Why can't we mimic even a fraction of our brain, yet

Four separate walls stand between a working simulation of one nerve cell and anything resembling a brain. Only one of them is about hardware — and it is the least interesting of the four.

Subject

Biological neurons vs. artificial ones; the limits of simulation

Compiled

13 August 2026

Status

Working draft — synthesis, not primary research

Numbers

Order-of-magnitude unless a source is named

It is a different object that shares one idea: weighted sum, then threshold. Everything else diverges, and the divergence is not a matter of detail still to be filled in. Deep learning stopped consulting biology somewhere in the 1980s. The word neural is vestigial — a courtesy to McCulloch and Pitts, who in 1943 tried to guess how the brain worked using what was known in 1943.

The artificial neuron holds a startlingly small amount of state: one weight per input, plus a bias. That is the whole object. No stored value, no clock, no history. In practice it is not even an object — it is one row of a matrix, and the activation function is code applied afterward, not a property the unit owns.

Where they part company

The right analogy is aviation and ornithology. Both a wing and a bird use lift — that shared physics is real, not metaphor. But aircraft do not flap, and nobody designs an airliner by studying pigeons. Deep learning grew out of neuroscience and left.

This is not speculative. Hodgkin and Huxley recorded the squid giant axon and in 1952 described the action potential with four differential equations: membrane voltage plus three gating variables tracking how open the sodium and potassium channels are. It reproduces the shape of a real spike quantitatively. It won the Nobel Prize in 1963 and it still runs.

A detailed single-cell model is a few thousand coupled ODEs. That runs on a laptop in minutes. Compute is not the constraint here, not remotely.

The ladder of detail

On that last rung: a cortical neuron contains on the order of 10¹⁴–10¹⁵ molecules. State-of-the-art molecular dynamics handles 10⁶–10⁹ atoms for nanoseconds. That is six to eight orders of magnitude short in size and another six in time. This is not a Moore's-law problem; it is a different category of problem.

Hole one: we fit what we cannot measure

Split "do we have the data" into four questions and the picture becomes uneven fast.

So the honest statement is narrow: we simulate a neuron in isolation, responding to injected current, very well. We cannot simulate a neuron in context — because a neuron in context is defined by its inputs, and we do not have them.

Hole two: matching the data does not mean the model is right

On human cells specifically

Almost all detailed physiology is rodent. Human cortical neurons are not scaled-up mice: dendritic trees are substantially longer and the cable properties differ, with dendrites more electrically isolated from one another (Beaulieu-Laroche et al., 2018).

And one result closes a loop worth noticing. Gidon and colleagues (Science, 2020) recorded dendrites of human layer 2/3 pyramidal neurons and found calcium spikes with an unusual tuning: the response grows with input strength and then falls. That curve implements XOR.

XOR is precisely the function Minsky used in 1969 to discredit the perceptron — the one requiring a hidden layer. A single dendritic branch of a human neuron does it alone.

Four independent walls, in increasing order of how permanent they are.

Wall 1 — arithmetic (the soft one)

Blue Brain simulated a microcircuit of rat somatosensory cortex in 2015: 31,000 detailed neurons, requiring a supercomputer, and running slower than real time. Call it roughly 0.3 CPU cores per biophysical neuron merely to keep pace with biology.

And that is inference only — running it once, at human speed, already trained. Training a language model means thousands of passes over terabytes. Multiply by another 10⁴–10⁵.

Wall 2 — there is no training signal (the hard one)

This matters more than compute, because hardware gets cheaper and mathematics does not.

A language model can speak because it was trained by gradient descent on enormous corpora. The only known way to assign credit across billions of parameters is to take a derivative. A spike has no useful derivative — it is a step function, zero slope everywhere, undefined at threshold. Gradients do not flow through it.

