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One thing we'd share with any alien species is our perception of the universe, and stars and galaxies are eminently countable, so the development of numbers see

One thing we'd share with any alien species is our perception of the universe, and stars and galaxies are eminently countable, so the development of numbers seems inevitable. There is the example of the sheepherder who cannot count but ensures all sheep are accounted for by with the bag of pebbles: as the sheep leave the enclosure in the morning, a pebble is placed in the (initially empty) bag; as the sheep return, a pebble is removed for each sheep, and if none are missing, the bag ends up empty. This quickly fails for many issues, such as two sheepherders wishing to discuss the relative size of their flocks, however. Regardless, an alien species might have started from entirely different premises then numbers. A lot of the images in this article are graphs, node-and-edge constructions, but it's a bit odd that graphical algorithms are a relatively new feature of human mathematics - Dijkstra's algorithm was only described in 1956. https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm What if the ancient Greeks had instead started there, what would mathematics look like today? An alien species might have done so, leading to system in which number theory would be of much less importance than graph theory.

cscheid 4y ago
You can't do graphs without numbers, so the history makes sense. Finite graphs are relations over finite sets. You can't do much with finite sets before inventing numbers.
- jacobolus 4y ago
  You are mixing up what something is with how it is conventionally formally modeled or defined. This is easy to do in modern mathematics, where students are trained from early on to develop every concept from basic axioms, imposing an ordered structure of definitions for convenience of exposition and proof without worrying as much about the inherent nature of the objects under study. A concept of number is not required to draw or describe graphs. Indeed, if you wanted you could define numbers in terms of graphs. For example, you could start with the combinatorial game Hackenbush and build up numbers from there. https://en.wikipedia.org/wiki/Hackenbush https://en.wikipedia.org/wiki/Hackenbush
openquery 4y ago
> One thing we'd share with any alien species is our perception of the universe, and stars and galaxies are eminently countable, so the development of numbers seems inevitable. I don't this is immediately obvious. There is an assumption here that stars and galaxies are these inherently well defined things, therefore they are countable. I don't think that's necessarily true. Where does a galaxy really begin and end? Or a star for that matter? If there is a solar flare occurring and solar matter is being ejected into the surrounding area is that matter still part of the star? We have this faculty which seems to be quite good at taking complex systems and approximating them to singular entities (planet, star, galaxy, table, audience, country), we can reason about. It seems to be a core aspect of human cognition but I'm not sure if this is a prerequisite for cognition in general.

cscheid 4y ago

You can't do graphs without numbers, so the history makes sense. Finite graphs are relations over finite sets. You can't do much with finite sets before inventing numbers.

jacobolus 4y ago
You are mixing up what something is with how it is conventionally formally modeled or defined. This is easy to do in modern mathematics, where students are trained from early on to develop every concept from basic axioms, imposing an ordered structure of definitions for convenience of exposition and proof without worrying as much about the inherent nature of the objects under study. A concept of number is not required to draw or describe graphs. Indeed, if you wanted you could define numbers in terms of graphs. For example, you could start with the combinatorial game Hackenbush and build up numbers from there. https://en.wikipedia.org/wiki/Hackenbush https://en.wikipedia.org/wiki/Hackenbush

openquery 4y ago

> One thing we'd share with any alien species is our perception of the universe, and stars and galaxies are eminently countable, so the development of numbers seems inevitable. I don't this is immediately obvious. There is an assumption here that stars and galaxies are these inherently well defined things, therefore they are countable. I don't think that's necessarily true. Where does a galaxy really begin and end? Or a star for that matter? If there is a solar flare occurring and solar matter is being ejected into the surrounding area is that matter still part of the star? We have this faculty which seems to be quite good at taking complex systems and approximating them to singular entities (planet, star, galaxy, table, audience, country), we can reason about. It seems to be a core aspect of human cognition but I'm not sure if this is a prerequisite for cognition in general.