Zerah Colburn’s greatest achievement may have been defeating William Rowan Hamilton in feats of calculation. Colburn was a nineteenth century American child prodigy. As a young boy he could multiply large numbers in an instant, compute square roots of large numbers, and determine the number of hours or seconds between distant dates. Colburn’s father capitalized on his son’s astonishing mental capabilities, taking him on tours across the country and in Europe for others to see, and sometimes to compete with the lightning calculator.
But the local talent was not always a walk-over. While in Dublin, Colburn went up against the twelve year old Hamilton. While Colburn mostly was victorious, the older Irish boy was sometimes the faster of the two. The matchup was probably the first time that Hamilton, who knew a dozen languages by that time, had been shown up in anything intellectual and it may have motivated him.
Hamilton went on to become one of the greatest mathematicians in history. He is probably most famous for his reformulation of Newtonian mechanics and today the Hamiltonian operator is well known to physicists everywhere. Hamilton also discovered quaternions while on a Sunday stroll with his wife. The fundamental relationships
came to him in a flash and he immediately carved them into the Brougham bridge so as not to forget them. Though quaternions have rather narrow applications today, where used they are quite valuable in providing faster and more robust computations. For instance, from molecular dynamics to computer graphics to spacecraft navigation, coordinate transformation algorithms are required. Quaternion-based transformations both minimize the number of multiplications and avoid singularities.
Hamilton also was interested in early forms of the traveling salesman problem. The problem was well known to salesmen of the day, but had not yet been formalized in mathematics. Hamilton invented a mathematical puzzle called the icosian game in which the objective was to create a path that visits twenty points without doubling back on itself.
The traveling salesman problem is interesting, and important, because the seemingly obvious strategy of simply moving to the next closest location after each visit does not generally work. The traveler’s objective is to minimize the total distance traveled, or more generally the total cost. The cost may be directly proportional to the distance traveled, or it may be more complicated. For instance, the cost of travel may vary by location and direction of travel (going uphill versus downhill, for instance).
In computer science the problem is known to be what is called NP-hard. It's complexity is thought to increase exponentially with the number of locations to be visited.
All of this makes new findings, that bees regularly solve their own routing problem, rather remarkable. As one report explained:
Bees can solve complex mathematical problems which keep computers busy for days, research has shown. The insects learn to fly the shortest route between flowers discovered in random order ... Bees manage to reach the same solution using a brain the size of a grass seed.
Dr Nigel Raine, from Royal Holloway’s school of biological sciences, said: “Foraging bees solve travelling salesman problems every day. They visit flowers at multiple locations and, because bees use lots of energy to fly, they find a route which keeps flying to a minimum.”
Using computer-controlled artificial flowers to test bee behaviour, his wanted to know whether the insects would follow a simple route defined by the order in which they found the flowers, or look for the shortest route.
After exploring the location of the flowers, the bees quickly learned to fly the best route for saving time and energy.
How does the bee, with a brain the size of a grass seed, optimize its route?
“Despite their tiny brains bees are capable of extraordinary feats of behaviour,” said Raine. “We need to understand how they can solve the travelling salesman problem without a computer.”
Indeed, we do need to understand the amazing feats of bees. The bee’s routing problem is much less complex than the problems today’s computers solve. But the bee does solve its routing problem. Did random mutations just happen to construct what our greatest minds have been unable to conceive (no, natural selection doesn’t help)? Perhaps, but this certainly is not a fact as evolutionists insist it is. Far from it. Religion drives science, and it matters.