Archive for August, 2021

Why doesn’t philosophy progress from debate to consensus? | Aeon Essays

Wednesday, August 18th, 2021

Source: Why doesn’t philosophy progress from debate to consensus? | Aeon Essays

My first thought on this article was to be puzzled by the idea that Molyneux problem is not trivial. Surely any person handling and feeling a sphere will notice the continuous symmetry of that experience relative to rotations of position relative to the object whereas that of handling the cube is only discrete (one feels edges and corners at different positions depending on one’s orientation relative to the cube). And similarly. the visual experience of thesphere is the same from all directions but that of the cube is not. So why would anyone not immediately make the correct identification on first seeing and comparing the objects?(but see third comment below!!)
 
My thought on progress in philosophy is that once a question becomes sufficiently well defined for consensus to be possible it becomes, by definition, a question of what we now call science. What is now called ‘Philosophy’ thus remains the domain where we try to come to grips with what is really meant by questions posed in the languages that we inherit from our almost pre-human ancestors with words like “should” and “good” and “why” which often express a mix of feelings that may vary from person to person and tribe to tribe.

The world can learn from South Africa’s ideal of nonracial democracy | Aeon Essays

Tuesday, August 17th, 2021

Challenging perspectives (|and contrary comments) on a deeply painful situation that provides a reflects our own – albeit in a strongly distorting mirror.

Source: The world can learn from South Africa’s ideal of nonracial democracy | Aeon Essays

(239) If two more particles bond together to make a bigger particle, what happens to their wave functions? – Quora

Monday, August 9th, 2021

The quantum state of a system of two particles is represented by a vector in the tensor product of their individual sate spaces.This is made up of linear combinations of products of state vectors (including integrals as well as finite sums), and if the individual states are represented in terms of (say) position observables by functions \psi_1(x_1) and \psi_2(x_2) , then a general state for the composite system is a function \psi(x_1,x_2) where the special case in which \psi(x_1,x_2)=\psi_1(x_1)\psi_2(x_2)

Source: (239) If two more particles bond together to make a bigger particle, what happens to their wave functions? – Quora

The quantum state of a system of two particles is represented by a vector in the tensor product of their individual sate spaces.

This is made up of linear combinations of products of state vectors (including integrals as well as finite sums), and if the individual states are represented in terms of (say) position observables by functions \psi_1(x_1) and \psi_2(x_2) , then a general state for the composite system is a function \psi(x_1,x_2) where the special case in which \psi(x_1,x_2)=\psi_1(x_1)\psi_2(x_2) corresponds to two separately identifiable particles.

If there is no interaction between the particles then this product form of a “pure tensor” is preserved by the time evolution of the system, but if there is an interaction term in the Hamiltonian then the evolution may carry such a pure tensor into a linear combination (or integral superposition) in which \psi(x_1,x_2) is more conveniently represented in a form like \psi(x_1,x_2)=\psi_{cm}(x_{cm})\psi_{rel}(x_{rel}) where x_{cm} and x_{rel} are the coordinates of the centre of mass and of the internal coordinates describing the relative positions of the two particles.

\psi_{cm}(x_{cm}) is then the wave function of the new composite particle and \psi_{rel}(x_{rel}) is the internal wave function which determines its possible energy levels etc.