Read the equation
The origin distance compares the present representation to a fixed historical baseline. The current distance compares it to the reference extracted from the present system state. A changing but accurately tracked system can have a large origin displacement and a small current mismatch, so the two should not be interpreted interchangeably.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| delta_origin | Distance from fixed baseline |
| delta_current | Distance from present reference |
| z_t | Current representation |
| r_0 | Fixed baseline |
How it works
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Assumptions & limits
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Original context
Read the surrounding source passage
These are interfaces, not recovered fully specified equations. Until F, H, and D are defined, this notation names the desired operations without providing an executable theory. There are two different reference choices. An origin reference freezes the state declared at an initial time, r0=ztD. A current reference tracks a specified measurable property of the actual system, rt=ϕst. The latter requires a measurement map ϕ into the same representational space as zt. δtorigin=dzt,r0, δtcurrent=dzt,ϕst. A changing, accurate estimate can differ permanently from its initial value. Conversely, an unchanged estimate can become inaccurate when the world changes. These two discrepancies cannot be substituted for one another. “Different from yesterday” and “incorrect about the present” are different empirical assertions. Likewise, zt≠st is not automatically a meaningful error: a short representation and the physical/computational system it describes may be different types of object. A map can accurately represent selected properties of a city without being a city. Non-identity of representation and referent does not establish falsity. 2.2 Declaration, onset, and persistence
Exact original notation
{\delta }_{t}^{origin}=d\left({z}_{t},{r}_{0}\right), {\delta }_{t}^{current}=d\left({z}_{t},ϕ\left({s}_{t}\right)\right).Sources & provenance
{\delta }_{t}^{origin}=d\left({z}_{t},{r}_{0}\right), {\delta }_{t}^{current}=d\left({z}_{t},ϕ\left({s}_{t}\right)\right).
{\delta }_{t}^{origin}=d\left({z}_{t},{r}_{0}\right), {\delta }_{t}^{current}=d\left({z}_{t},ϕ\left({s}_{t}\right)\right).