Category: Maths

Science Isn’t Broken: It’s just a hell of a lot harder than we give it credit for.

August 19, 2015

“Taken together, headlines like these might suggest that science is a shady enterprise that spits out a bunch of dressed-up nonsense. But I’ve spent months investigating the problems hounding science, and I’ve learned that the headline-grabbing cases of misconduct and fraud are mere distractions. The state of our science is strong, but it’s plagued by a universal problem: Science is hard — really fucking hard.

“If we’re going to rely on science as a means for reaching the truth — and it’s still the best tool we have — it’s important that we understand and respect just how difficult it is to get a rigorous result. I could pontificate about all the reasons why science is arduous, but instead I’m going to let you experience one of them for yourself. Welcome to the wild world of p-hacking.”

http://fivethirtyeight.com/features/science-isnt-broken/

Planet Money Podcast: Episode 644: How Much Does This Cow Weigh?

August 9, 2015

An interesting phenomenon that has been proven true many times over but seems so counterintuitive it is hard to believe. When asked to guess the weight of a cow or the number of jelly beans in a jar, often the average of all the guesses is extremely close to the correct answer. Even more accurate than many “experts'” guesses. This is an interesting case in which we can prove something true mathematically but still have a hard time believing. Overall great podcast.

http://www.npr.org/sections/money/2015/08/07/430372183/episode-644-how-much-does-this-cow-weigh

The Fallen of World War II

June 12, 2015

A really interesting video giving visual representations of the deaths during World War II. Watching this raises many interesting questions.

How do these visual representations give us a different sense of the war than history books would or simply looking at numbers on a page?

How can we accurately communicate truth?

What does it mean that after a certain point, numbers get so large that that we lose any sense of reality with them?

What is also interesting is that our sense of World War II is painted by our involvement in the war but when you look at the number of people killed, the United States was far from the worst off nation. Because the Soviet Union became our enemy after the war was over, we never really learn about (or care about) how disastrous the war was for them or how much they lost during the war.

How does our historical perspective distort our sense of accuracy and historical truth? What role do our emotions play when it comes to topics like this?

Steven Strogatz on the Elements of Math

June 10, 2015

“Steven Strogatz, an award-winning professor, takes readers from the basics to the baffling in a 15-part series on mathematics. Beginning with a column on why numbers are helpful, he goes on to investigate topics including negative numbers, calculus and group theory, finishing with the mysteries of infinity.”

http://topics.nytimes.com/top/opinion/series/steven_strogatz_on_the_elements_of_math/index.html

Does the Golden Ratio Not Measure Up?

June 10, 2015

“The professor has also conducted numerous experiments in Stanford’s psychology department wherein he asks students to pick out which rectangle they like best out of a diverse group. He said the ones they select are always random and frequently change. If the golden rectangle were really the most pleasing, wouldn’t students choose it every time?”

http://hyperallergic.com/211921/does-the-golden-ratio-not-measure-up/

Don’t Expect Math to Make Sense: On Pi Day, Celebrate Math’s Enigmas

March 15, 2015

“Pi also opens a window into a more uncharted universe, the one consisting of transcendental numbers, which exclude such common irrationals as square and cube roots. Pi is one of the few transcendentals we ever encounter. One may suspect that such numbers would be quite rare, but actually, the opposite is true. Out of the totality of numbers, almost all are transcendental. Pi reveals how limited human knowledge is, how there exist teeming realms we might never explore.”

Mathematical model explains marital breakups

March 10, 2015

“Most people know love takes work, and effort is needed to sustain a happy relationship over the long term, but now a mathematician in Spain has for the first time explained it mathematically by developing a dynamical mathematical model based on the second law of thermodynamics to model ‘sentimental dynamics.’ The results are consistent with sociological data on marriage breakdowns.”

http://phys.org/news193298961.html

ARE TODAY’S MOST ADVANCED MATHEMATICAL PROOFS IMPOSSIBLE TO VERIFY?

March 10, 2015

“While mathematics remains our most rigorous form of knowledge, the extreme complexity and length of some recent proofs have made them nearly impossible to check. As proofs continue to grow more complicated, mathematicians worry they will have to accept a greater degree of uncertainty than they’ve traditionally been comfortable with.”

http://seedmagazine.com/content/article/mathematical_uncertainty