Denkwerkzeug
72 cards from across every topic, each citing a source. Tap one to open it in the feed.
- "What if not?" is a measuring tool, not a game.
To say how important a cause was, you have to ask what would have happened without it. In 1964 economist Robert Fogel …
- A coin in a grave doesn't give you a year, only a boundary.
Historians often date not with a point but with two limits. Terminus post quem: if a grave holds a coin from 312, it …
- A fingerprint lies less often than a letter.
Sources split into two kinds. Relics arise incidentally: tools, rubbish, invoices, fingerprints. Narratives are told …
- A language model only ever guesses the next word.
Large language models like ChatGPT were trained on billions of sentences to predict the most likely next word fragment. …
- A number without a plus-minus isn't a measurement, it's a claim.
Every measurement is uncertain, no matter how expensive the instrument. That is why labs worldwide agree: a result is …
- A theory that can explain everything explains nothing.
Karl Popper, 1934: a statement is scientific only if some observation could refute it. A thousand white swans don't …
- Adaptation isn't free. It runs up a bill.
Bruce McEwen and Eliot Stellar coined the term allostatic load in 1993. Homeostasis is the stable target state …
- An accident needs holes that happen to line up.
James Reason described safety systems around 1990 as a stack of cheese slices: each layer is a barrier, each hole a …
- An object with no history is an object with no value.
Provenance is the unbroken chain of ownership and location of an object. It decides authenticity, market value and …
- Ask your 80-year-old self before you decide.
Jeff Bezos described the regret minimization framework for his 1994 decision to leave a safe job for Amazon: imagine …
- Check the units before you trust the number.
Every meaningful physical equation has the same units on both sides: metres stay metres, seconds stay seconds. If your …
- Chesterton's fence: don't remove what you don't understand.
In 1929, G. K. Chesterton described a fence in the middle of a field. The modern reformer says: 'I don't see the use of …
- Convert prices into hours of your life, not euros.
This mental tool comes from the bestseller 'Your Money or Your Life': divide your net income by all the hours your job …
- Creativity has two gears – don’t use both at once.
In 1956 psychologist J. P. Guilford distinguished divergent thinking – generating many possible answers – from …
- Diagnosed earlier does not mean lived longer.
If a disease is normally found at 60 and someone dies at 65, the statistic records five years of survival. If screening …
- Disturb a system at equilibrium and it pushes back.
Henry Le Chatelier stated in 1884: change the pressure, temperature or concentration of an equilibrium and it shifts so …
- Do great men make history, or does history make great men?
In 1840, Thomas Carlyle declared that world history was 'the biography of great men'. Herbert Spencer countered in …
- Earth's entire history compressed into one day.
Squeeze Earth's 4.54 billion years into 24 hours. The first life appears around 4 a.m. Multicellular animals don't show …
- Encryption explained with an open padlock.
Imagine handing out open padlocks that only your key can open. Anyone can lock a box with one, but only you can unlock …
- Everything is poison. Only the amount matters.
The physician Paracelsus wrote in 1538: all things are poison, and the dose alone makes a thing not a poison. Too much …
- Evolution wants nothing. It only sorts.
A common mistake: species "develop" traits because they need them. In reality, variants arise at random and the …
- Extraordinary claims require extraordinary evidence.
Carl Sagan made the line famous in 1980 in his series 'Cosmos', discussing alleged alien visits. The idea is older …
- Four rules that separate cause from coincidence.
Robert Koch and Friedrich Loeffler set out four conditions in 1884: the microbe is found in all the sick, can be grown …
- How many countries are there? Depends who you ask.
The United Nations has 193 member states plus two observers (Vatican City, Palestine). Kosovo is recognised by around …
- How many must take a treatment for one to benefit?
The Number Needed to Treat (NNT) answers exactly that. If a treatment cuts an event from 5 % to 4 %, the absolute …
- How many piano tuners are in Chicago? Work it out.
Enrico Fermi estimated unknowns by breaking them into quantities he roughly knew: population, households, pianos per …
- Ice cream sales and drownings rise together. Ice cream is innocent.
Two things occur together – that doesn't prove one causes the other. Often a third factor lies behind both: for ice …
- Longue durée: reading history at three speeds.
In 1949, the French historian Fernand Braudel distinguished three layers of time: events like battles and elections …
- Magnitude 7 isn't "a bit stronger" than 6.
The magnitude scale is logarithmic. One step up means ten times the ground motion and about 32 times the energy …
- More energy out than in? Look for the hidden source.
Two laws of thermodynamics have never been broken: energy does not arise from nothing, and heat flows by itself only …
- More lanes don't make the traffic jam smaller.
Widen a road and travel time drops briefly. That very drop attracts new trips: people switch from the train, drive at …
- Most cases come from the group with the small risk.
Geoffrey Rose described it in 1981: a measure can do almost nothing for any individual and still do a great deal for a …
- No single water molecule is wet.
Wetness only appears when billions of molecules act together. An ant colony builds roads though no ant knows the plan …
- Nobody ever woke up in the Middle Ages.
Periods are retrospective filing aids, not natural boundaries. In the 14th century Petrarch coined the idea of a dark …
- Nobody mentioning it almost never proves it did not happen.
A source's silence carries weight only under three conditions: the author meant to be exhaustive, would have noticed …
- North is only "up" because we're used to it.
