Natural Sciences

Methods & Tools

Sean Coleman

2026-04-30

“That’s funny…” vs. “Eureka!”

“The most exciting phrase to hear in science, the one that heralds new discoveries, is not ‘Eureka!’ but ‘That’s funny…’“ — attributed to Isaac Asimov

“That’s funny…” = the sound of something not fitting.

A contradiction. An anomaly. Something catching in your brain.

When the science is done, the reaction shifts to:

“Ah — now I understand.”

That move — from puzzle to understanding — is the basic structure of scientific explanation.

Don’t explain it — just read it and let it land. Then ask: “Can you think of a moment in science class where something just didn’t fit?” That’s where science begins. Today we’re examining how science produces knowledge: through explanation, experiment, theory, and — sometimes — revolution.

Today’s Questions

1. What does it mean to explain something in science?
2. Is there a single scientific method — and does science work the way the textbook says?
3. What are theories and laws, and do they describe reality?
4. How does science change — and can it make real progress?

Four questions, four blocks. Keep the roadmap visible — this is a lot of ground for 45 minutes. Pace tightly.

What Is a Scientific Explanation?

From Puzzle to Understanding

A scientific explanation resolves cognitive dissonance — a mismatch between expectation and observation.

Lightning — the phenomenon: A bright flash connecting clouds and the ground.

That’s funny… why does that happen?

Lightning — the explanation: - Constitutive: a rapid electrical discharge between cloud and earth - Causal: air particles rubbing together → charge builds up → air fails to resist → discharge

Ah, now I understand.

One explanation now covers trillions of events: sparks from hair brushing, arc welding, train junctions, and lightning. The world becomes a much simpler place.

Make the lightning example concrete. Maybe ask: “What’s the phenomenon? What’s the explanation?” Check they can distinguish them. The power of explanation is that one concept (discharge) unifies countless individual events.

Two Types of Explanation

Constitutive

What is the phenomenon made of?

→ Lightning is an electrical discharge

→ What kind of thing is it?

Causal

What caused the phenomenon?

→ Charge built up because air particles rubbed together

→ How did it happen?

Good scientific explanations are often both — they tell us what something is and what caused it.

These two types often work together. Make sure students can apply both to the lightning example before moving on.

Reductive vs. Holistic Explanation

Reductive (physics, chemistry)

Explain the whole by its component parts

→ The clockwork worldview

→ “Lightning is electrons moving”

→ Goes down to smaller things

Holistic (ecology, climate, biology)

Explain the system by the interactions of its parts

→ Interactions change the environment, which changes the interactions — a dynamical system

→ Goes up to the whole

James Lovelock: applying reductive explanations where they don’t apply has contributed to the climate crisis.

Key insight: the appropriate type of explanation depends on the subject matter. Ecology cannot be explained reductively in the same way a chemical reaction can. This is a genuinely important methodological point — not just a philosophical curiosity.

What Makes a Better Explanation?

• Simpler — uses fewer theoretical pieces (Occam’s Razor)
• More intelligible — easier to grasp
• More powerful — covers more phenomena
• Better supported — produced by a theory with stronger evidence

Occam’s Razor: If two explanations explain the same thing equally well, prefer the simpler one.

Ad hoc: an explanation invented for just one phenomenon — the worst kind.

E.g., “God Thor struck his hammer” explains only lightning — nothing else.

Occam’s Razor is a useful heuristic — but it’s not a law. Sometimes the more complex theory turns out to be right. Newton vs Einstein on gravity: Newton’s simpler maths works fine for everyday motion; Einstein’s more complex theory is needed for black holes and GPS satellites.

Do Explanations Need to Be True?

No. And this is a genuinely surprising result.

Physics textbooks calculate the falling apple by assuming:

• The apple is a point particle — false
• There is no air resistance — false

The explanation is a useful fiction.

Like a map: technically false (it omits everything), yet a good map gets the important features right. That is what we mean by truth in this context.

