In 1943, the Statistical Research Group sat in rooms calculating optimal curves for aircraft gunsights, minimum armour loads, and strategic bombing patterns. Alan Turing broke the Enigma code in 1941. This shortened the war by two to four years and saved ~14 million lives. The atomic bomb was built by running calculations on chain reactions, blast radii, and fission rates. History rewards the armies with better maths, not better speeches. And your life is no different. 5% more accuracy, 5% less waste, and 5% better timing – such edges compound until they look like genius. Math is not just beautiful equations. It’s infrastructure. Your Life Sucks Because Your Math Sucks Your Life Sucks Because Your Math Sucks Every mistake you’ve made can be traced back to one failure: you couldn’t correctly compute the cost of your decision. You operate on gut feeling, social proof, and vibes. This is why you’re stuck. The business you started was three years too late because you didn’t calculate the cost of waiting. The skill you never learnt because you couldn’t see the compounding returns. The price you charged left $50,000 on the table because you guessed instead of computed. You Already Do Math; You Just Do It Badly You Already Do Math; You Just Do It Badly School might teach you that maths is a list of rules to memorise and obey. If you get the rules wrong, you get a C-. But maths is about computing efficiently and using that computation to solve problems, build things, and make better decisions. You think you don’t use the maths from school. Wrong. You use it constantly. You just don’t call it maths. Every decision you make is a computation. Every risk you evaluate is a probability calculation. Every goal you set is an optimisation problem. Every trade-off you weigh is an equation. Every decision you make is a computation. Every risk you evaluate is a probability calculation. Every goal you set is an optimisation problem. Every trade-off you weigh is an equation. You’re just doing it unconsciously, sloppily, and badly. If you solved a problem in your life this morning, you did maths. You’ll be better at it once you realise that’s what’s happening inside your head. Math Is Common Sense, Extended Math Is Common Sense, Extended Math is a form of modelling (or you can call it abstraction), a method we use to compress complexity so we can actually work with it. Modelling means isolating some key attributes of something, stripping away everything else, and running computations on what remains. We use models to explain, describe, predict and forbid things. Modelling Think: aeroplane models, architectural blueprints, fashion models, mental models, large language models, and so on. There are two fundamental ways that we model reality: 1. Verbal Modelling — using language to describe logic. Like when you argue or write essays. 1. Verbal Modelling 2. Mathematical Modelling — using equations to describe logic with precision. 2. Mathematical Modelling On top of these, you get graphical modelling (charts, diagrams), statistical modelling (computing relationships that aren’t perfectly predictable), physical modelling (miniatures that isolate variables), geographical modelling (maps), and much more. It took humanity tens of thousands of years to figure out how to walk and talk. It took another few thousand years for someone like Archimedes to figure out the area of a circle. Now a kid can learn both immediately by simply using the models they’ve created. Modelling is what makes knowledge grow exponentially. Why This Matters If You Want to Build Anything Why This Matters If You Want to Build Anything The vague advice the world gives you—”just be creative,” “follow your passion,” “hustle harder”—is verbal fog masquerading as wisdom. You don’t just wake up one morning and build a product. You don’t just sit down and write an essay that enlightens minds. Even if you think you do, this is what’s happening in the background: How Knowledge Is Actually Made How Knowledge Is Actually Made Knowledge is created by compressing reality into workable models, then breaking and rebuilding those models until they no longer fail where the old ones failed. Knowledge is created by compressing reality into workable models, then breaking and rebuilding those models until they no longer fail where the old ones failed. That’s it. That’s science. That’s engineering. That’s mathematics. That’s entrepreneurship. That’s it. That’s science. That’s engineering. That’s mathematics. That’s entrepreneurship. People romanticize creativity, intuition, inspiration… But the engine underneath all that mystique is modelling. Let me break it down cleanly: 1. Reality Is Too Big. So, we compress it. 1. Reality Is Too Big. So, we compress it. Your brain cannot compute the full universe (yet). So it throws away 99% of the detail and keeps only the levers you think matter. think That “throwing away” is the act of modelling. A model is not a mirror of reality.It’s a filter. filter A map filters geography into lines and symbols A blueprint filters a building into load-bearing constraints Newton’s laws filter the universe into point masses and forces An essay filters the world into ideas and arguments A business