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To find out more about this topic, we spoke to mathematician Spencer Greenberg, co-founder of Rebellion Research and a contributing member of AskAMathematician where he answers questions on math and physics. He has also created a free Bayesian thinking module that's available online.

The key to Bayesianism is in understanding the power of probabilistic reasoning. But unlike games of chance, in which there’s no ambiguity and everyone agrees on what’s going on (like the roll of die), Bayesians use probability to express their degree of belief about something.

When US presidential candidate Mitt Romney said last year that he was not even going to try to reach 47% of the US electorate, and that he would focus on the 5–10% thought to be floating voters, he was articulating a commonly held opinion: that most voters are locked in to their ideological party loyalty.

But Lars Hall, a cognitive scientist at Lund University in Sweden, knew better. “His calculation, only zeroing in on 10% of voters, is a risky proposition,” he says.

Countries with debt-to-GDP ratios above 90 percent have a slightly negative average growth rate, in fact.

This has been one of the most cited stats in the public debate during the Great Recession.

In a new paper, "Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff," Thomas Herndon, Michael Ash, and Robert Pollin of the University of Massachusetts, Amherst successfully replicate the results.

Some 45 years after Wise found the private edition of the Sonnets, two British book dealers, named John Carter and Graham Pollard, decided to investigate his finds. They re-examined the Browning volume and identified eight reasons why its existence was inconsistent with typical practices of the era. For example, none of the copies had been inscribed by the author, none were trimmed and bound in the customary way, and the Brownings never mentioned the special private printing in any letters, memoirs, or other documents.

The 1847 edition had to be a fake.

According to Gladwell, those experts' intuitions proved correct, and the initial scientific tests that authenticated the statue turned out to have been faulty.

As a formal system, pure math exists only inside our heads. We can try to apply it to the real world, but if we are misapplying it, nothing in the system itself will tell us that we're making a mistake.

When someone says "correlation", they are most commonly talking about Pearson's correlation coefficient, which seeks to gauge whether there's a linear relationship between two variables.

We have known for a long time that Prince Charles' empty sails are so rigged as to be swelled by any passing waft or breeze of crankiness and cant. He fell for the fake anthropologist Laurens van der Post. He was bowled over by the charms of homeopathic medicine. He has been believably reported as saying that plants do better if you talk to them in a soothing and encouraging way. But this latest departure promotes him from an advocate of harmless nonsense to positively sinister nonsense.

The heir to the throne seems to possess the ability to surround himself—perhaps by some mysterious ultramagnetic force?—with every moon-faced spoon-bender, shrub-flatterer, and water-diviner within range.

So this is where all the vapid talk about the "soul" of the universe is actually headed. Once the hard-won principles of reason and science have been discredited, the world will not pass into the hands of credulous herbivores who keep crystals by their sides and swoon over the poems of Khalil Gibran. The "vacuum" will be invaded instead by determined fundamentalists of every stripe who already know the truth by means of revelation and who actually seek real and serious power in the here and now.

First, the Bayesian formalisms in their full form are computationally intractable on most real-world problems.  No one can actually calculate and obey the math, any more than you can predict the stock market by calculating the movements of quarks.

It is facts, not opinions, results, not premises, that are of most importance to the conservative. Conservatives favor a type of freedom, a form of capitalism that works in the real world, not merely one that works according to the speculative “logic” of this or that intellectual.

The notion that trade can define most human relationships rests on the tacit assumption that the individual is a kind atomistic unit without any bonds or ties to the community at large which will profoundly influence his behavior.

Social organization through free contract implies that the contracting units know what they want and are guided by their desires, that is, that they are “perfectly rational,” which would be equivalent to saying that they are accurate mechanisms of desire-satisfaction.

according to Rand, it is better to be consistent in a bad cause than inconsistent in a good one. This has it's basis in one of Rand's oddest prejudices—namely, that human beings are the mere pawns of the logical deductions of their most basic premises.

Rational ignorance occurs when the cost of educating oneself on an issue exceeds the potential benefit that the knowledge would provide.

Much of the empirical support for the idea of rational ignorance was drawn from studies of voter apathy, which reached particularly strong conclusions in the 1950s.[2] However, apathy appeared to decline sharply in the 1960s as concern about issues such as the Vietnam War mounted , and political polarization increased [3]. This suggests that voters' interest in political information increases with the importance of political choices. Additionally, rational ignorance is scrutinized for its broadening effect on the decisions that individuals make in different matters. The investment of time and energy on the specified subject has ramifications on other decision areas. Individuals sometimes forget to take this into account when unconsciously assessing the investment cost versus payout. The external benefits are therefore not adequately taken into account.

If she had a clear, rational case against Libertarianism, wouldn’t she have presented such a case and left it at that? But she does no such thing. Instead, her arguments appear drenched in malice and petty resentment.

Now if Libertarianism really is as bad as Rand would have us believe, why did Rand have to resort to name calling and illogical guilt-by-association arguments? I have several conjectures on this score, as listed below.

There are three doors with a car and two goats placed behind them at random. The game show host knows which is placed where.You must start off by choosing a door.The game show host opens one of the two doors which you did not choose, revealing a goat. (He or she will always open a door that will reveal a goat. He will never open a door which will reveal the car.)The host then offers you the chance to change your original pick.The question is whether it is better to change or stick with your original choice. The answer — which can be and regularly has been demonstrated by running the scenario over and over — is that you are more likely to win if you change. But many, if not most people simply can’t process this and insist that it cannot make any difference whether or not you switch and that your chances of winning are the same either way.

What is physically behind the doors never changes. That’s why you can’t apply mathematical “logic” after the reveal and call it a 50-50 chance. The prize goes behind one door at the start. Either it’s behind the door you choose first, or it isn’t. What happens with the reveal doesn’t physically change that by making it more or less likely.

The seething anger that seems to be an indigenous aspect of the Tea Party movement arises, I think, at the very place where politics and metaphysics meet, where metaphysical sentiment becomes political belief.

When it comes to the Tea Party’s concrete policy proposals, things get fuzzier and more contradictory: keep the government out of health care, but leave Medicare alone; balance the budget, but don’t raise taxes; let individuals take care of themselves, but leave Social Security alone; and, of course, the paradoxical demand not to support Wall Street, to let the hard-working producers of wealth get on with it without regulation and government stimulus, but also to make sure the banks can lend to small businesses and responsible homeowners in a stable but growing economy. 

Mark Lilla argued that the hodge-podge list of animosities Tea party supporters mention fail to cohere into a body of political grievances in the conventional sense: they lack the connecting thread of achieving political power. 

It has many branches, but a prominent one and perhaps the earliest, suggests that we irrationally discard information that is in conflict with our preconceived ideas.

The “rational” (i.e. Bayesian) reaction is to weigh your prior belief in the alternatives.

If people judged war purely on the basis of its obvious, immediate consequences, then, pacifism would be almost universal.

My best explanation is that Bastiat's seen/unseen fallacy is not a general psychological tendency.  Instead, it's an expression of anti-market bias: Since people dislike markets, they're quick to dismiss claims about their hidden benefits. 

The first virtue is curiosity.

The second virtue is relinquishment.

The third virtue is lightness.