C++ and Linear Algebra
category: general [glöplog]
I must admit I never found the Hugi course so illuminating. Especially the fact that it starts with abstract algebra is a bit over-the-top.
From a different angle: so, it was boggling me for years, why programmers and mathematicians use or even understand mathematics differently?
My best conclusion: mathematics is the way it is, because it was fine tuned for making proofs and/or deriving new facts/properties, while most programmers don't have to do it (most of the time they just apply those facts/properties).
So, if you take an average joe programmer, he might even have heard about matrices, cross-product or dot-product and where to use them, but he would rarely have a clue why inverse-transpose matrix is used for transformation of normal vectors or be able to derive it.
Saying that, linear algebra is still a special branch of mathematics, that is relatively engineer-friendly. Mostly, because it has (historically) so many applications in many other engineering fields.
So, there you go, my pretentious 5 cents of a day ;-)
My best conclusion: mathematics is the way it is, because it was fine tuned for making proofs and/or deriving new facts/properties, while most programmers don't have to do it (most of the time they just apply those facts/properties).
So, if you take an average joe programmer, he might even have heard about matrices, cross-product or dot-product and where to use them, but he would rarely have a clue why inverse-transpose matrix is used for transformation of normal vectors or be able to derive it.
Saying that, linear algebra is still a special branch of mathematics, that is relatively engineer-friendly. Mostly, because it has (historically) so many applications in many other engineering fields.
So, there you go, my pretentious 5 cents of a day ;-)
Just get a math library on a topic of your choice to be included in c and read its source code where available.
Chances are that someone already solved your problem in code better than you could ever imagine.
Chances are that tour promlem is simpler than you think and you do not need to define a new branch of mathematics to solve your problem, such as statistics to predict from experiences.
I could never understand quaternions but I can easily understand a c function that rotates by a quaternion once I see its source code.
Of course mathematical axioms such as commutativity are never to be ignored.
Chances are that someone already solved your problem in code better than you could ever imagine.
Chances are that tour promlem is simpler than you think and you do not need to define a new branch of mathematics to solve your problem, such as statistics to predict from experiences.
I could never understand quaternions but I can easily understand a c function that rotates by a quaternion once I see its source code.
Of course mathematical axioms such as commutativity are never to be ignored.
The coders problem is that methods are developed for the tools that are used with them.
Mathematical methods were developed for tools such as writing in the sand with your finger, chizling hieroglyphs and Arabic letters into stone (stats why our decimal system has a different endianness) , painting with chalc, painting with a wuil of liquid ash on bamboo...
And for thousand years the mathematical glyphs were great for these tools.
But now most math is done in floating point binary CPUs. There are no infinitissimals and infinity is only modelabe as a constant.
Yet too many people still use the ancient glyphs and functions that work better for pen and paper than for ascii text.
The result is a lot of confusion just because of using different methods for different tools to commit near-identical operations and calculations to predict something or to divide something fairly.
Mathematical methods were developed for tools such as writing in the sand with your finger, chizling hieroglyphs and Arabic letters into stone (stats why our decimal system has a different endianness) , painting with chalc, painting with a wuil of liquid ash on bamboo...
And for thousand years the mathematical glyphs were great for these tools.
But now most math is done in floating point binary CPUs. There are no infinitissimals and infinity is only modelabe as a constant.
Yet too many people still use the ancient glyphs and functions that work better for pen and paper than for ascii text.
The result is a lot of confusion just because of using different methods for different tools to commit near-identical operations and calculations to predict something or to divide something fairly.
Maths, yeah. Papers have analogue differentials, while solution is discrete. Maths look cool. I like it.
Solution is to not be scared of maths