This often surprises students. The key move: a model doesn’t need to be literally true to be a good explanation. It needs to get the relevant features right — like a map that doesn’t include every blade of grass but does include the tube stations you need.

Real Fictions: Contradictory Explanations

Some scientific explanations are not just false — they are logically contradictory.

The double slit experiment:

• Photons are modelled as particles passing through two slits
• The screen is modelled as a solid harbour wall — not particles
• But the screen is made of particles

The model is internally inconsistent — yet it perfectly explains the interference pattern and makes accurate predictions.

Hans Vaihinger called these “real fictions” — self-contradictory models that still function as good explanations.

This is the deepest point in Block 1. Students often expect science to be clean and logical — this shows it isn’t. The takeaway: a model can be false, even contradictory, and still be knowledge. What matters is that it gets the important features right.

Discussion Question 1 (pairs · 90 sec)

“If a scientific model can be false — even self-contradictory — and still count as knowledge, what does this tell us about what knowledge is?”

Quick check — don’t let it run long. Listen for: the “map metaphor,” the idea that knowledge is about capturing the relevant features, not literal correspondence. This connects to the Core Theme’s notebook metaphor and the notion that knowledge doesn’t require certainty.

Experiment and Observation

Is There a Single Scientific Method?

The standard textbook diagram:

Observation → Hypothesis → Experiment → Analysis → Conclusion → ↩︎

But ask:

• How do you know what to observe?
• Where does the hypothesis come from?
• What do you do in cosmology, ecology, or palaeontology — where experiments are impossible?
• Where are the actual scientists, funding bodies, and politics?

The methods of science are best described as pluralistic — many, diverse, and possibly contradictory.

The point isn’t to dismiss the diagram — it captures something true. The point is that it oversimplifies. Different sciences really do use very different methods. Particle physics is almost entirely experimental and computer-controlled; ecology is mostly field observation; cosmology is mostly theoretical and observational.

Science Is More Like a Pinball Machine

The California Academy of Sciences describes science as a pinball machine, not a straight line.

• The conclusion of one study raises new questions
• The process circles back — it is never finished
• All scientific knowledge is provisional — science is unfinished business

What diverse methods share: data collection, analysis, and interpretation through theory.

The pinball image is memorable. Science bounces around — serendipity, dead ends, surprising results, collaboration — before something gets confirmed. Emphasise that “provisional” is a strength, not a weakness. It means science can correct itself.

Serendipity in Science

Science doesn’t always start with a deliberate hypothesis.

Percy Spencer (1945, Raytheon): Testing radar equipment → noticed the chocolate in his pocket had melted → investigated → helped invent the microwave oven.

Penzias & Wilson (1964, Bell Labs): Testing a horn antenna for radio communications → kept picking up an unexplained background hiss from every direction in space → turned out to be the cosmic microwave background radiation — the echo of the Big Bang.

Serendipity: the fact of finding an interesting or valuable phenomenon by chance.

Both examples are great: one mundane (melting chocolate), one cosmic (echo of the Big Bang). Both discovered accidentally while doing something else entirely. Ask: “Does serendipity suggest science is random? Or does it suggest scientists are alert to ‘that’s funny’ moments?”

Correlation ≠ Causation

A scientist drinks on five nights:

Night	Drink	Result
Monday	Whisky + tonic	Drunk
Tuesday	Gin + tonic	Drunk
Wednesday	Rum + tonic	Drunk
Thursday	Vodka + tonic	Drunk
Friday	Southern Comfort + tonic	Drunk

Conclusion: “Tonic makes you drunk.”

This is the correlation-causation fallacy — one of the most common errors in interpreting scientific results.

Students always laugh at this — good. Then push: “Can you think of a real-world example where this fallacy has been made?” E.g., ice cream sales correlate with drowning rates (both caused by hot weather). Or: studies that show correlation between X and Y and are reported as “X causes Y” in the news.

How to Sort Correlation from Causation

Correlations are symmetrical: if A correlates with B, then B correlates with A.

