I just like to keep an inch of coffee in my mug.

My understanding is three chapters behind in my hind brain, and three chapters ahead in my forebrain.
So much for linear thinking.

She sits there by the window
Her coffee keeps her warm,
With her books and study papers
Sheltered from the storm.

Dressed in winter colors
Sweatshirt dark and denim jeans,
Comfort found in simple threads
Where complexity convenes.

Steam rising from her coffee cup
Casts a shadow on the glass,
It shades the pure reflection
Of such a pretty lass.

She sits there by the window
Gazing out beyond the storm,
Her coffee cup is empty now
Her body finally warm.

I found how infrequently some points or lines could align with a hyperplane.
It sounds way harder than it was, probably because I used to not know the succession of steps to learn about R^n and the hyperplane.
They are easy to grasp but it used to not be as easy as 1,2,3.
But it really is a simple plane in n-1 dimensions of R^n.
Yet when I first encountered the word some years ago, it was quite mesmerizing.
I think math will always be mesmerizing except if I've encountered it in pedagogy.
With this understanding, I know that all math is stepwise succession within its branch.
But somehow this leaves things undone, probably because I can't cheat true and tried pedagogy.
That's what I really want to do.

What does it mean that my logic and reasoning could solve a problem?
Meaning the one who gave me the problem could solve it already.
Yet there are those who have gone through all the courses of problems, all ending in relatively the same place mentally.
However, there are still problems they can't solve.
What does it take for a breakthrough?

To know when to employ math known to mankind and when I can't.
To know when I need something new or when I can use something old.
This, I believe, is the crux of the matter.
Otherwise, I try to invent new what is already done and so go nowhere except to prove to myself what all these people knew from a different perspective.

Learning for me must come from a need to end my ignorance rather than to further my understanding inasmuch as furthering understanding is infinite while becoming tired of my ignorance happens after a period of time after learning something new.

The universe and all it's organizing power must sing in my soul it's anthem of mystery before I can crack a book.

Grassmannian scattering amplitudes.
Galaxies with momentum horizons.
Galaxies moving in different directions at different speeds.

Still haven't found the graviton.
Colliders.
Huge interferometers.

Any work here seems like a lot of teamwork in companies.
I'm a drop in the bucket, whose feeling is my enemy if I am to manage complexity.

So one part of me says "just do it, do the problems I have prepared to do".
But I feel I'm missing a level of management of the field, like I'm not getting the big picture.
It is said: from point to expanse to point and back again.
Am I looking for a shortcut?
Learning purifies, it reveals what is now impossible to see.

A lack of study?
I know all the fundamental theories of physics and elementary calculations.
I know of all the branches of math and where they lead.
All of my notes of formulas are unused.
It's good that I studied electronics to know what focusing on math and physics gets me after graduation.
What really stays with me is what electronics isn't, but also how basic it is.
This is what I now expect for this endeavor.
The less help I get in it, the longer it takes.
Muhammad, pbuh, said get half of your knowledge from others and half from yourself.
But it is hard to tell what is from me.
Is my work the only thing: He meaning only let help solve half my problems?

There is:
1. What I need to work on
2. What I want to work on
3. Gain a degree of simplicity
4. Understanding what work is not

Studies show that novices often pay attention to different elements in a problem than experts.
I gain more from being asked a question that is impossible to answer than solving a question for computation's sake.
How do I know why a plane tangent to a sphere can only intersect at one point?
I knew that before I did the problem, but I wasn't aware I was trying to disprove that!
Like trying to make black pigment out of only yellow and blue.
No, that's too simple.
It is like nothing I ever experienced!
I was unaware of the use of the elements.
It is one thing to read a theory, to copy an equation, but to go through problems makes me experience the elements in ways I never knew.
To know limitations I was blind to because I had never tried to connect them before.
That is why experts can zero in on a problem so fast, and why novices are snagged on basics.

This excursion into the expanse has ended with a knowledge of the love of math problems.

I should study
but honestly,
even you, fool,
make more sense than this