At some point over the past weeks, some of us might have paused over a sheet of cookie dough to ponder how best to cut out as many cookies as possible.
As sa国际传媒 Post’s holiday deadlines loomed, many of us might have stood next to cardboard boxes and wondered how to tightly and securely fit a dozen or so oddly shaped packages into them for family and friends.
In the coming days, we might even face the same problem trying to fit too many holiday leftovers into our refrigerators.
The good news is experts have been worrying away at these same critically important problems for decades. The conundrum might well occupy them because they want more cookies in their lives, enjoy holiday leftovers, or are frustrated with their packing skills. However, they’re probably working on it because the problem of packing things optimally is a critical business and industry consideration, with billions of dollars at stake.
In clothing manufacturing and metal processing, for example, cutting out materials with as little waste as possible increases efficiency and supports the bottom line.
The problem applies in shipping, too. Pack a shipping container tightly and securely, and the contents will help reinforce the strength of the containers’ own walls. Pack a container optimally, and the contents won’t shift as easily when, to use a recent and locally relevant example, the ship carrying the container starts rolling in high waves. That, in turn, lessens the likelihood the container will break free and go overboard.
The bad news is that not even the most pointy-headed mathematicians and computer scientists using today’s supercomputers have been able to find a good solution.
According to Danish mathematicians, science now confirms it is impossible, at this time with current technology, to figure out what works best for getting more than a handful of spicy gingerbread Santa or reindeer cookies from a single slab of cookie dough. Yup, the experts have given up on finding a computer algorithm to answer cookies’ geometric problem.
Today’s computers just aren’t good enough. In fact, human brains — even bog-standard human brains like yours and mine that don’t have higher degrees in mathematics or physics — continue to consistently outperform machines in determining solutions to this problem.
“While algorithms let us solve seriously complex problems, this is one that remains too much of a mouthful for today’s computers,” said University of Copenhagen computer scientist Mikkel Abrahamsen in a statement about his team’s finding. “For now, it isn’t possible to pack more than 5-10 objects [into a container] optimally. And, our result suggests that this number probably won’t increase much for the time being.”
To answer the question, one must know all the co-ordinates at which the cookies (or packages, pallets or containers of leftover food) can be placed and all the angles at which they can be rotated within a space. Even if all the intended cookies have simple and identical shapes and sizes, the possible combinations are infinite.
That means it’s impossible to know all the locations needed to try in order to find an optimal packing solution.
Instead, to solve these problems, the algorithms need to be more analytical. But analysis by computers takes time.
If you want your cookies Santa- or reindeer-shaped, today’s computers can find optimal solutions for up to four objects. As more cookies per sheet of dough are added, the time needed to calculate solutions increases exponentially.
“Not even the best computers can keep up,” Abrahamsen said. “Theoretically it’s possible. But based upon the speed at which computing power is growing, it will probably take millions of years before we are able to optimize the handling of a few additional objects.”
So take heart: when you stand at the kitchen counter with cookie cutter in hand, in front of your refrigerator with leftovers piled at your elbow, or by your suitcase or Christmas parcel, the solution you devise in the moment is likely to be as good as it gets.
