If your results are highly counterintuitive

http://su3su2u1.tumblr.com/post/114728408943/if-your-results-are-highly-counterintuitive

by luu • 11 years ago

60 23 11 years ago

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blackle3• 11 years ago

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.

hyperpape• 11 years ago

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

blackle3• 11 years ago

unless you're working modulo 1

sytelus• 11 years ago

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.

SideburnsOfDoom• 11 years ago

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

davidgerard2• 11 years ago

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."

tbrownaw3• 11 years ago

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.

steven2012• 11 years ago

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.

myhf• 11 years ago

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

slyall• 11 years ago

..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.

late2part• 11 years ago

For a counter-example, consider quantum mechanics.

tbrownaw3• 11 years ago

"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.

formulaT• 11 years ago

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.

rasz_pl• 11 years ago

Its like author rediscovered Survivorship bias on his own :)

waterisnewcloud• 11 years ago

This kind of thinking often promotes confirmation biases.

simonbyrne• 11 years ago

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.

amag• 11 years ago

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...

If your results are highly counterintuitive

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