19 ideas
| 15717 | Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan] |
| Full Idea: The problem with the Axiom of Choice is that it allows an initiate (by an ingenious train of reasoning) to cut a golf ball into a finite number of pieces and put them together again to make a globe as big as the sun. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 9) | |
| A reaction: I'm not sure how this works (and I think it was proposed by the young Tarski), but it sounds like a real problem to me, for all the modern assumptions that Choice is fine. |
| 15712 | 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan] |
| Full Idea: You have 1 and 0, something and nothing. Adding gives us the naturals. Subtracting brings the negatives into light; dividing, the rationals; only with a new operation, taking of roots, do the irrationals show themselves. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 1 'Mind') | |
| A reaction: The suggestion is constructivist, I suppose - that it is only operations that produce numbers. They go on to show that complex numbers don't quite fit the pattern. |
| 15711 | The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan] |
| Full Idea: The rationals are everywhere - the irrationals are everywhere else. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 1 'Nameless') | |
| A reaction: Nice. That is, the rationals may be dense (you can always find another one in any gap), but the irrationals are continuous (no gaps). |
| 15714 | 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan] |
| Full Idea: The 'commutative' laws say the order in which you add or multiply two numbers makes no difference; ...the 'associative' laws declare that regrouping couldn't change a sum or product (e.g. a+(b+c)=(a+b)+c ). | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Tablets') | |
| A reaction: This seem utterly self-evident, but in more complex systems they can break down, so it is worth being conscious of them. |
| 15715 | 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan] |
| Full Idea: The 'distributive' law says you will get the same result if you first add two numbers, and then multiply them by a third, or first multiply each by the third and then add the results (i.e. a · (b+c) = a · b + a · c ). | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Tablets') | |
| A reaction: Obviously this will depend on getting the brackets right, to ensure you are indeed doing the same operations both ways. |
| 15713 | The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan] |
| Full Idea: The claim that no number is greater than a million is confirmed by the first million test cases. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Intro') | |
| A reaction: Extrapolate from this, and you can have as large a number of cases as you could possibly think of failing to do the inductive job. Love it! Induction isn't about accumulations of cases. It is about explanation, which is about essence. Yes! |
| 20657 | There are 23 core brain functions, with known circuit, transmitters, genes and behaviour [Watson] |
| Full Idea: In 2014 the National Institutes of Mental Health published a list of 23 core brain functions and their associated neural circuitry, neurotransmitters and genes, and the behaviour and emotions that go with them. | |
| From: Peter Watson (Convergence [2016], 16 'Physics') | |
| A reaction: They were interested in the functions behind mental health, but I am interested in the functions behind our belief systems, which might produce a different focus. Sub-functions, perhaps. |
| 20656 | Traditional ideas of the mind were weakened in the 1950s by mind-influencing drugs [Watson] |
| Full Idea: One development in particular in the 1950s helped to discredit the traditional concept of the mind. This was medical drugs that influenced the workings of the brain. | |
| From: Peter Watson (Convergence [2016], 16 'Intro') | |
| A reaction: This explains Ryle's 1949 book, and the Australian physicalists emerging in the late 1950s. Philosophers don't grasp how their subject is responsive to other areas of human knowledge. Of course, opium had always done this. |
| 7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
| Full Idea: Libet himself points out that the conscious decisions still have the power to 'endorse' or 'cancel', so to speak, the processes initiated by the earlier cortical activity: no action will result if the action's execution is consciously countermanded. | |
| From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by David Papineau - Thinking about Consciousness 1.4 | |
| A reaction: This is why Libet's findings do not imply 'epiphenomenalism'. It seems that part of a decisive action is non-conscious, undermining the all-or-nothing view of consciousness. Searle tries to smuggle in free will at this point (Idea 3817). |
| 6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
| Full Idea: Libet found that a subject's conscious choice to move was about a fifth of a second before movement, and thus later than the onset of the brain's so-called 'readiness potential', which seems to imply that unconscious processes initiates action. | |
