The Study of Ignorance

To build knowledge, it is helpful to understand (and consciously experience) the nature of ignorance. To this end, consider the following tools; two “algebraic”, two “geometric” and one conceptual.

How would you understand X if all you know was Y?

In line with Brian Eno’s Oblique Strategies and Edward de Bono’s Lateral Thinking, populate the above with words from two lists – then scramble these lists, then merge them. Examples:

soccer, movement of the ball
soccer, movement of money
politics, movement of money
politics, needs of the people
computers, electricity accurately measured but only once a day
computer processing, looking only at power supply rail activity
diabetes, the taste of urine
the brain, electricity down axons

How would you understand X if you did not know Y?

Similar approach to above, slightly different “algebra”; sufficiently useful to list as a tool of its own. How would you understand computers if you did not know electricity, e.g. if you were from the pre-electric age of mechanics and happened to find a computer, tore it apart, and studied the circuit boards as “maps”?

The gamut graph

This is drawn like a radar display disc, with lines of various aspects radiating from zero at the center, to maximum at the edge. For example, a color gamut has wavelengths of visible light as the “spokes”, with perfection being the full disc; various sensors, display screens, printers etc. would have blind kinks where particular colors were sensed or displayed poorly. Consider mixing radiative vs. absorbed red and green, producing yellow and brown respectively; how would you print yellow if red and green were the “primary colors”? Where can you see brown in a rainbow?

The gamut graph is a useful way to consider dissimilar information across contexts, e.g. if you took the lists used to feed the first two tools and mapped their apparent usefulness, e.g. “soccer, looking only at power supply rail activity” might score 0, but “diabetes, electricity down axons” might eventually score higher than expected.

The triangular relationship

So many formulas are “X = Y times Z”, e.g. voltage = current x resistance, distance = speed x time, pressure = temperature x density, etc. and these often nest and feed into each other, e.g. power = current x current x resistance, or energy = space/time x space/time x mass.

In each case, the product of the multiplication starts as the top of the triangle; then you tumble the triangle to undermine notions of cause and effect.

This helps to break down dualistic thinking, including the observer in the apparent duality. It also helps spot when emergent factors start to break the expected behavior of the duality. Both of these tap into the last tool, described next.

Consider the duality of self and universe, with Zen as the observer. More prosaically, consider the standard duality of trade and commerce, that of service provider and consumer. Originally, the top of the triangle could be ignored, as the consumer paid the provider, but in today’s world, the funder is an independent (and often dominant) factor.

Layers of abstraction

I wrote about this here, but may describe it differently now. Each layer arises from a layer beneath and drifts or breaks into something else above. Within the layer, certain truths hold that may or may not apply elsewhere. You can study a layer from the top down, e.g. how you experience life, or from the bottom up, e.g. what you know about computer chips and logic to understand the infosphere. Each may be considered as a system, but Goedel may break conservation laws, and Heisenberg may break the top-down view while chaos breaks the bottom-up view.

Usually, you’d expect the dominant stresses within a layer to break everything down to a diffuse end state, but in practice, tensions between these may generate complexity. This complexity is inherently a learning system, where “what works” comes to persist and grow. This is life; to game the system into creating, maintaining and extending these islands of complexity, flowing against the expected grain of decay. Selfhood, sentience and consciousness may emerge as winning strategies in this learning game of life.

The layer of human experience is within mind and language, where we model our understanding of the universe. Zen points to that which exists outside language, a la Goedel – i.e. the system of language (and mind?) is incomplete. Our sentience and ethics are here, but rest on (and are betrayed by) layers below.

The body is that of a multicellular animal in the biosphere, glued to a conveyor belt of time while free to move about in space. This scale is the most familiar to our dominant senses, and where the mind/brain generally operates. But the energy needs of such a large and active body requires us to consume the biosphere, even though our sentience finds this unethical. The inescapable sin; we cherish life, but are obliged to destroy it to live.

Within the body are various macroscopic organs, mostly tubes of one kind or another. This extends down in scale to the cellular level, bounded by membranes separating watery and oily domains. This layer is made up of very large and complex molecules, growing into the microscopic from the nanoscale and below.

The next layer down is chemistry, which is all about electron shells; this, rather than macroscopic space and time, is where our bodies arise. The inward intelligence of our immune systems operates from here to the cellular scale, and our oldest and all-but-forgotten senses of smell and taste operate here as well.

Below chemistry is the nuclear scale, affecting which elements occur in what quantities, and whether these are still (radio-)active or not. Below this is the Planck scale, which we define as where physics ceases to be measurable or make sense to our minds.

The thing about these layers of abstraction is they may involve strange loops, where emergent layers affect the deeper levels from which they arise. As humans, we do this all the time – hence the need to “tip over the triangle”, to check our assumptions about what arises from what, and what if anything is “fundamental”.

It’s only by studying ignorance, that we can follow Goedel’s escape from the tyranny of the measurable.