Windowed functions are used to construct moving averages and similar concepts. The basic idea is that the full domain of numbers is often not the most useful way of describing a local effect. Windowing allows multiple points to contribute to an aggregate result by different amounts.
Some examples are in order:
Windowing is used in databases to process a subset of the records in a table.
In signal processing, time-based windows are used to identify frequencies present at specific times. Your ears do something similar: As music plays, you can pick out a sequence of distinct notes, along with identifying lyrics or instruments. As speech or music gets faster, or as distinct pieces in a medley are cut together, the individual pieces blur into noise.
The same sort of thing can happen for a rapid sequence of images, and explains why you can’t see motion above a certain rate, and why we subconsciously interpolate many still images in a movie to be understood as if it was changing smoothly.
Your eyes work in an analogous way to detect color: Different cones in your eye are sensitive to different wavelengths of light. They’re integrating the energy received to sense “total brightness”, but different wavelengths contribute differently to the total. Each type of cone uses a different windowing function, and we perceive the result as red, green, or blue according to the type of the cone.
The concept of the Overton Window is well-known in political discussions. It’s the range of opinions which are considered normal / reasonable / acceptable. What is considered acceptable or radical changes over time. Among the weaknesses of the Overton Window is the problem that different groups perceive different ranges of policy to be acceptable. Also, there’s a smooth transition between what is and isn’t acceptable, rather than hard boundaries. The potential boundary is bedeviled by complications like “How is it justified?” “How is it implemented?” “Is it opt-out, opt-in, or one-size-fits-all?” “Does it apply to everyone equally?” “Who is supporting it?” “Who explains it?” and “Who implements it?” To handle the concept of different groups having different Overton windows, I envision what I think of as a “Dunbar window”: What you consider acceptable is likely framed by the range of opinions within your social circle. Things which most of your friends & family consider acceptable are likely acceptable to you. The closer a social relationship, the more it influences you. News organizations and politicians you trust count as social connections (in my Overton/Dunbar blending) and influence your beliefs. Those you ignore or distrust have a much lesser influence, or possibly even a reversed influence.
To be a bit more topical, you might think of your chance of catching a disease to be windowed integration over the people you’ve come in contact with: Although it’s possible to catch a disease from passing contact, it’s most likely when you spend substantial time in close proximity to an infected person. The closer the contact, the higher the chance of communicating the disease. The more people you come into contact with, the higher your chances overall. Hygiene and masks work to reduce the degree of contact with individual carriers to whom you’re exposed. Social distancing, isolation, and quarantine work to expose you to fewer carriers. Together they limit the windowed aggregate of your contact with other people, decreasing your likelihood of catching the disease.