There is no up in space. Medieval European maps often put east at the top, and Islamic cartographers like al-Idrisi put …
- Not every study carries the same weight.
From the bottom up: expert opinion, case report, cross-sectional survey, case-control study, cohort study, randomised …
- One detail in the wrong era exposes any forgery.
An anachronism is an object, word or custom that did not yet exist in the depicted period. Renaissance painters show …
- One healthy person in twenty falls outside the normal range.
A standard reference range is defined so that 95 percent of a healthy comparison group falls inside: 2.5 percent below …
- Presentism: judging the past by today's yardstick.
Presentism means judging people of the past as if they had your knowledge and your values. A doctor in 1750 who …
- Read every statement in its most reasonable interpretation first.
The principle of charity from philosophy says: when a statement is ambiguous, choose the reading under which it is most …
- Some places matter more than what happened there.
The historian Pierre Nora published "Les Lieux de mémoire" from 1984 to 1992 and coined the site of memory: a place …
- Source criticism: four questions before you believe a source.
Historians test every source with fixed questions: Who wrote it? When, and how close to the event? For whom, and with …
- The good old days were never as good as you remember.
In studies by Mitchell and Thompson, travellers rated the same trip far more positively afterwards than during it – …
- The invisible corridor every deal lives in.
The ZOPA (Zone of Possible Agreement) is the range between the maximum a buyer would pay and the minimum a seller would …
- The older an idea, the longer it will probably live.
The Lindy effect, named after a New York deli where comedians speculated about how long shows would run: for …
- The opposite of a straw man – and why it makes you smarter.
Steelmanning means stating the opposing view in its strongest form – so well that the other side says “yes, that’s …
- The real price of anything is what you give up for it.
Opportunity cost is the value of the best alternative you don't choose. A €20,000 car also costs what that money would …
- The trap of reading history as a road leading to us.
In 1931, the historian Herbert Butterfield criticised 'Whig history': narratives in which everything earlier is merely …
- The web is not the internet.
The internet is the road network: cables, routers and protocols that have linked computers since the 1970s. The World …
- Two circles that decide whether you wear yourself out.
Stephen Covey separates the circle of concern – everything on your mind – from the smaller circle of influence, where …
- Weather is mood, climate is personality.
Weather is what happens today: rain, 12 degrees, wind from the west. Climate is the statistics of that, usually …
- What is asserted without evidence can be dismissed without evidence.
Hitchens’s razor, named after writer Christopher Hitchens, sums up the burden of proof: whoever makes a claim has to …
- Who "discovered" America – and for whom?
Eurocentrism means treating the West as the yardstick and centre of world history. Hegel read history as a path from …
- Why '8% guaranteed' is always a lie.
Return is the payment for bearing risk. Safe assets like savings accounts pay little because nobody needs to reward you …
- Why a tax refund feels different from salary.
Mental accounting means you sort money into mental buckets even though every euro is worth the same. A €500 refund gets …
- Why country comparisons in absolute numbers almost always mislead.
A country with 1.4 billion people tops nearly every total: cars, emissions, accidents. That says little about any …
- Why doubling is so hard to picture.
In 1965 Gordon Moore noticed that the number of transistors on a chip doubled at a regular pace, roughly every two …
- Why every collapse looks 'inevitable' in hindsight.
Hindsight bias makes you treat an outcome you know as having been predictable. The fall of Rome, the Reformation, the …
- Why every disaster looks predictable in hindsight.
Hindsight bias: once you know the outcome, it seems like the most likely one all along. Baruch Fischhoff showed in 1975 …
- Why nobody knows the weather 30 days out.
In 1961 Edward Lorenz typed 0.506 instead of 0.506127 into his weather simulation. Shortly afterwards the weather …
- Why nobody may make, enforce and judge laws at once.
Montesquieu described three powers in 1748: the legislature (parliament) passes laws, the executive (government …
- Why the past seems to consist entirely of stone palaces.
What you know of an era is what survived: stone churches rather than wooden huts, letters of the literate rather than …
- Why the third slice of pizza is worth less than the first.
Marginal utility is the extra benefit from the next unit of a good, and it almost always falls. The first glass of …
- Why vitamin pills work in observations but not in trials.
People who voluntarily take vitamins usually also exercise more, smoke less and see doctors more often. In …
- Why we do things because we've always done them.
Path dependence means early decisions lock in later ones, even when better alternatives exist. The 1,435-millimetre …
- Why you take €100 today but want €110 in a year.
Question 1: €100 today or €110 in a week? Most take the €100. Question 2: €100 in 52 weeks or €110 in 53? Now almost …
- Without the natural course you can't spot an effect.
The natural history of a disease is the path it takes without treatment – from onset through the symptom-free phase to …
- Your strongest negotiating weapon is plan B.
BATNA stands for “Best Alternative To a Negotiated Agreement” – your best option if the negotiation fails. Fisher and …
- Your vaccination protects people you'll never meet.
A pathogen needs unprotected hosts. Once enough people are immune, it can't find a chain and dies out locally. The …
- “My grandpa smoked and lived to 95” is not an argument.
You only hear from the smokers who grew old – the others no longer tell stories. That's survivorship bias: you see only …
- “Risk cut by 50 %” can mean 1 person in 1,000.
Relative risk compares groups: if a disease drops from 2 to 1 per 1,000, that's “50 % less”. In absolute terms it's 0.1 …