26 ideas
| 20457 | Zeno assumes collecting an infinity of things makes an infinite thing [Rovelli] |
| Full Idea: One possible answer is that Zeno is wrong because it is not true that by accumulating an infinite number of things one ends up with an infinite thing. | |
| From: Carlo Rovelli (Reality is Not What it Seems [2014], 01) | |
| A reaction: I do love it when deep and complex ideas are expressed with perfect simplicity. As long as the simple version is correct. |
| 17453 | The meaning of a number isn't just the numerals leading up to it [Heck] |
| Full Idea: My knowing what the number '33' denotes cannot consist in my knowing that it denotes the number of decimal numbers between '1' and '33', because I would know that even if it were in hexadecimal (which I don't know well). | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: Obviously you wouldn't understand '33' if you didn't understand what '33 things' meant. |
| 17457 | A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck] |
| Full Idea: An appreciation of the connection between sameness of number and equinumerosity that it reports is essential to even the most primitive grasp of the concept of cardinal number. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) |
| 17448 | In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck] |
| Full Idea: One need not conceive of the numerals as objects in their own right in order to count. The numerals are not mentioned in counting (as objects to be correlated with baseball players), but are used. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3) | |
| A reaction: He observes that when you name the team, you aren't correlating a list of names with the players. I could correlate any old tags with some objects, and you could tell me the cardinality denoted by the last tag. I do ordinals, you do cardinals. |
| 17455 | Is counting basically mindless, and independent of the cardinality involved? [Heck] |
| Full Idea: I am not denying that counting can be done mindlessly, without making judgments of cardinality along the way. ...But the question is whether counting is, as it were, fundamentally a mindless exercise. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: He says no. It seems to me like going on a journey, where you can forget where you are going and where you have got to so far, but those underlying facts are always there. If you just tag things with unknown foreign numbers, you aren't really counting. |
| 17456 | Counting is the assignment of successively larger cardinal numbers to collections [Heck] |
| Full Idea: Counting is not mere tagging: it is the successive assignment of cardinal numbers to increasingly large collections of objects. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: That the cardinals are 'successive' seems to mean that they are ordinals as well. If you don't know that 'seven' means a cardinality, as well as 'successor of six', you haven't understood it. Days of the week have successors. Does PA capture cardinality? |
| 17450 | Understanding 'just as many' needn't involve grasping one-one correspondence [Heck] |
| Full Idea: It is far from obvious that knowing what 'just as many' means requires knowing what a one-one correspondence is. The notion of a one-one correspondence is very sophisticated, and it is far from clear that five-year-olds have any grasp of it. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4) | |
| A reaction: The point is that children decide 'just as many' by counting each group and arriving at the same numeral, not by matching up. He cites psychological research by Gelman and Galistel. |
| 17451 | We can know 'just as many' without the concepts of equinumerosity or numbers [Heck] |
| Full Idea: 'Just as many' is independent of the ability to count, and we shouldn't characterise equinumerosity through counting. It is also independent of the concept of number. Enough cookies to go round doesn't need how many cookies. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4) | |
| A reaction: [compressed] He talks of children having an 'operational' ability which is independent of these more sophisticated concepts. Interesting. You see how early man could relate 'how many' prior to the development of numbers. |
| 17459 | Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck] |
| Full Idea: The interest of Frege's Theorem is that it offers us an explanation of the fact that the numbers satisfy the Dedekind-Peano axioms. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) | |
| A reaction: He says 'explaining' does not make it more fundamental, since all proofs explain why their conclusions hold. |
| 17454 | Children can use numbers, without a concept of them as countable objects [Heck] |
| Full Idea: For a long time my daughter had no understanding of the question of how many numerals or numbers there are between 'one' and 'five'. I think she lacked the concept of numerals as objects which can themselves be counted. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: I can't make any sense of numbers actually being objects, though clearly treating all sorts of things as objects helps thinking (as in 'the victory is all that matters'). |
| 17449 | We can understand cardinality without the idea of one-one correspondence [Heck] |
| Full Idea: One can have a perfectly serviceable concept of cardinality without so much as having the concept of one-one correspondence. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3) | |
| A reaction: This is the culmination of a lengthy discussion. It includes citations about the psychology of children's counting. Cardinality needs one group of things, and 1-1 needs two groups. |
| 17458 | Equinumerosity is not the same concept as one-one correspondence [Heck] |
| Full Idea: Equinumerosity is not the same concept as being in one-one correspondence with. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) | |
| A reaction: He says this is the case, even if they are coextensive, like renate and cordate. You can see that five loaves are equinumerous with five fishes, without doing a one-one matchup. |
| 20468 | Quantum mechanics deals with processes, rather than with things [Rovelli] |
| Full Idea: Quantum mechanics teaches us not to think about the world in terms of 'things' which are in this or that state, but in terms of 'processes' instead. | |
| From: Carlo Rovelli (Reality is Not What it Seems [2014], 04) |
