The Incredible Power of Being Wrong

Ytopou get very little credit for being wrong. This post is going to look at a couple of situations where being wrong was incredibly important and useful. This usefulness arises from the different way that mathematics treats being wrong, in one special way. Two claims that are supported by mathematical reasoning are these: there are no trees on earth, there is no multi-cellular life on earth. The post looks at why these claims are worth considering, since they are obviously false, and then ends showing an example of how being wrong is actually a core technique in math.

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Image of the Week #190

 

Additional exploration of the cubic Julia conjugate of the cubic Mandelbrot.

IOTW

Sorting Fractions, an Activity

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This post is intended for the teachers of students who are just starting out with fractions, or who need to improve their understanding of fractions. The basic idea is simple: sort a list of fractions into ascending order. This can be done a number of ways, from reducing the fractions to decimal numbers and then sorting those, to using the cross-multiplication trick shown near the bottom of the post. There are also several special purpose shortcuts that solve parts of the problem, making this an exercise in problem solving as well, especially if the fraction sorting is done as a race or under time pressure.

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Being gifted can be a curse, without help.

topThis post begins Occupy Math’s fifth year of publication and it’s on a serious topic: support for gifted kids. The post is motivated by a confrontation at a school board meeting in which the parent of a child with severe learning disabilities took the parent of a gifted child to task. The parent of the disabled student was obscenely and profanely certain that money spent on the gifted student ensured that her child would not get the help they needed. They also felt that being gifted was a privileged state and so support for the gifted was robbing the needy to help those who were already ahead. There are a number of problems with that argument, and that is the subject of this post. Occupy Math has been an advocate for gifted children for decades and so this matter is near to his heart.

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Medicine can learn statistics or kill people — their choice!

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In the first post Occupy Math did on dodgy statistics, Occupy Math talked about the problem of using statistics without understanding them. This leads to the publication of results that are simply wrong. In this post we will look at some other issues –particularly effect size — which lead to the publication of results that are almost worthless. Further, we will find that this lack of interest in the mechanisms of evidence creates a situation where more than half of all treatments prescribed by doctors lack any evidentiary support and a few are actively harmful.

There are two different issues at stake in reporting that a scientific or medical finding is real. The first is to ask what the chance it that the result happened by accident, instead of because some treatment was used. The second is to ask how much difference the effect made — and that is effect size.

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Image of the Week #188

A spiral of spirals of spirals. This fractal uses a Julia-Mandelbrot-Julia iterator. Much of this fractal is pretty boring but it has some highly interesting views deep inside. This is one of them.
IOTW

And now for something completely different … heh, heh!

Occupy Math and his editor debated this post quite a bit. If you get through this post with no issues, without needing to re-read paragraphs, there is a decent chance you are a natural mathematician. More people should be able to get through the post, however, because Occupy Math’s editor made him revise this post more times than any other, ever. If you’re not feeling up to a challenge today, read the last paragraph and go make some hot chocolate or whatever your comfort beverage is.

We are used to multiplying numbers, as in 5×7=35, but there are many different kinds of multiplication in mathematics. That immediately causes a serious problem in understanding: people are so strongly conditioned to thinking of multiplication as something you do with, and only with, numbers that multiplying other types of objects is just weird. In math, multiplication can be any way of taking two objects A and B and getting back a third object C. We use the same notation: C=A×B but the symbol × has thousands of different possible meanings. The good news? This post is only looking at one of them. Occupy Math picked out this one, particular type of “multiplication” because it shows up all over both abstract mathematics and in natural science.

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