75 ideas
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
9605 | If a proposition is false, then its negation is true [Brown,JR] |
9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
9630 | The most brilliant formalist was Hilbert [Brown,JR] |
9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
18671 | The ground for an attitude is not a thing's 'goodness', but its concrete characteristics [Ewing] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
21167 | Gravity is unusual, in that it always attracts and never repels [New Sci.] |
21176 | In the Big Bang general relativity fails, because gravity is too powerful [New Sci.] |
21147 | Quantum electrodynamics incorporates special relativity and quantum mechanics [New Sci.] |
21155 | Photons have zero rest mass, so virtual photons have infinite range [New Sci.] |
21161 | In the standard model all the fundamental force fields merge at extremely high energies [New Sci.] |
21146 | Electrons move fast, so are subject to special relativity [New Sci.] |
21148 | The strong force is repulsive at short distances, strong at medium, and fades at long [New Sci.] |
21151 | Gluons, the particles carrying the strong force, interact because of their colour charge [New Sci.] |
21152 | The strong force binds quarks tight, and the nucleus more weakly [New Sci.] |
21142 | Classifying hadrons revealed two symmetry patterns, produced by three basic elements [New Sci.] |
21143 | Quarks in threes can build hadrons with spin ½ or with spin 3/2 [New Sci.] |
21150 | Three different colours of quark (as in the proton) can cancel out to give no colour [New Sci.] |
21145 | The four fundamental forces (gravity, electromagnetism, weak and strong) are the effects of particles [New Sci.] |
21153 | The weak force explains beta decay, and the change of type by quarks and leptons [New Sci.] |
21154 | Three particles enable the weak force: W+ and W- are charged, and Z° is not [New Sci.] |
21156 | The weak force particles are heavy, so the force has a short range [New Sci.] |
21164 | Why do the charges of the very different proton and electron perfectly match up? [New Sci.] |
21170 | The Standard Model cannot explain dark energy, survival of matter, gravity, or force strength [New Sci.] |
21140 | Spin is a built-in ration of angular momentum [New Sci.] |
21149 | Quarks have red, green or blue colour charge (akin to electric charge) [New Sci.] |
21158 | Fermions, with spin ½, are antisocial, and cannot share quantum states [New Sci.] |
21165 | Spin is akin to rotation, and is easily measured in a magnetic field [New Sci.] |
21157 | Particles are spread out, with wave-like properties, and higher energy shortens the wavelength [New Sci.] |
21163 | The mass of protons and neutrinos is mostly binding energy, not the quarks [New Sci.] |
21168 | Gravitional mass turns out to be the same as inertial mass [New Sci.] |
21138 | Neutrons are slightly heavier than protons, and decay into them by emitting an electron [New Sci.] |
21144 | Top, bottom, charm and strange quarks quickly decay into up and down [New Sci.] |
21141 | Neutrinos were proposed as the missing energy in neutron beta decay [New Sci.] |
21169 | Only neutrinos spin anticlockwise [New Sci.] |
21166 | Standard antineutrinos have opposite spin and opposite lepton number [New Sci.] |
21171 | The symmetry of unified electromagnetic and weak forces was broken by the Higgs field [New Sci.] |
21179 | Supersymmetric string theory can be expressed using loop quantum gravity [New Sci.] |
21178 | String theory is now part of 11-dimensional M-Theory, involving p-branes [New Sci.] |
21175 | String theory might be tested by colliding strings to make bigger 'stringballs' [New Sci.] |
21177 | String theory offers a quantum theory of gravity, by describing the graviton [New Sci.] |
21162 | Only supersymmetry offers to incorporate gravity into the scheme [New Sci.] |
21159 | Supersymmetry has extra heavy bosons and heavy fermions [New Sci.] |
21173 | Supersymmetry says particles and superpartners were unities, but then split [New Sci.] |
21172 | The evidence for supersymmetry keeps failing to appear [New Sci.] |
21160 | The Higgs field means even low energy space is not empty [New Sci.] |
21174 | Dark matter must have mass, to produce gravity, and no electric charge, to not reflect light [New Sci.] |