Recall the end of week 1#

A finite system must discard most of its world, and the discarding is not reported. We found one instance with a card.

The question we left open

Is that a fact about eyes, or about any system that has to sense at all?

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.

What a sense organ is for#

SLOP3233 · Week 2 · Rosalind Achebe

A bacterium solves this with one number#

The entire decision rule: if things are improving, keep going; otherwise turn at random.

What is and is not in that rule#

It climbs a gradient with no ability to sense which way the gradient points.

Watch your verbs#

Where the memory actually is#

The comparison needs a stored past, and in E. coli it is receptor methylation.

Ligand binding drives a fast response; methylation state adapts on a slower timescale, restoring the baseline. The difference between the two timescales is the memory — a few seconds of it.

So “is it getting better?” is implemented as “does current occupancy exceed what the methylation state has adapted to?”

Which is worth dwelling on#

The memory is not a record. It is an adaptation offset, a moving baseline that the current signal is compared against.

Nothing stores a value. Nothing is retrieved. And it is enough.

Macnab & Koshland, PNAS 69(9), 2509–2512 (1972); Berg, E. coli in Motion (2004).

The numbers, because they constrain the story#

A cell that reorients every second cannot be using a spatial comparison across its own body — it is far too small and too fast. Temporal comparison is the only option its physics leaves open.

Von Uexküll’s term for this#

The Umwelt: not the environment, but the world as it exists for that organism, built entirely from the distinctions its receptors can make.

His example is a tick, whose world reduces to butyric acid, warmth, and hair. Not an impoverished version of our world. A different one, complete in itself.

A Foray into the Worlds of Animals and Humans (1934).

So the question changes shape#

Not “how much of the world does this organism perceive?”

But “which distinctions did it commit to paying for?”

That reframing is what makes the next animal comprehensible rather than absurd.

Twelve channels against your three#

Gaussian approximations at published peak positions — for channel shape and spacing, not digitised microspectrophotometry.

Why channel shape decides what you can resolve#

Colour discrimination in us works by comparing across channels. Broad, overlapping sensitivities mean a small wavelength shift changes the ratio between two channels measurably.

Narrow, barely-overlapping channels give you excellent identification of which band a wavelength fell in, and almost no information about where inside the band it fell.

Discrimination, measured#

Thoen et al., Science 343(6169), 411–413 (2014). Bars are indicative of the reported ten-fold ratio rather than digitised values.

The hypothesis predicts a number#

If the animal reads which bin fired hardest and cannot resolve within a bin, then its discrimination threshold should be about one bin wide.

spectral range covered  =  720 − 300  =  420 nm
receptor classes        =  12
bin width               =  420 / 12   =  35 nm

Check it against the measurement#

predicted Δλ (one bin)        ≈  35 nm
measured Δλ (Thoen et al.)    ≈  25–30 nm
comparison animals            ≈   1–4 nm

The prediction lands in the right place, and the comparison animals are an order of magnitude away from both.

That is a great deal better than the hypothesis merely sounding plausible, and it is why this is [C] rather than [S].

The moral#

A story about a mechanism becomes a scientific claim when it commits to a number you can be wrong about.

“It scans like a barcode reader” is a metaphor. “Its threshold should be about one bin wide” is a prediction, and the prediction can be checked.

Ask this of every mechanism in the remaining ten weeks.

Two ways to use twelve channels#

Why you would build that#

The thing they can do that we cannot#

Stomatopods are sensitive to polarisation, including circular polarisation, the only animals known to be.

Which is the same story from the other side: the channels they built are excellent for a distinction we cannot make at all, and poor for one we make easily.

Neither system is better. They are priced differently.

A case where nobody knows the answer#

Magnetoreception. Many animals demonstrably use the geomagnetic field to navigate. Two candidate mechanisms have been argued for decades:

A sense we are certain exists and cannot explain. [C], and a useful reminder that this course’s confidence varies by topic.

What would falsify the barcode account?#

Worth asking, because this is the first [C] claim you are asked to hold.

• Behavioural discrimination that is fine within a single receptor band would break it — the account predicts you cannot resolve inside a bin
• Neural evidence of opponent comparison between adjacent channels would break it
• A species with the same twelve channels and good discrimination would break it

None of those has been shown either way, which is what [C] means here.

The lesson that carries to week 7#

This is a News and Views claim#

A popular statement that inverts its source is exactly the shape your week 7 investigation is looking for.

And note the trap in the brief: a popular version that is merely less detailed is not wrong, and a thousand words discovering that journalists simplify has found nothing.

The mantis shrimp is not available, it is the worked example.

Three Umwelten, priced differently#

None of the three rows is a deficient version of another. Each is a budget spent.

Which is the question to carry into week 3#

Not how much does this organism perceive.

What did it commit to paying for, and what did that purchase cost it?

Every remaining week of the course is a version of that question, including the weeks about you.