blueollie

How I try to determine what is “right”….

Here is what I am talking about: there is a major issue (say, vaccines, climate change,GMOs, or perhaps a claim from Keynesian economics, or a claim made in the social sciences) and I want to decide: where IS the truth? It is absolute or statistical? The problem is, of course, that many of these claims require a technical background to evaluate properly; one’s “common sense” is woefully insufficient. And, given that my training is narrow (mathematics; in particular, topology) I often do not have the professional background to properly evaluate such claims. Yes, I am subject to being fooled, especially if the conclusion is what I want to hear, or what “feels right” to me, or even, “makes sense” to me. “Figure it out for yourself” has some serious limitations, though there IS a place for it.

Here is an example of a popular math video which, while interesting, valuable and well done, does make an error:

The value is that it shows how something which, while involving infinity, can lead to something practical when one takes a finite approximation. Note: Fourier series is also like that.

The error is technical. Yes, “space filling curves” exist, but it can be shown that they can never be “one to one”.

For the experts: an onto continuous function from a compact space to a Hausdorff space is a homeomorphism (topological equivalence) if and only if the function is one to one. To prove this, note that the continuous image of a compact set is compact and compact sets in a Hausdorff space are closed, hence one to one implies that one has a one to one closed map which makes the inverse map continuous as well.

So: the limit function described in the video cannot have an inverse, though all of the approximating curves can, and these approximating curves can come as close to “filling” the square as one pleases, in terms of running them through a given finite lattice of points.

And the discussion of the “serpentine” curves is excellent; very well done. I’ll used that the next time I teach topology or analysis.

But, most non-mathematicians wouldn’t be able to evaluate this properly and realize that the presentation was just a tiny bit flawed, and yet very good and valuable.

And so, when I read an article on GMOs (appears to be a good article to me) which makes the point that organic foods may well use worse pesticides than GMO ones, among many, many other excellent points (e. g. organic foods could have had deliberately induced mutations via radiation) I really can’t do a technical evaluation of the article.

The same goes for this article on why poor people make so many bad decisions in life (basically, basic survival uses up most of their thought processing abilities).

So, this is how I go about deciding:

1. WHO is writing the article? Is it a journalist (who often will misunderstand technical details) or a specialist? If it is a journalist, I might go see if the the specialists have anything to say.
2. Where die the article appear? Is is in Scientific American? The New York Times? Natural News? (lol).
3. If the author is a specialist:
a. What are the author’s credentials?
b. Is the author STILL respected within the community? Yes, even Nobel laureates in science can go “off of the rails” and go crackpot, but this is usually picked up by the rest of the community.
c. Does the result conform to current consensus? Is there currently a debate within the community? Or is the result really an exciting new conjecture that is still being vetted by the other top guns within the community? Most new conjectures are false, but a few past the test of peer vetting.
4, Who are the critics? Are they themselves specialists or people who just don’t like the results for social or political reasons? (think: some of the criticisms of Steven Pinker’s stuff)

And yes, even with all of this, I am going to get things wrong from time to time.

June 10, 2016 - Posted by | politics/social, science, social/political, Uncategorized

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