Causation is asymmetrical: if A causes B, it is not usually true that B causes A.

Lightning and thunder: Lightning always precedes thunder. But lightning doesn’t cause thunder.

Both are caused by a third variable: the electrical discharge.

What we need: a piece of theory — from other experiments — that tells us the causal mechanism.

Observation finds the correlation. Theory finds the cause.

The lightning/thunder example is elegant: lightning doesn’t cause thunder any more than thunder causes lightning — they are co-effects of the same cause. The general principle: you need theory to interpret data. Data alone doesn’t tell you what’s causing what.

Replicability

A result obtained at one location, at one time, by one team might be a fluke.

Replication: repeating an experiment in a slightly different context to check the result is real, not an artefact of the experimental setup.

If results cannot be replicated by any team → flagged as doubtful → rejected as knowledge.

If results are replicated using different methods → strong evidence the result is a real feature of the world.

Replication is a first step toward objective knowledge — knowledge independent of the observer.

The IT department analogy in the reading is useful: if a software error can be reproduced on another computer, it’s a system problem, not a local one. If it can’t be reproduced, the problem is local. Replicability works the same way.

Case Study: Michelson-Morley (1887)

Scientists believed light (a wave) needed a medium — the ether.

Prediction: the speed of light should be different in the direction of Earth’s travel versus at right angles.

Result: no difference. The ether appeared not to exist.

Replicated over decades — with mirrors, masers, lasers — by multiple independent teams.

1973: speed of light constant to within 2.5 cm/sec — one part in 12 billion.

The null result paved the way for Einstein’s special theory of relativity.

A landmark experiment — simple in concept, revolutionary in consequence. The result was so unexpected (and so inconvenient) that it needed massive replication before the scientific community accepted it. This is science working correctly: a result you don’t want to be true, confirmed again and again until you can’t ignore it.

Science Is Collaborative

Three forms of collaboration in modern science:

1. Scientists working side by side in the same lab
2. Scientists separated by space, collaborating across borders
3. Scientists separated by time — building on previous results

2020 Nobel Prize in Chemistry: Charpentier & Doudna

• Microbiologist + structural biologist
• Discovered that a bacterial virus-defence mechanism could be repurposed as programmable genetic scissors
• Result: CRISPR-Cas9 — now used in cancer treatment and potential cures for hereditary disease

“Crossing borders between countries and disciplines is instrumental to opening doors.” — Charpentier

CRISPR is a perfect example: it required expertise from two different fields (microbiology and structural biology). Neither could have done it alone. The collaborative, cumulative nature of science is part of what makes it reliable — it’s not just one person’s judgment.

Discussion Question 2 (whole class · 2 min)

“If there is no single scientific method, is there anything that makes scientific knowledge distinctive?

Or is the difference between science and other AoKs less clear-cut than we thought?”

This question connects back to the Scope readings (01–03). Students should be reaching for: replicability, peer review, the requirement for natural explanations, tentative and self-correcting. But they should also feel the pressure: those features exist in other AoKs too, just to different degrees.

Theories, Laws, Models, and Assumptions

‘Theory’ — A Critical Clarification

Two uses of the word ‘theory’:

Everyday: “Oh, it’s only a theory” = speculation, not yet knowledge

Scientific/ToK: A systematic body of knowledge — concepts + laws + methods + standard examples

The theory of evolution has as much evidential support as the theory that water is H₂O.

It is not a speculation awaiting confirmation.

The confusion has been exploited — especially in arguments against evolution on religious grounds.

Spend 30 seconds here — this is a frequent misconception. In ToK we always use the technical meaning. The word “theory” in everyday speech is almost the opposite of its scientific meaning.

What Is a Theory?

A theory is bigger and more structured than a fact.

Newton’s three laws of motion:

1. A body moves in a straight line at constant velocity unless a force acts on it.
2. Force = mass × acceleration.
3. Bodies in interaction apply equal and opposite forces on each other.

