inv-02

A

B

C

Here’s a clean, high-resolution way to think through your A + B packet using the invariant we’ve been developing: input → throughput → output, where throughput = Δ(value)/Δt, the rate of transformation.

Let me walk through PJM’s pathway as a cognitive-processing throughput system and extract the metrics you’re pointing toward.


1. INPUTS (PJM’s Early Life Constraints)

On paper his inputs were objectively low:

Structural Inputs

Positive Inputs

Relative to people who reach UC Berkeley Econ PhDs, his measurable inputs were orders of magnitude lower.


2. THROUGH­PUT (PJM’s Cognitive Processing Rate)

This is the extraordinary part. His throughput must have been extremely high to compensate for low inputs and still generate elite outputs.

We can think of cognitive throughput here as:

\[\text{Cognitive Throughput} = \frac{\Delta(\text{Conceptual Mastery})}{\Delta t}\]

or even more concretely:

Possible throughput metrics

  1. Learning velocity Rate at which he compressed unfamiliar information into structured, usable knowledge.

  2. Abstract synthesis rate Ability to generalize from small, noisy data (his environment) into large-scale models.

  3. Resilience-to-progress conversion rate Hard environments tend to degrade throughput; in him it accelerated it.

  4. Opportunity conversion efficiency When a new node appeared (e.g., Kikuyu College), he converted it rapidly into leverage.

  5. Signal extraction from sparse data A hallmark of high-throughput cognition is: the less information you need to form correct intuitions, the higher your throughput.

  6. Compression ratio How much conceptual output per unit of educational input?

Measured this way, PJM’s cognitive throughput was pathologically high.


3. OUTPUTS (What Actually Emerged)

These are downstream results conditioned by throughput:

The output is, in formal terms:

\[\text{Output} = \int \text{Throughput} , dt\]

And his integral is unusually large given the boundary conditions.


4. What Does This Say About Secondary School Education?

Here’s the provocative but mathematically clean insight:

High-throughput individuals do not need long ramps.

They need:

Secondary school adds latency to the system. Latency is poison to high-throughput learners.

For a sufficiently motivated, high-throughput person:

Formally:

If

\[\frac{\Delta K_{\text{school}}}{\Delta t} \Bigg|*{\text{secondary}} < \frac{\Delta K*{\text{self-taught}}}{\Delta t} \Bigg|_{\text{PJM}}\]

then the schooling system is throughput-inhibiting.

Secondary school is a bandwidth normalizer: it tries to equalize rates across students. High-throughput individuals break such systems because their natural dK/dt is far above the enforced pace.


5. So What Was PJM?

A high-throughput, low-latency learner whose system was constrained by:

But who compensated with:

His map looks like this:

Phase Input Throughput Output
Childhood Low resources Very high Conceptual intuition
Mwiri Very short time High Partial formal grounding
Lost years Minimal structure High self-study Preparedness for Kikuyu
Kikuyu Alternative pathway Extreme Makerere admission
Makerere High signal Extreme Top of class
Berkeley Very high signal Elite PhD (1980)

All consistent.


6. The Deeper Point You Are Circling

You are asking:

Is secondary school necessary for a high-throughput mind?

Answer:

No — secondary school is a throughput dam for self-propelled systems. It exists to increase minimum throughput, not maximum throughput.

High-throughput learners only need:

  1. Access to signal
  2. A feedback channel
  3. A pathway to formal certification

Everything else is redundant.

PJM solved 1–3 manually.


7. If You Want, I Can Go Further

I can:

Just tell me: “Continue.”