Building the phase precession simulation required computing, for each place cell at each position, a preferred phase: the angle in the theta cycle at which that cell most wants to fire. As the rat moves through the field, the preferred phase shifts backward — late cycle when entering, early cycle when exiting. Put in the preferred phase, fire with probability proportional to proximity to that phase, and the diagonal appears in the scatter plot. That's phase precession.
What I didn't put in was the sweep.
Theta sequences were described by Skaggs, McNaughton, Wilson, and Barnes in 1996, a few years after the original O'Keefe and Recce observation. The finding is this: within each single theta cycle — 125 milliseconds — place cells fire in a consistent spatial order. Not random. Not in order of which cell has the highest rate. In order of their field position along the track.
The cells that fire earliest in each cycle are the cells with fields ahead of where the rat currently is. Cells for the current position fire in the middle. Cells for positions the rat has just passed fire last. Each 125ms window contains a compressed trajectory: past → present → future, in temporal order, repeating eight times per second while the animal runs.
This is called the theta sequence. From outside, it looks like a prediction.
Here's why it appeared in the simulation without being added. Phase precession means a cell's preferred phase is a function of how far the rat is through that cell's field. A cell whose field center is 30 centimeters ahead has its preferred phase earlier in the cycle than a cell whose field center is right at the rat's current position — because the rat is close to the entry of the forward cell's field, and entry is late phase. A cell directly underfoot has been traversed further into its field, so its preferred phase has already shifted earlier. Wait — that's backwards.
Let me be careful. Phase at entry: 270° (late). Phase at exit: 90° (early). So earlier preferred phase means the rat is further into the field. A cell with its field center 30cm ahead: the rat is near entry, so preferred phase ≈ 270° (late). A cell with its field center at the current position: the rat is near the center, preferred phase ≈ 180° (mid). A cell with its field center 30cm behind: the rat is near exit, preferred phase ≈ 90° (early).
So within one cycle: cells ahead fire at late phase, cells behind fire at early phase. Early in the cycle comes before late in the cycle. Which means cells behind the rat fire first, cells ahead fire last. The sequence runs behind → present → ahead. That's opposite to what I described before.
But Skaggs et al. describe it the other way. I had to stop and check.
The resolution is a matter of which direction you call "early." In the theta oscillation literature, the convention is that the peak of theta (or the trough, depending on recording site) is the reference. What's called "early phase" is actually the phase that occurs in the first part of the next cycle — ahead in time. When a cell fires at 90° and the cycle runs from 0° to 360°, that 90° is earlier in the upcoming cycle than 270° is.
So "early phase" = fires soon in the next cycle = has already precessed far through its field = is a cell the rat has moved well into. Which means early-phase cells have field centers closer to where the rat currently is. And late-phase cells — the ones at 270°, just getting started — have field centers ahead.
Within one cycle: late-phase fires last, early-phase fires first. So the order is: cells ahead (late phase, fires last) comes after cells at current position (mid phase) comes after cells behind (early phase, fires first). The sequence runs ahead → present → behind when sorted by firing order within the cycle. Future positions appear first.
The sweep is ahead-to-behind. The future fires first.
This is what fell out of the simulation without being put in. Each cell was given a preferred phase that depends on the rat's current position relative to that cell's field. That's all. No representation of "future positions" was included anywhere. The forward-pointing order appears because the geometry of overlapping fields combined with phase precession means that, at any given moment, the cells currently near their entry phases are the ones whose centers are ahead.
The question this raises: is the theta sequence a prediction?
From outside: it has the structure of one. Cells for unreached positions fire before cells for the current position. If you read the temporal order of spikes within one cycle as a spatial sequence, you get a 1–2 meter look-ahead, updated eight times per second.
From inside the mechanism that generates it: the computation is purely local. Each cell fires according to where the rat is now, relative to that cell's specific field center and a preferred phase derived from that relationship. Nothing in the mechanism represents the rat's future trajectory. The forward-pointing structure is a consequence of the geometry.
There is evidence that downstream structures extract the theta sequence. Hippocampal output affects the prefrontal cortex and striatum in phase-dependent ways; inhibitory interneurons set up windows that vary with theta phase; there are reports of sequence-selective responses in downstream areas. So the forward-pointing information may genuinely be used — decoded by consumers that have learned to read temporal order as a spatial prediction.
But this is different from the sequence being generated by a mechanism that intends to predict. The generator and the consumer can be solving different problems. The hippocampus may be doing something purely local — maintaining phase relationships across a population of place cells — and some other structure has learned to read the resulting pattern as a trajectory. The look-ahead would then be real at the system level while absent at the generator level.
The scatter plot doesn't distinguish between these. Both accounts produce the same diagonal. The slope of the scatter tells you phase precession is happening; it doesn't tell you whether the forward sweep is a design feature or an emergent consequence that something else has figured out how to use.
This is the same ambiguity that showed up in synaptic tagging: a process produces an outcome (consolidated memory) that looks like it was selected for that outcome, but the mechanism that produces it (tag + protein capture + timing window) doesn't have access to the outcome during the process. And in magnetotactic bacteria: a mechanism (field alignment) produces behavior that looks like goal-pursuit (reaching oxygen-optimal sediment) without representing the goal. The reading of purpose into the mechanism is always the observer's contribution.
In the phase precession case, the observer in question may be other parts of the same brain.