Three laws → explain virtually all motion on Earth → predict positions of planets, comets, stars, and galaxies.

Yet Newton’s theory is false for objects near the speed of light, or near black holes.

“Literally false, but it does a wonderful job.” — we leave Einstein to handle the extreme cases.

The beauty of Newton’s laws is their scope. Three simple statements cover an enormous range of phenomena. Then the kicker: the theory is false in certain regimes. Even our best theories are approximate maps of reality, not reality itself.

Scientific Laws: Real or Invented?

Realist view

Laws are built into the fabric of the universe.

A universe with different laws would look completely different.

Astronomer Martin Rees: six numbers are built into the universe — change any one slightly and we would not exist.

Anti-realist view

Laws are idealisations we invent to make sense of data.

The second law of thermodynamics applies to closed systems — but there are no truly closed systems in the universe.

Boyle’s law applies to ideal gases at constant temperature — no real gas qualifies.

Laws apply only in idealised situations that do not exist.

The anti-realist point is subtle but powerful: if laws only apply to idealised situations that don’t actually exist anywhere, in what sense are they “real”? You can’t see the law of gravity — you only see its effects. Does that make it real or just a useful tool for prediction?

Models as Metaphors

A model takes a familiar situation and uses its structure to illuminate an unfamiliar one.

Just like literary metaphor:

“Shall I compare thee to a summer’s day?” — Shakespeare, Sonnet 18. The structure of the seasons illuminates thoughts about human mortality.

The Bohr atom: The atom as a miniature solar system

• Nucleus = Sun; Electrons = planets
• False — atoms are not solar systems — but useful for predicting chemical properties

The key: know the limits of the model. A metaphor only works in certain respects.

The metaphor connection is something students can relate to from Group 1. The point: models in science do the same thing metaphors do in poetry — they use a known structure to make sense of an unknown one. Both are useful; both are ultimately false in a literal sense; both can mislead if taken too literally.

The Assumptions Behind Science

To do natural science at all, we must assume:

1. The world is rationally comprehensible by human beings. (Einstein: “The most incomprehensible thing about the universe is that it is comprehensible.”)
2. The laws of physics are the same everywhere — Earth is not a special case.
3. The laws don’t change radically over time — tomorrow follows from today.
4. Everything can be explained by natural processes — no supernatural causes needed.
5. Science is self-correcting — errors eventually disappear.

These are not scientific results. They are presuppositions that make science possible.

This is a deeply philosophical point: science rests on assumptions it cannot itself prove. Ask: “Is assumption 5 (self-correction) obviously true? What if powerful institutions or funding bodies prevented the correction of errors?” This connects to Knowledge and Responsibility.

Theory Choice and Paradigm Shifts

How Do We Choose Between Theories?

When two theories compete to explain the same phenomenon, compare them on five criteria:

Criterion	What it means
Predictive power	Accurately describes and predicts — especially novel phenomena
Explanatory power	Explains a broad range of phenomena
Consistency	No internal contradictions; coheres with other accepted theories
Simplicity	Fewest theoretical concepts (Occam’s Razor)
Fruitfulness	Generates further insights beyond its original scope

The most persuasive evidence: novel predictions — predicting phenomena no one has seen yet.

Run through these quickly — students can refer to the reading. Spend a little more time on novel predictions: Einstein’s prediction that gravity would bend light was a completely new and unexpected consequence of General Relativity. It could have been wrong. When it turned out to be right (1919 eclipse), it was extraordinarily powerful evidence for the theory.

Case Study: Big Bang vs. Steady State

From the late 1940s to the mid-1960s, two theories competed to explain the expanding universe:

Steady State (Bondi, Gold, Hoyle)

As the universe expands, new matter fills the gaps.

The universe looks the same at all times and distances.

Prediction: powerful radio galaxies at all distances.

Big Bang (Lemaître, 1927)

Universe began in a single explosion.

The universe looks different at different stages of its history.

