19 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. |
| 17486 | Supervenience is simply modally robust property co-variance [Hendry] |
| Full Idea: Supervenience is not an ontological relationship, being just modally robust property co-variance. | |
| From: Robin F. Hendry (Chemistry [2008], 'Ontol') | |
| A reaction: I take supervenience to be nothing more than an interesting phenomenon that requires explanation. I suppose Humean Supervenience is a priori metaphysics, since you could hardly explain it. |
| 17481 | Nuclear charge (plus laws) explains electron structure and spectrum, but not vice versa [Hendry] |
| Full Idea: Given relevant laws of nature (quantum mechanics, the exclusion principle) nuclear charge determines and explains electronic structure and spectroscopic behaviour, but not vice versa. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: I argue that the first necessary condition for essentialism is a direction of explanation, and here we seem to have one. |
| 22717 | Self-interest can fairly divide a cake; first person cuts, second person chooses [Poundstone] |
| Full Idea: To fairly divide a cake between two children, the first divides it and the second chooses. …Even division is best, as it anticipates the second child will take the largest piece. Fairness is enforced by the children's self-interests. | |
| From: William Poundstone (Prisoner's Dilemma [1992], 03 'Cake') | |
| A reaction: [compressed] This is introduced as the basic principle of game theory. There is an online video of two cats sharing a dish of milk; each one drinks a bit, then pushes the dish to the other one. I'm sure two children could manage that. |
| 22718 | Formal game theory is about maximising or minimising numbers in tables [Poundstone] |
| Full Idea: At the most abstract level, game theory is about tables with numbers in them - numbers that entities are are efficiently acting to maximise or minimise. | |
| From: William Poundstone (Prisoner's Dilemma [1992], 03 'Curve') | |
| A reaction: A brilliant idea. The question is the extent to which real life conforms to the numberical tables. The assumption that everyone is entirely self-seeking is blatantly false. Numbers like money have diminishing marginal utility. |
| 22719 | The minimax theorem says a perfect game of opposed people always has a rational solution [Poundstone] |
| Full Idea: The minimax theorem says that there is always a rational solution to a precisely defined conflict between two people whose interests are completely opposite. | |
| From: William Poundstone (Prisoner's Dilemma [1992], 03 'Minimax') | |
| A reaction: This is Von Neumann's founding theorem of game theory. It concerns maximising minimums, and minimising maximums. Crucially, I would say that it virtually never occurs that two people have completely opposite interests. There is a common good. |
| 22720 | Two prisoners get the best result by being loyal, not by selfish betrayal [Poundstone] |
| Full Idea: Prisoners A and B can support or betray one another. If both support, they each get 1 year in prison. If one betrays, the betrayer gets 0 and the betrayed gets 3. If they both betray they get 2 each. The common good is to support each other. | |
| From: William Poundstone (Prisoner's Dilemma [1992], 06 'Tucker's') | |
| A reaction: [by Albert Tucker, highly compressed] The classic Prisoner's Dilemma. It is artificial, but demonstrates that selfish behaviour gets a bad result (total of four years imprisonment), but the common good gets only two years. Every child should study this! |
| 22721 | The tragedy in prisoner's dilemma is when two 'nice' players misread each other [Poundstone] |
| Full Idea: The tragedy is when two 'nice' players defect because they misread the other's intentions. The puzzle of the prisoner's dilemma is how such good intentions pave the road to hell. | |
| From: William Poundstone (Prisoner's Dilemma [1992], 11 'Howard's') | |
| A reaction: I really wish these simple ideas were better known. They more or less encapsulate the tragedy of the human race, with its inability to prioritise the common good. |
| 22722 | TIT FOR TAT says cooperate at first, then do what the other player does [Poundstone] |
| Full Idea: The successful TIT FOR TAT strategy (for the iterated prisoner's dilemma) says cooperate on the first round, then do whatever the other player did in the previous round. | |
| From: William Poundstone (Prisoner's Dilemma [1992], 12 'TIT') | |
| A reaction: There are also the tougher TWO TITS FOR A TAT, and the more forgiving TIT FOR TWO TATS. The one-for-one seems to be the main winner, and is commonly seen in animal life (apparently). I recommend this to school teachers. |
| 22723 | Do unto others as you would have them do unto you - or else! [Poundstone] |
| Full Idea: TIT FOR TAT threatens 'Do unto others as you would have them do unto you - or else!'. | |
