https://www.vectors-of-reality.com/about https://www.vectors-of-reality.com/pictures-website/web-pic-7.jpeg Julius T. Geiger Julius T. Geiger standing in a gallery between two paintings, looking aside. https://www.vectors-of-reality.com https://www.vectors-of-reality.com/pictures-website/web-pic-landing-page-fade-background.jpeg Julius T. Geiger Portrait of Julius T. Geiger, author of the essays at Vectors of Reality. https://www.vectors-of-reality.com/essays/opportunity-quotient https://www.vectors-of-reality.com/essay-glyphs/opportunity-quotient.png How high is your Opportunity Quotient? On seeing the options that were there all along. https://www.vectors-of-reality.com/email-figures/opportunity-quotient/MentalModelLensDiagram.png A lens ground out of an idea A lens standing between two versions of the same scene. On the left, the raw situation: a loose scatter of grey dots with no order. In the centre, a convex lens labelled mental model. On the right, the very same dots, now resolved into a rising blue curve, made visible. Faint rays gather the scattered points into the lens and project them back out in order: nothing is added, the lens only rearranges what was already there. https://www.vectors-of-reality.com/email-figures/opportunity-quotient/OQComponentsDiagram.png What a high OQ is built from Four muscles a high Opportunity Quotient is built from, arranged in a two-by-two grid whose cells meet at a central blue OQ node: cognitive flexibility top left, combinatorial chemistry top right, comfort with ambiguity bottom left, agency and execution bottom right. https://www.vectors-of-reality.com/email-figures/opportunity-quotient/SeeingOpeningsWallPullDiagram.png Seeing openings One situation at the left, drawn as a single node, with routes leaving it toward a wall built of twelve courses of slate brick, each brick an assumption. Eleven grey routes run at the standing courses and stop dead against them, each ended by a small cross. One brick is caught in the air below and to the right of the wall, with the slot it came out of dashed above it, high on the wall. A single blue route bends up out of the node, threads that slot and carries on off the right edge, labelled opening. It is the only way through the scene and it did not exist until the brick came out. https://www.vectors-of-reality.com/email-figures/opportunity-quotient/TwoKindsOfWallDiagram.png Two kinds of walls Two walls standing on one ground line, built out of different things. The long wall on the left, drawn in blue and labelled soluble, a knowledge problem, is brick and it is breached in four places, each hole as far along as the knowledge that bought it: a full doorway at boiling the water, most of the way through at the reusable rocket, a small notch at fusion power and a single brick out at reverse ageing. The holes step along the brick joints and the wall runs off the left edge of the frame because that pile has no end. The short block on the right, drawn in ink and labelled fixed, is not brick at all but one uncut mass, hatched the way a drawing hatches solid material, with no course, joint or opening anywhere in it and a heavier outline closing it on all four sides, with gravity ticked beneath it. https://www.vectors-of-reality.com/essays/maximal-reproducible-return https://www.vectors-of-reality.com/essay-glyphs/maximal-reproducible-return.png Maximal Reproducible Return A brilliant Tuesday bought with Wednesday and Thursday. https://www.vectors-of-reality.com/email-figures/maximal-reproducible-return/RecoveryAsymmetryDiagram.png The climb back is bigger than the fall How far a loss has to climb to get back to where it started. A 10 percent loss needs an 11 percent gain to recover, a 30 percent loss needs 43 percent and a 50 percent loss needs a full 100 percent. The fall and the climb cover the same distance, but as a percentage the climb back is always larger and it accelerates as the loss deepens. https://www.vectors-of-reality.com/email-figures/maximal-reproducible-return/RunnerPacingDiagram.png Two ways to run the same distance Pace across one run. Runner one holds a steady pace just under the lactate threshold the whole way and finishes strong. Runner two surges over the threshold early, then the pace collapses to a walk and only partly recovers. Despite the early surge, runner two's average pace ends up well below runner one's steady line. https://www.vectors-of-reality.com/email-figures/maximal-reproducible-return/ThresholdDomainsDiagram.png Three kinds of lines Three kinds of threshold, each plotting capacity over time after a crossing. Reversible: the capacity falls and climbs all the way back to where it started, but the climb takes much longer than the fall. Irreversible: it recovers only part-way and settles at a floor below the original ceiling. Absorbing: it falls to the floor and stops, with no recovery at all. https://www.vectors-of-reality.com/essays/failure-modes-of-decision-models https://www.vectors-of-reality.com/essay-glyphs/failure-modes-of-decision-models.png Failure Modes of Decision Making And why error detection is the most important