The Explanation Test
Judge a theory by what it explains, never by what it can predict
- Difficulty
- Moderate
- Time to result
- ~weeks to results
- Steps
- 5
- Confidence
- 74%
Deutsch's test separates two things that get conflated: predicting what a system will do, and explaining why it does it. Darwin's theory is not a theory that predicts elephants, it is a theory that explains them, and the explanation does more than any prediction possibly could. Run a supercomputer over the plains of Africa until it prints a picture of an elephant and it has explained nothing about what happened or why. His domino illustration is sharper still: you can trace every domino striking every other and correctly predict that one particular domino never falls, and still understand nothing about prime numbers, which are the actual reason. The corollary is that explanations live at levels. Thermodynamic irreversibility is invisible in a single molecule; acids are real explanatory objects even though chemistry reduces to physics. Importing a verdict from the wrong level is a category error, not rigour.
Origin
Extracted from Naval. Deutsch draws the domino and prime numbers illustration from his own book The Beginning of Infinity and uses Darwin and elephants as his favourite counterexample to the initial-conditions-plus-laws-of-motion picture of science.
Core principles
- 01A prediction that comes with no account of why is not understanding.
- 02Explanations exist at their own level; some are not available lower down.
- 03Reducing a phenomenon to particles can be both computationally impossible and explanatorily empty.
- 04A missing constant or parameter does not make an explanation incomplete.
- 05Judging high-level theories from the level of physics is a category error.
How to run it
- 1
Separate the two questions
Write down separately what your model predicts and what it explains. Many models score highly on the first column and leave the second one empty.
Pro tip A useful prompt: if this model were perfectly accurate forever, what would I now understand that I did not before?
- 2
Run the elephant test
Imagine the model producing exactly the right output. If the output arriving would still leave you unable to say why it arrived, the model is a predictor, not an explanation.
Watch out Accuracy is seductive. A simulation printing a correct picture is the clearest case of prediction without any explanation at all.
- 3
Find the level the explanation lives at
Ask which level of description contains the concepts the explanation needs. The dominoes needed prime numbers; irreversibility needed thermodynamics, not a single molecule.
Pro tip If the explanation requires a concept your chosen level cannot even name, you are at the wrong level.
- 4
Check the reduction is possible and useful
Reduction can fail twice over: the computation may be larger than the universe, and even a successful computation may carry no explanation. Both failures are real and independent.
- 5
Refuse cross-level verdicts
Reject conclusions about high-level matters that are pronounced from a lower level, such as claims about responsibility derived from the behaviour of atoms. Argue those questions in their own domain.
Pro tip Name the category error explicitly; it is usually the fastest way to end an unproductive reductionist argument.
In the wild
In The Beginning of Infinity, Deutsch describes an arrangement of dominoes that computes something about prime numbers, where a particular domino stands up rather than falling. You could follow every single domino striking every other domino and correctly work out that this domino will never fall over, and you would have predicted it. You would still not understand anything about prime numbers, and would not even know that primes were involved. He adds that for some arrangements, nobody will know for the next ten thousand years why that domino stands, yet the explanation is there and it has nothing to do with dominoes.
→ A perfect low-level prediction leaves the explanation completely untouched, which shows the two are different achievements.
Newton's theory of gravity contained an arbitrary constant, now called G, whose value Newton did not know. Cavendish later designed an ingenious apparatus and measured it to an accuracy Deutsch calls amazing for the period. Deutsch argues Newton's discovery was not incomplete for lacking the number: the discovery was the explanation, and that explanation is the same before and after Cavendish. Cavendish's creativity was real but it was creativity about brass balls and wires, not about gravity.
→ Parameters get measured later; the explanation was already whole, which is why a model's fitted constants are not the thing that gives understanding.
Common mistakes
Treating accuracy as understanding
A model that reproduces the data can still be silent on why the data look that way. Accuracy and explanation are independent properties.
Assuming the lowest level is the truest level
Thermodynamics and chemistry carry real explanations that do not exist at the level of individual particles. Reducing further can destroy the explanation rather than deepen it.
Importing verdicts across levels
Deriving conclusions about morality or responsibility from the fact that we are made of atoms is a category error, and it produces policy backed by rubbish arguments.
Is it for you?
Best for
Anyone evaluating models, simulations or reductive arguments and needing to tell genuine understanding apart from accurate output.
Not ideal for
Purely operational settings where an accurate forecast is all that is required and no one needs to know why.
From the transcript
“Darwin's theory of evolution is not the theory that predicts the existence of elephants it's a theory that explains the existence of elephants”
“you will have predicted it but you still won't understand anything about prime numbers”
“it prints out a picture of elephant it hasn't explained anything about what has happened or why”
From the episode
The Deutsch Files II