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Study Suggests the Number-Line Concept Is Not Intuitive
An anonymous reader writes "The Yupno people of New Guinea have provided clues to the origins of the number-line concept, and suggest that the familiar concept of time may be cultural as well. From the article: 'Tape measures. Rulers. Graphs. The gas gauge in your car, and the icon on your favorite digital device showing battery power. The number line and its cousins – notations that map numbers onto space and often represent magnitude – are everywhere. Most adults in industrialized societies are so fluent at using the concept, we hardly think about it. We don't stop to wonder: Is it 'natural'? Is it cultural? Now, challenging a mainstream scholarly position that the number-line concept is innate, a study suggests it is learned."
Any measuring cup will tell you a number line can be very intuitive. Stacking objects, filling a container; many everyday tasks are perfect physical examples of a number line.
Rulers are another example, though perhaps a bit less physical or intuitive.
How can I believe you when you tell me what I don't want to hear?
No. The science which maps real-world phenomena onto artificial symbols and concepts is known as physics. Mathematics is only concerned with the artificial symbols and concepts, independent of whether they can be mapped to real-world entities (many things cannot).
Yes. And mathematics is about the map and its rules, without caring about the territory, or even if it corresponds to a territory at all. If you want to learn about the territory, use physics. And yes, you'll use maps (i.e. mathematics) there, too. But those maps are not arbitrary, but carefully adapted to the territory as far as we know it, and actively developed to improve how well it maps the territory.
So in the map/territory picture you have:
Mathematics: The science of maps. Doesn't care about what the maps mean, or if they mean anything at all. As long as a map is consistent, it is accepted as valid map.
Physics: The science of territory. Uses maps to describe the territory. A map is considered valid only if it describes the relevant aspects of the mapped territory sufficiently well.