Recall the end of week 7#

The self-model is necessarily a summary, and introspection reads the summary rather than the process.

The question we left open

Seven weeks built one account. Does any of it describe minds that are not vertebrates?

Where this week sits#

The third part is not a tour. It is the only place a bound is visible from outside, which is what the fourth part needs.

A million neurons is plenty#

SLOP3233 · Week 8 · Rosalind Achebe

Where we are#

Seven weeks built an account. From here to week 10 we stop adding to it and start testing it.

If it only describes vertebrates, it was never an account of intelligence.

And the intuition it cuts against#

Counts from Chittka & Niven, Current Biology 19(21), 2009.

An old and bad answer#

1850 — Dujardin proposes the mushroom bodies are the “organs of intelligence” in arthropods, partly because they are enlarged in social insects.

1929 — Pandazis notes the largest mushroom bodies belong to horseshoe crabs.

Pandazis’s own resolution#

Size doesn’t matter; wiring does.

Insect mushroom bodies contain cells with extensive dendritic ramifications and connections to all major brain centres — as a centre of higher-order integration requires. Limulus mushroom bodies do not.

That is the move this whole lecture makes, repeatedly.

Where a bee’s neurons actually go#

Counts from Chittka & Niven 2009, Fig. 1.

Do the arithmetic#

optic lobes      3 × 216,000  =  648,000
mushroom bodies  2 × 170,000  =  340,000
protocerebrum                 =   19,000
antennal lobes                =    4,500
motor neurons                 =    2,500
                                ---------
                                  1,014,000

Sanity check: Chittka & Niven give “fewer than a million neurons” for a ~1 mm³ brain. The parts add to about that, so we have the whole budget and not a subset of it.

Read the first line again#

648,000 / 1,014,000  =  0.64

64% of the budget is optic lobes.

Lamina, medulla and lobula: ~216,000 cells each.

Two-thirds of the brain is spent before any integration happens at all.

What is left to think with#

Nineteen thousand neurons, for everything the mushroom bodies don’t do.

And it runs 59 distinct behaviours#

Chittka and Niven enumerate them. A sample:

aggressive flight · alarm fanning · antennation · attend dance · beg food · brief piping · brood incubation · build comb · buzz run · cap brood · colony fission · corpse removal · dorsoventral abdominal vibration · expulsion of drones · guarding · lateral shake · robbing other hives · scouting for food · sickle dance · sterzeln · tremble dance · waggle dance · worker policing

Mostly: more of the same#

Finer resolution, higher sensitivity, more precision. Not new operations.

The same pattern centrally#

Primary visual cortex area:

mouse 4.5 mm² → macaque 1200 mm² → human 3000 mm²

A ~670-fold increase, largely engaged in low-level feature extraction, without necessarily increasing the diversity of ways information is processed.

Convergence worth noticing#

Insects and vertebrates arrived at the same architecture independently: retinotopic maps built from local circuits — “cartridges” or columns — repeated hundreds or thousands of times.

Same solution, and no common ancestor that had it.

Skeletal muscle counts#

An insect sits inside the mammalian range. Chittka & Niven 2009, Fig. 3.

With strikingly few neurons controlling them#

Desert locust flight:

• 72 motor neurons innervating 34 muscles
• the flight central pattern generator is 3 neurons

Vertebrate limb muscles are typically innervated by tens of motor neurons; highly innervated insect muscles have fewer than fifteen.

Why that matters for the account#

Novel behaviour does not require novel hardware.

It can come from few neurons recruiting existing motor circuits in a different order — which is cheap, and which is why repertoire size does not track brain size.

Repertoire against brain mass#

The number to remember#

A million-fold increase in brain mass buys a mammal two to three times the number of behaviour types.

Not a million times. Two to three.

Delayed matching-to-sample, in a bee#

Train: see pattern A, then choose between A and B. A is rewarded.

Then: bees generalise to “choose the same one” with entirely different stimuli — pattern C, then C and D — having never seen them.

They transfer the sameness rule across modalities, from olfactory entrainment to visual test. And they learn the inverse: choose the odd one.

Two objections you must be able to state#

Grade the sameness-concept claim [C] and say what would move it.

Srinivasan’s inversion#

The interesting possibility isn’t that bees manage rules despite small brains.

It’s that rule learning, concept formation and categorisation may be adaptive because of miniaturisation, combining objects under one category economises on memory, rather than storing each instance.

Constraint as the cause of abstraction. Keep that for week 12.

Olkowicz et al., 2016#

28 avian species, isotropic fractionator.

• Parrot and songbird brains hold roughly twice the neurons of primate brains of equal mass
• A higher proportion sits in the pallial telencephalon
• So large parrots and corvids match or exceed monkeys with far larger brains on forebrain neuron count

PNAS 113(26), 7255–7260.

Which is what this part is for#

Our intuitions about which minds are capable were tracking the wrong quantity for decades.

We found that out by measuring a lineage from outside it. Nobody discovered it by introspecting about brains.

