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.
1) this doesn't work for cases where your data are positive-definite.
However, let's set that aside. I apologize for being a bit obfuscatory. My point is: If this is the case, then the explanation in the OP is totally misleading, because your data shouldn't look like an ellipsoid, but rather a circle. PCA should only be used in situations where there is a reason to believe there is a mechanistically justifiable "hidden value" that underlies otherwise uncontrolled "independent variables", thus making a dimensional reduction reasonable.
This is not at all the situation that the OP goes over in the first part of the post.
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.
> 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.
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.
America doesn't have a free market healthcare system. It is heavily regulated.
The fact of the matter is that we've somehow managed to end up with a set-up that has just the bad parts from both models. All the runaway costs of regulatory capture, and all of the gross inefficiency of entrenched bureaucracy.
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 am not sure this story is really about the need for socialized medicine. This is more about the need of specialist care and second opinions. If most doctors he saw determined that he most likely would not survive treatment, a socialized medical program may have very well denied payment for such treatments, and he would have had to resort to fundraising anyways.
Maybe if the system was flexible, nimble and could make judgement calls on the side of compassion, it might work, but this is difficult in both public or private sector institutions.
When I was obviously ill and in pain in class the other day (I have some ongoing health issues), I had one of my classmates tell me that Obamacare was going to "destroy the entire country" (exact words) because people like me having health insurance would make doctors become underpaid. I mentioned that my health insurance paid $40,000+ to a certain hospital lately, and he complained that it all went to the hospital, not the doctors.
Then he went on some rant about how all the Canadians have to come down here for health care, and that was why you never hear of Canadians having surgery up there. I mentioned I had a Canadian friend who had a 3 part bowel surgery done recently, with very reasonable waiting times, and that of my several dozen Canadian friends, all but one was satisfied with their system, and he was just like, well, that's anecdotal, the statistics don't bear that out. That's not true at all, but he wouldn't hear of it.
Even before my health problems started, I was pro-single payer. But people like my classmate are everywhere, and seem to think that health care SHOULD be expensive and hard to get. It's inordinately cruel.
I've lived here all my life, but I'm actually moving out of state next month partially because my state's refusing to accept federal funds to cover my demographic next year, and I can't live without the medication I'm on. (Plus going to college out of state is cheaper than going to college in state (!). And they wonder why they have such a brain drain problem...)
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.
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.
The scientist behind this hypothesis makes no such claim:
"For my own part, curiosity has carried me away from my old idea of reality. I no longer know what to believe. Is it possible that so many biologists might be wrong about the nature of human origins? Is it possible for a pig to hybridize with a chimpanzee? I have no way of knowing at present, but I have no logical or evidential basis for rejecting the idea. Before dismissing such a notion, I would want to be sure on some logical, evidentiary basis that I actually should dismiss it. The ramifications of any misconception on this point seem immense." --from macroevolution.net
He says it would be possible and there's evidence in physiology. Saying there's no way or that it would be a miracle (and dismissing it for that) is showing a misunderstanding of evolution. Given enough time and enough tries, it could happen.
A bacterium becoming a mitocondrium within a cell is one of the most astounding miracles of life and scientists have never been able to reproduce it (and mind you, generations of cells come by far easier and faster than of chimps and pigs), yet it happened, perhaps exactly and only once, but it happened and that's why all animals exist.
I think, like the author, that some curiosity and imagination is never a bad thing. It's led to our most interesting discoveries.
1 people think hybrids are sterile, but they're not
2 people think hybrids don't occur in nature, but they do
3 people think only plants hybridize, but animals do to
From this basis, he concludes that a chimp-pig hybrid is plausible, and proceeds to lay out his theory.
The problem is the three facts he starts with are trivial compared to the obstacles raised by PZ Meyer. To take just one, there is the difference in chromosome number. In most cases, if a human ends up with the wrong number of chromosomes, it's a lethal condition. Or you end up with Down's syndrome. With one extra chromosome. The hybrid this guy posits has a dad with 38 chromosomes and a mom with 48.
I could argue that that's not a big deal. In the plant groups I study stranger things happen. But that's in plants. Primates, as I understand it, are much more sensitive to chromosomal abnormalities.
There are many logical, evidential reasons to discount this hypothesis. Again, check out the pz meyer post linked elsewhere. Claiming I don't understand evolution because "given enough tries anything is possible" is facile. Of course anything is possible. But what is probable here?
I think we agree it's highly improbable, but then all major leaps of life and evolution have been. From that ground, I don't see why you seem to be angry at the guy for making a (minimally plausible, not because of the obstacles, but because of what the theory would explain) leap of faith and then wanting to prove his way there scientifically, tagging the whole ordeal 'absurd' and 'ridiculous.'
Sure the hybrid has parents wildly different genetically. But if two individuals who have a high chance of producing fit offspring may by chance produce unfit individuals, then we also agree the hybrid would have to have been a minimally fit individual by chance born from two parents who have a very low chance of doing so. A person with Down syndrome is not a catastrophe of nature, and not fundamentally a disease, such that through successive backcrossing (women with Down syndrome are usually fertile) it could theoretically produce a different kind of Homo that would be fit for some imaginary environment conditions. Or at least would still be a far more intelligent creature than all other animals we have on this planet.
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.
Well that's an interesting point. There is survivorship bias. If the key event for life to thrive never happened, then we wouldn't be here to talk about it, but maybe some other world would have evolved intelligent life instead and they would be.
If you assume that a hybrid is necessary for intelligent life (which is a crazy, unlikely, implausible assumption, I know) then it doesn't matter if it only happens in one out of a billion worlds, on the one world it does happen in, there will be intelligent people around to talk about how unlikely it is.
Now maybe it's not so implausible. Pigs are some of the smartest animals, and something weird happened a few million years ago to jump start human evolution such a crazy amount. Still seems pretty unlikely IMO though, but I'll raise my probability estimate of it slightly.
The thing I find most depressing about these crackpots is that some otherwise productive scientist has to spend an evening debunking their nonsense. And it still doesn't stop.
I taught evolution for undergrads, and occasionally had to deal with these issues from students. It takes time to look into them, and no matter how thoroughly debunked the theory, some kids find them too irresistible to let go of. It undermines real education in the end.
What often distinguishes the crackpot from the visionary is whether they are eventually vindicated. The latter usually begins their career being perceived as the former.
This is a tautology. Of course visionaries are the ones who were vindicated.
That doesn't mean that being perceived as a crackpot is a reliable indicator of being a visionary. It's similar to the argument that opposition equals confirmation -- some religious groups and conspiracy theorists argue that the fact that people oppose them means they are right.
I never said crackpots are guaranteed to be visionaries, though I'm sure it made a convenient strawman for you to argue against. My only point was that you can't be certain either way a priori, to be sure you must actually investigate it (and history tells us even then that's not always going to guarantee certainty).
The depth of investigation should be proportional to the probability of correctness, weighted by the cost of being wrong. Crackpots are called such because the probability of correctness is very low.
Given all the evidence, I consider the MFAP origin hypothesis to be significantly less likely than the primate evolution theory. Extraordinary claims require extraordinary evidence.
to play devil's advocate: consider the extreme absurdity of einstein's theory of relativity, the theory that time may speed up or slow down depending on your velocity.
> some kids find them too irresistible to let go of. It undermines real education in the end.
Teaching is not my cup of tea but isn't an important life lesson teaching kids how to smell bullshit? If they can do that, surely they will know what books to pick and what to learn.
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.
Agree. Debunking this sort of thing would be a fabulous way of describing all manner of genetic principles, particularly the structure of chromosomes, recombination hotspots and haplotypes.
