#math research

[hexiflexi]

guys...

my good friends...

my professor has overrided the system to let me do research with him next semester...

more to come...

[liskantope]

Today I had one of those social events (did a hike as a local Meetup group event) which was a reminder of the default drudgery of going to events made for meeting new people when the people going are selected only for age (20's and 30's in this case, not age-selected at all in some other cases) but aren't selected for anything else in common besides interest in the immediate physical activity the event is arranged around. The conversations I had were almost as forgettable as it gets. Just yesterday I was re-watching the second-to-last episode of Better Call Saul, and I can draw an analogy between what I'm trying to describe and the social dynamics Kim Wexler's new workplace (which are depicted in an almost too over-the-top manner). If my social interactions at LessOnline at the start of this summer were on one end of the spectrum of being engaging and mind-expanding, this event was on the other end of that spectrum for my summer.

Maybe the number one thing I miss about being a student (undergrad or grad), and having groups of fellow students at the same place form most of my social interactions, is that every conversation with a new person doesn't have to be a discussion of each of our jobs. That's not all of it, but it's pretty close to the heart of why meeting-new-people socializing as an adult in his 30's is so dreary sometimes.

Not that anyone or any of our interactions were less than perfectly pleasant, to be clear. But my recent claim to not remember the last time I was asked by a new person what kind of music I'm into, or when it has ever happened since I was 22, is dated now. (At least the asker was asking me and someone else together, and the other guy gave an answer that was followed by a change of subject, so I didn't have to try to put together an answer.) Also today's interactions featured the time-honored standards and my two other very least favorite questions in a general context: "What do you like to do in your free time?" (I can't really answer, "Uh, I like posting on Tumblr") and "What is math research exactly and what kind of math problem do you work on and what are its applications?"

[art-of-mathematics]

The fano plane in Octonian algebra - hypercomplex numbers [8D]

Octionions are non-commutative and non-associative, say, the order of calculating is important.

x·y ≠ y·x (non-commutative),

x·(y·z) ≠ (x·y)·z (non-associative)

For multiplication in the fano plane, you take two neighbouring elements on a line and the resulting value is the third element that closes the loop. Moving with arrows gives a positive value, moving against arrows gives a negative value.

Interestingly the symmetry on those values is still there, only inverted. As example:

e_3·e_4=e_6 and e_4·e_3= (-e_6)

Hence:

e_n·e_m=e_l and e_m·e_n= (-e_l)

This inverted symmetry, or antisymmetry, could be what I refer to as the anthitetics states, the butterfly clones in information weaving/butterfly progression.

[greenglasstudy]

- simulation time! -

we have finally started doing numerical tests for stability so catch me running 100s of tests to even see if a rogue wave is created. it’s so nice today i hate to stay inside but it ees what it ees.

[vanessainstem]

Made a cute cover for my summer math research log book (The circles were a template in GoodNotes, I just picked it out, put the logo and text on top)

[vacuously-true]

Diagrams from some of my number theory research this semester regarding the density of the rational points on a circle.

[art-of-mathematics]

How Mathematicians Make Sense of Chaos | Quanta Magazine

Illuminating mathematics, physics, biology and computer science research through public service journalism.

Funny how every week I find articles by quanta magazine with concepts that often overlap heavily with my own. This one is a nice addition to some of my concepts - or my ideas are a nice addition to these concepts.

[greenglasstudy]

- scratch work -

i finally got all the relations i’ve been working for in this paper and i’m v happy. it’s a shame there are 8 more pages left and this one section took me two weeks.