I'd like to take this analogy a bit further. Imagine that we are 15th century explorers setting foot in the New World for the first time. Now instead of finding a passage to the Orient, King Ferdinand and Queen Isabella wants us to find extra-terrestrial species. In this alternate Universe, the Church has reason to believe that there are creatures descending from outer space and they want to discover them. Since these alien species haven't been discovered, they don't have a great idea what they look like.
The challenge is that there are a lot of different species of plants and animals that are from this world, but look rather different than what we've seen before. So the challenge is to not have too many false discoveries. The other challenge is that we don't know what alien species look like! We've never seen one before. Now as a conquistador tromping through the Amazon, you are overwhelmed with the possibilities, but and you're searching through unfamiliar land and searching for something that you can't quite identify. It's a real challenge to even define how you go about starting!
Now one way to go about searching for aliens, is to listen to the friars at the monastery back in Espanga who have their own opinions about what extra-terrestrial life looks like. The problem is that their opinions are driven by almost certainly wrong assumptions. Furthermore, every friar you ask has a different opinion. You'll end up with tomes of drawings and the chances that any one of their pictures of a space alien will match up with a real space alien hiding out in the Amazon are zero to nil.
Another way is to make a list of all normal species and then systematically add to it all the normal species that you can identify one-by-one, a long and arduous process. This will definitely discover an alien while if they're out there, but it may take years to go about doing it. Furthermore, since you haven't specified what an alien could be, you might accidentally sort an alien into your dictionary and it might take decades to sort itself out. (Think of the Burgess Shale and the delay in discovering the Cambrian Explosion).
Yet another way is to take the long list of aliens that your friars created and deconstruct them down to their bare anatomies -- find the essential commonalities between all the different models of aliens. You find the essential features that makes something an extraterrestrial and look for that alone, rather than being distracted by superfluous specifications that the friars came up with. May be it's the green blood. Or may be the 3 arms. This approach isn't perfect because you still have to rely on the friars, but you're looking at coarser features than their elaborate drawings that they come up with. This approach is also much faster because you don't have to understand everything before you can start looking for aliens -- after all, falling out of favor with the King during the Inquisition isn't completely ideal *wink-wink*.
So these three different approaches are being used at the LHC to search for new physics. The first approach is a model dependent search. A theorist (one of the sage, but insane friars) comes up with a model that should be searched for. The experimentalist (the conquistador) then has to go and look for that wonderful model, even though it has almost no chance of being precisely right. The next theorist comes along with a slightly different model and the experimentalist has to do a similar search.
The second approach is a model independent search. Here, you take in all the data and you just make sure that it agrees with the Standard Model of Particle Physics prediction. The problem here is that it is really difficult to know what the Standard Model predicts. You have the possibility of normalizing away signals, particularly if you aren't looking for anything in particular.
The final approach is one that I've been championing for several years. Here we strip out all of the details of models and get the essential aspects of the theories down to their cores. We call these stripped down theories Simplified Models. These Simplified Models capture most of the details of full theories, but captures many different theories at the same time. Here you know what you're looking for, but are doing so in a general enough way that you may discover new physics even if you haven't explicitly proposed the correct model, but were in the right ballpark.
Right now Simplified Models have gained a lot of traction at both experiments at the LHC. I'm about to put out a paper soon extending the set of Simplified Models that should be considered. I was also invited to a workshop on the Epistemology of LHC Physics in Aachen, Germany in January, 2012 to speak about what Simplified Models imply for the philosophy of physics.
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