twstws

The example was a little clunky, but I don't find it misleading. A biplot of two normalized variables is elliptical, if the variables are correlated. This particular hand-drawn example does indeed look a bit weird, but that doesn't detract from the main point. It clearly shows the relationship between the original data and the ordination; it's a rigid rotation.

This is easily grasped with a 2d example, despite the fact that PCA makes no sense with only two variables.

It's not dimensionally invalid if you remove the dimensions via normalization.

Each variable is standardized to mean = 0, standard deviation =1. If you reject this as arbitrary, you are rejecting correlation analysis as a whole - this is exactly the same standardization done to two variables in bivariate correlation, extended to a multivariate data set.

PCA is a form of (or at least related to) correlation. With standardization the resulting transformation hihlights variables in the original data that are most highly correlated. Without standardization you're visualizing covariation. Unlike correlation, covariation is influenced by the magnitude of the variables.

By standardizing, you control for differences in the magnitude of the variables, and focus on their inherent variation instead.

In most cases each variable is standardized to put them all on a comparable scale.

> we can't determine if a computed result is actually a sought result or its reflection/negative

That's not how I'd explain it. The 'sought result' and its reflection are not two different things. They are the same thing, differing only in a trivial detail of orientation. The 'negative' of the result conveys exactly the same information as the result.

Good point. I do think the frequency of cases where the only option is private fund raising is much reduced under public systems.

I suspect it is because those with the means to move are generally doing well enough to avoid the failings of the US system.

I can't understand how Americans, who have the least efficient, most expensive health care system in the world, are so quick to write off public healthcare. The idea that government healthcare is more wasteful than a private system is not supported by facts, but the theory is too hard to let go of.

Which is not to say there is a perfect solution. But just about any of the alternatives would be better than the US system.

Except for the US, most of the developed world does, via public health care. It's not perfect, but better than the alternative.

This is truly a wonderful story. But it makes you wonder how many others in a similar situation weren't so fortunate.

I lived in the US for two years, and I never understood the aversion to government healthcare. The Canadian system is far from perfect, and I know there are failures. But it's still a lot better than soliciting for online charity on a case by case basis.

I'm impressed and humbled that it worked in this case. Just a little disturbed that it was necessary at all.

I expect quinoa will be selected for environmental tolerance first. Given how difficult it is to grow in th US, top priority would be getting consistent high yield in North American conditions. Breeding has to meet the farmer's needs before you start considering the consumer.

True, to a point. Debunking one of these in a class is a good exercise. Preparing a lesson takes time, though, especially when you have to respond to something out of the blue. You could easily get caught spending all your limited spare time discussing why these theories aren't science, instead of the ones that are. Evolution is a big topic, and I'd rather spend my limited time dealing with the substantive bits.

This bothers me as a former professor, because these fringe ideas undermine teaching and waste time. Imagine trying to present a lesson on evolution, and one of your students brings this up. You spend a few minutes discussing it. Of course, you've never heard of it before, because it's beyond implausible. So you spend your evening looking into it, and the holes in the theory. Next class you spend more time discussing it. If you're good, the student understands and you move on. If not the student leaves thinking this is a valid alternative viewpoint. And no, an idea does not become valid simply because it's not impossible. It's not unreasonable to demand more than a faint hope probability before judging an idea worth serious discussion.

This happens once, and you can make it a teachable moment. But when the scenario starts to repeat itself it undermines the effort you're putting into teaching real science.

This. The author makes the absurd claim that because many hybrids are fertile, any hybrid could be fertile. Using hybridization between two closely related birds to support the notion that pigs and apes could breed is ridiculous.