Idkintervallum

Idkintervallum is a fictional mathematical construct used in thought experiments and online discussions to explore interval-based reasoning under uncertainty. In its simplest form it models a quantity as a closed interval on the real line, but with an explicit indication of epistemic doubt. The term blends idk, an internet abbreviation for "I don't know," with intervallum, Latin for interval.

In practice, an idkintervallum attaches a confidence tag to the interval, signaling whether the endpoints are firmly established or provisional. When all information is available, an idkintervallum reduces to a standard interval [a, b]. When information is partial, the representation may be written with an idk marker, or as an annotated interval that encodes a higher degree of uncertainty.

Operations on idkintervallum objects are often described by borrowing rules from standard interval arithmetic, with the caveat that the indeterminacy tag propagates conservatively. This means that combining two idkintervallum intervals tends to preserve or expand uncertainty to avoid overconfident conclusions.

Applications of idkintervallum appear mainly in pedagogy and theoretical discussions rather than formal practice. It is used to illustrate how knowledge gaps influence bounds, decision making, and robust computation. The concept serves as a mnemonic for the idea that not all bounds carry the same level of trust.

Example: if a sensor reports a measurement x in [2.0, 3.0] but calibration is uncertain, one might represent idkintervallum(x) as [2.0, 3.0] with an idk marker, which could narrow to [2.5, 2.9] as calibration confidence improves. See also interval arithmetic, uncertainty quantification, epistemic uncertainty.