Wealth as the Set of Possible Transformations
Measure wealth as everything you could bring about, not as a number
- Difficulty
- Moderate
- Time to result
- ~ongoing to results
- Steps
- 5
- Confidence
- 70%
In constructor-theoretic terms, the wealth of a person, a country or the world is the set of all the possible transformations it could bring about, if it wanted to. It will never bring about all of them because there are exponentially too many, and it has to have the right problems before it acts. Given the right problems, it uses knowledge plus the physical assets it holds to cause physical transformations, and if it also has the right solutions, the set grows. Where the process demands creative leaps, knowledge grows too, which grows the set again. The sharp consequence is that wealth cannot be quantified as a number, because a set is not a number. Deutsch's illustration is that you cannot say in absolute terms whether Mozart was richer than Nathan Rothschild: both created knowledge out of nothing, in domains whose transformation sets barely overlap.
Origin
Deutsch derives this from constructor theory, using the same notion of transformation that he uses to define knowledge as information necessary for a physical transformation. Extracted from Naval.
Core principles
- 01Wealth is a set of transformations you could bring about, not a scalar.
- 02Knowledge plus physical assets is what turns a possible transformation into an actual one.
- 03Without the right problems, capability sits idle.
- 04Creative leaps taken while growing wealth grow knowledge, which grows wealth again.
- 05Two sets of capability that barely overlap cannot be ranked against each other.
How to run it
- 1
Enumerate the transformations, not the assets
Write out what you could actually cause to happen in the physical world. That list, not a balance, is the object being measured.
Pro tip Include transformations you could perform but currently have no reason to; the set is about capability, not intention.
- 2
Decompose each into knowledge and assets
For every transformation, note which knowledge it requires and which physical assets it consumes. Both are needed; neither alone is sufficient.
- 3
Find the knowledge-blocked transformations
Isolate the ones you could not perform even with unlimited assets. Those mark the frontier where new knowledge, rather than more capital, expands the set.
Pro tip This is the most actionable output: it tells you when buying more will not help.
- 4
Match the set to your real problems
Capability only converts into transformation when you have the right problem. Name the problems that would call on the transformations you can already perform.
Watch out A large capability set with no live problems produces nothing, which is why counting assets misleads.
- 5
Track growth as set expansion
Record wealth growth as specific new transformations entering the set, and note which of them arrived through a creative leap that also grew knowledge.
Watch out Do not collapse the set back into a single figure for convenience; that reintroduces exactly the error the model is correcting.
In the wild
Deutsch asks whether Mozart was richer, in this fundamental sense, than Nathan Rothschild. Rothschild had knowledge of banking which he created out of nothing; Mozart had knowledge of musical beauty which he created out of nothing. Both were improving on previous ideas, as all knowledge does, and both created something that was not there before. But because their sets of possible transformations barely overlap, Deutsch concludes you cannot say that one of them had more knowledge, or was wealthier, than the other. The comparison is not merely hard, it is undefined.
→ The set-based definition explains why a single wealth number cannot rank fundamentally different kinds of capability.
A hardware startup lists what it can bring about: it can manufacture at volume, ship worldwide and support customers. It also lists what it cannot: a specific sensor calibration that no amount of capital will buy, because nobody has solved it. Applying the model, the founders stop treating a funding round as the lever and route effort into the one transformation blocked by missing knowledge rather than by missing assets.
→ Capital allocation shifts toward the creative leap that would actually enlarge the transformation set.
Common mistakes
Collapsing the set into a number
As soon as wealth is quantified, the information about which transformations are available disappears, and with it the ability to see where knowledge is the binding constraint.
Counting assets without knowledge
Physical assets only cause transformations in combination with the knowledge of how to use them. An asset list overstates capability wherever that knowledge is missing.
Ranking non-overlapping capability sets
Comparing two people or two countries whose transformation sets barely intersect produces a confident answer to a question that has none.
Is it for you?
Best for
Founders, investors and policymakers who want a definition of wealth that explains capability rather than just recording a balance.
Not ideal for
Accounting, tax and reporting contexts that legitimately require one comparable figure.
From the transcript
“the set of all the possible Transformations that it could bring about”
“wealth can't be Quantified as a number wealth is a set a set of Transformations”
“Nathan Rothchild had knowledge of banking which he had created out of nothing and Mozart had knowledge of musical Beauty”
From the episode
The Deutsch Files II