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Notation study

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This thread is an attempt to quantify the methods used to communicate a mathematical concept to another person for the purpose of applying the concept.

Each response should ideally contain:

  • A single math concept, as you would present it to an inexperienced colleague in your field, who asks for help.
  • Any additions that you would include for the average person.
  • Optional comments.

Provide as many examples as you like, including historical examples, but please send each as its own post for ease of evaluating responses.

There are no restrictions on field or complexity.  The only restrictions on length and format are the practical limitations of this forum.  You may provide links to external resources.  Any document over 10 pages provided as a link or attachment should call out the most relevant page numbers in the body of the post.

We specifically request examples that include unconventional, obsolete, historical, experimental, graphical, scanned handwritten, 3 dimensional, or otherwise odd notation provided it is useful to explain a math related practical concept.  Computer code from any language is welcome.  Please note if you would use computer code exclusively, or coupled with traditional notation.  Please identify the notation type or language if it is not obvious to an English speaking C/C++ coder.

We understand there is ambiguity in the question, such as "What is a single math concept?"  Use your personal judgement.  Disambiguation is another feature of the thread.

Thank you.  I hope the results are interesting.

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I demonstrated the concept of subtraction to my children by eating their French fries. It worked quite well, and served the parallel purpose of being an education in social interaction with people more powerful,than you... that life isn’t always fair. 

Sorry... yours is a weird OP

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Yes, it is a weird question.  Stealing fries is a useful communication of the subtraction concept.  It is an example of what I am looking for.  I am trying to get back to first principles in a field with a great deal of adopted convention.  I'm trying to see if any of those conventions have become a crutch or shortcut for those in the know that slow or inhibit understanding by those unfamiliar or uncomfortable with the conventions. 

An example:  Traditional single letter variables, even with sub- and super- scripts do not convey much information and require mental symbol substitution to process.  Multi-character computer variables say what the variable is and leverage the highly practiced mental processes involved in reading and forming mental images from what is read.  Symbol substitution is fast for some and slow to others.  Perhaps this fact is unintentionally sorting people into scientific vs computer careers.  If science were done with variables composed of whole words rather than single letters would the field have access to a different set of minds?  Would existing scientists better grasp concepts because they access their emotional reading imagination, or are less burdened by cold symbol substitution.

Of course reading is also symbol substitution, but many that see single letter variables first convert to the words the variables represent then do a second substitution from the word to the meaning represented by the word.  The single letter variable convention has great space efficiency because it is unnecessary to demarcate the beginning and end of variables.  Is that better than mental efficiency?  I

Single letters allow 2 letters together to imply multiplication, which must be explicit with multi-character variables.  Do we need implicit multiplication?  Is there a different way to imply coefficients with multichar variables?  Can we settle on one representation of division?  Are there better keyboard layouts for math that just work without LaTeX?  PEMDAS applied blindly to endless practice problems (inconsistently between texts) confuses many and seems to delay understanding of how to properly form unambiguous equations.  Order of operations is not fundamental and not necessary, just convenient.  Is there value in experiencing the inconvenience?

Tackling one notation convention at a time is doomed to failure.  Tackling them all at once, is likely still doomed, but might produce some insight along the way to failure.

I wish to compile several unconventional ways to do math, present them to test subjects, and see if any of those alternate methods are more efficient or intuitive than conventional notation.  The results of that may inform development of a math software package.

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34 minutes ago, slomobile said:

Yes, it is a weird question.

So it is difficult to know how or even if to answer.

So it good that your second post has improved my understanding over your first one.

Have you considered looking at history and the development of Maths teaching in schools ?

Much of what you describe already happens so is there to be studied.

Also you should review your conception of 'first principles'.

Maths has advanced to the point where many of the most basic principles are also the most difficult.


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