanese tolerate the same sort of misspellings for fluent readers?
New Math was the same sort of thing. It pushed a much broader view of what math was than just the algorithms. Look, long division is done the way it is because hundreds of years of experience informs us that it's the best way to get the right answers when you have to do a hundred division problems a day, day after day. New Math failed when the teachers pushed the broader view but didn't teach the mechanics.

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"it radically rewrote the rules of literacy for tens of thousands of children seemingly overnight."
There are always stories about how miraculous various programs and phonics in particular are in teaching reading. But surely such programs would have been adopted by now and thus must have been producing undeniable results somewhere. Wouldn't phonics have been adopted in red states (there is an obvious partisan divide on this) and shouldn't those states now be much better in reading performance?
Spanish is almost perfectly phonetic so why do international comparisons put reading performance in Spain below that in the US? Can Japanese and Chinese (who do well on the international comparisons) only learn to read after seeing the romanized versions? Surely people in China were able to read before it was exposed to the West.
"Whole language" may have been a wrong turn if it really resulted in ignoring phonetics (I doubt that it really did in practice), but the fact is that proficient reading requires recognition of whole words. Most children can learn new words both audibly and in symbols very fast, but some may require more help from phonetics.
By the way the Roman alphabet is very poor for most languages (including English), which typically have more sounds. Few languages have only five vowels sounds, like Spanish and Italian (and presumably Latin). Phonetics is presumably helpful in deciphering foreign words, but the simple Roman alphabet will never describe them (except Spanish, etc) accurately even with code books. However some alphabets, such as Arabic, may be even simpler, omitting vowels altogether at times.

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It's just convention that one does not write railwaystation or particleaccelerator or internalcombustionengine but imo those are perceived as units.
German also has the useful convention of capitalizing nouns. Using Internalcombustionengine would at least signal it's a noun, even though it starts off with an adjective. Camel notation* from computer programming would possibly be better: InternalCompustionEngine.
The example everyone remembers from college German is Handschuh (hand shoe) as a generic glove/mitten term, Fingerhandschuh for gloves, Fausthandschuh for mittens, Panzerhandschuh for armor, etc. The German is at least consistent. In English, it's another of the English/Norman dualities. Glove is from Old English; mitten is from Norman for mitten; gauntlet is from the Norman for glove. I understand there are more types of Handschuh that correspond to some of the other uses English has piled on gauntlet, like "throw down the gauntlet" or "run the gauntlet".
I'll just go ahead and invite Hartmut to explain how wrong I am :^)
* Off and on for a half-century now I have occasionally tried to adopt camel notation when I'm writing code. It never lasts, and I always go back to underscores: source_index rather than sourceIndex in something I've been writing this week.

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A couple of things about reading. It's a bit like second language acquisition, in that no one is guaranteed to acquire reading. There is a basic idea that reading is a interactive process that bounces back and forth between bottom up and top down, but beyond that, there is not much. There is an notion of orthographic depth, but it's often by speakers of one language (usually English) projecting onto other languages.
I tend to think of it a lot like umwelt, which is the unique subjective experience that an organism has that can not be understood by any other organism. Though it doesn't use the word, "What Is It Like to Be a Bat?" by Thomas Nagel gets at that point. I'll leave it to Harmut to explain umwelt, along with merkwelt and wirkwelt in Uexküll's biosemiotic theory and I've never heard of any linguist taking this up, but I definitely will in another life where I am multi-lingual...

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"A very rare exception is suovetaurilia"
Thanks, Harmut for introducing us to the ancient Roman form of Turducken.

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wj, imo English de facto has composite words, just not writing them as such (keeping the parts separate, not even using hyphens). It's just convention that one does not write railwaystation or particleaccelerator or internalcombustionengine but imo those are perceived as units. Latin has very few of those and they are usually fixed terms of noun and adjective (e.g. res publica = state, res novae = coup d'etat, homo novus = upstart). A very rare exception is suovetaurilia (sacrificing a pig, a sheep and a bull together) but that is in essence a proper noun, a name.

