25 ideas
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |
| 23429 | The environment needs localised politics, with its care for the land [Dobson] |
| Full Idea: More localised politics helps to generate the disposition of care for the land which is a core feature of environmental politics. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 4) | |
| A reaction: I currently live in a time when localised politics is hugely devalued, because centralisation and privatisation are cheaper. It seems obvious that many human needs require a commitment to a particular locality. |
| 23424 | An ideology judges things now, and offers an ideal, with a strategy for reaching it [Dobson] |
| Full Idea: An ideology generally has three components: a judgement (usually critical) of how things are, a picture of the ideology's ideal society, and a strategy for progressing towards the ideal. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 2) | |
| A reaction: Conservatives tend to think we are already living in the ideal, and they reject most ideologies for being 'idealistic' (which presumably means delusional). I'm a fan of ideals, but combined with cool judgement. |
| 23426 | Ecologism is often non-liberal, by claiming to know other people's best interests [Dobson] |
| Full Idea: Liberals say that their preferences are their interests, and resist the idea that anyone could know their interests better than they can. …To this degree, ecologism might be regarded as 'non-liberal'. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 2) | |
| A reaction: There are lots of other cases where liberal citizens may not realise their best interests, such as in the control of traffic, or of drugs. |
| 23427 | Socialism can be productive and centralised, or less productive and decentralised [Dobson] |
| Full Idea: Marx and his heirs promote a productivist socialism, but utopian socialists such as William Morris offer a less productivist and more decentralised form of socialism. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 2) | |
| A reaction: Modern history teaches us to be very cautious about the centralised version. Presumably you could be decentralised but still value production highly, even if it is a bit less efficient. |
| 23428 | Difference feminists say women differ fundamentally from men [Dobson] |
| Full Idea: Difference feminists argue that men and women are fundamentally different. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 2) | |
| A reaction: You can be significantly different without being 'fundamentally' different. Personally I don't see a huge difference, even though history may have greatly exaggerated and dramatised what differences there are. |
| 23422 | For the environment, affluence and technology matter as much as population size [Dobson] |
| Full Idea: Although bare population figures are important for environmental impact, the level of affluence and the technology are also crucial factors. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 2) | |
| A reaction: It is worth noting that the technology can also have a good impact, though affluence is nearly always bad. |
| 23425 | Ecologism says growth must be reduced, and efficiency is not enough [Dobson] |
| Full Idea: A central belief of the ideology of ecologism is that aggregate growth must be reduced, and that this is very unlikely to be achieved by efficiency gains alone. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 2) | |
| A reaction: He argues that efficiency gains invariably lead to increased production. Trickle down economics needs huge growth to deliver a good life for the poorest sector. Ecologism has to be fairly egalitarian about wealth. |
| 23430 | A million years is a proper unit of political time [Dobson] |
| Full Idea: We must acknowledge that a million years is a proper unit of political time. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 5) | |
| A reaction: [He cites Colin Tudge] Such thinking is almost impossible, but owners of large aristocratic estates seem to have thought in centuries, because they were confident of continuity. The more we identify with all of humanity, the more this is possible. |
| 23423 | We currently value the present fourteen times more highly than the future [Dobson] |
| Full Idea: At current rates we seem to value present concerns as fourteen times more valuable than future concerns. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 2) | |
| A reaction: A sobering figure, which sounds about right. This directly influences how much we spend on future concerns. One thought is that future generations may be much more affluent than us! |
| 21202 | The strong force has a considerably greater range than the weak force [Martin,BR] |
| Full Idea: The strong nuclear force has a range of 10^-15 m, considerably larger than the range of the weak force. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: This is because the bosons transmitting the weak force (W+, W-, W°) are much heavier than the gluons of the strong force. |
| 21211 | If an expected reaction does not occur, that implies a conservation law [Martin,BR] |
| Full Idea: If some reaction is not observed when there is apparently nothing to prevent it occurring, it is an indication that a conservation law is in operation. | |
| From: Brian R. Martin (Particle Physics [2011], 07) |
| 21209 | Electron emit and reabsorb photons, which create and reabsorb virtual electrons and positrons [Martin,BR] |
| Full Idea: In QED an electron constantly emits and reabsorbs virtual photons and these photons constantly create and reabsorb pairs of virtual electrons and positrons, and so on. | |