thing. https://www.vectors-of-reality.com/email-figures/failure-modes-of-decision-models/AgencyFailureDiagram.png Influence mistaken for control A large dashed circle labelled believed under control holds a small solid blue disc labelled actually under control. Blue dots sit inside the small disc; grey dots fill the crescent gap between the two circles and scatter across the space outside, labelled chance. Most of the variables lie outside the agent's real control. https://www.vectors-of-reality.com/email-figures/failure-modes-of-decision-models/BoundedRationalityDiagram.png Bounded Rationality A field of alternatives narrowing left to right. An even field of option-seeds fills the wide mouth; as it passes three constraint bands — limited knowledge, cognitive capacity and time limits — the cone narrows, options that fall outside it are shed in grey and the blue survivors converge into a single decision. https://www.vectors-of-reality.com/email-figures/failure-modes-of-decision-models/CircleofcompetenceDiagram.png Circle of Competence Two nested circles in blue. The larger circle, a light blue wash, is what we think we know; the smaller circle inside it, a deeper blue, is the much smaller set of what we actually know; and the open space beyond both circles, labelled on the right, is everything we don't know. https://www.vectors-of-reality.com/email-figures/failure-modes-of-decision-models/EpistemicFailureDiagram.png Four shapes of epistemic failure Four labelled cards in a 2×2 grid, each naming an epistemic failure mode — false coherence, unknown unknowns, untested belief and premature closure — with a three-line description of the mechanism and, under a divider, a one-line consequence: worst under time pressure; not knowing what you don't know; confirmed, never tested; it sounds done, so we act. https://www.vectors-of-reality.com/email-figures/failure-modes-of-decision-models/FeasibilityFailureDiagram.png Penrose Tribar A Penrose tribar — an impossible triangle of three bars in graded VOR blue, meeting at three valid right-angle corners, yet forming a solid that cannot exist in space. https://www.vectors-of-reality.com/email-figures/failure-modes-of-decision-models/OntologicalFailureDiagram.png Geocentrism vs heliocentrism Ptolemy ran the calendars for centuries with the earth in the wrong place. A model can be useful and still be wrong about what sits at the centre. https://www.vectors-of-reality.com/email-figures/failure-modes-of-decision-models/PredictionFailureDiagram.png The cone of potential futures A cone of potential futures fanning out from the present and narrowing backward into historic evidence. The forward mouth is banded into a dense probable core, a wider plausible zone and an outermost possible boundary, with two rare events pinned to that outer edge. https://www.vectors-of-reality.com/essays/measured-against https://www.vectors-of-reality.com/essay-glyphs/measured-against.png What is a good decision? And what apples and yardsticks have to do with it? https://www.vectors-of-reality.com/email-figures/measured-against/DecisionMeasuresDiagram.png Four counter weights The same decision weighed on four balance scales, one for each measure: Outcome, Given Information, Goals and Values, from shallow to deep. The identical blue decision token sits on the left pan of every scale, weighed against a standard that grows heavier the deeper the measure. The beams tilt differently: at the surface the decision's pan sinks, so it measures up and at the deeper measures the standard's pan sinks, so the decision falls short. The verdicts disagree, sliding from pass to fail as the measure deepens. https://www.vectors-of-reality.com/email-figures/measured-against/ValuesVirtuesDiagram.png Values vs. Virtues The same mark in two states. On the left a hollow blue circle floats inside a thought bubble, labelled VALUES, the ideal held in the mind. An arrow crosses to the right, where the same circle is now solid and rests on a ground line, labelled VIRTUES, the act shown in reality. A value becomes a virtue when it is lived out. https://www.vectors-of-reality.com/essays/optimal-stopping-theory https://www.vectors-of-reality.com/essay-glyphs/optimal-stopping-theory.png The Math of making the most optimal decision When does "I could do better" have to surrender to "This is as good as it gets"? https://www.vectors-of-reality.com/email-figures/optimal-stopping-theory/BestChoiceCurve.png A curve of win probability against the fraction of candidates you skip before accepting. It rises from zero, peaks at a fraction of about 0.37 where the win probability is also about 0.37, then falls back toward zero. The single peak is marked at 1 over e. https://www.vectors-of-reality.com/email-figures/optimal-stopping-theory/BestInLookWindow.png This time the tallest slip of all sits inside the first 37%, so you can't take it. As nothing after the window ever reaches it, you have to take the last slip you are handed. https://www.vectors-of-reality.com/email-figures/optimal-stopping-theory/GateAxisDiagram.png On the left the gate sits on the time axis, the 37% rule. On the right the gate sits on the value axis, a level you set