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I'm puzzled by this. I'm not good at languages, relative to my other skills, but switching alphabets - Cyrillic, Greek, Georgian... is trivial.
It's not onerous, no, but it is a factor on at least two levels in my experience.
First off, it can create some noise when particular letters look similar to letters in the other language that are not phonetically equivalent, and that usually triggers a bit of recursion in the reading process. It's not a lot of load on the system, but it is processing power that is not being used to make sense of the meaning. Writing English using the Greek alphabet barely affects reading comprehension when deciphering the message when one is fluent in English. Combine a lack of fluency with the need to decipher and the effects compound.
Second of all, it messes with the pattern recognition that one relies upon when skimming a text. When I'm reading Swedish or Spanish, I can skim the text fairly easily and a lot of the language has enough root-equivalency to make those reading skills transfer. That sort of whole-word pattern recognition doesn't fire the same way when I am faced with another alphabet.
All of these things mess with your language in the same way that when a student is asked to write about an unfamiliar topic with its own technical vocabulary, they often end up writing language that has a greater number of grammar and spelling errors than when they are writing about familiar topics. The familiar has a much simplified processing economy.
And again, with functional and transactional language, these difficulties are much less pronounced than when dealing with more complex and nuanced subjects.
At least that is my experience, and it seems to match with my observations of how my non-native student writers interact with texts. Actual linguists would likely have a lot to say about the places where I'm wallpapering over some complex topics, or missing the boat entirely.

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In Latin one has to invent new words for concepts Cicero&Co. did not yet possess and would probably not understand. Greek (unlike classical Latin) allows composite words that can transport about any meaning with little to no loss.
No offense, but I wonder if being a native speaker of German might be coloring your view here. Composite words being one of the most noticable things (after gendered nouns) for English speakers when learning it.
I admit that I don't have a wide enough base to know how common composite words are in languages generally.

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...the alphabet contributes somewhat to that difficulty...
I'm puzzled by this. I'm not good at languages, relative to my other skills, but switching alphabets - Cyrillic, Greek, Georgian... is trivial.
(I struggle with Hebrew, where some of the letters are just too alike.)

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India, with its huge population, already uses it because its people speak 5 mutually unintelligible native languages
Off the top of my head, Hindi, Urdu, Bengali, Gujarati, Punjabi, Malayalam, Tamil, Telugu. There are many others.

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It occurs to me that a lot of education should be guiding people to what they are good at. I always thought I was good at languages, but I realize that I am really good at the languages that are in roman letters. Had I known, I might have opted for vietnamese instead of thai, or even earlier, dove into chinese first (I have several english native friends who have fluency in Japanese and Chinese and all of them did Chinese first and I don’t know anyone who went the opposite way).

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Ancient Greek is far more versatile than Latin but also quite a bit more difficult. I never really got the hang of it (in 3.5 years at school compared to 9 years of Latin).
I think there is little to-day that could not be directly translated into ancient Greek while Latin would require massive reformulation to do the same and much would get lost doing it. In Latin one has to invent new words for concepts Cicero&Co. did not yet possess and would probably not understand. Greek (unlike classical Latin) allows composite words that can transport about any meaning with little to no loss. Latin is the hammer of a blacksmith, ancient Greek is a jeweller's toolset.

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Instant translation is fine for functional and transactional language, but it hits its limits pretty quickly as language complexity increases and becomes problematic for understanding as soon as there is an intertextual element at work. I see this a lot with my international students when they are working their way through English texts with the help of translation software. They miss a lot of the features that the authors are using to communicate - parallelisms, homophones, puns, etc.
To be fair, a lot of my native language domestic students miss those things too, but the international students have the reading skills to catch those elements in their own languages, and would notice those things if they were actually working with the original text.
One thing I can add that speaks to lj's first point. Language-wise I've studied Spanish, French, Swedish, and Ancient Greek. I can muddle through in Spanish, and would probably be able to attain fluency in any of the first three in a few months with immersion. Greek, however, never sticks particularly well, and the alphabet contributes somewhat to that difficulty. It's one more unfamiliar element (deciphering) that takes up processing power that would otherwise be used for linguistic sense-making.

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Why learn, if there is an instant translator?
I don't see that happening in complex, real-life contexts. It's hard enough to make sense of people in one's native language sometimes, lol.

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In case anyone is interested in the subject (and in lieu of fraught AI summaries):
https://en.wikipedia.org/wiki/English_as_a_lingua_franca
It's entirely possible that English will become the lingua franca for international communications, but if it does, I'd expect, like Hartmut, that it continues to shed irregular constructions and colloquialisms and that native dialects will be treated as quaint variants with charming local color. I also predict that both Americans and Brits will complain bitterly that ELF is "not proper English" when that happens, and resent any standard that treats ELF as the paradigm.

*Comment archive for non-registered commenters assembled by email address as provided.