Has cosmic fine-tuning been refuted?

Introduction

Is the universe fine-tuned for intelligent life? In 2016, astrophysicist Geraint Lewis and cosmologist Luke Barnes, both at the University of Sydney, Australia, waded into this perplexing and controversial arena in a new book entitled A Fortunate Universe: Life in a Finely Tuned Cosmos [Lewis2016]. The core of the Lewis-Barnes book and an accompanying technical paper by Luke Barnes [Barnes2012] is their review of the “cosmic coincidences”:

Carbon resonance and the strong force. If the strong force were slightly stronger or slightly weaker (by just 1% in either direction), there would be no carbon or any heavier elements anywhere

Continue reading Has cosmic fine-tuning been refuted?

Do probability arguments refute evolution?

Introduction

Both traditional creationists and intelligent design writers have invoked probability arguments in criticisms of biological evolution. They argue that certain features of biology are so fantastically improbable that they could never have been produced by a purely natural, “random” process, even assuming the billions of years of history asserted by geologists and astronomers. They often equate the hypothesis of evolution to the absurd suggestion that monkeys randomly typing at a typewriter could compose a selection from the works of Shakepeare, or that an explosion in an aerospace equipment yard could produce a working 747 airliner [Dembski1998; Foster1991; Hoyle1981;

Continue reading Do probability arguments refute evolution?

Evolutionary computing and artificial intelligence

Courtesy Ahmed Medhat Othman

Evolutionary computing

Evolution has been studied mathematically since the early 1900s, with works by D’Arcy Thompson, Ronald Fisher and others. Among other things, these analyses quantified estimates of how many generations of a given species would be required to achieve a certain level of observed change. With the rise of computer technology in the 1960s, computational simulations were devised to study evolution.

From here is was a relatively straightforward step to apply these same evolution-mimicking simulations to other applications as well, an approach originally termed genetic algorithms. In a typical application, potential engineering design parameters

Continue reading Evolutionary computing and artificial intelligence

The future of artificial intelligence: Utopia or dystopia?

MIT cosmologist Max Tegmark is no stranger to controversy. In his 2014 book Our Mathematical Universe, Tegmark proposed that our universe and everything in it are merely mathematical structures operating according to certain rules of logic. He argued that this hypothesis answers Stephen Hawking’s question “What breathes fire into the equations?” — there is no need for anything breathing fire into mathematical equations to create the universe, because the universe is a set of mathematical equations.

In his latest book, Life 3.0: Being Human in the Age of Artificial Intelligence, Tegmark surveys some of the recent advances of the AI

Continue reading The future of artificial intelligence: Utopia or dystopia?

Fine tuning and Fermi’s paradox

A “freakishly” fine-tuned universe

Ever since the time of Copernicus, the overriding worldview of scientific discovery has been that there is nothing special about Earth and humanity: the Earth is not the center of the solar system — we are merely one of several planets orbiting the Sun; the Sun is not the center of the Milky Way — it is merely one of over 100 billion stars in the galaxy; the Milky Way is not the center of the universe — it is merely one of over 100 billion galaxies in the universe; etc. Indeed, this “Copernican principle” has

Continue reading Fine tuning and Fermi’s paradox

New Go-playing program teaches itself, beating previous program 100-0

A potentially momentous milestone has been reached in the decades-old battle between human intelligence and artificial intelligence.

Go playing board

Until 18 months ago ago, the ancient Chinese game of Go had firmly resisted attempts to apply computer technology — the best human players were substantially better than the best computer programs. This changed abruptly in March 2016, when a Google computer program named “AlphaGo” defeated the reigning world champion 4-1, a defeat that shocked many observers, who had not expected to see this for many years.

Now a new computer program, called “AlphaGo Zero,” which literally taught itself

Continue reading New Go-playing program teaches itself, beating previous program 100-0

Fibonacci: A man of numbers

Keith Devlin, well-known mathematician and author, has published two books on Leonardo Pisano (Leonardo of Pisa), better known to many today as “Fibonacci,” short for “filius Bonacci” (son of the Bonacci family), a name ascribed to Leonardo by the 19th century French historian Guillaume Libri. Devlin argues that Leonardo deserves to be ranked among the all-time most influential scientists and mathematicians, mainly for his key role in popularizing the Hindu-Arabic decimal system to Western Europe during the early Renaissance.

Devlin’s books are:

The Man of Numbers: Fibonacci’s Arithmetic Revolution Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who

Continue reading Fibonacci: A man of numbers

Origin of decimal arithmetic with zero pushed back to 3rd century CE

The Bakhshali manuscript

The Bakhshali manuscript is an ancient mathematical treatise that was found in 1881 in the village of Bakhshali, approximately 80 kilometers northeast of Peshawar (then in India, now in Pakistan). Among the topics covered in this document, at least in the fragments that have been recovered, are solutions of systems of linear equations, indeterminate (Diophantine) equations of the second degree, arithmetic progressions of various types, and rational approximations of square roots (more on this below).

The manuscript features an extensive usage of decimal arithmetic — the same full-fledged positional decimal arithmetic with zero system that we

Continue reading Origin of decimal arithmetic with zero pushed back to 3rd century CE

Does mathematical training pay off in the long run?

The California Community College mathematics controversy

Eloy Ortiz Oakley, the Chancellor of the California Community College system, recently recommended that intermediate algebra should no longer be required to earn an associate degree, excerpt for students majoring in some field of mathematics, science or engineering (see also this Physics Today report):

College-level algebra is probably the greatest barrier for students — particularly first-generation students, students of color — obtaining a credential. … [I]f we know we’re disadvantaging large swaths of students who we need in the workforce, we have to question why. And is algebra really the only means we have

Continue reading Does mathematical training pay off in the long run?

Pi and the collapse of peer review

The 1897 Indiana pi episode

Many of us have heard of the Indiana pi episode, where a bill submitted to the Indiana legislature, written by one Edward J. Goodwin, claimed to have squared the circle, yielding a value of pi = 3.2. Although the bill passed the Indiana House, it narrowly failed in the Senate and never became law, due largely to the intervention of Prof. C.A. Waldo of Purdue University, who happened to be at the Indiana legislature on other business. The story is always good for a laugh to lighten up a dull mathematics lecture.

It is worth

Continue reading Pi and the collapse of peer review