Paradoxes of set theory | Paradoxes of infinity
Galileo's paradox is a demonstration of one of the surprising properties of infinite sets. In his final scientific work, Two New Sciences, Galileo Galilei made apparently contradictory statements about the positive integers. First, some numbers are squares, while others are not; therefore, all the numbers, including both squares and non-squares, must be more numerous than just the squares. And yet, for every number there is exactly one square; hence, there cannot be more of one than of the other. This is an early use, though not the first, of the idea of one-to-one correspondence in the context of infinite sets. Galileo concluded that the ideas of less, equal, and greater apply to (what we would now call) finite sets, but not to infinite sets. In the nineteenth century Cantor found a framework in which this restriction is not necessary; it is possible to define comparisons amongst infinite sets in a meaningful way (by which definition the two sets, integers and squares, have "the same size"), and that by this definition some infinite sets are strictly larger than others. The ideas were not new with Galileo, but his name has come to be associated with them. In particular, Duns Scotus, around 1302, compared even numbers to the whole of numbers. (Wikipedia).
Relativity: how people get time dilation wrong
Einstein’s special theory of relativity is notorious for being easy to misuse, with the result that sometimes result in claims of paradoxes. When one digs more carefully into the theory, you find that no such paradoxes actually exist. In this video, Fermilab’s Dr. Don Lincoln describes a
From playlist Relativity
Twins Paradox: The Complete Explanation
The twins paradox is easily the most famous paradoxes of all time. Using spacetime diagrams and the rules of relativity, we can show the paradox only happens because people are being lazy with special relativity. http://brilliant.org/ScienceAsylum ________________________________ VIDEO ANN
From playlist Einstein's Relativity
The Raven Paradox - A Hiccup in the Scientific Method
Sign up to brilliant.org with this link to receive a 20% discount! https://brilliant.org/upandatom/ This video has been heavily influenced by the introductory Philosophy of Science book "Theory and Reality" by Peter Godfrey-Smith. I highly recommend this book to anyone interested in philo
From playlist Paradoxes
What is General Relativity? Lesson 69: The Einstein Equation
What is General Relativity? Lesson 69: The Einstein Equation Having done so much work with the Einstein tensor, the interpretation of the Einstein equation is almost anti-climatic! The hard part is finding the Newtonian limit in order to understand the constant of proportionality between
From playlist What is General Relativity?
Even More Paradoxical: The Twin Paradox in Curved Spacetime
The Twin Paradox gets a stranger, even more mind-bending upgrade in General Relativity's world of curved spacetime. We explore the surprising and relatively unknown results to these new scenarios, while getting our toes wet in some of GR's conceptual frameworks. And finally, after several
From playlist Summer of Math Exposition Youtube Videos
So with these enormous numbers, it means there should be lots of chances for life to spark and exist, but where are all the aliens? This is the Fermi paradox. In this video, we discuss a very short introduction to the Fermi paradox and talk about basic background information about the spac
From playlist Faster Than Light Into the Past?
Mario Livio on Galileo, Science Denial, and the Future of the Universe | Closer To Truth Chats
Mario Livio talks Galileo, the Hubble Telescope, modern and historical science denial, and the far future of life in the universe. He also discusses his book, Galileo: And the Science Deniers, which provides a fresh interpretation of the life of Galileo Galilei, one of history's greatest a
From playlist Closer To Truth Chats
The Role of Theory in Science - David Gross
Speaker : David Gross (KITP, Santa Barbara) Date and Time : 28 Dec 2009, 05:30 PM Venue : J. N. Tata Auditorium, IISc, Bangalore On the occasion of the inauguration of the International Centre for Theoretical Sciences, TIFR, I shall share some of my observations and conclusions as to the
From playlist Public Lectures
Umberto Bottazzini, The immense sea of the infinite - 10 aprile 2019
https://www.sns.it/it/evento/the-immense-sea-of-the-infinite Umberto Bottazzini (Università degli Studi di Milano) The immense sea of the infinite Abstract In a celebrated talk Hilbert stated that the infinite was nowhere to be found in the real, external world. Yet from time immemorial
From playlist Colloqui della Classe di Scienze
Phsyics 20B. Cosmology. Lec. 5: Isaac Newton
UCI Physics 20B: Cosmology (Winter 2015) Lec 05. Cosmology -- Isaac Newton View the complete course: http://ocw.uci.edu/courses/physics_20b_cosmology.html Instructor: James Bullock, Ph.D. License: Creative Commons CC-BY-SA Terms of Use: http://ocw.uci.edu/info More courses at http://ocw.
