Monday, December 1, 2014

The Lock Mess Monstrosity

I came across this story, with a moral so unintentionally genetic that I had to pass it on.  Exercise, Aesop's fable-style.
"I had just finished taking a nice, long, luxuriant hot and foamy shower after working up a hearty sweat at the local gym.  I got my towel and began to dry myself off, in a soft, slow, leisurely way, before leaving.   Then, having largely dried my (lissome) body, I felt a bit chilled and, covering myself somewhat modestly with the (one small) towel wrapped around my waist, I returned to my locker.  Or I thought I did...
I don't go to the gym all that often, since I can get the sort of exercise I like, and also nice languid baths or showers, at home, sometimes with company--if you know what I mean.  But this time I paid the price for my irregular gym workouts.  I could not remember exactly which locker I had used, and of course, like everyone else, I'd locked it.  But now, to my sheer, or one might say naked, horror, I looked down upon row after row of lockers.  Which one was mine? 

OMG!  They're all exactly the same!!
You might think that some sort of trial and error would help, but unfortunately, all the lockers looked exactly the same, and the gym used the same type of lock on each one.  When you arrive, they give you a towel and a slip of paper with the locker number and lock combination on it.  Of course, stupid me!, I had read the number, thought I knew it, and left the paper in the locker when I shut the door, and slithered off to the shower.
So what was I to do? I could make a guess at which locker was mine, and try the combination, or, rather, various combinations that seemed like what I remembered.  But that's like trying to remember the phone number of someone you met last night at a bar and wanted to meet again, but knowing you didn't have all the digits lined up correctly (in your mind).  I mean, how many numbers can you try, or do you just go back to the same bar and hope you find your ideal there again--but you really can't remember exactly how that perfect person looked (it was dark, you'd had a few, you know?).
Could I try every possible combination on every lock on every locker? In fact, I finally had to give up and, rather chilled and hardly 'decent' (I had just the one small towel), slithered out into hallway to the custodian's office, my smooth skin still moist and glistening, and asked for help. They know the combinations, of course!  And there's no guessing with locks, once you know the lock, if you also know the combination, you're sure to be able to open it.  But since I didn't remember the locker number....
For me this really was a lock mess monstrosity: it's what is called a many-to-many problem among locks and combinations.  If you really want to be able to open each lock predictably, there needs to be another way.   
And there is: the lock company also put a key slot in the bottom of the lock, and the custodian had the master key.  When I discovered this, I was more than a little embarrassed, and blushed all over, but I was saved!"
Moral:  Every lock looks the same, but appearances are deceptive.

All the same, yet all different.  Source: Google images
This is a simple story, but a complex parable, which shows not only how important it is to remember the combination to your lock, but also how much trouble you can get into if you are not careful about predictability and causation.  Not a moral you'd have predicted, I am sure.

Of course, here we're dealing with mundane aspects of predictability.  As far as we know, a combination lock is not capricious (though you have to oil it or keep it from rusting or acquiring moisture and freezing in cold weather, or from being gummed up with sticky goo). The lock will open every single time, no exceptions, if its correct combination is entered.  So, it is completely true that while all combination locks may look essentially the same, or may have some exactly similar features, each lock is 100% determined by its combination.

This is curious, because if you know the combination of the lock in your hand, you can open it, but if you know just a combination, you can't tell other than by trial and error which lock it will open, and you cannot tell from looking at a lock what combination will open it.  So, we might say that you can't predict the combination from seeing the lock, and you can't tell without trying which lock a given combination will actually open. That's why it's a many-to-many problem.  This, of course, is where our parable becomes a tale about genetics.

Of course, there are many different kinds of combination locks made by different companies.  Some have separate wheels that have to be put in a particular position in order to open the lock.  You can buy sets of locks with the same combination, like twins, but if you don't know that, or mix them with other locks, it's no help because they just look like any other locks--indeed, if you could predict the combination from looking at them, they'd hardly be of much use for protecting one's wallet at the gym.

There are many different types, or 'species', of combination locks, not to mention other types of locks such as those opened by their unique key.  But the same characteristics apply.  Indeed, it's rather the nature of locks that they are not predictable in this way.  In that sense, the system is robust. If they were more predictable, they'd be rather useless.

