Scientific reasoning across the multiverse
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With a hat tip to Bruce Webster, more cartoons for the weekend, this time from Jonathan Rosenberg's Scenes from a Multiverse:
Selection bias and confirmation bias (both old favorites in these parts, especially in connection with people's estimates about who says what, how often, and how long they've been doing it), all in one four-panel strip. And then a well-known problem in hypothesis testing that arises repeatedly in reasoning about language:
In the starkly simple form here, this is: if X then Y; Y is true; therefore X is true. That's just affirming the consequent, which is invalid as a general line of inference. Of course, if you discuss alternatives to X and what follows from them, and if you flesh out predict as something more interesting than mere implication, and if you take into account what would make X false, then maybe we can talk.
Matt Enlow said,
July 30, 2010 @ 7:07 pm
This post needs a "Like" button :)
A mathematician said,
July 30, 2010 @ 7:40 pm
That's not modus tollens (which is a perfectly valid form of reasoning)!
Last second update: I notice that you've already corrected yourself. Humph. Where's the fun in that?
Kylopod said,
July 30, 2010 @ 7:52 pm
Is that second strip alluding to string theory?
Sili said,
July 30, 2010 @ 7:59 pm
The accompanying blogpost refers to a new paper that doesn't seem to have much to do with String Theory, but I haven't seen this particular one picked up by any of my regular blogs, yet. I thought it was gonna be about the attempt to explain gravity as an entropic effect, actually. The comments on the linked article doing away with the Big Bang and Dark Energy immediately decry is as crackpottery. I'm not in a position to judge it beyond invoking Sturgeon's Law.
But String Theory works as well (as the butt of the joke, not jury's still out on whether it's a good description of reality as we know it).
Lance said,
July 30, 2010 @ 8:47 pm
And don't miss the mouseover on today's comic!
D.O. said,
July 31, 2010 @ 3:29 am
But, the rabbit black hole does NOT predict that chocolate is delicious. That's a more serious mistake than the reverse modus ponens.
nonpoptheorist said,
July 31, 2010 @ 5:50 am
http://szamitogepesnyelveszet.blogspot.com/2010/07/scientific-approaches-in-syntax.html Something I read recently talking about Abductive Reasoning that helps explain the remaining odds and ends of life?
"The hypothesis to be tested is p, if p is true then, on the basis of the other well-established assumptions, we will expect to observe q, r, s, t …as well. If p is false, there is no obvious connection between q, r, s, t… Yet q, r, s, t…are all true. The likelihood that p is true is therefore increased, inasmuch as it explains the otherwise apparently random coexistence of q, r, s, t…. "
Ahruman said,
July 31, 2010 @ 8:27 am
To be fair, if chocolate had not been tested for deliciousness at the time the prediction was made, and the prediction was backed by an actual chain of reasoning, and chocolate was subsequently found to be delicious, that would be evidence (not proof) in the sense of the hard sciences. Not very strong evidence, mind you.
Apart from, possibly, string theory, the comic lampoons the simulation argument.
rone said,
July 31, 2010 @ 3:45 pm
Holy crap, this is my favorite new comic strip. Thank you, Arnold!
Tom Moertel said,
August 2, 2010 @ 11:56 am
To take the comic strip about scientific evidence entirely too far, let's give it the Bayesian treatment:
A theory predicts that chocolate tastes good. Now an experiment confirms the prediction. In light of this experimental evidence, how much more should we believe the theory?
It depends on our prior beliefs. That is, our new (degree of) belief in the theory should be as before but updated for this new evidence, in light of what we already knew.
This updating boils down to computing an adjustment factor, the ratio of two probabilities: (1) the probability of observing the evidence (that chocolate tastes good), given that the theory is true and (2) the probability of observing the evidence in any case.
Since we already knew that chocolate tastes good, both of these probabilities turn out to be 100%, and the adjustment factor turns out to be 100% / 100% = 1. Our belief in the theory, then, should be adjusted by a factor of 1: not changed at all.
In other words, the new evidence carries no weight. We already knew that chocolate tastes good, so this redundant evidence shouldn't surprise us or cause us to alter our beliefs that depend upon our beliefs about chocolate.
As scientific evidence, it's empty calories.