https://synapse.cafe/@axoaxonic/110195562798838650 @[email protected]: “But what are we studying when we are doing mathematics?”
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Musing on mathematics, as our map of the territory of maps.
background
A comprehensive mechanistic account of the mind (and cognition) requires comprehensive study of both map and territory – the following is a summary.
Consider:
- Territory aligns, our maps ought to
- Valid perspectives of the same phenomenon ought to be continuable, to other valid perspectives
mathematics
Forms of mathematics are continuable to other forms of mathematics. Further, we might also say “mathematical perspectives are continuable to territory” (which is kinda the point of maps, but to extend) “to occasionally absurd degrees of precision”.
The basic premise of any map, is one of alignment – between map and territory – such that each map intersects territory at least twice, origin and destination; of course territory is the substrate of persisted and integrated map, in which case, thrice.
maps are multi-phase {persisted; integrated; operational; adopted; $\ldots$ }
$$\ldots$$ The “absurd alignability” between mathematics and territory is curious ^[ I have a take on why and how, which I’ll hold back for the time being ].
Consider that both mathematics and territory must follow the similarly equivalent rules – that both comply with the similarly equivalent constraints.
Constraints limit the space of all legal form. Form instructs behaviour. All are constrained, as constraints propagate (and evolve) through form and behaviour (and subsequently phase).
$$\ldots$$ Are maps free form? Is mathematics free-form?
The “space-of-all maps” is vast. Do all conform to a common set of constraints? Is the space-of-all maps finite-infinite or infinite-infinite?
$$\ldots$$ Thinking abut the substrate of maps, leads to a poetic expression: “the fabric of cognition”, such that what we are considering here – is the (occasionally absurd) alignment between “the fabric of cognition” and “the fabric of territory”.
If we consider that “the fabric of cognition” is a physical substrate – what it is of maps, which aligns with territory – is other territory, not free-form, but constrained to same finite legal forms (and respective behaviours) as all territory.
In which case, the occasionally absurd alignment between mathematics and territory is not so mysterious, and innate, and we only really ever get in our own way (by contrived complexity).
further, in the context of education, by promoting adherence to traditional ways as a virtue, (at times in isolation of application to territory) we might miss “what it is of mathematics that is fundamental”, altogether
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“But what are we studying when we are doing mathematics?
Consider that what we study is the very fabric of cognition – the substrate of us; of direct phenomenological experience; of consciousness; and all evolved biological cognition – the constraints of which are sufficiently equivalent, and directly instructive, to those of territory, and all subsequent phases.
active draft. for corrections or suggestions, contact: @[email protected]