| 20467 | Quantum mechanics describes the world entirely as events [Rovelli] |
| Full Idea: The world of quantum mechanics is not a world of objects: it is a world of events. | |
| From: Carlo Rovelli (Reality is Not What it Seems [2014], 04) | |
| A reaction: I presume a philosopher is allowed to ask what an 'event' is. Since, as Rovelli tells it, time is eliminated from the picture, events seem to be unanalysable primitives. |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| Full Idea: Hermarchus said that animal killing is justified by considerations of human safety and nourishment and by animals' inability to form contractual relations of justice with us. | |
| From: report of Hermarchus (fragments/reports [c.270 BCE]) by David A. Sedley - Hermarchus | |
| A reaction: Could the last argument be used to justify torturing animals? Or could we eat a human who was too brain-damaged to form contracts? |
| 20469 | There are probably no infinities, and 'infinite' names what we do not yet know [Rovelli] |
| Full Idea: 'Infinite', ultimately, is the name that we give to what we do not yet know. Nature appears to be telling us that there is nothing truly infinite. | |
| From: Carlo Rovelli (Reality is Not What it Seems [2014], 11) |
| 20461 | The basic ideas of fields and particles are merged in quantum mechanics [Rovelli] |
| Full Idea: The notions of fields and particles, separated by Faraday and Maxwell, end up merging in quantum mechanics. | |
| From: Carlo Rovelli (Reality is Not What it Seems [2014], 04) | |
| A reaction: This sounds to me just like Anaximander's 'apeiron' - the unlimited [Rovelli agrees! p.168]. Anaximander predicted the wall which enquiry would hit, but we now have more detail. |
| 20462 | Because it is quantised, a field behaves like a set of packets of energy [Rovelli] |
| Full Idea: Since the energy of the electromagnetic field can take on only certain values, the field behaves like a set of packets of energy. | |
| From: Carlo Rovelli (Reality is Not What it Seems [2014], 04) |
| 20463 | There are about fifteen particles fields, plus a few force fields [Rovelli] |
| Full Idea: There are about fifteen fields, whose quanta are elementary particles (electrons, quarks, muons, neutrinos, Higgs, and little else), plus a few fields similar to the electromagnetic one, which describe forces at a nuclear scale, with quanta like photons. | |
| From: Carlo Rovelli (Reality is Not What it Seems [2014], 04) | |
| A reaction: According to Rovelli, this sentence describes the essence of physical reality. |
| 20464 | The world consists of quantum fields, with elementary events happening in spacetime [Rovelli] |
| Full Idea: The world is not made up of fields and particles, but of a single type of entity: the quantum field. There are no longer particles which move in space with the passage of time, but quantum fields whose elementary events happen in spacetime. | |
| From: Carlo Rovelli (Reality is Not What it Seems [2014], 04) | |
| A reaction: If you are not a scientist, there is (I find) a strong tendency to read and digest stuff like this, and then forget it the next day, because it so far from our experience. Folk like me have to develop two parallel views of the nature of reality. |
| 20460 | Electrons are not waves, because their collisions are at a point, and not spread out [Rovelli] |
| Full Idea: Schrödinger's wave is a bad image for an electron, because when a particle collides with something else, it is always at a point: it is never spread out in space like a wave. | |
| From: Carlo Rovelli (Reality is Not What it Seems [2014], 04 note) | |
| A reaction: And yet there is the diffusion in the two-slit experiment, which Thomas Young discovered for light. I must take Rovelli's word for this. |
| 20459 | Electrons only exist when they interact, and their being is their combination of quantum leaps [Rovelli] |
| Full Idea: Electrons don't always exist. They exist when they interact. They materialize when they collide with something. The quantum leap from one orbit to another constitutes their way of being real. An electron is a combination of leaps between interactions. | |
| From: Carlo Rovelli (Reality is Not What it Seems [2014], 04) | |
| A reaction: If a philosopher with an Aristotelian interest in the nature of matter wants to grasp the modern view, the electron looks like the thing to focus on. You can feel Rovelli battling here to find formulations that might satisfy a philosopher. |
| 20466 | Quantum Theory describes events and possible interactions - not how things are [Rovelli] |
| Full Idea: Quantum Theory does not describe things as they are: it describes how things occur and interact with each other. It doesn't describe where there is a particle but how it shows itself to others. The world of existence is reduced to possible interactions. | |
| From: Carlo Rovelli (Reality is Not What it Seems [2014], 04) | |
| A reaction: Fans of 'process philosophy' should like this, though he is not denying that there may be facts about how things are - it is just that this is not mentioned in the theory. There is not much point in philosophers yearning to know the reality. |
| 20465 | Nature has three aspects: granularity, indeterminacy, and relations [Rovelli] |
| Full Idea: I think that quantum mechanics has revealed three aspects of the nature of things: granularity, indeterminacy, and the relational structure of the world. | |
| From: Carlo Rovelli (Reality is Not What it Seems [2014], 04) |
| 20458 | The world is just particles plus fields; space is the gravitational field [Rovelli] |
| Full Idea: The world is made up of particles + fields, and nothing else; there is no need to add space as an extra ingredient. Newton's space is the gravitational field. | |
| From: Carlo Rovelli (Reality is Not What it Seems [2014], 03) | |
| A reaction: I get the impression that particles are just bumps or waves in the fields [yes! Rovelli p.110], which would mean there are fields and nothing else. And no one seems to know what a field is. |
| 20470 | Only heat distinguishes past from future [Rovelli] |
| Full Idea: It is always heat and only heat that distinguishes the past from the future. | |
| From: Carlo Rovelli (Reality is Not What it Seems [2014], 12) | |
| A reaction: I can remember the past but not the future - so can that fact be reduced to facts about heat? |