The Infinite Pocket Watch

Consider the following story.  On your eighth birthday your grandfather gives you a gift.  You unwrap it and find an antique pocket watch.  It hangs from a silver chain, and it has a beautiful carving of a clipper ship on the lid.  The back is engraved with the words, "The Best of Times."  It's a nice gift, but you're eight.  You wanted a toy truck.  From that day forward you vow revenge on this old coot.  If it takes you the rest of your life, you're going to crack the secret of time travel and then travel back and give him a present when he was eight, a bullet to the head.  Sure it's little extreme, and sure you might be nullifying your own existence, but to hell with the consequences!  You were really counting on getting that truck.  So, you tinker away in your basement on your time machine, plotting your revenge, and you carry the watch for thirty years, as a reminder of your vow.  Finally, everything is ready.  You travel back sixty years to the day your grandfather turned eight.  You find him playing in the dirt in his front yard, playing with a toy truck of all things, what nerve!  You walk up to him and throw the pocket watch in his face and yell, "Happy birthday Jerk!", as you raise the gun to fire.  Just then, a meteor falls from the sky and lands right on top of you.  Your eight year old grandfather blinks in surprise at the giant smoking rock in his front yard.  Then he notices the pocket watch laying in the dirt beside his truck.  He picks it up and dusts it off.  He holds on to this watch for the rest of his life, as a memento of this strange incident.  On his grandchild's own eighth birthday, he presents it to you as a gift.

So now you see the new can of worms we've opened.  We've disposed of the grandfather paradox with the idea that whatever happened in the past, already happened and can't be changed.  You can't kill your grandfather because you already tried and you ended up getting flattened by a meteor.  That's what happened.  But now we have a new problem.  In the process of your assassination attempt, you gave your grandfather a pocket watch, the same pocket watch he gave you.  So this raises the obvious question: where the heck did this pocket watch come from?

This is what is known as the ontological paradox.  This is where information or objects loop through time without a clear origin.  The ontological paradox and its close cousin, the predestination paradox are the result of the theory where the time traveler was always in the past.  The grandfather paradox arises from an inconsistency between cause and effect which results from a change in the time line.  The effect cancels out the cause.  With these new paradoxes you have the opposite problem.  In the predestination paradox, you have the effect causing itself.  In the ontological paradox, you have an object or information originating with itself.  In both cases, you have a closed loop where the past is fulfilled by the future that has resulted from it.  The constant and unchangeable nature of time, which was once the handy solution, has now become the problem.  Sure, it's already happened, that's why it's going to happen.

Now, my first, intuitive reaction to the ontological paradox is simply to dismiss it as a cute little trick of fiction.  Yeah, it's neat and everything that the grandfather gives you the watch he got from you, but is this really a legitimate concern?  Could it actually happen in the scenario?  Well, remember the "links" I put in the post at the beginning of the month?  Suppose I had been able to read the posts before I wrote them.  I'd know what I was going to write, and then I could have just gone back and written it based on what I read.  But then, where would the words and ideas have actually come from?  They would loop around through time, originating with themselves.  I would just be copying from myself what I had already copied from myself, without ever actually writing the original material.

Okay, so that covers information, but what about an object.  Well, suppose you stole the Mona Lisa from the Louvre.  Then you take it back in time and leave it on Leonardo Da Vinci's  doorstep.  Now, Leonardo could preserve his integrity and simply throw the thing away, but even so, he couldn't forget what he saw.  The Mona Lisa would inevitably influence his painting of the Mona Lisa, perhaps even giving him the idea.  So, at the very least, you'd still have information running in a loop.  But what if Leonardo wasn't so scrupulous?  What if he just looked this way and that, took the painting inside, and then eventually passed it off as his own?  Now you've got a solid object, paint and canvas, looping around through time, and God only knows where it came from.  So yes, the ontological paradox is definitely a real problem.  All it would take is setting the Mona Lisa on Da Vinci's doorstep.

If you look closely, you'll notice a mathematical problem that arises from this as well.  Take a look at our pocket watch again.  Between the day your grandfather picks it up and the day you take it back in time with you, sixty years elapses.  The hour hand has made 43, 800 rotations around its face.  So that means that the watch is at least sixty years old when you throw it at your grandfather.  So it was already sixty years old when he picked up, then  it was carried around for another sixty years before it was taken back in time.  Okay, so the hour hand has made 87,600 rotations and the watch was at least 120 years old when your grandfather picked it up.  But then it was carried for another sixty years, so it was really 180 years old.  Round and round it goes until you're forced to conclude that the hour hand has made an infinite amount of rotations around the face.  Not even the best made watch could last forever, let alone one that wasn't made in the first place. 

The problem here is that you have no starting point to calculate the watch's age from.  It's not that the loop itself keeps repeating.  The events only happen once, but yet the numbers keep piling up.  You can never establish exactly how old the watch is at any one point, so you're forced to keep compounding the time it traveled around the loop.  So, not only does this watch have no beginning; it has no ending either.  It exists for eternity in an isolated circle of events.

Or how about this: Let's say you work as a scientist in a lab.  You come in on Monday and find a mysterious petri dish on the table.  You take the dish back to Sunday and leave it on the table for yourself to find on Monday and bring back to Sunday.  The microbes in this dish double once a day.  So, if there were at least two microbes on Sunday, then there were four by Monday, which means there were at least four on Sunday, which means there were eight on Monday, which means there were at least eight on Sunday, which means there were 16 on Monday, which means....Yes, quite a can of worms indeed.

I wish I had a solution to offer for this, but honestly, I'm stumped this time.  I have no ideas or theories at the moment.  Even the multiverse won't save us this time.  We can't skip over to the universe next door, because we aren't changing anything.  And yet, solve it we must, for one could argue that our entire existence is the ultimate ontological paradox.  You know the old conundrum: what caused the thing that caused the thing that caused The Big Bang?  Where did the stuff come from, that all this...stuff came from?  You could go around with it forever, but here we are, the most infinite pocket watch of all.  So, the solution is out there.  Maybe I'll find a note on my refrigerator tomorrow morning, explaining it all.  After I read it the next day, I just have to remember to travel back to yesterday and leave it on the refrigerator.

(This post is also available in extra cheesy version.)