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One of the things I find interesting about ancient Chinese math is how computational it was (in modern terminology we would say they were only interested in com
by betterunix2 8y ago
One of the things I find interesting about ancient Chinese math is how computational it was (in modern terminology we would say they were only interested in computable numbers); AFAIUI the ancient Chinese were vaguely aware of numbers that could not be computed exactly (i.e. irrationals) but mostly cared about being able to compute approximations up to whatever precision was required for a given task. So while Western mathematicians were struggling in vain to find a way to double a cube using a compass and straightedge or to derive a quintic formula, the Chinese mathematicians were satisfied with an algorithm that found useful approximations. There is a profound difference in philosophy, as evidenced by the title of this entire thread: the Chinese were "solving" 14th degree polynomials, but only in the sense of having an algorithm for doing so (as opposed to having a formula like the quadratic formula; in fact there is no such formula for degree 14 polynomials, or for any polynomials beyond the quartic).
- how_to_bake 8y agoHate to be annoying, but I'm a native English speaker and I just skipped over "AFAIUI" because it was too much work to guess what it meant. "As far as I understand it" ? RIP if you're not a native speaker.
- twtw 8y agoRIP if you are a native speaker too.
- Asooka 8y agoIRC-speak is its own language :)
- deleted 8y ago[deleted]
- plussed_reader 8y agoA predecessor of pager code.
- idoescompooters 8y agoHaha yeah I actually chucked at that one. Amazes me how many acronyms people come up with for that simple kind of statement.
- mr_overalls 8y agoI think it actually points to a hole in English - the lack of a short word that expresses a bit of uncertainty regarding one's own statement. Anyone want to coin a word (or point one out that we're all apparently unfamiliar with)?
- whatswrongwitu 8y agoCovfefe
- erikpukinskis 8y agoYes sir, dispatching the operative now.
- deleted 8y ago[deleted]
- jacquesm 8y agoAFAIUI seems to solve the problem nicely. Not a native speaker and yet I understood it right away.
- interfixus 8y agoTTBOMK, TANST.
- laretluval 8y agoMaybe
- betterunix2 8y agoI think it is a relatively common abbreviation used in informal writing online, similar to "AFAIK" or "AFAICT" (maybe those are not so common?) but admittedly less common than "QED" or "etc." Yes, it means "as far as I understand it."
- waterphone 8y ago"AFAIUI" is nowhere even close to as common as your other examples. I have never encountered it before, and Google Trends doesn't even register it in a comparison between the others. https://trends.google.com/trends/explore?date=all&geo=US&q=afiak,afaict,afaiui https://trends.google.com/trends/explore?date=all&geo=US&q=a...
- rtkwe 8y agoTrends isn't the best for this as it's search results not occurrences so really all this will show is the number of people confused by the term for weird contractions like this. "AFAIUI" could theoretically just be completely understood by the community using it.
- waterphone 8y agoNumber of search results: AFAIK: 8,600,000 AFAICT: 346,000 AFAIUI: 14,600
- rtkwe 8y agoShould have made it more clear that I meant that in the general case not in this particular. I've never seen AFAIUI.
- waterphone 8y agoOh, I understood what you meant, I was just providing an additional data point for this particular conversation in response to what you were saying re: search queries vs. results.
- overcast 8y agoAgreed, so sick of these internet acronyms. This isn't text messaging, it's an intelligent discussion forum. Type out what you're saying.
- skh 8y agoIn case someone is wondering about your wording. A computable number is one whose decimal approximation can be computed to arbitrary precision with a finite, terminating algorithm. All algebraic numbers and some transcendental numbers are computable. Thus being irrational does not imply not being computable. One more pedantic note. There are algebraic formulas for solving polynomials of higher degree than 4. For instance, you can find a formula to solve x^n = 0 for n a positive integer. You can’t find a general, algebraic formula to solve polynomial equations of degree n where n > 4.
- malmsteen 8y agoIs there "not computable" numbers ? Example ?
- wetmore 8y agoThere are "more" non-computable numbers than computable one. Chaitlin's constant is an example.
- skh 8y agoI can give you many more examples of specific computable numbers than I can of noncomputable numbers. This is a bit surprising when one learns that the set of noncomputable numbers is much larger than computable ones. Most of the numbers you’ve dealt with are computable. Every noncomoutable is close to a computable number where close means as close as you want. There is also the notion of definable numbers which is different than computable. There are people who study these things and the implications they have in mathematics and computer science. I’m not one of these people so beyond what I’ve said I don’t dare comment.
