Applying Calculus in Intelligence Calculations
(The Question of a Coup)
Coups in Africa
Let's examine some well-documented coups in Africa where post-event investigations, memoirs, and expert analyses exactly show the slow-burn patterns of coups:
Elite whispers
Performative loyalty
Silence from insiders, and
Danger being misjudged rather than unseen.
Here are specific, widely studied cases, with the pattern made explicit:
Not arranged in any particular order:
AI-generated image. The image of the military officer is for illustrative purposes only and does not represent any real person or country.
NIGERIA COUPS
A Typology of Nigerian Coups
SIX COUP TYPES | SIX FAILURE MODES
Coups rarely come out of nowhere—they happen when leaders misjudge how quickly or how drastically conditions are changing. Unknown to many intelligence analysts, tools from calculus, the mathematics of change and accumulation, offer a useful lens for understanding these moments. In Nigeria, for example, each coup reflects a point at which those in power misread the pace, scale, or direction of political shifts. Calculus concepts like rates of change, momentum, tipping points, and buildup over time could have helped clarify how serious the threats were and when they might peak. From this perspective, many Nigerian coups, therefore, were not unavoidable—they succeeded because rigorous analytical reasoning (at least, those with mathematical precision) was absent at the top.
THIS IS NOT A CAPTURE-ALL REVIEW
. The six coup types discussed here are not meant to capture every coup or coup attempt that has taken place in Nigeria. Also, the Shagari-overthrow coup of 1983 features twice, not because it happened twice, but because two principal failure modes played out concurrently.
A calculus-based synthesis of coups
Across all six types of military coups in Nigeria, the shared mistake is the same: leaders treat political danger as a still photograph when it is actually a moving video. In doing so, they substitute momentary snapshots for sustained and sophisticated trend analysis.
Coups do not erupt because intelligence is missing. They erupt because leaders look at where things are instead of where things are going—and how fast.
This is where calculus-based thinking quietly matters.
1. Derivatives: Track rates of change, not levels
What is the calculus idea here?
The derivative measures how fast something is changing—public opinion, voting numbers, economic hardship, public safety concerns, grumblings within the military, or policy approval, not how big it is.
Why does it matter for coups?
Leaders often track levels—approval ratings, number of protests, and who is protesting, loyalty statements, etc. Coups tend to follow accelerations, which are measurable mathematically.
What is the applied insight for intelligence analysis?
A military that is “mostly loyal” but quickly losing its loyalty is more challenging for the besieged leader than one that is stably skeptical.
A quiet elite whose resentment is accelerating is more dangerous than a noisy but static opposition.
What intelligence failure does this correct?
Mistaking “things still look okay” for “things are stable.”
2. Second Derivatives: Measure acceleration and stored instability
What is the calculus idea here?
The second derivative captures acceleration—how fast the rate of change itself is changing.
Why does it matter for coups?
Silence, discipline, or calm can coexist with rapidly increasing internal pressure.
What is the applied insight for intelligence analysis?
Fewer complaints + rising removals + tighter control may indicate accelerating elite exit.
Stability can be a pre-coup compression phase.
What intelligence failure does this correct?
Treating calm as equilibrium instead of as energy that is being stored for the "D-Day."
3. Determine and monitor thresholds and discontinuities
What is the calculus idea here?
Systems can behave smoothly until they hit a critical threshold, after which behavior changes abruptly.
Why does it matter for coups?
Coups are not linear events. Below a threshold, nothing happens; above it, everything happens at once.
What is the applied insight for intelligence analysis?
Legitimacy does not need to hit zero—only a minimum viable level.
Loyalty does not need to collapse everywhere—only at the final veto node.
What intelligence failure does this correct?
Assuming tomorrow will look like today because today looks like yesterday.
4. Integration: Calculate and monitor accumulated pressure over time
What is the calculus idea here?
Integration sums small changes over time into a total effect.
Why does it matter for coups?
Grievances, rumors, slights, and mistrust compound even when each instance seems minor.
What is the applied insight for intelligence analysis?
Repeated “low-confidence” warnings can add up to a high-confidence risk.
Time itself is a variable; prolonged inaction increases cumulative danger.
What intelligence failure does this correct?
Evaluating warnings individually instead of as an accumulated trajectory.
5. Monitor boundary conditions and constraints
What is the calculus idea here?
A system’s behavior is constrained by boundary conditions, regardless of internal dynamics.
Why does it matter for coups?