plan filters chaos into revenue, cost, conversion rates, churn A mental model filters life into heuristics Your beliefs, religion, political opinions, and so on. are models you’ve created and/or adopted. A map filters geography into lines and symbols A blueprint filters a building into load-bearing constraints Newton’s laws filter the universe into point masses and forces An essay filters the world into ideas and arguments A business plan filters chaos into revenue, cost, conversion rates, churn A mental model filters life into heuristics Your beliefs, religion, political opinions, and so on. are models you’ve created and/or adopted. You never operate on reality. You operate on your model of reality. your model This is why people fail: Their model is wrong, incomplete, or unfalsifiable. 2. Every Model is an Oversimplification: But That’s the Point 2. Every Model is an Oversimplification: But That’s the Point Wrong/Right is a spectrum, not binary. All explanations are wrong, but some are good because they fail in ways that matter less. good Bohr’s atom model was wrong, but it unlocked chemistry. wrong Newton’s gravity was wrong, but it unlocked engineering. wrong Ptolemaic astronomy was wrong, but it predicted planetary motion for centuries. wrong Progress doesn’t come from “finding the ultimate truth”. It comes from building a model that fails more gracefully and explains more phenomena with fewer assumptions. building a model that fails more gracefully and explains more phenomena with fewer assumptions 3. Falsifiability = Knowing Where the Model Should Break 3. Falsifiability = Knowing Where the Model Should Break A model must rule out possible worlds. If it can’t be wrong, it can’t be right. A model must rule out possible worlds. A good model is fragile in the correct places. Bad model: “Everything happens for a reason. ”Good model: “Demand decreases when price exceeds perceived value.” All knowledge is an oversimplification because that’s how it was created (via modelling). But subsequent models become more accurate by failing better. That’s the mechanism of progress. 4. Creativity Is Just Model Mutation 4. Creativity Is Just Model Mutation People over-mystify creativity. Strip off the poetry, and here’s the engine: Creativity = generating variations on an existing model. Creativity = generating variations on an existing model. Criticism = checking where those variations fail. Criticism = checking where those variations fail. Selection = keeping the variation that fails least. Selection = keeping the variation that fails least. That’s evolutionary epistemology. Model → Variation → Criticism → Selection → Improved Model Model → Variation → Criticism → Selection → Improved Model The magic is that this loop works for everything. everything Pixar iterates story models SpaceX iterates failure models Einstein mutated Lorentz transformations Every great creative you admire works this way. Architects redraw. Writers redraft. Engineers prototype. Musicians riff. Founders iterate. The breakthrough looks like intuition from the outside, but on the inside it’s the quiet brutality of model mutation: kill the version that breaks, keep the one that doesn’t. 5. A Mathematical Model Is the Most Precise Model 5. A Mathematical Model Is the Most Precise Model Like matrix algebra converts 3D to 2D, we convert reality into compressed models so we can compute them. Math is the ultimate compression codec. Verbal models are lossy. Visual models are intuitive but vague. Statistical models capture correlations without mechanism. Mathematical models capture structure with precision. Math isn’t “numbers”. Math is structure. structure Structure is what stays true after you compress reality. 6. The Fundamental Recipe for Knowledge Creation 6. The Fundamental Recipe for Knowledge Creation Step 1: Distill Step 1: Distill Ignore 99% of reality. Zoom in on what matters. Name the variables. Step 2: Constrain Step 2: Constrain Define what must be true. Define what can’t be true. Remove wiggle room. Step 3: Compress Step 3: Compress Find the smallest structure that explains the largest chunk of reality. That’s the model. Find the smallest structure that explains the largest chunk of reality. Step 4: Compute Step 4: Compute Run the model. Solve, simulate, graph, test. Step 5: Criticize Step 5: Criticize Look for failure modes. Where does the model break? Why does it break? Step 6: Mutate Step 6: Mutate Generate new variations. Change the assumptions. Try another abstraction. Try a different representation. Step 7: Select Step 7: Select Keep the version that fails least. This is your new understanding. Repeat forever. This is how humans, science, startups, and civilisations progress. Start Computing. Start Computing. Your life changes when your model changes. model Stop running vibe-driven models that have bad explanations and predict nothing. Start building models that constrain reality and give you leverage over it. Sell the models you develop to others and make their lives easier too. Every breakthrough product, writing, research or design starts with a good model. If you’d like to build yours, Check out my free newsletter: https://crive.substack.com Enjoy, —Praise J.J.