| From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.9 | |
| A reaction: Of great interest to philosophers! It seems to make conscious choices epiphenomenal. The key move, I think, is to give up the idea of consciousness as being all-or-nothing. My actions are still initiated by 'me', but 'me' shades off into unconsciousness. |
| 20655 | Humans have been hunter-gatherers for 99.5% of their existence [Watson] |
| Full Idea: Anthropology shows that the hunter-gathering lifestyle has occupied 99.5 per cent of the time humans have been on earth. | |
| From: Peter Watson (Convergence [2016], 13 'Emergence') | |
| A reaction: If you are trying to understand humanity, you ignore this fact at your peril. Even agriculture is only a tiny part of our history, and that only disappeared as a major human activity (in many nations) in the last hundred years. |
| 20650 | The Uncertainty Principle implies that cause and effect can't be measured [Watson] |
| Full Idea: The Uncertainty Principle implied that in the subatomic world cause and effect could never be measured. | |
| From: Peter Watson (Convergence [2016], 05 'Against') | |
| A reaction: The fact that it can't be measured does not, presumably, entail that it doesn't exist. Physicists seem to ignore causation, rather than denying it. Can causation be real if it only exists at the macro-level, as an emergent phenomenon? |
| 20649 | The interference of light through two slits confirmed that it is waves [Watson] |
| Full Idea: Thomas Young in 1803 confirmed the idea of Huyghens that light is waves, showing how light passing through two slits produces an interference pattern that resembles water waves sluicing through two slits. | |
| From: Peter Watson (Convergence [2016], 04 'Conception') | |
| A reaction: The great puzzle emerges when it also turns out to be quantised particles. |
| 20661 | Electrons rotate in hyrogen atoms 10^13 times per second [Watson] |
| Full Idea: In the hydrogen atom the electron rotates some 10,000 billion times per second. | |
| From: Peter Watson (Convergence [2016], 18 'Evolutionary') | |
| A reaction: That's an awful lot. Is it at the speed of light? |
| 20647 | Quantum theory explains why nature is made up of units, such as elements [Watson] |
| Full Idea: Planck's quantum idea explained so much, including the observation that the chemical world is made up of discrete units - the elements. Discrete elements implied fundamental units of matter that were themselves discrete (as Dalton had said). | |
| From: Peter Watson (Convergence [2016], 4 'Intro') | |
| A reaction: The atomic theory was only finally confirmed by Einstein in 1905. This idea implies that the very lowest level of all must have distinct building blocks, but so far we have got down to 'fields', which seem to be a sort of 'foam'. |
| 20654 | Only four particles are needed for matter: up and down quark, electron, electron-neutrino [Watson] |
| Full Idea: We need twelve particles in the master equation of the standard model, but it is necessary to have only four to build a universe (up and down quarks, the electron and the electron neutrino (or lepton). The existence of the others is 'a bit of a mystery'. | |
| From: Peter Watson (Convergence [2016], 11 'First Three') |
| 20651 | The shape of molecules is important, as well as the atoms and their bonds [Watson] |
| Full Idea: Pauling showed that the architecture - the shape of molecules was relevant (as well as the bonds). This meant that molecules were just as important as atoms in the understanding of matter. Molecules were not just the sum of their parts. | |
| From: Peter Watson (Convergence [2016], 05 'Three') | |
| A reaction: If Aristotle struggled to understand matter, then so should modern philosophers. This involves thermodynamics and chemistry, as well as quantum theory. |
| 20652 | In 1828 the animal substance urea was manufactured from inorganic ingredients [Watson] |
| Full Idea: In 1828 Wöhler, in an iconic experiment, had manufactured an organic substance, urea, hitherto the product solely of animals, out of inorganic materials, and without any interventions of vital force. | |
| From: Peter Watson (Convergence [2016], 06 'Inorganic') | |
| A reaction: For reductionists like me, the gradual explanation of life in inorganic terms is the great role model of explanation. I take it for granted that the human mind will go the same way, despite partisan resistance from a lot of philosophers. |
| 20658 | Information is physical, and living can be seen as replicating and preserving information [Watson] |
| Full Idea: In passing information, physical changes take place, and information is thus physical. On this account, the act of living can be seen as replicating and preserving the information that a living body is comprised of. | |
| From: Peter Watson (Convergence [2016], 17 'Dreams') | |
| A reaction: [He emphasises 'the act' of living, rather than a life] |