yourself. https://www.vectors-of-reality.com/email-figures/optimal-stopping-theory/OptimalStoppingSimulation_1.png https://www.vectors-of-reality.com/email-figures/optimal-stopping-theory/OptimalStoppingSimulation_2.png https://www.vectors-of-reality.com/email-figures/optimal-stopping-theory/SettleForMarginal.png Here the first 37% is full of weak slips, so the bar sits low. The first slip that beats it is barely better than what you already saw and the rule stops there. The real best arrives a few slips later, far taller but you have already committed to one candidate. https://www.vectors-of-reality.com/email-figures/optimal-stopping-theory/ThirtySevenPercentRule.png You only look at candidates and reject them by default, but let the tallest set the bar. After the first 37%, the rule takes the first one that is taller than the set bar. https://www.vectors-of-reality.com/email-figures/optimal-stopping-theory/TwoValuesDiagram.png A row of candidate bars from early to late. Each bar is split into two values: a slate part for its worth as data and a deep blue part for its worth as the catch. Early bars are mostly data, late bars mostly catch and the handover between them slides earlier or later as the horizon is set shorter or longer. https://www.vectors-of-reality.com/essays/the-good-kind-of-uncertainty https://www.vectors-of-reality.com/essay-glyphs/the-good-kind-of-uncertainty.png Why We Actually Crave Uncertainty Why we love Uncertainty or at least some type of it. https://www.vectors-of-reality.com/email-figures/the-good-kind-of-uncertainty/DeliberateIgnorance.png What you choose not to know Three nested circles. The outer set holds every question a person could ask about their life, the middle set the questions they cannot answer and the innermost set, drawn in blue, the questions they could answer but choose not to, which is deliberate ignorance. https://www.vectors-of-reality.com/essays/lessons-in-probability-from-the-serengeti https://www.vectors-of-reality.com/essay-glyphs/lessons-in-probability-from-the-serengeti.png Working Hard Is Not Enough Effort is a lever, but a small one compared to the underlying generator. https://www.vectors-of-reality.com/email-figures/lessons-in-probability-from-the-serengeti/UniversalGeneratorDiagram.png The universal generator A vertical pen-blue portal on the left emits a stream of circles rightward along a horizontal thread. Filled pen-blue circles are successes; hollow circles are misses. The proportion of fills tracks the probability parameter set by the slider below. https://www.vectors-of-reality.com/essays/the-geometry-of-luck https://www.vectors-of-reality.com/essay-glyphs/the-geometry-of-luck.png The Geometry of Luck On path-dependent outcomes, luck surface area and the conversion of randomness into result. https://www.vectors-of-reality.com/email-figures/the-geometry-of-luck/SinnvollLebenDiagram.png Where effort ends and luck begins A rectangle divided diagonally. Below the diagonal is the effort field; above, the luck field. A vertical band at the plane of action shows the split between effort and luck at one specific point. https://www.vectors-of-reality.com/essays/Ergodicity-Intro https://www.vectors-of-reality.com/essay-glyphs/Ergodicity-Intro.png The Room with the Revolver and other Non-Ergodic Systems On ergodicity, time averages and the lie hiding inside expected value. https://www.vectors-of-reality.com/email-figures/Ergodicity-Intro/ErgodicityDefinitionDiagram.png Two ways a path moves through a space Two circles. Left, non-ergodic, a woven mesh of chords that all keep clear of the centre, leaving a hollow disk in the middle. Right, ergodic, scatters random chords that fill the entire disk. https://www.vectors-of-reality.com/essays/protean-uncertainty https://www.vectors-of-reality.com/essay-glyphs/protean-uncertainty.png Until the God speaks - Protean Uncertainty Why the future does not just hide from us. https://www.vectors-of-reality.com/email-figures/protean-uncertainty/UncertaintyTaxonomy.png Three kinds of uncertainty Three panels comparing risk, fogged-over uncertainty and a field of many shifting distributions. https://www.vectors-of-reality.com/essays/distributional-thinking https://www.vectors-of-reality.com/essay-glyphs/distributional-thinking.png Every success has siblings and often you only meet one An introduction to Distributional Thinking https://www.vectors-of-reality.com/email-figures/distributional-thinking/DistributionGaussian.png Gaussian Distribution A symmetric distribution. The mean and the median sit in the same place, so the average lands where intuition expects it. https://www.vectors-of-reality.com/essays/why-dying-is-often-hard-but-sometimes-easy https://www.vectors-of-reality.com/essay-glyphs/why-dying-is-often-hard-but-sometimes-easy.png Why dying is often hard, but sometimes easy On decision-making under unknown time horizons. https://www.vectors-of-reality.com/email-figures/why-dying-is-often-hard-but-sometimes-easy/HorizonDiagram.png Expected against actual Time axis with two draggable markers, expected and actual horizon. The strategy band runs from now to expected; the hatched slice between expected and actual is the misallocation.