General > General Technical Chat
Admit your Brain lock
IanB:
--- Quote from: tggzzz on April 04, 2024, 02:44:12 pm ---In my day it was "follow the algorithm" - which was admittedly useful when I've had to implement floating point arithmetic! Nowadays they are taught that you can get the right answer by several different "successive approximations", e.g. 99y is easily calculated as 100y-y. That encourages a much better "feel" for the "shape" of numbers and arithmetic.
--- End quote ---
On a related note, when I watch (the UK quiz show) Countdown, I am always impressed at how adept Rachel Riley is with her mental arithmetic. She can, in the moment, multiply say 47 by 83 and write down the answer while speaking to camera. I think she must dream numbers in her sleep.
nctnico:
--- Quote from: Zero999 on April 04, 2024, 01:53:39 pm ---There are 26 letters in the alphabet, which should be more than enough.
--- End quote ---
But who says the alphabet you are using is THE alphabet to use for math? There are so many different sets of symbols in use across the globe. Think about Arabic, Cyrillic, Greek to name only a few. Unicode defines about 150000 different characters for a good reason. In math and science quite a few Greek characters have a special meaning like lowercase tau, upper case delta and last but not least, lower case pi. You really have to consider math a language in itself.
Zero999:
--- Quote from: nctnico on April 04, 2024, 03:21:26 pm ---
--- Quote from: Zero999 on April 04, 2024, 01:53:39 pm ---There are 26 letters in the alphabet, which should be more than enough.
--- End quote ---
But who says the alphabet you are using is THE alphabet to use for math? There are so many different sets of symbols in use across the globe. Think about Arabic, Cyrillic, Greek to name only a few. Unicode defines about 150000 different characters. In math and science quite a few Greek characters have a special meaning like lowercase tau, upper case delta and last but not least, lower case pi. You really have to consider math a language in itself.
--- End quote ---
The Latin alphabet is used over much of the globe, for the purposes of information exchange. Until fairly recently, virtually all text was ASCII. A good number of those Unicode symbols look virtually identical, which is also a security vulnerability: look up homoglyph attack. There's no need for that crap in the field of mathematics. It's pure obfuscation. :palm:
CatalinaWOW:
Absolutely not intentional obfuscation. There are more than 26 unique concepts/entities in math and physics. The people who started the use of these "special" characters did it to provide shorthand and avoid confusion with other entities. The usage was productive and therefore adopted by others, eventually becoming widespread, used by people whose written language did not involve those characters.
In today's world of ubiquitous data processors there is an argument that multi-character identifiers could be used, and commonly is for some symbols like pi. But this all started when you had to write your ideas on paper with a pencil or pen and a terse notation is a benefit to avoid getting bogged down in the mechanics of writing equations. Having a different notation for notebooks/scratch pads and publication made (and makes) no sense so it stuck.
I am unconvinced that long variable names would be an improvement.
Area_of_Circle Is_Identically_Equal_To Distance_Around_The_Rim Times The_Square_Of(Distance_From_Rim_To_Center) Times The_Ratio_Of_Circumference_To_Diameter
This expression still requires prior knowledge of terms like Equal, Identially, Rim, Square, Center, Ratio, Circumference and Diameter and is horribly unwieldy. Imagine the fun for a truly complex expression.
Finally, as a native speaker of English, I will point out the 26 characters is not enough even to encode the languages common in Europe. Even leaving the Greeks and Slavs out there are enough umlauts and tildes and diacritical marks to exhaust that limited set. Unicode may go too far, but was done in a time when it had been found that even the expanded 255 characters in a byte weren't really enough and the obvious idea is to dedicate two bytes.
coppice:
--- Quote from: Zero999 on April 04, 2024, 01:53:39 pm ---If a maths teacher only gives 93% or over 100%, when all the answers are correct, complete with working, then he or she doesn't deserve their job, because they clearly don't understand percentages.
--- End quote ---
There can ALWAYS be greater clarity in the workings. There is ALWAYS the possibility of an insightful way to speed up the derivation of an answer that would deserve an extra mark or two. 100% says nothing could be better. I award you 0%, must try harder.
Navigation
[0] Message Index
[#] Next page
[*] Previous page
Go to full version