From playlist Physics 20B: Cosmology
Relativity & Gravity - The Complete History
Einstein (and his friends) came to some pretty crazy conclusions about gravity. By the end of this video, you'll have no choice but to come to the same conclusions. We'll start with a little background though: From Galileo in 1632 all the way to Einstein in 1905 and 1915. _________________
From playlist Einstein's Relativity
Russell's Paradox - A Ripple in the Foundations of Mathematics
Bertrand Russell's set theory paradox on the foundations of mathematics, axiomatic set theory and the laws of logic. A celebration of Gottlob Frege. Thank you to Professor Joel David Hamkins for your help with this video. Hi! I'm Jade. Subscribe to Up and Atom for physics, math and com
From playlist Math
Aristotle's Wheel Paradox - To Infinity and Beyond
Sign up to Brilliant with this link to receive a 20% discount! https://brilliant.org/upandatom Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :) https://www.patreon.com/upandatom Visit the Up and Atom store https://store.nebula.app/collectio
From playlist Math
The Nature of Infinity: Hilbert's Hotel and Equinumerosity
We follow the allegory of Hilbert's hotel and the paradox of Galileo and what these teach us about equinumerosity and the varying nature of infinities. 0:00 Hilbert's Hotel 04:01 The Infinite Bus 08:06 The Infinite-Infinite Train 12:30 Equinumerosity & The Infinity of the Irrationals
From playlist Summer of Math Exposition 2 videos
Astronomy Cast Episode 314: Acceleration
Put that pedal to the metal and accelerate! It's not just velocity, but a change in velocity. Let's take a look at acceleration, how you measure it, and how Einstein changed our understanding of this exciting activity.
From playlist Astronomy Cast
Aristotle vs. Galileo- The Race of All Time
Do all objects fall at the same rate, regardless of weight or size? License: Creative Commons BY-NC-SA More information at http://k12videos.mit.edu/terms-conditions
From playlist Physics
Astronomy - General Relativity (3 of 17) What is the Equivalence Principle?
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn The Equivalence Principle in 3 examples: 1) The observers can not tell the difference of playing volleyball on Earth or
From playlist ASTRONOMY 32 GENERAL RELATIVITY
Professor Adrian Moore journeys through philosophical thought on infinity over the last two and a half thousand years. This comes from a BBC radio series. For a good introduction to the philosophy of mathematics, check out: https://www.youtube.com/watch?v=UhX1ouUjDHE 00:00 Horror of the I
From playlist Logic & Philosophy of Mathematics
What IS a Number? As Explained by a Mathematician
NEXT VIDEO IN SERIES https://www.youtube.com/watch?v=QO9a7h87DbA See how we develop even more concepts from this mathematical foundation. Ever wondered how numbers are actually defined? In this video, you'll learn the most common way it's done by mathematicians. MY PATREON IS NOW LIVE! B
From playlist Summer of Math Exposition 2 videos
Teach Astronomy - Thought Experiments
http://www.teachastronomy.com/ Scientists make measurements and observations and they do experiments. However sometimes they also do thought experiments or Gedanken experiments in the German. A thought experiment is a situation where a scientist uses an idealized situation to understand
From playlist 01. Fundamentals of Science and Astronomy