Predictions: distant objects differ from nearby ones; a detectable thermal echo — cosmic microwave background radiation (CMB).

1964: Penzias & Wilson detect the CMB while testing a horn antenna — serendipity. Radio galaxies only visible at great distances. Steady State falsified. Big Bang wins.

The irony: the name “Big Bang” was coined by Hoyle (a Steady State advocate) as a dismissive term. It stuck. The decisive evidence — the CMB — was found by accident.

Why Theories Don’t Change Overnight

Changing a theory has enormous costs:

• The new theory must explain everything the old one did, and more
• Experimental methods, apparatus, and textbooks must change
• Scientists have reputational and financial stakes in their theories

Result: a successful theory can survive anomalous observations for a long time.

“The theory is pretty good — there are just a few exceptions in extreme situations.”

Anomalies accumulate. Eventually, influential scientists abandon the old paradigm. Competing theories emerge. One wins.

This is Kuhn’s great sociological insight: science is not purely a rational process. It’s a human, social activity. People don’t abandon theories just because there’s contradicting evidence — they resist, they explain away anomalies, until the evidence becomes impossible to ignore.

Paradigm Shifts (Thomas Kuhn)

A paradigm shift is a revolution not just in theory, but in:

• Methods of investigation
• Standard examples (template problems)
• Experimental instrumentation
• The kinds of questions that can be asked
• Fundamental perspectives (scope)

Kuhn compared it to a political revolution:

Old order → build-up of grievances → overthrow → chaotic competing factions → new order

“Normal science” → anomalies pile up → “revolutionary science” → new paradigm → new normal science

The political revolution analogy is vivid. Before: established order, everyone knows the rules. During: chaos, competing factions. After: new order settles in. Science works the same way. Ask: “Can you think of a paradigm shift from your science classes?”

Two Case Studies

Copernican Revolution

Geocentric → Heliocentric

Changed: theories, methods, instruments, the kinds of questions astronomy could ask.

Took: Copernicus → Kepler → Galileo → Newton.

Postscript: the Sun isn’t the centre of the universe either.

Miasma → Germ Theory

“Bad air” → microorganisms

John Snow (1854): cholera spread through water, not air.

Pasteur, Koch: identified specific microbes causing anthrax, tuberculosis, cholera.

Better explanations → better prevention.

These are classic paradigm shift examples. The Copernican one is in the reading; the miasma one is more recent and relatable (students know about disease). Ask: “What would it take for scientists to shift away from germ theory today?” (This is also relevant during a post-COVID world.)

Kuhn’s Radical Claim: Incommensurability

Kuhn argues we cannot use the five criteria to compare paradigms.

A paradigm includes the notion of what counts as a good theory or a good method.

→ There is no neutral standpoint from which to make the comparison.

Incommensurability: different paradigms cannot be directly compared — there is no common standard.

Implication: scientific change is not progress — just change.

Peter Galison (1997) disagrees: theory can change without method changing, allowing meaningful comparison.

Incommensurability is Kuhn’s most radical and controversial claim. Students find it unsettling — which is the right reaction. If we can’t compare paradigms, how do we know science is getting better? Is the switch from geocentric to heliocentric astronomy actually progress? Galison’s response: not everything changes at once, which gives us footholds for comparison.

Discussion Questions

At this point in the lesson you know which threads your students have been most engaged by. Pick accordingly. Question A connects to Block 1, B to Block 2, C to Blocks 3–4.

Question A — Explanation and Truth

“We have seen that scientific models can be false, even self-contradictory, and still count as good explanations.

Does this mean that the goal of science is not truth but usefulness? Or are these the same thing?”

Follow-up: If all models are fictions, what makes a bad model? Is there any limit?

Students who go for “usefulness” should be pressed: a horoscope can be “useful” in the sense of making people feel better. What makes a scientific model specifically useful? The answer: it gets the causally relevant features right. It can be tested. It makes predictions that pan out.

