If your results are highly counterintuitive | Hacker News Reader

If your results are highly counterintuitive

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60 pointsluu23 comments

..then call the lab's publicist and get your paper out as quickly as possible.

This is where those "A Pepperoni Pizza per day prevents Cancer" headlines come from.

Funny, in pure mathematics the opposite is true. Examples of intuition defying theorems include the Banach–Tarski paradox, cantor sets, uncountability of the reals, gabriel's horn, the list goes on.

That said, when you prove 1 = 0, it's still often wrong.

unless you're working modulo 1

There's no 1 in modulo 1.

fine, 1 ≡ 0

Pretty much every great result in Physics had been counter-intuitive: Gravity, relativity, quantum mech, nuclear physics, semi-conductors, super conductors... I'd say every major advance is science destroyed some conventional wisdom and proved previous intuition wrong.

> every major advance is science destroyed some conventional wisdom and proved previous intuition wrong.

true, but not in contradiction to the original statement that counter-intuitive claims are very likely to be wrong.

Carl Sagan said it well: "But the fact that some geniuses were laughed at does not imply that all who are laughed at are geniuses. They laughed at Columbus, they laughed at Fulton, they laughed at the Wright brothers. But they also laughed at Bozo the Clown."

http://rationalwiki.org/wiki/Galileo_gambit

Yes, but "counter-intuitive" means "probably wrong."

There are many great results that are counter-intuitive, but there are vastly more completely stupid ideas that are counter-intuitive. Ask any academic about their green ink file.

Most new ideas are bad. That doesn't mean "give them a serious look", but it does mean "though you probably won't get far with them."

What is a "green ink file"? Google isn't helping.

A British journalistic term for the frothing of lunatics; may or may not actually be written in green. http://rationalwiki.org/wiki/Green_ink Academics tend to get a lot of correspondence from cranks, often enough to accumulate a collection.

Banach–Tarski paradox

This relies on declaring that 2x == x for sufficiently large x. Which is clearly bullshit: they're not the same, you just can't tell the difference.

cantor sets

The wikipedia page doesn't make clear what's supposed to be contrary to intuition about this. Unless you mean the 2x == x issue wrt cardinality?

gabriel's horn

This one isn't counterintuitive at all; smaller things always have more surface area.

Calculus with infinitesimals works by discarding (symbolic) terms known to be (numerically) below epsilon. Adding things to infinity works the same way.

Both of these will be intimately familiar to anyone who works with algorithmic complexity ("big-O notation") or the IEEE 'float' or 'double' data types.

I'm pretty sure it's not just "sufficiently large x" but rather as x approaches infinity. The properties as you approach infinity are completely different, and counterintuitive, to simply a very very large number.

For the Banach–Tarski paradox it's not enough to have an x that is a \HUGE number of elements, you need an actual infinite. For this and most (all?) of the unintuitive results that use the Axiom of Choice, it is even not enough to have a countable number of elements, like the integer numbers or the rational numbers. You need a bigger infinite like the number of elements in the real number. In this case the number of points in a sphere of real numbers in R^3.

(More info about the different types of infinites: http://en.wikipedia.org/wiki/Cardinal_number )

The "odd" or "counterintuitive" properties as you approach infinity, are a perfectly reasonable consequence of the general agreement to throw away information and treat infinity as all the same.

But they're not all the same, they're simply large enough that any non-infinite numbers are below epsilon.

Much like how infinitesimals are all equal to zero (below epsilon for any non-infinitesimal), but if they were all the same calculus wouldn't work.

In mathematics we don't say that something is "clearly bullshit." We say that it "requires the axiom of choice."

Its like author rediscovered Survivorship bias on his own :)

To me, these examples vividly illustrate the limitations of working with observational data, and are an extension of the standard "correlation vs causation" problem.

I think the pertinent lesson here is that these are still very real problems in the world of "big data": just because you're map-reducing, and throwing around petabytes of data, what you can learn is still limited by the regime under which the data were collected.

Interesting, I wonder if not the latest Spotify Insight is exactly a case of this: https://insights.spotify.com/us/2015/04/22/music-taste-matur...

Endogeneity is not unique to big data. If your results are counterintuitive, it could be because of endogeneity, or your data is just generally messed up, or more subtle statistical issues. Or maybe your analysis is right.

This kind of thinking often promotes confirmation biases.

For a counter-example, consider quantum mechanics.

"Intuitive" means "consistent with prior experience".

If that prior experience is using a prism in a box to take the spectrum of the sun or various kinds of electric lights, and then studying where the bright and dark bands come from? Or shining a laser pointer at a hair to see the diffraction pattern?

Well, playing with that stuff for fun means that a lot of the QM stuff doesn't seem nearly as bizarre as it's said to be.

But then, heavier-than-air flying machines were for a while considered impossible, rather than merely counterintuitive. And now you can get kits to make small ones at the toy store.

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