7 ideas
12427 | All of mathematics is properties of the whole numbers [Kronecker] |
Full Idea: All the results of significant mathematical research must ultimately be expressible in the simple forms of properties of whole numbers. | |
From: Leopold Kronecker (works [1885], Vol 3/274), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 09.5 | |
A reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date. Natural numbers have a special status, but not sufficient to support this claim. |
10091 | God made the integers, all the rest is the work of man [Kronecker] |
Full Idea: God made the integers, all the rest is the work of man. | |
From: Leopold Kronecker (works [1885]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Intro | |
A reaction: This famous remark was first quoted in Kronecker's obituary. A response to Dedekind, it seems. See Idea 10090. Did he really mean that negative numbers were the work of God? We took a long time to spot them. |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
21730 | A 'field' is a property with a magnitude, distributed across all of space and time [Baggott] |
Full Idea: A 'field' is defined in terms of the magnitude of some physical property distributed over every point in time and space. | |
From: Jim Baggott (Farewell to Reality: fairytale physics [2013], 2 'Quantum') | |
A reaction: If it involves a 'property', normal usage entails that there is some entity which possesses the property. So what's the entity? Eh? Eh? You don't know! Disappointed... |
21731 | Fields can be 'scalar', or 'vector', or 'tensor', or 'spinor' [Baggott] |
Full Idea: Fields can be 'scalar', with no particular direction (pointing, but not pushing or pulling); or 'vector', with a direction (like magnetism, or Newtonian gravity); or 'tensor' (needing further parameters); or 'spinor' (depending on spin orientation). | |
From: Jim Baggott (Farewell to Reality: fairytale physics [2013], 2 'Quantum') | |
A reaction: [compressed] So the question is, why do they differ? What is it in the nature of each field the result in a distinctive directional feature? |
21732 | The current standard model requires 61 particles [Baggott] |
Full Idea: The current model requires 61 particles: three generations of two leptons and two flavours of quark, in three different colours (making 24); the anti-particles of all of these (48); 12 force particles (photon, W1, Z0, 8 gluons), and a Higgs boson. | |
From: Jim Baggott (Farewell to Reality: fairytale physics [2013], 6 n) |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |