darikwaEdward Madziwa
E = mc2
Every landing page promises to save you time. This one explains why time is negotiable.
Push the throttle. The stars ahead bunch up and turn blue, the ones behind thin out and turn red, and your clock runs slow against everyone you left at home. The sky, the clocks and the light paths are not decoration: they all come from Einstein's equations. Each chapter below ends with the same principle put to work in a business.
- Speed
- 60,647 km/s
- Lorentz factor
- γ = 1.02
- One hour on board
- 1.02 h at home
- A metre on board
- 97.9 cm to home
The rest mass
Start with what a thing is.
Everything a thing can do is already in what it is. Physics calls it rest mass: the one property every observer agrees on, however fast they move past it. Energy and momentum change with the viewpoint. Mass does not.
Shopify, the accounts and the warehouse each see the same product from their own position, with their own dates and figures. What they must all agree on is the product itself: its barcode, what it is made of, how it behaves, how long it takes to come back. Get that record right and sales, stock and cash follow from it. It is the first thing I build.
An analogy from physics, not a claim that physics predicts business results.
Nothing on Earth converts mass to energy completely. A nuclear reactor manages a fraction of a percent, and only in specific isotopes. The exchange rate is real all the same: the Hiroshima bomb released the energy of about 0.7 g of mass, and the Sun turns 4.3 million tonnes of itself into light every second.
Time dilation
Speed slows your clock. Everyone else's keeps going.
Light always travels at the same speed, whoever measures it. A clock that ticks by bouncing light between two mirrors therefore ticks more slowly when it moves past you, because its light has further to go. The factor is γ, and it turns up in everything that follows.
Different systems measure the same sale differently. Translation between them only works once the product has one identity.
γ from 1 at rest to 8 as v nears c
General relativity, 1915
Mass bends space, and light follows the bend.
Gravity is not a force pulling things down. Mass tells spacetime how to curve, and curved spacetime tells everything, light included, how to move. Move the mass and watch the rays of light steer around it. Rays that come too close never leave.
One wholesale order, one hero product or one big customer distorts everything around it, and a straight-line average walks straight past the distortion. Good tools show the curvature instead: concentration, weighting, what is really pulling demand. That is the difference between a dashboard and a decision.
Move your pointer over the grid, tap it, or use the arrow keys to place the mass. The gold ring is the event horizon. The dashed ring marks one and a half Schwarzschild radii, the photon sphere of the exact solution; this weak-field sketch swallows rays that stray anywhere near it.
Black holes
Squeeze anything hard enough and it disappears.
Every mass has a radius at which its escape velocity reaches the speed of light. Compress the object inside that radius and nothing, light included, can get out. Karl Schwarzschild worked this out at the end of 1915 while serving on the Russian front. It was published in January 1916 and he was dead by May; the radius still carries his name.
Stock that sits long enough crosses a line after which no price clears it and the cash never comes back. Every line has its own radius, set by its season, its margin and its rate of sale. The aged-stock reports I build show how close each line is to that horizon while there is still time to act.
6.0 × 10²⁴ kg
The radius scales with mass and nothing else. Double the mass, double the radius. That is why the black hole at the centre of our galaxy, at 4.3 million solar masses, has a horizon eighteen times wider than the Sun, a fifth of the way out to Mercury, rather than a town.
Gravitational time dilation
Gravity slows time too, and your phone knows it.
Clocks run slower deeper in a gravitational well. A satellite clock therefore runs fast because it is higher up, and slow because it is moving quickly. GPS satellite clocks gain about 38 microseconds a day on the clocks below them, and if nobody corrected for it, satnav would drift by kilometres every day.
GPS only works because someone corrects 38 microseconds a day; left alone, the error grows into kilometres. Reporting drifts the same way: a mis-mapped category, a duplicated return, a currency rate a month out of date. Each is tiny, and every one compounds. Reconciling to the source every period is the correction, built into the system rather than left to memory.
Drawn to scale, geostationary orbit at the edge
The two effects cancel at 3,186 km, one and a half Earth radii from the centre. Below that, speed wins and the clock runs slow; above it, altitude wins and the clock runs fast.
