joe12south wrote:Cary Knoop wrote:It is not false
I believe you misunderstand what information means.
Then define "information".
information theory is getting way out of scope let me just say within the context of what we are discussing that an algorithm never increases the amount of information.
i just asked my big friend ChatGPT to make a relevant example that hopefully explains it to you:
Scenario: Temperature Data Between CitiesSuppose we have a dataset containing the average daily temperatures for a particular day from several cities along a straight highway: City A, City B, and City C. These cities are equidistant from each other, and we have exact temperature measurements for each city.
Dataset Original:
City A: 70°F
City B: 75°F
City C: 80°F
Algorithm Application: Spatial InterpolationWe decide to interpolate temperatures for multiple points between these cities to create a more detailed temperature map of the area. An algorithm is used to estimate temperatures at several points between each pair of cities based on a linear gradient between the known temperatures of these cities.
Expanded DatasetAfter applying the spatial interpolation algorithm, our dataset now includes temperatures not just for Cities A, B, and C, but also for several points between them. For example, halfway between City A and City B, the temperature is interpolated to be 72.5°F, and so on along the highway.
Analysis of Information ContentOriginal Information: The original dataset contained exact, measured temperatures for each city.
Expanded Information: The new dataset contains estimated temperatures for points between the cities. These interpolated values are based on a simple average of the temperatures of the nearest cities.
Key Points on Information ContentNo New Measurements: Like in the time-based interpolation example, the spatially interpolated temperatures are not new measurements; they are estimates based on existing data between known points. No additional temperature measurements were taken at these new points.
Predictability and Redundancy: The interpolation introduces predictability; the temperatures at interpolated points are predictable if one knows the temperatures at Cities A, B, and C. This redundancy means that the interpolated values are heavily dependent on the original data and do not introduce new independent data.
No Resolution of Additional Uncertainty: The interpolated points do not resolve any additional uncertainties about temperature variations that were not already implicit in the measurements from Cities A, B, and C. The new data points are derived and do not add information about anomalies, microclimates, or other factors that could be present if actual measurements were taken at those points.
ConclusionIn this spatial interpolation scenario, while the dataset grows larger and provides a smoother gradient of temperature data across a geographic region, the actual informational content — insights into the temperature variations that are independent of the known city data — does not increase. This illustrates how spatial interpolation, like demosaicing in imaging, uses existing data to create a fuller but not necessarily more informative dataset. The true information content, which would involve capturing new and independent data points, remains the same as before the interpolation was applied.