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a hypothesis is an expected answer to a question, usually based on some theory or prior research. hypothesis testing is a method of determining the viability of a hypothesis. let’s use the us presidential election as an example. there are many hypotheses (questions) about how people feel or whom they will vote for. the only way to know the 100% “truth” about the answers to these questions is to ask every single possible voter – something that is impossible, expensive, time consuming etc. instead, we take samples and use statistics to make “best guesses” about the answer to a particular hypothesis. we never know for sure if our conclusion is right at the time we accept/reject it, but these techniques, when used appropriately can get us close to the truth most of the time (which is a lot better than guessing, flipping coins or throwing darts to get answers).

the tricky part about hypothesis testing is that we have to think somewhat backwards about it – we have to test what is known as the “null hypothesis”. as an example, the hypothesis might be “obama is more popular than romney” while the null hypothesis is “there is no difference in popularity between obama and romney”. we focus on the null hypothesis because it tells us exactly what the expected value of our tests should be (obama popularity = romney popularity) and we can collect data and see if it comes out that way (see next section on “significance”). if it does, then we “accept the null hypothesis” and reject our original hypothesis. if the null hypothesis is disproven, we look at the data to see if our original hypothesis holds (obama> romney).

the revival of interest in greek and roman influences also stimulated developments in math and science. the mathematical traditions that governed the conception of the universe were based in greek mathematics that had been preserved and built upon by scientists in muslim lands, such as nasir al-din in the 13th century. the catholic church endorsed the views of ptolemy, the greek philosopher and astronomer who constructed a geocentric theory where all planets, the moon, and the sun revolved around the earth. using calculations from al-din, polish monk and mathematician, nicholas copernicus, concluded that the geocentric theory did not make sense. instead, his data indicated that the earth and all the other planets rotated around the sun, a conclusion that he did not share widely, for fear of retaliation from the church. in fact, his heliocentric theory was not published until after his death in 1543.

the scientist that really got into trouble over the heliocentric theory was italian galileo galilei, who strengthened and improved copernicus' theory. other scientists, such as johannes kepler, had demonstrated that planets also moved in elliptical orbits, and galileo confirmed those theories as well. perhaps most famously, he built a telescope that allowed him to observe the phenomena directly, recording details of heavenly bodies that the ancients could never have known about. galileo's theories were published in the starry messenger in 1610, a highly controversial book criticized by other scientists, as well as officials of the church. galileo made the mistake of making fun of people that disagreed with him, and he was arrested and put on trial, eventually recanting his theory publicly in order to save his own life.