The new riddle of induction

Suppose every blueberry you've observed to date has been blue. You take this to be evidence for:

(H1) All blueberries are blue.

As a consequence, you predict:

(P1) The first blueberry I observe on February 11, 2012 will be blue.

Now, define "bleen" to mean "blue until February 10, 2012--green thereafter". By this definition, every blueberry you've observed to date has been bleen. You take this to be evidence for:

(H2) All blueberries are bleen.

As a consequence, you predict:

(P2) The first blueberry I observe on February 11, 2012 will be bleen.

A blueberry that will be bleen on February 11, 2012, though, will be green--not blue. Thus, (P2) flatly contradicts (P1). Is there any evidence that favors (H1) over (H2)? We might complain that (H2) is couched in terms of a derivative property--"bleen" is defined in terms of "blue" and "green". We might take this observation to favor (H1), and therefore (P1).

But define "grue" to mean "green until February 10, 2012--blue thereafter". Imagine a culture that only understands "bleen" and "grue"--not "green" and "blue". To them, "green" means "grue until February 10, 2012--bleen thereafter", while "blue" means "bleen until February 10, 2012--grue thereafter". Their complaint about (H1) is that it is couched in terms of a derivative property--"blue" is defined in terms of "bleen" and "grue". They take this observation to favor (H2), and therefore (P2). Could we really be right, and they really be wrong?

What else could favor (H1) over (H2)? If nothing, isn't this a problem for every hypothesis of the form "All X are Y"? And don't we (implicitly) make predictions founded upon such hypotheses in our everyday reasoning? Doesn't this problem undermine the very way in which we learn from our observations and experiences?

Nukes for the environment

So the US approved the first nuclear reactors since 1979 with the Three Mile Island boogie. The real question is why this is the first approval since then? Why does this approval come so close to the near catastrophe in Japan? Heck Germany (the ones trying to tell everyone else how to run their balance sheets) has gone as far to say they are going to shut down all of their reactors to avoid the same potential fate as Japan. Now that the approvals are out in the open, I suspect you'll start seeing more sensational news reporting on radiation leaks at existing plants - heck in VT there were reports of radioactive fish being caught right outside the cooling towers sparking mass hysteria. A majority of media outlets are leaving out details, such as testing at the facilities report no radiation leaks and that other fish in the same stream at the other end of the state, 150 miles away, have the same radiation levels - good little tidbit which changes the severity of the situation. Not to mention, in America we don't build reactors on fault lines or earthquake central.

Not all that long ago, I lived 10 miles from an aging plant. Sure it wasn't the greatest landmark the area has known, but I really didn't mind it. Some of my lesser intelligent friends were even concerned for my life, I was moving so close to a reactor after all. These same friends also think that radiation causes three legged frogs and birth defects: lead and fertilizers cause that stuff, all radiation does is kill you or give you cancer. All I have to say is it's about damn time the flukes on capital hill moved along something that is actually beneficial to the prosperity of this great nation. There has never been a better thing for the environment than nuclear power - it's basically steam on steroids. No real waste products, no hazardous green house gases and jigga-what-whats (see what I did there?) of power for the masses. Sure you need to bury the spent fuel rods in barren deserts forever, but is that really all that bad?

All I can say is, mother nature loves nuclear power and I'm sure the tree huggers are loving this. Plus it just might drive the cost of electricity down to where plug-in electric cars are cost effective in a person's lifetime.

Why isn't mathematics sensitive to experimental scrutiny?

Suppose I have two containers, both full of (what I believe to be) a single fluid. Each container's volume is 500 mL. I then empty the contents of the two containers into a third, the volume of which is 1000 mL. To my surprise, the container is only 75% full--it holds just 750 mL of the fluid. How should I revise my beliefs in light of this discovery?

Among my presumptions was that volume is additive when mixing a single fluid. One conclusion that suggests itself is that the two containers in fact contained different fluids. Another is that volume is not necessarily additive.

A third conclusion, however, does not suggest itself: 500 + 500 = 750. Why not? What is it about 500 + 500 = 1000 that justifies my willingness to concede that the fluids were different, or that volume is not necessarily additive, but not that 500 + 500 = 750? The surprising outcome of my experiment shows that at least one of my presumptions is incorrect, but it does not indicate which. What is it about this experiment that prevents it from lending support to the hypothesis that 500 + 500 = 750?

I just wanna note real quick...

