Based on this image, the following thoughts occurred to me.

Multidimensional scaling means that an increase of the base means a huge collective result. That is, doubling length of a square, quadruples area, or doubling length of a cube multiplies volume by eight. Doubling length of a ten dimensional space increase volume by a thousand and doubling length of a thirty dimensional space increases volume by over a billion. This is interesting if a dimensional social space is defined by the number of people, if each person is going in a different “direction”.

The image comes from this post, which I read subsequently.

The post is interesting, and is nice composition of concepts. Still too much category thinking. Effectively, people need to be aware of their scale, and whatever inventions they make, it is wise to think about scalability issues sui generis. It’s not something to be tagged on, some social solution replicated across different spaces and cultures. Neither is it a goal or target, but rather a natural extension of a process if the social conditions are sensitively included.

What has this to do with math? Not much. It is mostly to do with organisational limits, solutions consultants come up with in order to fit into the organisational complexity that is the modern world.

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Leon Conrad(08:36:54) :David – you wouldn’t be posting this, nor would they, probably, if people used the Aristotelian categories of being – which are as hard-wired into our brains as metaphors are – to explore the world of thought. Genus and Species are 2 of these categories and contain within them the concept of scaling. Cicero took this further (as did the Atomists) in terms of looking at different ways of defining things – breaking them down into constituent parts. All points to 1 in the end.

happyseaurchin(12:40:11) :hmmm… not sure if genus and species fit what i was trying to say in this post… as far as i can tell, the species/genus is effectively a nested hierarchy… whereas, the insight i was trying to get across in this post was the simultaneous connection between altering the base and effecting the whole — eg changing length of square quadruples the area, or changing the “magnitude” of a social vector (perhaps translated as motivation) expands the total social space (perhaps translated as energy)… which suggests phase change, that elusive thing which i have been hovering around with adults since i experienced it so graphically with kids in classrooms…

david(15:30:44) :another observation after returning to this post just now:

1^30 is simply one

doubling the base produces a billion-fold increase in “space”

2^30

the difference between 1^1 and 1^30 is the dimension

which would be represented by the unit normally

eg 1^2 cm would be 1 square cm

eg 1^3 cm would be 1 cube cm

what if we conceived of the culture space to be

1^7billion for the planet

or

1^5 for a small team of players

ie

the “space” does not increase

that is

the sum is the same as each of the parts

in a way

there is a way of talking about the dimensionality of roughness

mandelbrot etc

so 2.3 means a plane which is quite bumpy