If neurons are treated as computing components, the brain hardly looks like a good machine.
When von Neumann wrote The Computer and the Brain in the 1950s, a neuron took four to five orders of magnitude longer to respond than a vacuum tube or transistor. Neural signals were not especially precise either. By his estimate, numerical representations inside the brain retained only two or three significant digits. Yet this collection of slow and imprecise components could reliably perform complex tasks that contemporary computers could not approach.
The real question is not how the brain compensates for poor component performance. It is whether the brain has been performing a different kind of computation from the start.
Von Neumann did not simply compare the brain to a computer. His comparison led him to a more consequential conclusion: if a system tolerates imprecision in its components, messages, and intermediate results, its organization cannot merely be a cheaper version of a precise computer. The brain is reliable not because it gets every step right, but because an error in one step is unlikely to change the meaning of the whole.
A Single Pulse Is Not a Binary Digit
Neural pulses invite an intuitive analogy: a neuron either fires or does not, so is that not simply 0 and 1? If the basic signal is all-or-none, the brain seems naturally to be a digital computer.
Von Neumann began there as well. He treated the presence or absence of a pulse as two states and acknowledged that the nervous system initially displays digital characteristics. But he quickly added a qualification: this digital character exists only at the surface.
The reason is that producing a pulse is not merely the operation of a simple logic gate. A neuron receives many inputs, and whether it responds may depend on their number, location, timing, and the neuron’s prior fatigue. Multiple pulses that arrive within a summation interval may act together; an earlier pulse does not necessarily lose its influence immediately when the interval is longer. An approximately discrete output does not imply that the process producing it is clean Boolean logic.
More importantly, an individual pulse is often not the whole message. Von Neumann used sensory nerves transmitting stimulus intensity to illustrate this point: a stimulus can be converted into the frequency of a pulse train. Each pulse still has only two possibilities, present or absent, but a continuous quantity is encoded in a statistical property over time. He also suggested that correlations among different pulse sequences, not just their frequencies, might carry information.
This is fundamentally different from a binary digit in a digital computer. Flipping a bit at an exact position can change the meaning of an entire number or instruction. In a statistical message, an occasional missing or extra pulse usually shifts the frequency only slightly. The carriers may be discrete without the meaning being determined symbol by symbol.
The brain therefore does not laboriously assemble reliable bits out of unreliable pulses. A more plausible direction is that it uses a representation in which no single pulse must be perfectly reliable.
The Problem of Precision Is Really a Problem of Depth
Why do artificial computers depend so heavily on precision? The intuitive answer is that their tasks require exact results, but von Neumann pointed out that the precision required of an external result is not the same as the precision required during internal computation.
The inputs to many physical problems already contain measurement error, and their outputs need only limited precision. A computer nevertheless has to retain many digits internally because a long serial computation continually accumulates rounding error, while later operations can magnify errors introduced early on. The task itself may not require ten decimal places; the long chain of computation does.
This reframes the question of how the brain operates at low precision. If the brain truly tolerates only low precision, it cannot routinely rely on very deep serial computations. Otherwise, errors would propagate along dependency chains and quickly overwhelm the result.
Von Neumann called the number of sequential arithmetic operations arithmetic depth and treated it as part of logical depth. His eventual inference was not that the brain secretly possesses more precise components, but that its logical structures must be shallower than the mathematical derivations and machine programs familiar to us.
Here, “shallow” does not mean simple or incapable. It means that a complex result cannot be obtained primarily through a long chain of dependencies. The complexity has to live somewhere else.
Slow Components Force the Structure Toward Parallelism
Von Neumann compared the neurons and electronic components of his time: artificial components were few and fast, whereas biological components were numerous and slow, with enormous advantages in volume and energy consumption. Those specific orders of magnitude belong to the 1950s and should not be used directly to judge modern chips. The method of deriving structure from constraints, however, has not become obsolete.
When components are slow but can be deployed in vast numbers, a suitable organization naturally tends to acquire and process as much information as possible at once. When components are expensive but fast, it is more economical to reuse a small number of them in sequence. Natural systems therefore lean toward parallelism, while artificial computers lean toward serial operation.
Parallelism, however, does not mean distributing a sequence of steps evenly across many neurons. If a later step depends on the result of an earlier one, it still cannot happen in advance. Von Neumann specifically warned that converting a serial process into a parallel one often requires changing its “logical method and organization” as well. Merely adding execution units does not shorten the dependency chain that determines how errors accumulate.