And the same argument, pointed at us#

Herculano-Houzel — a co-author on that paper — on the human brain:

an ordinary primate brain scaled up, with no special encephalisation.

What is unusual is the absolute cortical neuron count, and the metabolic budget required to run it.

Two quantities, two mechanisms#

Cataglyphis fortis, Saharan salt-pan forager. No pheromone trail — too hot, too volatile.

The second one is the claim that needed proving.

The design is the argument#

Wittlinger, Wehner & Wolf, Science 312, 1965–1967 (2006).

Work the stilts#

Say an ant walks 10 m out with a natural stride of 10 mm. Its integrator therefore holds:

strides counted  =  10.0 m / 0.010 m  =  1,000

Glue on stilts so the stride becomes 13 mm, then let it run home. It runs until the count is repaid:

distance covered  =  1,000 × 0.013 m  =  13.0 m
overshoot         =  13.0 − 10.0      =   3.0 m

And the stumps#

Trim the legs so the stride becomes 7 mm:

distance covered  =  1,000 × 0.007 m  =   7.0 m
undershoot        =  10.0 − 7.0       =   3.0 m

Sanity check: the error is proportional to the stride change, and to the outbound distance. A longer foraging trip makes the same manipulation worse in absolute terms — which is what the experiments found.

The moral#

The ant is not measuring distance. It is counting a proxy and multiplying by an assumed constant.

Change the constant after the count and the arithmetic is still perfect. The answer is simply wrong, and nothing inside the calculation can notice.

Why the control is the clever part#

Manipulating before the outbound run leaves navigation intact.

The ant counts the same stride length in both directions, so the error cancels.

That single condition rules out optic flow, energy expenditure and elapsed time in one move.

Robust in ways that are informative#

The distance estimate survives:

• carrying heavy prey
• walking backwards
• losing one or two legs

It’s a stride integrator that compensates for stride length and walking speed, not a naive step counter. Follow-up: J Exp Biol 210(2), 198–207 (2007).

And bees do it completely differently#

Walking insects integrate strides. Flying insects use optic flow.

Same computational problem, two unrelated solutions, chosen by what the body makes available.

Not a route#

Which has a consequence you can compute#

Simulation: per-step heading error SD 6°, step-length error SD 4%, seeded.

The result is not what you would guess#

The integrator is good. Errors partly cancel on a wandering path, so the miss grows roughly as √n and stays within a few body lengths.

It is still not good enough — because the target is a hole.

Past ~50 steps the expected error exceeds the nest entrance.

So the spiral is not a failure#

Arriving in the right place stops being the same as finding it.

The systematic search at the end of the homeward run is the only available remedy for an accumulator with no external reference.

Take that sentence to week 12#

No independent reference means no error signal.

No error signal means the failure is invisible from inside, and no amount of better engineering within that design removes it.

You can see the ant’s bound because you are outside it.

Because that was a cognitive profile#

Everything in Part 8 maps onto the sections of the assessment you are writing. Deliberately, so you have seen one done before you attempt one.

The mapping, section by section#

And the sections where marks concentrate#

Read section 3 again#

stores a vector, not a route

That is a claim about what is held in the animal. Not about what it does.

“It navigates accurately” would be a behavioural claim, and it is the single most common way this section is failed.

And read section 7 again#

the accumulator has no independent reference

Not “the ant sometimes gets lost”. A structural limit: no better engineering inside that design removes it, because the checking would have to come from outside the thing being checked.

Section 7 is where weak profiles collapse, and that sentence is the standard.

Bumblebees roll balls#

Galpayage Dona et al., Animal Behaviour 194, 239–251 (2022).

• 45 tagged bees; individuals rolled between 1 and 117 times
• they detoured into a ball chamber past a clear path to food
• a second experiment (42 bees) showed colour-chamber preference for balls
• younger bees rolled more; males rolled for longer

No proboscis extension, no biting — so not food-directed. Frequency rose then fell, matching play rather than exploration.

Jumping spiders may dream#

Rößler et al., PNAS 119(33), e2204754119 (2022).

The method is the finding: salticids cannot move their lenses, but they can move their retinal tubes, and newly emerged spiderlings are unpigmented enough to watch it happen.

34 spiders showed regular bouts of retinal movement with limb and spinneret twitching, lengthening through the night.

Grade both honestly#

[C] and [C].

Note the asymmetry even here. We can state precisely what evidence would settle the question for a bee.

For the same question about ourselves, we cannot say what would count.

Neither tells us what we want it to. “Play” and “REM” are both defined by criteria developed on mammals, and the question of whether those criteria travel is exactly the question.

Seminar: what evidence would move either?

Four things#

1. A small brain is not a scaled-down large one — it is differently apportioned, and mostly it is sensors.
2. Scaling buys resolution, not new operations, more glomeruli, more ommatidia, more cortex doing low-level extraction.
3. Counting neurons rather than grams dissolves the corvid puzzle — and makes our own brain unnotable for its lineage.
4. A system with no external reference cannot detect its own error, the ant, stated once, and the whole of week 12.