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> any math constructions brought in should be checked against the physical reality But that's not how things work in practice. Parts of the mathematical framew

> any math constructions brought in should be checked against the physical reality But that's not how things work in practice. Parts of the mathematical framework used for describing a particular physical phenomenon are always a kind of mental scaffolding and do not have a direct representation in reality. This is how math always works in science. Think of the complex numbers, for example: they are used extensively in quantum physics and electrical engineering, but that does not mean that you can see them, touch them or measure them.

CraneWorm 6y ago
> Think of complex numbers I'd say naturals are abstract enough :)
- Koshkin 6y ago
  I would disagree: if you close your eyes you can still tell the difference between 2 and 3 - by touch!
  - trhway 6y ago
    sorry, man, no :) https://www.newscientist.com/article/mg20126997-300-tactile-illusions-1-the-aristotle-illusion/ https://www.newscientist.com/article/mg20126997-300-tactile-... "One of the oldest tactile illusions is the Aristotle illusion. It is easy to perform. Cross your fingers, then touch a small spherical object such as a dried pea, and it feels like you are touching two peas. This also works if you touch your nose."
    - Izkata 6y ago
      I dunno if I'm doing it wrong or what, but that illusion doesn't work for me.
trhway 6y ago
>Think of complex numbers, for example: they are used extensively in quantum physics and electrical engineering, but that does not mean that you can see them, touch them or measure them. yes, we use complex numbers there only because we have a very consistent mental map between their properties/behaviour in the math model and the physical reality. The physical reality doesn't obey the math model, it is a successful and useful math model which seems to consistently describe and predict the reality in some range of conditions. So when a new model is brought in you'd want it to have at least some partial consistent mapping to reality, and with refining of a model the mapping is expected to improve. If refining of a model turns instead into rounds and rounds of complexity growths without matching massive improve in the consistency of mapping to physical reality, you'd naturally start to question the model, and may be think, kind of VC style, about spending say a few percent of resources going into that massive complexity growth of the currently dominating, yet still far from working that good, model into exploring some alternative models.

CraneWorm 6y ago

> Think of complex numbers I'd say naturals are abstract enough :)

Koshkin 6y ago
I would disagree: if you close your eyes you can still tell the difference between 2 and 3 - by touch!
- trhway 6y ago
  sorry, man, no :) https://www.newscientist.com/article/mg20126997-300-tactile-illusions-1-the-aristotle-illusion/ https://www.newscientist.com/article/mg20126997-300-tactile-... "One of the oldest tactile illusions is the Aristotle illusion. It is easy to perform. Cross your fingers, then touch a small spherical object such as a dried pea, and it feels like you are touching two peas. This also works if you touch your nose."
  - Izkata 6y ago
    I dunno if I'm doing it wrong or what, but that illusion doesn't work for me.

trhway 6y ago

>Think of complex numbers, for example: they are used extensively in quantum physics and electrical engineering, but that does not mean that you can see them, touch them or measure them. yes, we use complex numbers there only because we have a very consistent mental map between their properties/behaviour in the math model and the physical reality. The physical reality doesn't obey the math model, it is a successful and useful math model which seems to consistently describe and predict the reality in some range of conditions. So when a new model is brought in you'd want it to have at least some partial consistent mapping to reality, and with refining of a model the mapping is expected to improve. If refining of a model turns instead into rounds and rounds of complexity growths without matching massive improve in the consistency of mapping to physical reality, you'd naturally start to question the model, and may be think, kind of VC style, about spending say a few percent of resources going into that massive complexity growth of the currently dominating, yet still far from working that good, model into exploring some alternative models.