Originally Posted by Autumn
The way Fallacy of Composition and Fallacy of Division are made for each and every person testing as INTP ... regardless of brain hemisphere dominance, multiple intelligences, learning modalities, childhood traumatization in formal-education institutions, enneagram type, etc?
Though fond of sequences I'm reminded of how easily people are trapped by/in metaphors.
As a kid I learned about `the food chain' then latter heard about a `food web'.
The `chain' metaphor may be preferred by linear, left-brain thinkers even though `web' is a better metaphor than a chain for what happens in the eat-and-be-eaten ecology.
A sequence of numbers may be beheld as such, but what if each number were factorized into primes and diagrammed as a ramifying non-linear tree?
The use of sequences can induce sequential bias which demotes noticing non-sequential factors and phenomena.
Not that I'm against learning sequences and progressions, I'm just making note of a hidden paradigm trap which can emerge if one is not careful.
(more videos about basic mathematics by numberphile)
Chain rule: Derivatives
U Substitution: Integrals
I'd suggest, as others have suggested, that it's best to try to make sense of the subject on your own. When you learn at your own pace and take the time to understand everything properly, you will start to understand mathematics more generally. Of course, that takes effort and self-discipline and, as an INTP, I predict you'll be bored before achieving true understanding (sorry).
On a side note...
I love this! However, methinks it should read
"I'm left with the sense that there is something fundamentally missing or incomplete or ...flawed ... about REALITY (starting and following from its axioms); my mind just doesn't take it in, as presented, nor as I can manipulate it in attempts to find a proper axiomatic base. Let's simplify it and assume objectivism."
First of all, it's almost certainly true that you don't understand mathematics completely. I consider myself good at maths, but I don't claim to understand it completely and I certainly wouldn't make the outrageous statement that the whole field is flawed... although I might state that it could be taught better. Secondly, you can't reduce all of mathematics to a set of axioms: David Hilbert is a mathematician that tried to do that (see "Hilbert's program"), but Godel proved that it's impossible with his incompleteness theorem.
It's nice to think that everything should be reduced to a finite set of axioms. I wish the world were that simple. Ah, to be naive again.
I - 89 % N - 100 % T - 89 % P - 100 %
Does anything on this Geometric modeling page evoke any passion, mthomps?
How about the notion of music, DAWs, computers as quantizers, computers as data loggers, computers as sequencers, and computers as ubiquitous general purpose DWIM servants as targets of applied mathematics?
download this app for your phone called "Math Workout", its a very easy way to improve your maths skills
gps, understanding anything envokes passion for me. To me anything that can be detected by a human as sensory input can be deduced down to a shape, or at least, be manifested as a shape. In my simple mind, everything in the humans world is a simple pattern , or cycle which can be built in to complex ones. Or simple to complex shapes. Of course these "shapes" I see are not accurate of their actual mathematical shape, but that's the idea anyways.
I'm very sure that this is true (but not 100%). But, you see, and I am now willing to admit this, I am not educated. There are large gaps of data in my educational background. Saying this is due to a lack of intelligence is just an excuse, a better excuse, however, would be that I have never found a means of instruction that satisfies my own personal abstractions of the world. And by world I mean math.
Gene, you fucker. Stop playing in the mud
But Matt, thars math in that thar mud.
Why bother with cuneiform symbols in clay when one may use a stick or stylus to draw shapes in said mud ... then erase, and re-use it.
Mud is just mother nature's etch-a-sketch ... as well as building material for mud and wattle.
Mud is simply THERE TO BE PLAYED WITH ... and INTPs have a play ethic.
And where there is mud there is water ... and perchance Princesses and Frogs!!
I saw a few potential princesses while creek/stream sculpting recently.
I was tempted to go Gabriel on one of them, but couldn't get puffed up enough to start my croaking.
Hint: For the language-based, double entendres are a great way to induce the brain to generate simultaneous solutions.
To string them along like Peter Gabriel is to build a system or network of equations.
There's mathopoetic (EG akin to `mythopoetic') stuff in the lyrics of Gabriel.
Let it be an inspiration to you
`So Like Candy' is pretty much a running metaphor of double entendres -- some couched within similes -- as well.
Simultaneity is where you find it ... or generate it.
The math-minded -- algebra-minded, really -- do it with symbolic expressions; lyricists, on the other hand, do it with symbolic expressions crafted in so-called `natural' languages.
Be at one with the mud, Matt.
Use the force; use the mud.
Life is for learnin'.