All different.  Source: Google images

This means that you can't tell a lock from its color, so to speak.  You can't tell the combination by looking at how old a lock is, or what sort of bike or gym locker you find it on, nor whether it's all scratched up, nor even what brand it is.

For Master locks, with a combination of 3 numbers ranging from 0 to 39, there are 64,000 different combinations.  In a way, that makes the 'predictive' power of a combination (whether it'll open a given lock), 1/64,000=0.000016.  Even if each lock is perfectly deterministic!  And, though you can't tell which is which, because millions are made, many different locks of the same type have the same combination (indeed, I myself had two Master locks, years apart and in different places, with the same combination: 36-38-20) -- but, of course, you could not tell that by looking at them, nor would that combination open the next lock you came across.  Nor would you know whether two lockers in the same gym had locks with the same combination.

Not entirely deterministic
Likewise, of course, in my experience, combination locks are also somewhat capricious.  Environmental factors like moisture, physical bashing around, and so on make a lock hard or sometimes impossible to open even if you know its combination.  So even in a thoroughly mechanistic situation like this, the probability that the lock will open even if you know the combination, is far from 100%.  And this assumes you don't fumble, as I do, while turning the wheel, which for some of us is no easy trick. If you do, you may fail and fail again and come to believe, as our storyteller would have had he tried to find his lock, that either you've forgotten the combination or are trying to open the wrong locker in the gym!  That environmental aspect can be most discomfiting if it happens after you've just come out of the shower and want to dress and go home--or if you're at the wrong locker and its rightful owner comes along and doesn't appreciate your fiddling where you don't belong!

Many-to-many causation: found in Nature, too!
With regard to locks, many-to-many causation means many different combinations open the same kind of lock, and many different locks and kinds of locks have the same combination.  In fact, unlike, say, people, even if each lock looks a bit different from every other lock, you can't use that to predict its combination.  If it's a key-type lock, and you have the key, you're on easy street. Otherwise even having a key is of little use, as is having a lock without the key.

Of course, you can use tools to force open the case, one might say to 'dissect' the lock experimentally.  If you're not too destructive and know how combination mechanisms work, you can perhaps figure out what the combination was.  But then, of course, you've destroyed the lock.  And since each lock is basically different, that experimental confirmation of mechanism will perhaps tell you the way that all the locks work. But it will not really help you open the next lock.  There's a difference between understanding a general mechanism, and knowing a given instance of it.

In fact, the innards of a lock are not all that complicated.  And, unlike your innards, their operation is mainly deterministic; they're hard-wired to open with a pre-specified combination.  Neither probability nor sampling are very helpful in understanding locks.  There is no 'personalized' combinatorial formula that you can know just by looking at it.  Indeed, think how we'd be in the soup if the innards of locks that determine the exact combination stop points typically jiggled around, say, if you bumped or shook the lock or closed it too hard.  Then 'the' combination would actually change, maybe just a little, but that could be very frustrating.

In fact, even combination locks don't seem to be all that precisely determined.  In my experience, some locks are very sensitive to how exactly you get to each number before you turn the dial back towards the next number.  In that sense, their combinations aren't 100% deterministic.

And, while all analogies limp, that is why the kinds of promises of personalized genomic medicine being made are a diversion from proper understanding of the underlying science.  And when it comes to inferring evolution, where the events are not even observable, promises that we are unlocking the secret of genomes are at least misleading--and, since (like locks) new combinations are always arising--we may never unlock that secret.  Unfortunately, while we have a good theory for the nature of locks, that explains the lock mess monstrosity retold above, we have no such precise theory for life.

And the moral of this tale is: if you're not careful asserting causal connections, you might be caught with your pants down.


John R. Vokey said...

It is not a combination lock, but it is one of the best visual explanations I have ever seen:

Ken Weiss said...

Thanks. But I don't think you are implying anything different from what we said, are you?

John R. Vokey said...

No, I agree completely. As you pointed out, understanding the locking mechanism is of no help if you can't match the key to the lock.