Question B — Method and Objectivity

“If there is no single scientific method, and science is driven by funding bodies, politics, serendipity, and personal reputation…

…can scientific knowledge really be objective? Or is it just the dominant paradigm of its time?”

Follow-up: Is the fact that science is self-correcting enough to rescue objectivity? Can science police itself?

This is the Kuhn question, but also connects back to scope (01). The strong programme in sociology of knowledge says no — science is just a powerful social institution like any other. Most scientists and philosophers reject this but can’t fully dismiss it. Peer review, replication, the requirement for natural explanations — these are the defences of objectivity.

Question C — Paradigm Shifts and Progress

“Kuhn says paradigm shifts cannot be compared — they are just different, not better.

If Kuhn is right, in what sense — if any — is science making progress?”

Follow-up: Are we more confident in germ theory than miasma theory? In heliocentrism than geocentrism? If yes, why — and does that confidence count as progress?

The most philosophically rich question. Students who feel the pull of Kuhn’s incommensurability should be pressed: do you actually think we know no more about disease than people in 1400? If not, what does that additional knowledge consist in? Is it just more of the same paradigm, or genuine improvement?

Exit

Three Things to Leave With

1. Explanation: A good scientific explanation moves us from puzzle to understanding. It need not be literally true — models are useful fictions. What matters is getting the relevant features right.

2. Method: There is no single scientific method. What methods share is data, analysis, and theory. Replicability and peer review are the engines of objectivity — but science is also social, provisional, and driven by human beings.

3. Theory and change: Theories are systematic bodies of knowledge — not speculations. Laws may or may not be ‘built into’ the universe. When theories change, the change can be minor (theory swap) or revolutionary (paradigm shift). Whether revolutions count as progress is genuinely open.

One sentence each. Then straight to the exit ticket.

Exit Ticket

Write 2–3 sentences — choose one:

Option 1: “Give an example of a scientific model you have used in class. In what sense is it a fiction? In what sense does it still count as knowledge?”

Option 2: “A new study claims: ‘Students who eat breakfast get better grades.’ Is this a correlation or a causation claim? What would you need to know to be more confident?”

Option 3: “Was the shift from miasma theory to germ theory a paradigm shift in Kuhn’s sense? Justify your answer using at least two criteria.”

2 full minutes. Options 1 and 3 are the hardest — push stronger students toward them. Option 2 is more accessible and directly tests one of the session’s key concepts.

Reference

Key Terms — Explanation

Term	Definition
	What a phenomenon is made of
	What caused the phenomenon
	Explains the whole by behaviour of its parts
	Explains a system where parts depend on the whole
	Prefer the simpler of two equally good explanations
	Invented for just one phenomenon — the worst kind
	A self-contradictory model that still functions as a good explanation

Key Terms — Method and Theory

Term	Definition
	Finding a valuable phenomenon by chance
	Assuming that because A and B are correlated, A causes B
	Repeating an experiment in a different context to check the result
	Formal evaluation of research by other specialists
	A systematic body of knowledge: concepts + laws + methods + examples
	A general, experimentally confirmed description of a feature of reality
	An idealised, usually false representation that illuminates real phenomena
	Radical change in theory, method, scope, instrumentation, and perspective
	Kuhn’s claim that different paradigms cannot be directly compared
	Scientific activity governed by a dominant accepted paradigm

TOK Connections

• Knowledge and the Knower — Does serendipity suggest scientific discovery is partly personal?
• Methods and Tools — How do methods shape what kinds of knowledge are possible?
• Core Theme: Knowledge and Language — How does the word ‘theory’ shape public understanding of science?
• Core Theme: Knowledge and Responsibility — Who decides which paradigm gets funding? Who pays for ‘normal science’?
• Human Sciences AoK — Do the social sciences face the same replication problems as natural sciences?
• Ethics — Joseph Rotblat resigned from the Manhattan Project. When is a scientist responsible for the application of their knowledge?
• History AoK — How do historians of science decide which paradigm shifts were genuine progress?