Technology, algorithms and AI · Methods and tools
How far should we trust tools whose workings we cannot check?
Students use calculators and software that give answers in an instant. Few users could explain how the device computes a sine or a square root. This question asks what kind of knowledge we have when we rely on such tools.
Claims
- Calculators are tested and reliable, and relying on them is like relying on any expert source; it frees us to think about the problem.
- We can check tools indirectly, by estimation or by comparing methods, so trust need not be blind.
Counterclaims
- Hardware and software can contain errors, and people who cannot estimate cannot notice when a tool is wrong.
- Relying on tools may change what we understand: knowing how to get an answer is not the same as knowing why it is right.
Real-life situations from mathematics
The Pentium division bug
In 1994 the mathematician Thomas Nicely noticed that some Intel Pentium processors gave slightly wrong answers to certain divisions. Intel eventually offered to replace the chips, at great cost.
Spreadsheet errors
Errors in spreadsheet formulas have affected business and research decisions. In 2020 a file format limit in a spreadsheet caused thousands of positive COVID-19 test results in England to be left out of daily figures for several days.
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 technology and knowledge, or about trust in sources.
Exhibition. Your own graphic display calculator is a natural, personal object for a technology prompt.
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 technology Methods and tools
How mathematical knowledge is produced and justified.