This takes the claim that the brain “depends entirely on parallelism” one step further. Parallelism is not just a way to accelerate slow neural components; it is a prerequisite for low-precision computation to work. It simultaneously employs large numbers of components and forces problems into shallower, more distributed representations.
Reliability Does Not Mean No Errors; It Means Errors Do Not Matter
In the earlier essay The General and Logical Theory of Automata, von Neumann had already noticed that natural systems and artificial machines take different attitudes toward errors.
Traditional computers try to expose an error immediately because a local failure can invalidate everything that follows. Natural systems appear instead to weaken the consequences of local errors through their organization, allowing the system to continue before gradually isolating or repairing a failure. The former requires components to be as correct as possible; the latter first requires that an error not easily spread into a catastrophe.
He used majority voting among three identical computing units to show how redundancy can improve reliability. An individual unit may fail, but the majority remains correct unless two units make an error at the same step. This example describes a fault-tolerance scheme for artificial automata, not the literal structure of the nervous system. It demonstrates a more general principle: reliability can be a statistical result produced by many unreliable events rather than a premise requiring every event to be reliable.
This connects directly to representing information through pulse frequency. A missing pulse is diluted into a small change in a statistic; parallelism and redundancy across many components keep local failures from occupying a decisive position. The system gives up arithmetic precision in exchange for logical reliability.
This difference can be compressed into two minimal models that change only the organization. Adjust the same local error rate: the serial model requires all three steps to succeed, while the redundant model lets three units work separately and takes the majority. To isolate the effect of organization, the model assumes that failures are independent. These are not structural diagrams of a computer and a brain. They isolate the difference between errors propagating through a dependency chain and being diluted by a group.
Every step must succeed for the final result to remain correct.
The result remains correct when any one unit fails.
“Reliable” still does not mean infallible. Redundancy can reduce the probability of error, not eliminate it. The genuine change is that the system no longer stakes correctness on any single component, pulse, or long computational chain.
Do Not Complete von Neumann’s Answer for Him
Looking back from the present, it is tempting to summarize the brain as “in-memory computing” and then read that answer back into von Neumann’s text. Yet he was exceptionally cautious when discussing memory. He listed persistent activity in neural circuits, connection states, chemical changes, and genetic mechanisms as possibilities, then explicitly admitted that we do not know the basic physical entities responsible for memory in the nervous system. He even emphasized that the elements underlying memory need not be the same as those performing basic operations.
Likewise, saying that “the language of the brain is not the language of mathematics” does not mean the brain cannot be described mathematically. His point was closer to this: the mathematics we consciously use may be only a concise code built on top of the nervous system’s native representation. The language actually used inside the brain has lower logical depth, lower arithmetic precision, and a more statistical character, so it need not be isomorphic to formulas on paper or computer instructions.
He even expected the mathematical study of the nervous system eventually to change how we understand mathematics and logic themselves. This was not a rejection of mathematical modeling, but a doubt that our existing mathematical expressions were sufficient.
From “Better Components” to “Making Errors Irrelevant”
Treating the brain as a slow, low-precision computer leaves only a puzzle: how can such poor hardware be so capable? Von Neumann’s genuinely new perspective was to reject the assumption that the two systems must be carrying out the same kind of computation.
Digital computers exchange precise symbols and relatively deep serial sequences for reproducible results. The nervous system he envisioned instead uses statistical messages, shallow logic, parallelism, and redundancy so that local imprecision is no longer fatal. The brain’s advantage is therefore not that it beats a machine at every step, but that it redesigns the question of which steps must be absolutely correct.
This intuition extends beyond the brain. When a system becomes so complex that local errors cannot be eliminated, increasing the precision of every component is often prohibitively expensive. Another path is to change how information is represented, shorten the dependency chains that amplify error, and use parallelism and redundancy to keep errors local. The most reliable system need not possess the most reliable individual parts. It may simply be the system least likely to make any one part irreplaceable.
Further reading: John von Neumann, The Computer and the Brain, Yale University Press, 1958; John von Neumann, The General and Logical Theory of Automata, 1951. The former is an unfinished manuscript for the Silliman Lectures, published after the author’s death. The historical measurements and neurophysiological claims discussed here are presented in their original context and should not be treated as conclusions of contemporary neuroscience.