The tower of Hanoi
A test of design, planning, and purpose
The tower of Hanoi, also known as Lucas’s tower1 or the Tower of Brahma, is a game or puzzle requiring considerable skill and mental aptitude. By assessing the number of steps one takes to move the discs to another pole while following certain rules, this game tests one’s cognitive functioning as well as programming skills.
It eventually became included in the Cambridge Neuropsychological Test Automated Battery (CANTAB) developed in the 1980s to measure memory, attention, reaction time, decision making, and response control.2
Used by many psychologists today, the game, as is suggested by its multiple names, appears to have its roots within varying cultures. It is also an unspoken testament that all we know of could only have been created by an all-powerful, super-intelligent God.
Nothing to everything, by itself?
Atheistic evolutionists believe that our world came from nothing. And they believe that later, whatever something there was organized itself by random processes, constrained only by the physical laws, to form the complex world around us. Since they insist that no supernatural intelligence was involved, and since this world is indeed very complex, they believe that billions of years are required in order for chance to make these complex systems possible.
But randomness does not observe rules,3 whereas such rules are all around us. Seashells, trees and many other things in the natural world grow in patterns that follow the mathematical Fibonacci sequence.4 All of life follows the highly complicated processes of DNA replication, transcription, and translation. There is a rule of life, known as the Law of Biogenesis; life only ever comes from life. No matter has ever been observed to assemble itself into anything approaching the complexity of even the simplest living thing.5
Life is full of ordered processes with rules and sequential order governing them. The first self-reproducing entity in evolution could not have had the help of any selection or mutation, because natural selection only applies to living things. Therefore only chance can be invoked.
But for pure chance to build the sorts of systems required for a self-reproducing organism, not even ‘zillions’ of years would be plausible, much less the few billion years pushed by evolutionists.
To highlight this, consider the following. According to one legend, there is a room in the Hindu temple of Kashi Vishwanath in India with three rods and 64 golden discs, said to be moved by Brahmin priests according to the rules of this puzzle. (This is a possible explanation for the name ‘Tower of Brahma’.) Let’s assume we were to move these 64 discs at a rate of one disc per second, and by applying very high intelligence, we were to ensure that the smallest number of moves is required. It would still take 18,446,744,073,709,551,615 turns or 585 billion years—some 40 times longer than the assumed evolutionary age of the whole universe!
Imagine how inconceivably much longer it would take for chance to achieve this same solution in, say, a situation in which the choice of disc were random, with no intelligence or intelligent programming to ensure the smallest number of turns.
Small wonder that the legend states that the tower was created at the beginning of the world, and that the world would end when the puzzle was completed. Yet any of the basic processes required of life, such as DNA replication, transcription, and protein translation, easily outstrip the complexity of the Tower of Hanoi task—by orders of magnitude.6
Time related to intelligence
Furthermore, since the time (and number of moves) taken to complete the Tower of Hanoi task gives some idea of a person’s cognitive capabilities, having all of creation made in just six days tells us of God’s unfathomable power and intelligence.
For any creative task, whether solving a puzzle, making a table or indeed a universe, the more power and intelligence that is at work, the shorter the time needed—and vice versa. Thus, for a very gifted adult, figuring out the Tower of Hanoi solution for a handful of discs might take only a few hours at most.7 Yet the same solution might readily take the average seven-year-old (assuming no lapse in concentration, ever) every waking hour of ten years.
Had God used evolution, and taken billions of years to create as theistic evolutionists believe, it would clearly rob Him of His glory. The all-powerful, all-intelligent God Who created time itself could even have accomplished all of creation in ‘no time’ if He had so wished.8
The Tower of Hanoi is generally accepted as a cognitive test by psychologists, many of whom are atheists. It is a wonder that they cannot see that all of creation, being much more wonderfully structured and with processes that require much more complex ‘instructions’ than are needed to solve this puzzle, is a huge testament to God’s power and His creative designing intelligence.
Testing and brainpower
The Tower of Hanoi puzzle comprises three identical rods, and a number of different-sized discs which can slide onto them. Starting with all discs on one rod in ascending size to make a cone shape, the idea is to move the whole stack to another rod under these rules:
- Only one disc moves at a time.
- Each move involves taking (only) the uppermost disc of any stack and putting it on top of another.
- No disc can be put on top of a smaller one.
- The minimum number of moves needed to solve the puzzle is 2n–1, where n is the number of discs (e.g. 5 discs would require at least 31 moves).
References and notes
- After French mathematician Édouard Lucas who popularized this puzzle in the late 1800s, and is known for his study of Fibonacci sequences (see Ref. 4.) Return to text.
- The CANTAB can use either the Tower of Hanoi or its simplified cousin, the ‘Tower of London’, which is thought to give a “purer test of planning ability”—see Ozonoff, S. et al., Performance on Cambridge Neuropsychological test automated battery subtests sensitive to frontal lobe function in people with autistic disorder: Evidence from the collaborative programs of excellence in autism network, Journal of Autism and Developmental Disorders 34 (3):139–150, 2004. Return to text.
- Macroscopic systems do reflect the ‘rules’ of probability applied to large numbers of random processes; see Wieland, C., World Winding Down: a layman’s guide to the Second Law of Thermodynamics, Creation Book Publishers, Powder Springs, GA 2013. Return to text.
- Wieland, C., and Grigg, R., Golden numbers, Creation 16(4):26, 1994; creation.com/golden. Return to text.
- Dr Craig Venter did create a simple form of synthetic life, but this involved huge amounts of directed intelligence in copying the original design. See Sarfati, J., Was life really created in a test tube? And does it disprove biblical creation? creation.com/venter, 25 May 2010. Return to text.
- Thus by 10, 100, 1,000, 10,000 times or more. Return to text.
- This assumes they are unaware of the various ‘rules’ for its inevitable solution others have calculated. Return to text.
- The obvious question is, ‘Why then did He take six days?’ The answer seems to be found in Exodus 20:11 (part of the Ten Commandments delivered to the Israelites), where the six days of God’s work and one day of rest are given as the basis for man’s work and rest in the Sabbath Commandment. Return to text.