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Spirals
What repeats as something grows? Which parts are mathematical structure, and which are the result of material, environment and time?
Try Noticing Maths
Take a question with you.
Six small investigations you can adapt to a garden, classroom, kitchen, newspaper, spreadsheet or conversation. The goal is not to finish quickly. It is to look more carefully.
01 · Symmetry
Is nature really symmetrical?
Find the symmetry. Then find where it fails.
Mark one line or rotation that seems to preserve the pattern. Now identify a petal, leaf, angle or spacing that breaks it. Does the imperfect pattern still deserve to be called symmetrical?
Take it further: photograph something else that looks symmetrical and compare the departures from perfect symmetry.
02 · Scale
What would you measure first?
A measurement is useful only if it answers the question.
Height is only one description. What about spread, branch length, number of leaves, spacing or rate of growth?
Create one ratio, such as canopy width ÷ height. Repeat later. Does proportion remain stable as the plant grows?
03 · Sampling
How many flowers are in a field?
Count a small patch and scale up. Then ask whether the patch you chose was typical.
A tidy answer can still come from a poor sample.
What would make the estimate more trustworthy?
Use several locations. Decide how they are selected. Notice clustering. Compare estimates. Report a range rather than pretending the field contains an exact number.
Return to the same place. Change becomes visible.
04 · Change
When does a model stop describing the real thing?
A model is an argument with assumptions — not reality itself.
Plot something you can observe repeatedly: plant height, daylight, temperature, water level or growth. Where does the trend change? What else would you need to know before explaining why?
05 · Evidence
“90% effective.” Should we be impressed?
Percentage of what — and based on how many?
Ask about the denominator, comparison group, selection process, uncertainty and what “effective” actually means.
Questions beside an impressive number
Where did it come from?
Compared with what?
How was it measured?
What is missing?
What am I being invited to believe?
06 · Human vs machine
AI answer: Area = 12.4 m
Before recalculating, what is already wrong?
Would you sign your name to it?
Mathematics is not finished when the arithmetic stops.
Start with the units. Then check the shape, measurements, assumptions, precision and whether the conclusion answers the actual question.
A recurring collection
Spirals · Seeds · Stars
Three old ways into new mathematical questions — growth, scale, pattern, navigation and the stories we place around what we observe. Rooted in the west of Ireland without pretending every pattern has a single historical explanation.
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Seeds
How does a small beginning become a question about number, scale, probability, survival or change?
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Stars
Which pattern is in the sky — and which part did we put there when we joined the points and told the story?
eˣ — Grow at your own rate.