| From: Brian R. Martin (Particle Physics [2011], 06) | |
| A reaction: 'And so on'! These virtual particles have energy, and hence mass. |
| 21201 | A 'field' is just a region to which points can be assigned in space and time [Martin,BR] |
| Full Idea: The word 'field' is simply a shorthand way of saying that a physical property is assigned to the points of space and time in a region. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: This is disappointing because I had begun to think that fields were foundational for modern ontology. Turns out they are operational abstractions (according to Martin). Note that a field extends over time. |
| 21212 | The Higgs field, unlike others, has a nozero value in a state without particles [Martin,BR] |
| Full Idea: The Higgs field has the property of having a nonzero value in a state without particles, the vacuum state. Other fields are assumed to have a value zero in a vacuum state. | |
| From: Brian R. Martin (Particle Physics [2011], 09) | |
| A reaction: This seems to make a big difference to our concept of a field, since it has a measurable reality even when there are no particles. So it isn't just a geometrical frame for locating particles. |
| 21205 | Many physicists believe particles have further structure, if only we could see it [Martin,BR] |
| Full Idea: Although standard particles are assumed to be structureless, many physicists believe that if distances could be probed down to 10^-35 m structures would be discovered. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: Such probing is said to be probably impossible. And does the division then come to a halt? Aristotle's meditations on this are not irrelevant. |
| 21203 | Uncertainty allows very brief violations of energy conservation - even shorter with higher energies [Martin,BR] |
| Full Idea: The uncertainty principle states that energy conservation can be violated, but only for a limited period of time. As the energy violation increases, the time period within which 'borrowed' energy has to be 'paid back' decreases. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: This is the only reason modern physicists ever seem to mention the uncertainty principle. You can ask why this debt must be paid, but it seems to be hidden where the laws of physics may not even apply. |
| 21207 | The Exclusion Principle says no two fermions occupy the same state, with the same numbers [Martin,BR] |
| Full Idea: The 'exclusion principle' initially stated that no two electrons in a system could simultaneously occupy the same quantum state and thus have the same set of quantum numbers. The principle actually applies to all fermions, but not to bosons. | |
| From: Brian R. Martin (Particle Physics [2011], 02) | |
| A reaction: This principle is said to be at the root of atomic structure, making each element unique. What exactly is a 'system'? Why does this principle hold? How do you ensure two women don't wear the same dress at a party? |
| 21204 | The standard model combines theories of strong interaction, and electromagnetic and weak interaction [Martin,BR] |
| Full Idea: As presently formulated, the standard model is two theories. One operates in the sector of strong interaction, and the other in the sector of the electromagnetic and weak interactions. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: The first is Quantum Chomodynamics (QCD). The second is Quantum Electrodynamics (QED). Interesting that the weak interaction is included in the latter, which (I take it) means there is an electro-weak union. Interactions are the heart of the model. |
| 21208 | Eletrons don't literally 'spin', because they are point-like [Martin,BR] |
| Full Idea: The picture of a particle spinning like a top is sometime useful, but it is not consistent with the idea of the electron being point-like. In fact there is no analogy for spin in non-quantum physics. | |
| From: Brian R. Martin (Particle Physics [2011], 02) | |
| A reaction: If we take this stuff literally then it blow traditional metaphysics to bits, because an electron has properties without being a substance. In what sense can an electron 'have' properties if it is a point? In interactions they cease to be points. Eh? |
| 21210 | Virtual particles surround any charged particle [Martin,BR] |
| Full Idea: A cloud of virtual particles always surrounds a charged particle. | |
| From: Brian R. Martin (Particle Physics [2011], 06) | |
| A reaction: Here's a nice fact for aspiring Buddhists to meditate on. |
| 21206 | The properties of a particle are determined by its quantum numbers and its mass [Martin,BR] |
| Full Idea: In quantum theory, the full set of quantum numbers defines the state of the particle and, along with its mass, determines its properties. | |
| From: Brian R. Martin (Particle Physics [2011], 02) |
| 21213 | String theory only has one free parameter (tension) - unlike the standard model with 19 [Martin,BR] |
| Full Idea: Unlike the standard model, with its 19 free parameters (including the masses of quarks, coupling constants and mixing angles), string theories have a single free paramater: the string tension. | |
| From: Brian R. Martin (Particle Physics [2011], 10) | |
| A reaction: This must be one feature in favour of string theory, despite its problems. |
| 21200 | An 'element' is what cannot be decomposed by chemistry [Martin,BR] |
| Full Idea: In the modern sense 'element' means a substance that cannot be decomposed by the methods of chemistry. | |
| From: Brian R. Martin (Particle Physics [2011], 01) |