Being and Becoming · Episode 7 of 10 · 7:09
How does a model stay useful through change?
Did the state change, or did the evidence change our estimate?
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Why this question matters · 0:00
When feedback is noisy, a surprising report need not mean the world has changed. Reliable prediction requires an estimate that can respond to evidence without treating every report as a new physical event. Watch the distinction between changing a state, updating its estimate and revising the model itself.
Declare M1 · 0:21
Keep the same PULSE and RESET rules, with no spontaneous changes. Replace the exact reader with a noisy one. We label this noisy-reader variation M1. In this teaching variation, it reports the true lamp value with probability eighty percent and the opposite value with probability twenty percent. Reads still leave the device unchanged. When the hidden configuration is held fixed, the report errors are independent: an earlier error does not change the probabilities of the next report for that fixed configuration. The transition rules and sensor probabilities are supplied assumptions; we have not learned them from the reports.
Prior and prediction · 1:03
Begin a new run with half the starting probability on u and half on v. This equal prior is a new assumption, not something implied by the two state names. Prior means the estimate before the next piece of evidence. Execute PULSE. The half assigned to u moves to w; the half assigned to v stays at v. Before any new report, the predicted current probabilities are half w and half v. No probability is lost. The reader reports one.
Report and likelihood · 1:33
If the current state is w, that report has probability eighty percent, because w has lamp one. If it is v, the report has probability twenty percent, because the reader can misreport its zero lamp. These conditional report probabilities are likelihoods. Keep the one actual received report separate from the two possible explanations. Both w and v remain possible, with different support from this evidence. To make the update visible, scale the starting probability to one hundred equal units of model weight: fifty for w and fifty for v.
Work the first update · 2:03
These are drawing units for probabilities, not a hundred observed devices or experiments. For the w case, eighty percent of its fifty weight units correspond to report one. That gives forty units of weight for w together with this report. For v, twenty percent of its fifty units correspond to report one, giving ten units. The remaining model weight belongs to report zero, which is not the report received in this step. Among the weight matching report one, there are forty units for w and ten for v, fifty in total. The w share is forty divided by fifty: eighty percent. The v share is twenty percent. These are the updated state probabilities. Is the state now certain to be w? No. Both states remain possible. Now suppose the prior had been different. Would the same reader and report always give eighty percent on w? No. The eighty-percent result used our half-and-half prior as well as the specified sensor. A different prior can give a different updated probability with the same reader and report.
Second report, unchanged state · 3:35
Take another reading, with no action or state change between readings. Use the same sensor rule with a fresh error draw for that unchanged state. It reports zero. Use the previous updated estimate as the new prior: eighty percent on w and twenty percent on v. On the same one-hundred-unit scale, w contributes eighty times twenty percent, or sixteen units. The v case contributes twenty times eighty percent, also sixteen units. For this second update, the total matching weight is thirty-two units. Each state gets sixteen of those thirty-two units, so the updated probabilities return to one half each. Our model allowed different reports without a physical change. The disagreement alone therefore does not prove the device changed. A controller can predict, receive a report, update its estimate and choose its next operation.
Loop and task · 4:30
If its goal is to report the hidden current condition, another reading might help. Whether it is worth taking depends on the decision rule and its costs. If the goal is instead to turn the lamp on, RESET followed by PULSE succeeds under our known rules, even without feedback. That changes the device; it does not reveal its origin. A loop diagram by itself does not establish a benefit over alternative plans.
Estimating versus learning · 5:04
Our worked calculation estimated the current state using a supplied transition rule and sensor model. Learning a previously unknown response rule is a different task. Finish the operating example before considering that new question. Imagine extra calibration equipment that can prepare a known v and record responses to PULSE. Those trials could help compare candidate response rules. This preparation access was not available to the operating observer, and RESET does not prepare v. No such experiment has been run here.
Revise description versus adjust estimate · 5:39
A future investigation might find that prediction requires an unrecorded mode or recent history. Adding such a variable would revise the model’s state description. It would be a new model to justify and test, not a hidden change to the rules of our existing example. Noise, an incorrect response rule and an omitted variable are different possible explanations for discrepancies. Evidence must help compare them. Updating the state estimate, learning a rule and revising the variables should not be treated as the same operation.
Classify the levels · 6:13
Classify these operations: change the probabilities on w and v; estimate a previously unknown PULSE response rule; add memory of the previous output to the description. Which is state estimation, rule learning and model revision? Changing the probabilities is state estimation. Estimating the response rule is rule learning. Adding memory revises the state description. None of those descriptions alone says that a physical action was executed. Episode eight introduces a separately specified threshold-and-memory example. Episode nine then changes to the R4 actuator case, with its own dynamics, probabilities and evidence. Carry the distinctions forward, and introduce each new model on its own terms.