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Is Infinity Real?

There is an interesting discussion at Quanta “Solution: ‘Is Infinity Real?’” – Is infinity a real physical phenomenon outside our models? Max Tegmark doesn’t think so – while admitting it is indisputably useful for mathematical models of physics, he believes that nothing is truly continuous – including space and time.
infinity_500Would an infinitely X* phenomenon be amenable to observational evidence? Perhaps not – and if so, we can never count one infinity, making it difficult to assign a likelihood that infinity exists in the territory and not as just convenient approximations in our maps.
Max believes also there are good philosophical reasons to ditch infinity and pitfalls in assuming infinity in mathematical models. Four points that should be understood (which are detailed in the linked Quanta article):
1. The map is not the territory.
2. Infinity is valid in mathematical models and can be very useful.
3. In the physical world, there are compelling practical and philosophical reasons to reject infinity as a default assumption.
4. There will be limiting cases where the mathematical infinity assumption and the physical absence of infinity result in different answers.
 
Finite models are proposed as solutions to replace infinite solutions for a few mathematical problems: Hilbert’s hotel, the 100, 200, 300 Triangle, and the Elliptical Pool Table.
“So the bottom line is: Infinity is permissible in mathematics applied to physics because it makes things convenient and tractable in most cases. However, we must be alert for limiting cases where our models are bound to fail, and we will then need to apply different methods.”
 
*X could represent huge, small, powerful etc..
 
 
I had a discussion about this with a friend Adam Karlovsky – and I was surprised when this just came up on my radar – it’s an interesting read.  We discussed the possibility that infinite randomness would produce an infinite amount of copies of Adam Karlovsky – doing an infinite amount of things.  He said that at one stage this thought kept him up at night.  I have had my doubts about the realism of infinity.

So what do you think?

Is Infinity Real?

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The Simpsons and Their Mathematical Secrets with Simon Singh

You may have watched hundreds of episodes of The Simpsons (and its sister show Futurama) without ever realizing that cleverly embedded in many plots are subtle references to mathematics, ranging from well-known equations to cutting-edge theorems and conjectures. That they exist, Simon Singh reveals, underscores the brilliance of the shows’ writers, many of whom have advanced degrees in mathematics in addition to their unparalleled sense of humor.

A mathematician is a machine for turning coffee into theorems. Simon Singh, The Simpsons and Their Mathematical Secrets

The Simpsons and their Mathematical SecretsWhile recounting memorable episodes such as “Bart the Genius” and “Homer3,” Singh weaves in mathematical stories that explore everything from p to Mersenne primes, Euler’s equation to the unsolved riddle of P v. NP; from perfect numbers to narcissistic numbers, infinity to even bigger infinities, and much more. Along the way, Singh meets members of The Simpsons’ brilliant writing team—among them David X. Cohen, Al Jean, Jeff Westbrook, and Mike Reiss—whose love of arcane mathematics becomes clear as they reveal the stories behind the episodes.
With wit and clarity, displaying a true fan’s zeal, and replete with images from the shows, photographs of the writers, and diagrams and proofs, The Simpsons and Their Mathematical Secrets offers an entirely new insight into the most successful show in television history.

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An astronomer, a physicist, and a mathematician (it is said) were holidaying in Scotland. Glancing from a train window, they observed a black sheep in the middle of a field. “How interesting,” observed the astronomer, “all Scottish sheep are black!” To which the physicist responded, “No, no! Some Scottish sheep are black!” The mathematician gazed heavenward in supplication, and then intoned, “In Scotland there exists at least one field, containing at least one sheep, at least one side of which is black. Simon Singh, The Simpsons and Their Mathematical Secrets

 

 

Simon Singh is a British author who has specialised in writing about mathematical and scientific topics in an accessible manner. His written works include Fermat’s Last Theorem (in the United States titled Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem),The Code Book (about cryptography and its history), Big Bang (about the Big Bang theory and the origins of the universe), Trick or Treatment? Alternative Medicine on Trial[6] (about complementary and alternative medicine) and The Simpsons and Their Mathematical Secrets (about mathematical ideas and theorems hidden in episodes of The Simpsons and Futurama).

Singh has also produced documentaries and works for television to accompany his books, is a trustee of NESTA, the National Museum of Science and Industry and co-founded the Undergraduate Ambassadors Scheme.

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As a society, we rightly adore our great musicians and novelists, yet we seldom hear any mention of the humble mathematician. It is clear that mathematics is not considered part of our culture. Instead, mathematics is generally feared and mathematicians are often mocked. Simon Singh, The Simpsons and Their Mathematical Secrets

Science, Technology & the Future

Bayeswatch – The Pitfalls of Bayesian Reasoning – Chris Guest

Chris Guest - Headshot 1Bayesian inference is a useful tool in solving challenging problems in many fields of uncertainty. However, inferential arguments presented with a Bayesian formalism should be subject to the same critical scrutiny that we give to informal arguments. After an introduction to Bayes’ theorem, some examples of its misuse in history and theology will be discussed.

Chris is a software developer with an academic background in Philosophy, Mathematics and Machine Learning. He is also President of the Australian Skeptics Victorian Branch. Chris is interested in applying critical reasoning to boundary problems in skepticism and is involved in consumer complaints and skeptical advocacy.

 

Talk was held at the Philosophy of Science Conference in Melbourne 2014

Video can be found here.