Models and the real world · Methods and tools
Are units of measurement discovered in nature or decided by agreement?
A metre and a kilogram feel like natural facts, but they are defined by international agreement, and the definitions have changed. This question asks how much of quantitative knowledge depends on human conventions.
Claims
- The choice of unit is conventional, but the quantity measured is real, so measurement gives objective knowledge expressed in an agreed language.
- Modern definitions are tied to constants of nature, which makes them as objective as possible.
Counterclaims
- What we choose to measure, and how precisely, reflects human purposes, so measurement is never purely a reading of nature.
- Agreements need institutions; the authority of a measurement depends partly on trust in those institutions.
Real-life situations from mathematics
Redefining the kilogram
Until May 2019 the kilogram was defined by a metal cylinder kept near Paris. It was then redefined using the Planck constant, a constant of nature.
Defining the metre
Since 1983 the metre has been defined by the distance light travels in a vacuum in a set fraction of a second, so the speed of light is now exact by definition.
Check dates and figures in a reliable source before you use them, and cite that source.
Use this in your TOK work
Essay. Fits titles about conventions, objectivity or the role of institutions in knowledge.
Exhibition. A ruler or a kitchen scale makes a simple but rich object for a prompt about who decides what counts as knowledge.
Link it to the prescribed title or the exhibition prompt you are working on, in your own words. See using maths examples in your essay and choosing exhibition objects.
Themes and study heading
Knowledge and language Knowledge and politics Methods and tools
How mathematical knowledge is produced and justified.