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Galileo argued that the giants of folklore, taking human form but at much larger scale, are physically impossible. Similar ideas will lead us to many other paradoxes of dimension.
Joel David Hamkins
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Let us explore the nature of symmetry, beginning simply, but moving steadily to abstraction, eventually to the symmetries of the symmetries themselves…
Joel David Hamkins
Reaching into the higher infinite, we shall undertake various transfinite recursions—the alephs and the beths, the cumulative hierarchy, as well as some…
Joel David Hamkins
3
What is the spectrum of possible behavior at infinity for a real-valued function on the reals? What are the possible rates of growth? What is the…
Joel David Hamkins
Is there any infinity strictly between the infinity of the natural numbers ℕ and the infinity of the real numbers ℝ?
Joel David Hamkins
5
We shall fight the fearsome Hydra and in defeating it we shall see how the existence of transfinite numbers can have surprising consequences within the…
Joel David Hamkins
5
Shall we count together in the ordinals? Let us venture into that transfinite realm beyond infinity. Is infinity even or odd? Can we count to an…
Joel David Hamkins
2
Archimedes finds the area of a parabolic segment by exhausting it with triangles, anticipating key ideas of the calculus by two millennia. We shall…
Joel David Hamkins
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