“Today the major reason for our interest in Flatland is that for the first time we can achieve some of the dreams of our ancestors a century ago and obtain direct visual experience of phenomena in a dimension higher than our own.” FirstsReasonDreamTodayInterestAchieveCenturyHigherMajorsFirst TimeDirectLogicCertaintyUncertaintyReasoningVisualsDimensionsAncestorOntology Author:Thomas Banchoff
“My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. How do I know this? Because I have studied it from all sides for many years; because I have examined all objections which have ever been made against the infinite numbers; and above all because I have followed its roots, so to speak, to the first infallible cause of all created things.” KnowsYearsFirstsMadeSpeakCausesSidesNumbersRocksTheoryReturnRootsLogicInfiniteCertaintyUncertaintyFirmReasoningArrowsObjectionsInfallibleOntologyArcher Author:Georg Cantor
“This view [of the infinite], which I consider to be the sole correct one, is held by only a few. While possibly I am the very first in history to take this position so explicitly, with all of its logical consequences, I know for sure that I shall not be the last!” KnowsFirstsLastsViewsPositionConsequenceLogicInfiniteCertaintyUncertaintyReasoningLogicalSoleOntology Author:Georg Cantor
“The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.” WorldMindFirstsFormOrderThreeNumbersTypeLogicThirdsAbsolutesInfiniteIndependentAriseCertaintyMathematicalUncertaintyReasoningMagnitudeOntologyFinite Number Author:Georg Cantor
“Many of life's decisions are hard. What kind of career should you pursue? Does your ailing mother need to be put in a nursing home? You and your spouse already have two kids; should you have a third?such decisions are hard for a number of reasons. For one the stakes are high. There's also a great deal of uncertainty involved. Above all, decisions like these are rare, which means you don't get much practice making them. You've probably gotten good at buying groceries, since you do it so often, but buying your first house is another thing entirely.” NeedsShouldFirstsKindMeanDoeTwoHardReasonHomeKidsMotherHouseDecisionDealsNumbersCareersPracticeInvolvedThirdsPursueUncertaintyBuyingStakesSpouseNursingGroceriesNursing Home Author:Steven Levitt