The workarounds are real, and all of them are compromises:

• Surrogate gradients (Neftci, Mostafa & Zenke, 2019) — lie during the backward pass, substituting a smooth function for the step. This works, and is the dominant method today.
• ANN-to-SNN conversion — train a conventional network, then map activations to firing rates. Works, but defeats the purpose: you now run a conventional network inefficiently.
• e-prop (Bellec et al., 2020) — a local, online approximation to backpropagation through time. More biologically plausible, less accurate.

Critically, all of these operate on point neurons. Nobody trains networks of multi-compartment Hodgkin–Huxley cells by gradient descent. The one genuine exception, Jaxley (2024), is differentiable multi-compartment simulation built on JAX — and it exists to fit single cells to experimental data, not to train networks.

Wall 3 — time runs the wrong way

A transformer consumes a token in one forward pass. A spiking network must simulate tens to hundreds of milliseconds of biological time to settle on anything — hundreds of timesteps per token.

So on a GPU, spikes do not save energy; they add a hundredfold overhead. The efficiency argument only pays off on event-driven hardware where a silent neuron costs nothing. On a dense matrix multiplier you pay full price for every zero.

Wall 4 — biophysics is a bad parameterisation (the permanent one)

Return to the Beniaguev result: one cortical neuron ≈ an 5–8 layer network. Now invert it.

This is also the accumulated lesson of forty years of neural networks: the unit barely matters. Sigmoid, tanh, ReLU, GELU — differences of a few percent. Architecture, objective and data scale are what move results. Making the unit a thousand times more biologically faithful would not improve a language model; it would multiply the electricity bill.

The brain runs on about 20 watts — roughly a third of a single old 60 W incandescent bulb, burning continuously. Our simulations of it consume gigawatts. The natural question is why silicon is so hopeless.

The question contains a category error, and unpacking it is the most useful thing in this document.

The hurricane

A hurricane moves billions of tonnes of air and water. How many operations does it perform? None. It simply is — physics does the work at no computational cost.

Forecasting that same hurricane 24 hours ahead takes a supercomputer, megawatts and hours of compute. Nobody asks why weather models are so inefficient compared to the atmosphere, because the mismatch is obvious: the atmosphere does not solve Navier–Stokes. Navier–Stokes is our description of the atmosphere.

The brain is the same, only less obviously so. The brain does not compute the Hodgkin–Huxley equations. Ion channels simply open. Those equations are our attempt to describe them, and every simulation pays a translation tax the brain never sees.

The uncomfortable part: biology is not near any physical limit

Landauer's principle sets a floor: erasing one bit costs at least kT·ln2 ≈ 3 × 10⁻²¹ J at room temperature. Measured against it, the brain does badly.

Read that carefully. A transistor is closer to the thermodynamic floor than a synapse is — by roughly a thousandfold. A single spike burns on the order of a billion ATP molecules. And the neuron is slow: hertz, against a transistor's gigahertz.

Silicon beats biology on both the energy and the speed of the elementary event. So the brain's eight-order advantage comes from somewhere else entirely: architecture. Which is the same thing as saying it comes from a list of specific taxes our simulators pay and brains do not.

Tax 1 — we compute everything, always, whether or not anything happens

This is the single largest item. A cortical neuron fires at roughly 1 Hz and a spike lasts about 1 ms, so the cell is doing something one thousandth of the time; at any moment only 1–5% of neurons are active at all. Silence is nearly free.

A simulator at dt = 0.025 ms performs 40,000 updates per second per compartment, regardless. Multiply by a thousand compartments and one detailed cell costs 40 million updates a second, of which a handful mean anything.

Tax 2 — memory sits apart from computation

In the brain, a synapse both stores its weight and applies it. Same physical object; the data travels a distance of zero. In a computer the weights live in DRAM, get carried to an arithmetic unit and carried back.

Fetching an operand costs several hundred times the multiplication it feeds. And 10¹⁴ synapses do not fit in cache, so every synaptic event is a trip to main memory. In a brain simulation, essentially the entire energy budget is data transport. The arithmetic is a rounding error.

