Applying mathematics takes 'friendship paradox' beyond averages

The friendship paradox is the observation that the degrees of the neighbors of a node within any network will, on average, be greater than the degree of the node itself. In other words: your friends probably have more friends ...

New quantum theory heats up thermodynamic research

Researchers have developed a new quantum version of a 150-year-old thermodynamical thought experiment that could pave the way for the development of quantum heat engines.

The paradox of dormancy: Why sleep when you can eat?

Why do predators sometimes lay dormant eggs, which are hardy, but take a long time to hatch and are expensive to produce? That is the question that researchers from Singapore University of Technology and Design (SUTD) set ...

Deconstructing Schrödinger's cat

The paradox of Schrödinger's cat—the feline that is, famously, both alive and dead until its box is opened—is the most widely known example of a recurrent problem in quantum mechanics: its dynamics seem to predict that ...

Are we looking for happiness in all the wrong places?

If only we could win millions on the lottery—or failing that, at least convince our boss to give us a massive raise. And then, if we could just meet the love of our life on that new dating app, we could Instagram our perfect, ...

Quantum gas turns supersolid

Researchers led by Francesca Ferlaino from the University of Innsbruck and the Austrian Academy of Sciences report in Physical Review X on the observation of supersolid behavior in dipolar quantum gases of erbium and dysprosium. ...

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A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition. Typically, however, quoted paradoxical statements do not imply a real contradiction and the puzzling results can be rectified by demonstrating that one or more of the premises themselves are not really true, a play on words, faulty and/or cannot all be true together. But many paradoxes, such as Curry's paradox, do not yet have universally accepted resolutions. The word paradox is often used interchangeably with contradiction. Literary and other artistic uses of paradoxes imply no contradiction and may be used to describe situations that are ironic. Sometimes the term paradox is used for situations that are merely surprising. An example of a paradox is "This statement is false.", and is explained below.

The logician Willard V. O. Quine distinguishes:

Paradoxes in economics tend to be the veridical type, typically counterintuitive outcomes of economic theory, such as Simpson's paradox. In literature a paradox can be any contradictory or obviously untrue statement, which resolves itself upon later inspection.

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