Turn a proposal into a testable claim
Use the declaration manuscript to separate an event definition from its interpretation.
Course lessons · 1 of 5
Identify observations that support or contradict a stated event-order hypothesis.
Useful background: Distinguish parameters, memory, and context
Operational definitions make disagreement possible
The declaration study distinguishes an observed declaration from a persistent state discrepancy. Each needs a detector, a specified input record, and a rule that can return no event. A hypothesis about their order can then disagree with the observations.
If a persistence detector only starts after a declaration, it cannot discover persistence that began earlier. The recovered research explicitly allows the two detectors to examine their eligible records independently. This avoids building the desired order into the measurement.
Persistence requires all observations in a window
A persistence rule can require that every observed discrepancy in a window exceed a threshold. That differs from requiring only a large average. A window’s starting time may be labeled retrospectively, while confirmation is only available after its last observation.
Missing values are not zero discrepancies and are not proof of persistence. Define the eligible grid and gap policy first. Even a measured event order would support that operational finding; its relationship to conscious experience remains a further hypothesis.
Check a two-observation persistence window
1Specify the rule
Use threshold ε = 0.2 and window length W = 2. A valid window requires both consecutive discrepancies to exceed 0.2.
2Inspect the observations
At times zero, one, and two, suppose the discrepancies are 0.3, 0.4, and 0.1. The window beginning at zero passes; the next window fails.
3Separate start from confirmation
The passing window begins at time zero, but it is confirmed only after the observation at time one. Any online claim must respect that information delay.
Make the idea respond
The scalar lab does not automatically detect declarations or persistent discrepancy. For a manual detector exercise, keep the defaults s₀ = 0, a = 0.8, b = 0.2, and constant input 1. Define δ_t = |s_t − s₀|, threshold ε = 0.2, and a strict two-observation window. The states at t = 1, 2, 3 are 0.2, 0.36, 0.488. The window beginning at t = 1 fails because equality is not greater than 0.2; the first passing window begins at t = 2 and is confirmed at t = 3. This is a stipulated teaching detector, not an observed declaration event.
Change one input at a time. Predict what should happen, then compare the computed result with your prediction.
Teaching model · computed in your browser
Watch a state remember
Apply a sequence of inputs to one persistent number. Explore forgetting, oscillation, and unstable feedback.
s is the persistent scalar state; a controls the retained prior state; b scales the input u. The same stored state is updated at every step. For this linear recurrence, differences in initial conditions shrink when |a| < 1. This one-number demonstration is not a neural network, a trained model, or an operating Pantheon runtime.
Try this: choose a single pulse and compare a = 0.8, −0.8, and 1.2. Which settings forget an earlier state, and which amplify it?
Playback starts only when you choose Play. It pauses when this tab is hidden or the lab leaves view. Reduced-motion preferences slow the updates; Step always gives you direct control. Runs stop after 40 updates or at the display limit.
The default worked example is shown below.
Stable memory: differences in initial state shrink because |a| < 1. Press Step to apply the first input to the initial state. The constant-input fixed point is b / (1 − a) = 1; convergence to it requires |a| < 1.
| Update | Input u | Previous state | New state |
|---|---|---|---|
| 0 | Not yet applied | Initial condition | 0 |
Your turn.
Try an answer before opening a hint. Feedback will explain the result, and you can practice again.
Interactive practice is loading. The lesson, worked example, and printable questions remain available below.
View printable practice and solutions
Use these questions when studying without interactive controls. Opening a written solution does not earn progress.
For ε = 0.2 and W = 2, which window satisfies the strict persistence rule?
- (0.3, 0.1)
- (0.2, 0.4)
- (missing, 0.4)
- (0.3, 0.4)
Read the solution
Only (0.3, 0.4) contains two observed values above 0.2.
A two-observation window starts at time 5 and contains times 5 and 6. At what time can it first be confirmed?
Read the solution
It can be confirmed at time 6, after both observations exist.
Which detector design permits testing whether persistence preceded a declaration?
- Define every declaration as persistence.
- Replace missing earlier observations with desired values.
- Scan persistence over its full eligible record, including earlier times.
- Start looking for persistence only after declaration.
Read the solution
Scanning the full eligible record lets persistence occur before, after, or with declaration.
Observed declaration followed by measured persistence directly establishes which conclusion?
- Conscious experience has been proven.
- Every model will show the same order.
- All changes were caused by the declaration.
- The operational event order under the stated detectors.
Read the solution
It establishes the observed ordering under a particular measurement protocol.
Follow the original record
Use the definitions you just practiced to read the project’s own notation, assumptions, and evidence.
The ideas to keep
- Define detectors before interpreting events.
- Permit the data to contradict the proposed order.
- Distinguish event start, confirmation time, and causal interpretation.
Reading completion is separate from your practice evidence.
Progress is kept in this browser. How learning works