Tax 3 — precision we do not need

We compute in float64. Biology is filthy: vesicle release is probabilistic and often fails outright, channel gating is stochastic, spike timing jitters by milliseconds. Effective precision is perhaps 3–5 bits — and the noise is used, for exploration and regularisation.

Which produces a small absurdity: we spend 64-bit arithmetic plus an expensive random number generator in order to manufacture imprecision. Multiplier energy scales roughly with the square of bit width, which is exactly why quantisation is such a live topic in mainstream machine learning.

Tax 4 — physics could be doing the integration

A membrane is a capacitor. A capacitor with current flowing into it is an integrator — not a model of one. Add membrane leak and you have a resistor. Two components, continuous, no clock, picojoules.

Digitally: sample, multiply, accumulate, store, repeat 40,000 times a second. This is why Heidelberg's BrainScaleS is analogue — it builds circuits that behave like neurons rather than computing equations describing them, and consequently runs thousands of times faster than biology on very little power.

Tax 5 — communication and synchronisation

Two of these hurt disproportionately. Every simulation timestep is a barrier where all cores wait for the slowest. And distributing a clock signal across a die consumes a substantial share of a processor's power all by itself — an expense the brain, having no clock, never incurs.

Where the orders of magnitude go

Hardware that removes a term

Worth noticing: quantisation, sparsity and mixture-of-experts routing are already mainstream in ordinary machine learning. Industry arrived at the brain's answers independently, driven purely by electricity bills.

Spiking language models exist

SpikeGPT (2023, ~260M parameters), SpikingBERT, Spikformer, and spike-driven transformer variants are real published systems. They work. They are also nowhere near the frontier, and they use point neurons — leaky integrate-and-fire. Biophysical content: zero.

The transfer that actually works runs the other way

The productive direction is not simulating biology but stealing its architectural tricks and implementing them cheaply. The field has a name — NeuroAI, after Zador et al. (2023) — and it has results:

• Dendrites as a mechanism for local learning. Sacramento, Costa, Bengio & Senn (2018) showed dendritic cortical microcircuits can approximate backpropagation locally, without weight transport. A candidate answer to the objection that backprop is biologically impossible.
• Active dendrites against catastrophic forgetting. Work from Numenta found dendritic gating improves multi-task and continual learning — a genuine open problem in machine learning, with biology supplying the hint.
• Bursts as an error signal. Payeur, Naud and colleagues (2021) proposed burst-dependent plasticity as a biological carrier for a learning signal.
• Dendrocentric learning — Boahen (Nature, 2023), arguing the dendrite, not the neuron, should be the unit of computation.

The pattern is consistent: take the idea, discard the biophysics. Not "simulate the channels" but "a dendrite multiplies and gates — put multiplication in the layer."

Three claims worth carrying away.

First: the brain is not an efficient simulator of a brain. It is the thing being simulated. Comparing the two directly is comparing a hurricane to a weather forecast. Ask instead how much energy a system purpose-built for the function requires, and the gap becomes 10²–10³ — a tractable engineering problem, not a chasm.

Second: fidelity and capability are pulling in opposite directions. Biophysical realism costs a millionfold and buys no functional advantage, because forty years of evidence say the unit is not what matters. Anyone who wants both is holding two different research programmes.

Third: we currently possess both ends of the ladder and none of its middle. We can simulate one cell in exquisite detail. We can build something with broadly brain-like competence out of components that resemble neurons not at all. Between one cell and a cortical column, credit assignment, the inputs, and the interpretability all fail at once.

So the "yet" is honest, but it is not evenly distributed. Hardware efficiency will keep improving; that wall is soft. What does not obviously yield to time is the training problem — assigning credit across a spiking, recurrent, non-differentiable network without a global error signal. Biology solved it with mechanisms we have only recently begun to take seriously, and which we do not know how to scale.

That is the interesting part, and it is where the two ends of the ladder are most likely to eventually meet.