- lacker 8y agoIn math, infinite sets have different sizes. The number of computer programs is "countably infinite". The number of real numbers is "uncountably infinite". Since there are more numbers than computer programs, some numbers must be uncomputable. for more info see: https://en.wikipedia.org/wiki/Countable_set https://en.wikipedia.org/wiki/Countable_set
- qubax 8y ago> One of the things I find interesting about ancient Chinese math is how computational it was (in modern terminology we would say they were only interested in computable numbers); This isn't just the chinese. The ancient greeks rejected ( or ignored ) irrational numbers too. Also, western math was just as computationally driven. Pretty much all math everywhere developed for practical purposes ( ie to divide land, more accurate calendar, etc ). > There is a profound difference in philosophy, as evidenced by the title of this entire thread: the Chinese were "solving" 14th degree polynomials No there isn't. The ancient greeks also "solved" equations, such as for volume of geometrical objects, by approximation. That's why they didn't invent calculus ( though sometimes math historians try to twist the definition and meaning and understanding of calculus to claim ancient greeks did ). The fundamental difference is that ancient greeks developed explicit axiomatic mathematics while the chinese didn't. But practical computational mathematics is the foundation of all mathematics.
- empath75 8y agoI'd say the greeks used techniques (limits, for example) that would later be used in calculus, but the didn't systematize them.
- betterunix2 8y agoExcept that the Chinese did not reject irrational numbers, but simply did not find the distinction to be important enough to explore. They had a notion of numbers that could not be computed exactly (i.e. they could only get a sequence of better approximations) but they were satisfied as long as an algorithm existed (I imagine they might have rejected the concept of non-computable numbers, had such a concept existed at the time). There was a time when the Greeks firmly believed that all numbers are rational and explicitly rejected (not simply ignored) irrational numbers, and later they had a strong interest in the separation between rationals and irrationals. The difference between the Chinese and the Greeks was not just explicitly stating axioms (Chinese math was also a system built from basic principles, they just did not organize things as neatly as the Greeks), but their view of what computation is. The Greeks tried to map all computation onto Euclidean geometry, whereas the Chinese generally viewed computation as symbolic manipulation and tried to map all math (including geometry) into computation problems. I see that as a very big difference that had a big impact on how the two traditions developed.
- rasz 8y agochabuduo
- wumms 8y agochabuduo = close enough "Instead, the prevailing attitude is chabuduo, or ‘close enough’. It’s a phrase you’ll hear with grating regularity, one that speaks to a job 70 per cent done, a plan sketched out but never completed, a gauge unchecked or a socket put in the wrong size. Chabuduo is the corrosive opposite of the impulse towards craftmanship, the desire, as the sociologist Richard Sennett writes in The Craftsman (2008), ‘to reject muddling through, to reject the job just good enough’. Chabuduo implies that to put any more time or effort into a piece of work would be the act of a fool. China is the land of the cut corner, of ‘good enough for government work’." (https://aeon.co/essays/what-chinese-corner-cutting-reveals-about-modernity https://aeon.co/essays/what-chinese-corner-cutting-reveals-a...)
- echevil 8y agoZu Chongzhi derived pi should be between 3.1415926 to 3.1415927 back in 5th century. Well, that was pretty good precision at that time
- bmc7505 8y agoQin Shi Huang lifted the sword to the sky, and shouted: “Computer Formation!” Four giant bronze cauldrons at the corners of the platform came to life simultaneously with roaring flames. A group of soldiers standing on the sloping side of the pyramid facing the phalanx chanted in unison: “Computer Formation!” On the ground below, colors in the phalanx began to shift and move. Complicated and detailed circuit patterns appeared and gradually filled the entire formation. Ten minutes later, the army had made a thirty-six kilometer square computer motherboard… “This is really interesting,” Qin Shi Huang said, pointing to the spectacular sight. “Each individual’s behavior is so simple, yet together, they can produce such a complex, great whole! Europeans criticize me for my tyrannical rule, claiming that I suppress creativity. But in reality, a large number of men yoked by severe discipline can also produce great wisdom when bound together as one.” —Cixin Liu, The Three Body Problem (2008)