| From: William Poundstone (Prisoner's Dilemma [1992], 12 'TIT') | |
| A reaction: Essentially human happiness arises if we are all nice, but also stand up firmly for ourselves. 'Doormats' (nice all the time) get exploited. TIT FOR TAT is weak, because it doesn't exploit people who don't respond at all. |
| 17478 | Maybe two kinds are the same if there is no change of entropy on isothermal mixing [Hendry] |
| Full Idea: One suggestion is that any two different substance, however alike, exhibit a positive entropy change on mixing. So absence of entropy change on isothermal mixing provides a criterion of sameness of kind. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: [He cites Paul Needham 2000] This sounds nice, because at a more amateur level we can say that stuff is the same if mixing two samples of it produces no difference. I call it the Upanishads Test. |
| 17484 | Maybe the nature of water is macroscopic, and not in the microstructure [Hendry] |
| Full Idea: Some deny that that microstructure is what makes it water; substance identity and difference should be determined instead by macroscopic similarities and differences. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: Very plausible. Is the essential nature of human beings to be found in the structure of our cells? |
| 17479 | The nature of an element must survive chemical change, so it is the nucleus, not the electrons [Hendry] |
| Full Idea: Whatever earns something membership of the extension of 'krypton' must be a property that can survive chemical change and, therefore, the gain and loss of electrons. Hence what makes it krypton must be a nuclear property. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: A very nice illuminating example of essentialism in chemistry. The 'nature' is what survives through change, just like what Aristotle said, innit? |
| 17485 | Maybe water is the smallest part of it that still counts as water (which is H2O molecules) [Hendry] |
| Full Idea: If they do count as water, individual H2O molecules are the smallest items that can qualify as water on their own account. Hydroxyl ions and protons, in contrast, qualify as water only as part of a larger body. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: As Aristotle might say, this is the homoeomerous aspect of water. This is Hendry's own proposal, and seems rather good. |
| 17482 | Compounds can differ with the same collection of atoms, so structure matters too [Hendry] |
| Full Idea: The distinctness of the isomers ethanol (CH3CH2OH, boiling at 78.4°) and dimethyl ether (CH3OCH3, boiling at -24.9°) must lie in their different molecular structures. ...But structure has continuously varying quantities, like bond length and angle. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: [compressed] This seems to imply that what matters is an idealised abstraction of the structure (i.e. its topology), which is a reason for denying that chemistry is reducible to mere physics. |
| 17483 | Water continuously changes, with new groupings of molecules [Hendry] |
| Full Idea: Macroscopic bodies of water are complex and dynamic congeries of different molecular species, in which there is a constant dissociation of individual molecules, re-association of ions, and formation, growth and disassociation of oligomers. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: The point is that these activities are needed to explain the behaviour of water (such as its conductivity). |
| 17476 | Elements survive chemical change, and are tracked to explain direction and properties [Hendry] |
| Full Idea: Elements survive chemical change, and chemical explanations track them from one composite substance to another, thereby explaining both the direction of the chemical change, and the properties of the substances they compose. | |
| From: Robin F. Hendry (Chemistry [2008], Intro) | |
| A reaction: [The 16,000th idea of this database, entered on Guy Fawkes' Day 2013] |
| 17477 | Defining elements by atomic number allowed atoms of an element to have different masses [Hendry] |
| Full Idea: In 1923 elements were defined as populations of atoms with the same nuclear charge (i.e. atomic number), allowing that atoms of the same element may have different masses. | |
| From: Robin F. Hendry (Chemistry [2008], 'Chem') | |
| A reaction: The point is that it allowed isotopes of the same element to come under one heading. This is fine for the heavier elements, but a bit dubious for the very light ones (where an isotope makes a bigger difference). |
| 17480 | Generally it is nuclear charge (not nuclear mass) which determines behaviour [Hendry] |
| Full Idea: In general, nuclear charge is the overwhelming determinant of an element's chemical behaviour, while nuclear mass is a negligible factor. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: The exception is the isotopes of very light elements light hydrogen. |