6 ideas
13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
20945 | Belief is no more rational than is tasting and smelling [Hamann] |
Full Idea: Belief happens as little in terms of reasons as tasting and smelling. | |
From: J.G. Hamann (works [1770], v2:74), quoted by Andrew Bowie - Introduction to German Philosophy | |
A reaction: That is one idea definitively expressed! I take it as only a partial truth. Beliefs happen as a result of observation and experience. But someone can draw our attention to something (and we can hunt it out ourselves), which is giving a reason for belief. |
21236 | Instead of gravitational force, we now have a pervasive gravitational field [Farmelo] |
Full Idea: Physics replaced the notion that bodies exert gravitational force on each other by the more effective picture that the bodies in the universe give rise to a pervasive gravitational field which exerts a force on each particle. | |
From: Graham Farmelo (The Strangest Man [2009], 08) | |
A reaction: This still uses the word 'force'. I sometimes get the impression that gravity is the curvature of space, but gravity needs more. Which direction along the curvature are particles attracted? The bottom line is the power of the bodies. |
21235 | The Schrödinger waves are just the maths of transforming energy values to positions [Farmelo] |
Full Idea: Dirac showed that the Schrödinger waves were simply the mathematical quantities involved in transforming the description of a quantum based on its energy values to one based on possible values of its position. | |
From: Graham Farmelo (The Strangest Man [2009], 08) | |
A reaction: Does this eliminate actual physical 'waves' from the theory? |
21234 | Experiments show that fundamental particles of one type are identical [Farmelo] |
Full Idea: It is an established experimental fact ...that every single fundamental particle in the universe is the same and identical to all other particles of the same type. | |
From: Graham Farmelo (The Strangest Man [2009], 07) | |
A reaction: A loud groan is heard from the tomb of Leibniz. I'm unclear how experiments can establish this. If electrons have internal structure (which is not ruled out) then uniformity is highly unlikely. |
7666 | God is not a mathematician, but a poet [Hamann, by Berlin] |
Full Idea: Hamann's fundamental doctrine was that God was not a geometer, not a mathematician, but a poet. | |
From: report of J.G. Hamann (works [1770]) by Isaiah Berlin - The Roots of Romanticism Ch.3 | |
A reaction: [This idea is wonderfully expressed by D.H.Lawrence in his poem 'Red Geranium and Godly Mignonette]. The idea becomes attractive when you ask whether God would need to do mathematics. |