6 · Perpendicular Ghosts

Oh gosh — so the cross product is the potential height, considering the parallelogram formed by the two vectors. Maybe later we could extend that: the two dimensions of a Cartesian coordinate being the base of any three-dimensional format, and the triple scalar product being the height, like the manifestation of a 3D printer. One thing that is magnificently paradoxical is that dimensionality collapses when we look at it — a cross b is a vector whose magnitude is the area of the parallelogram formed by a and b. So is there any geometric relationship between the parallelepiped and the cross product vector? And why is it the case that the dot product of that new vector with a is zero, meaning they are perpendicular?

Why meaning and intention are key in life: when we confine interpretation to two dimensions, we see a surface — say a parallelogram — consisting of two direction vectors. Then there is an imaginary vector (not in the technical Argand-diagram sense, but colloquially) that penetrates that surface, normal to it, escaping the two-dimensional space. That cross product vector is a new vector; it opens up a new dimension. It is still a vector, but it has meaning. MEANING. So maybe a proposition can be derived here: something meaningful transcends dimensionality — and that might be applicable to other endeavours.

That same visualisation applies to 3D. Anything we see in three dimensions would also have a scalar triple product that goes into the fourth dimension — also imaginary. It's not that everything we see in life has a normal vector sticking out of it (that would be terrifying), but the INTENTION materialises that stretch, that quantum leap into the new dimension. The intention of crystallising the cross product — which was imaginary — into the actual third dimension was the ACTION of the product. That vector was not in the original 2D space. It was orthogonal to everything in that space. In a very real sense, it did not exist in the 2D world; it was imaginary relative to that plane.

So for the other vectors still living in two dimensions, it is totally logical for them to conclude that this new thing appears as a mere point — obscure, anomalous, futile and weird. And humans are vectors too, with the head pointing toward greed and the tail toward fear. When someone becomes the normal — "would not be normal" in colloquial terms — everything collapses, but that induces enlightenment in the other vectors, such that a new dimensionality can open up.

In pure sinusoidal waves, or those with exponentially increasing amplitude, you need to add a shift. The broke will continue to buy only what sits inside their comfort zone. I truly believe that for those with the audacity to buy things far beyond their current financial situation, the world will meet them there. Nothing changes if your entire selection of options is always the cheapest one. You need to do the complete opposite — choose the most expensive one, feed your system with the most value, and find a way to fulfil that order.

Plasma dynamics — unchartered territory for me, and it sounds interesting. Cryptography seems really interesting too, adjacent to CS, maths and physics; and cybersecurity is a niche as important as the wars, yet somehow rarely discussed.

The fundamentals of knowledge are maths, linguistics and theology. Master those three perfectly and you can do anything. I live by that truth. You don't need to rush into coding and programming and stats and everything else. Trust me: if you can tolerate abstractness at that level, everything else comes easily. Studying applied maths is like studying how to use a hammer when you could take the time to learn how to drive an earth auger and dig deep. Depth in maths and theoretical physics will take you to realms you can't even fathom as possible.