Formal authority operates within limits set by who controls force, access, and enforcement.
What is the applied insight for intelligence analysis?
Civilian rule within a military-controlled boundary will revert to full military rule under stress, e.g., in the event of national security emergencies, internal unrest or rebellion, external invasion or war, states of emergency or martial law, or weak institutions or legitimacy crises.
Elections cannot stabilize a system whose coercive boundaries are unchanged.
What intelligence failure does this correct?
Overestimating formal changes while ignoring structural constraints.
6. Multipliers: Track when one variable nullifies another
What is the calculus idea here?
In many models, variables multiply rather than add.
Why does it matter for coups?
Some factors act as zero-multipliers.
What is the applied insight for intelligence analysis?
Intelligence × enforcement capacity = deterrence.
If enforcement capacity is zero, intelligence—however perfect—has no effect.
What intelligence failure does this correct?
Believing that awareness alone changes outcomes.
AI-generated image. The image of the military officer is for illustrative purposes only and does not represent any real person or country.
The Core Insight
Most coups succeed not because the overthrown leaders knew nothing,
but because they misunderstood movements.
They read levels:
“Is loyalty high?”
“Is the army calm?”
“Is the state functioning?”
When they needed to read curves:
“Is loyalty shrinking faster than before?”
“Is calm masking coordination?”
“Is the system approaching a tipping point?”
This is why people trained to think in dynamics—engineers, analysts, systems thinkers, mathematicians—often spot danger earlier than politicians.
They are not smarter about politics.
They are simply trained to ask a different kind of question:
“What happens next if this trend continues?”
And that, more than ideology or intent, is what decides whether a coup fails—or succeeds.
AI-generated image. The image of the military officer is for illustrative purposes only and does not represent any real person or country.
Common patterns in the coups
Across these cases, experts consistently identify the same sequence:
Elite discontent becomes private, not public
Rituals of loyalty continue, but substance disappears
Advisers hedge, delay, or fall silent
Leaders mistake formality for fidelity
The coup appears sudden—only in retrospect
One day an administration stands; the next, it is gone.
This is why many coup experts argue that coups are not shocks but revelations: the moment when invisible shifts finally become undeniable.
Other Countries
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About the tool book
This free introductory manual starts where conventional intelligence analysis grows uncomfortable—and grinds to a screeching halt—and that is, sophisticated mathematics. No one likes maths, but it's maths that saves the day, every day. This manual takes a turn most intelligence analysts never expect: Calculus. This is not just equations; it's not academic maths, but a discipline designed to reason under uncertainty, thresholds, and hidden coordination.
Yes, many intelligence failures are driven less by missing information and more by a false sense of certainty.
Calculus accounts for what you do not know! In this case, calculus may be the missing tool leaders never realized they needed.
What intelligence analysts will get from this manual:
A disciplined way to treat coup risk as a continuously evolving process rather than a binary outcome.
A method for preventing repeated signals from masquerading as independent confirmation
Practical tools for integrating noisy, incomplete, and deceptive intelligence without forcing premature conclusions.
A calculus-based framework for handling hidden coordination, thresholds, and nonlinear escalation.
Protection against false certainty created by consensus, narrative dominance, or analytic momentum.
Clear guidance on when confidence is warranted, conditional, or unjustified.
An approach that strengthens judgment without replacing experience or tradecraft.
Techniques for briefing senior leaders that explain not just what you assess, but why that level of confidence exists.
Earlier warning without alarmism, even when visible indicators remain weak.
A way to stay analytically ahead of surprise rather than explaining it afterward.
Explore our other recent projects:
The Question of a Coup: Applying Calculus in Intelligence Calculations: A practical intelligence manual showing how calculus-based reasoning can prevent false certainty, expose hidden coordination, and reduce strategic surprise in coup analysis.
National socio-digital early warning and strategic foresight architecture: a computational intelligence ecosystem to anticipate mass sentiment shifts before coordinated unrest and destabilization emerge.
Understanding the Lockwood Analytical Method for Prediction (LAMP): my firsthand experience applying one of the intelligence community’s most rigorous forecasting methodologies.
Self-disruption research: Applied Whitney Johnson's four principles of self-disruption in addressing unconscious bias among intelligence analysts.
Intelligence training manual: Self-disruption as analytic tradecraft
Self-disruption as analytic tradecraft: Classified-style analytic vignettes and tradecraft alignment
Not Intelligence-Related:
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