Brownian motion, 1905
Uncertainty grows with the square root of time.
The same year as E = mc², Einstein explained why pollen grains in water jiggle: millions of molecules knock them at random, and the spread of where a grain ends up grows with the square root of time, not with time itself. That one result is the backbone of modern forecasting, and run backwards it is how AI image generators work, removing noise step by step until a picture is left.
Weekly sales move like those grains: a trend plus noise. So an honest forecast is a range that widens the further out it looks, and thirteen weeks ahead is about 3.6 times as uncertain as next week, not thirteen times. Buy stock and plan cash against the range, then re-forecast every week as actuals land. That is how the forecasting in the tools I build is designed.
The wall
The formulas behind each chapter, and what each one is for.
Fifteen equations. Between them they describe how fast clocks tick, why starlight bends and how a forecast spreads. Under each, the same idea put to work in a business: these are the principles the tools on this site are designed from.
Mass and energy are the same thing in different units. The conversion rate is c squared.
In business: Everything a product can earn starts with what it is. Get the product record right first, and the rest follows from it.
How much time stretches and lengths shrink for something moving at speed v.
In business: One factor that every downstream effect depends on. In a trading model it is the few drivers, like conversion and average order value, that everything else is built from.
A moving clock's tick (proper time τ) takes γ times longer as you measure it.
In business: The same week looks different from the till, the ledger and the warehouse. Name the frame before comparing numbers.
A moving object is shorter along its direction of travel, by the same factor.
In business: Measured in the wrong frame, a gap looks smaller than it is. A margin quoted ex-VAT against a price inc-VAT is the everyday version.
How to translate positions and times between two observers in relative motion.
In business: A fixed rule for converting one observer's numbers into another's: what reconciling Shopify to the accounts is, once both describe the same product.
The full version of E = mc². For something at rest, p is zero and it collapses to the famous one.
In business: Sales, stock and cash read differently depending on where you measure from. The product record underneath them does not.
The one distance every observer agrees on. Space and time trade against each other to keep it fixed.
In business: The product record is the business's invariant: every system sees it from its own position, and every system agrees on it.
Why the stars in the hero turn blue ahead and red behind as you accelerate.
In business: What is coming towards you reads differently from what is moving away. Forward orders and last season's sales need different lenses.
Curvature on the left, matter and energy on the right. Ten equations in one line.
In business: Ten coupled equations in one line, solved together, never one at a time. A buy plan, a cash forecast and a stock file are the same.
Compress a mass inside this radius and it becomes a black hole.
In business: Past a certain age no price clears a line. Aged-stock reporting shows how close each line is to that point.
How far a ray of light bends passing a mass at distance b. Confirmed in 1919.
In business: A big mass bends every path that passes it. One large customer or hero product bends your averages the same way.
Clocks closer to a mass run slower. Zero at the horizon.
In business: Tiny systematic errors compound. Correct them at the source every period, the way GPS corrects 38 microseconds a day.
Why the stars in the hero crowd towards the direction you are travelling.
In business: Speed changes what you see ahead of you. Grow fast and the next season's risks crowd into the same narrow window.
Einstein, 1905: random jostling makes the spread grow with the square root of time, not time itself.
In business: Why a forecast is a fan, and why thirteen weeks out is about 3.6 times as uncertain as next week, not 13 times.
Einstein's shorthand: a repeated index means add up over it. He invented it to tame the field equations.
In business: Every layer of a neural network is this line. AI code still calls it einsum, and the tensors it multiplies are the ones in his field equations.
First principles, then experience
Now, about your business.
None of this is decoration. Understand a principle well enough and it becomes a method: a core every observer agrees on, frames translated into one another, errors that compound unless corrected, uncertainty that widens with the horizon. Put that together with twenty years in retail, running operations, finance and merchandising across every kind of product for retailers large and small, and you get the systems I build, starting with a product record every other system agrees on, then a weekly trade report that goes out whatever the numbers say, monthly figures that tie back to the stock file so your accountant can trust and use them, and a seasonal buy planned against a range rather than a guess.