We arrive at mathematical truths through contemplation, experimentation, and incubation. Figuring things out is messy. Polished publications bely just how messy the discovery process is and, in so doing, are rendering a disservice to would-be adventurers.
Mathematics is a world unto itself. While human reasoning may be, by some distant principle, limited, that hasn't stopped people from constantly -- predictably, even -- discarding their worn out limits. The wisest among us unlearn the cumbersome concept of being limited completely. After all, who could possibly know what lies beyond that there thicket?
We're blessed with the ability to conceive of and chart new worlds. We also live in an age that enables these worlds to meet, in a language with agreed upon rules. And yet, despite the simplicity of this interface, these many worlds may be suited to so many dispositions. There's something for everyone.
What about when someone's something intrudes upon uncomfortable territory? Perhaps that someone would previously skirt this sinewy section of the jungle, yet now finds themselves in possession of a machete made just for this excursion. Seemingly disparate areas of mathematics have a tendency to meet at unexpected crossroads.
The term "applied mathematics" demands clarification. In academic parlance, it often refers to applying knowledge from one area of mathematics to another. In quarterly earnings parlance, it usually means finding ways of using so-called pure math, which might be considered applied math by those hoity-toity academic folk, to the "real world."
So, we have layers and we have direction.
Layerlyly, we can abstract entire operations and recognize that what we had previously thought was one thing was actually a subset of this other thing, and this other thing usually works in such and such way, and we can prove this from this other area of math that often deals with such other things, etc.
Directionally, we find Fourier gauging the temperature of Earth's surface leads to entire branches of analysis leads to improved image compression on our flashy beepy boxes.
How do we improve our ability to share and discover mathematical truths? How do we forge connections between lands? How do we prepare our mathematical weaponry for rarefied and unconquered expanses? Oh, and how do we peacock our fancy accoutrements? A healthy pride is welcome here. That's what this is all about, adventurer.
Mocap, gesture, waves, triangles
What is it about intervals such as an octave and a perfect fifth that makes them more consonant than other intervals? Is this cultural, or inherent in the nature of things? Does it have to be this way, or is it imaginable that we could find a perfect octave dissonant and an octave plus a little bit consonant?
~ Music, a mathematical offering, BensonI'll ask similar questions about poetry and sound, movement and gesture.
| Description | Sense | Emotion | Analogues |
|---|---|---|---|
| Major scale (3 half tones, 2 half tones) | Hearing | Happy | A sharp intake of breath; the rising tone that marks a question |
| Heroic head-count | |||
| Poetic pentameter | |||
| Tonal vs harmonic | |||
| Cat song | |||
| Kiki and bouba | |||
| Orange and cyan | |||
| Heart soaring |
A plant can be happy, if we remember that language is an interface. A burst of light doesn't burst to every living thing. A wave of sound is only described as such by wave-seers -- and describers. When we reduce all such mechanisms to signals and survival, we shoot ourselves in the distalmost, weight-bearing, locomotion-enabling sections of our musculoskeletal systems. Such deconstruction is critical for teasing out mechanisms, sure, provided that we don't lose meaning in the reconstruction. This is all leaving aside the heuristics that layer our conception of what it means to be individual.
But whatever. Let's forget for a moment that language is a lubricant. Let's also forget the inextricability of thing and place. We're left, then, with signals and receivers. Sensory variety runs a very quirky and bendy gamut. How do we mix and match signals that the receivers receive? If we reduce senses to primitives, beyond "light," even, down to the photon, or beyond vibration, even, accommodating those who aren't given to recognizing temporal patterns, how then can we combine these primitives, like a painter does paints? Is it possible to cancel out or arrange primitives, patterning new processes in the process?