In chapter 1 of Vision, "The Philosophy and the Approach" [1], David Marr wrote that trying to understand perception by studying only neurons is like trying to understand bird flight by studying only feathers: it can't be done. I read that as saying feathers are a lossy copy of flight, so measuring enough of them would eventually add up to an explanation.
It's the other way round. A complete description of the feathers leaves nothing out. What it lacks is a way to tell which of its facts matter, and the problem supplies one: flight needs lift, and aerodynamics says wing shape matters and feather color doesn't. Only with aerodynamics, Marr writes, do "the structure of feathers and the different shapes of birds' wings make sense."
Marr built this into three levels of explanation for any information-processing system, each answering its own question:
- Computational theory: what problem does the system solve, and why is that the right solution?
- Representation and algorithm: how are inputs and outputs encoded, and what procedure turns one into the other?
- Implementation: what physical device runs the procedure?
"Computational" is a misleading name: it means the problem, not the computing. It's the question the feathers couldn't answer, and it tells the other two what they're for.
His example is a supermarket cash register. You can state its problem without opening it: buying nothing should cost nothing, the order and grouping of your items shouldn't change the total, and a refund should cancel a price. Those requirements are exactly the rules of addition. Decimal and binary arithmetic are then two procedures for it, and a child with a pencil runs the same procedure on different hardware. The middle level has content of its own: the representation decides what is easy. In Arabic numerals it's easy to see whether a number is a power of 10 and hard to see whether it's a power of 2; in binary it's the reverse.
Two neuroscientists, Eric Jonas and Konrad Kording, tested their own field's methods where the right answer is known [2]. They took a chip understood at every level, the MOS 6502 processor that ran Donkey Kong and Space Invaders, and studied it the way neuroscience studies a brain. Removing transistors one at a time found some whose loss broke one game but not the others ("perhaps there is a Donkey Kong transistor"), and the analyses turned up structure in the data without describing how the processor works. Lesions and recordings are implementation-level methods: every transistor was measurable, and no measurement supplied the problem the chip solves.
The paper also spells out what understanding the chip looks like, and it answers Marr's three questions:
- Computational theory: the problem is running whatever program is in memory, and that is the right solution because one chip can then play any game.
- Representation and algorithm: instructions and data are encoded as bytes in memory and registers, and the procedure reads an instruction, decodes it, has the arithmetic unit act on the registers, stores the result and repeats.
- Implementation: the physical device is registers and adders, built from transistors.
Start from the first answer and the lesion result explains itself: a general-purpose processor has no game-specific parts, so a transistor whose loss breaks only Donkey Kong belongs to a circuit that only Donkey Kong's code happened to need.
References
The Philosophy and the Approach [link]
Marr, D., 2010. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. MIT Press.Could a Neuroscientist Understand a Microprocessor? [link]
Jonas, E. and Kording, K. P., 2017. PLOS Computational Biology, Vol 13(1), pp. e1005268. DOI: 10.1371/journal.pcbi.1005268