...that we nailed Nevada, Groundhog Day, and the Super Bowl winner. So...word to ya motha.

Onto Colorado and Minnesota we go:

1st: Rom Mittney

2nd: Sant Rickorum

3rd: Ging Newtrich

4th: Pan Roul

Same for bof states. Be amazed, y'all.

Groundhog Day 2012 prediction

Punxsutawney Phil, perhaps the most famous groundhog (aka whistle-pig), is due to make his appearance this Thursday, Feb. 2nd. The appearance the country is really awaiting with bated breath is that of his shadow.

[polldaddy poll=5900524]

The grand holiday of Groundhog day takes its roots from a similar European tradition, wherein a badger or some other non-groundhog little rat guy comes out, does a little dance and then the elders determine whether or not you're going to need to wear a parka for the next few days. The American version of this exciting time dates back to as early as the mid-19th century in the middle of nowhere, Pennsylvania. Since then, many cities have adopted their own groundhog to come out and try to spy his shadow. However, Punxsutawney Phil, or Seer of Seers Prognosticator of Prognosticators Weather Predictor Extraordinaire as he's sometimes known, is by far the most revered. He is so revered, in fact, that the so-called Inner Circle was established to protect and advise him. The Inner Circle is comprised of 15 members with such meaningful titles as "Stump Warden," "Thunder Conductor," and my personal favorite, "Big Chill."

(SPOILER ALERT: If you do not wish to know the outcome of this year's coming Groundhog day, navigate yourself away from this page. Perhaps one of our other gripping and timely posts would better interest you and possibly your friends.)

Here at Defeasible Reasoning, we take pride in knowing things before you do and then rubbing your face in it telling you about it. To that end, we've pored over recent trend data to bring you such predictions as the outcome for the Florida Republican Primary and the Nevada Republican Caucus. Whether Punxsutawney Phil will see his shadow is equally important. After months of observing the trends in atmospheric pressures, barometric altitudes, cloud form patterns, Sun illumination angles and temperature inversion data, we've come to the conclusion that Punxsutawney Phil will indeed see his shadow at approximately 7:22am EST. Go get those heavy winter coats out of the attic, folks, it's going to be a 6 week longer Winter.

 

 

EDIT: As predicted, Punx Phil crawled out of his hidey hole to be surprised by his shadow, thus predicting 6 more weeks of Winter. You're welcome for the heads up.

Two Americas

There are two kinds of Americans. The first are autistic. The second are drunk, drugged up, and manically depressed. Why? Don't ask me. But, here's a theory: the economy hates the second group, just like you hate your drunk, drugged up, and manically depressed cousin (and yes, the Oxford comma is absolutely essential) who just eats all your food and complains about life being unfair.

Now, Mr. Scientist (you might say), what use is this theory? Just seems like you're hating on people who already hate themselves. Well, I am doing just that. But, I'm also doing science. If my theory is right, here's a prediction it makes: the second group has shitty economic fortunes compared with the first. Ta da...

From personality to neuropsychiatric disorders, individual differences in brain function are known to have a strong heritable component. Here we report that between close relatives, a variety of neuropsychiatric disorders covary strongly with intellectual interests. We surveyed an entire class of high-functioning young adults at an elite university for prospective major, familial incidence of neuropsychiatric disorders, and demographic and attitudinal questions. Students aspiring to technical majors (science/mathematics/engineering) were more likely than other students to report a sibling with an autism spectrum disorder (p = 0.037). Conversely, students interested in the humanities were more likely to report a family member with major depressive disorder (p = 8.8×10⁻⁴), bipolar disorder (p = 0.027), or substance abuse problems (p = 1.9×10⁻⁶). A combined PREdisposition for Subject MattEr (PRESUME) score based on these disorders was strongly predictive of subject matter interests (p = 9.6×10⁻⁸). Our results suggest that shared genetic (and perhaps environmental) factors may both predispose for heritable neuropsychiatric disorders and influence the development of intellectual interests.

You know whose economic fortunes are better than humanities majors? Science majors. Just look at those p-values. Hot damn. I didn't pay much attention in AP statistics (I just remember gems like "power is desirable", and "we want small Ps"), but this looks pretty sciency to me. And the authors are from Princeton!

OK, so, my theory sucks. Granted. But how about them p-values? And for the record, I belong to the first group, have shitty economic fortunes, and I spend my days eating other people's food and complaining about the unfairness of life. I am the two Americas.