Evolution of the Calculator
Before the invention of the electronic calculator, people used a number of devices to help them with mathematical calculations
Humans have been using mathematics for so long that it is uncertain what the earliest aids to mental arithmetic were. But the first was probably our fingers, and the second was small piles of stones which were used to keep a record of the objects being counted. However, these methods were insufficient, only useful for minimal amounts and, in the case of fingers, could only be employed for short periods before sore muscles set in. With the advent of prehistoric agriculture, commerce and astronomy, maintaining large piles of stones for counting became cumbersome and hopelessly inadequate.
A rudimentary version of the abacus, or counting frame, dating to around 2,500 BCE, was developed in Sumeria (present day Iraq) and subsequently spread to Europe and the rest of Asia. As the abacus was refined with the use of string and beads, calculations that had been considered extremely difficult became routine. For the next 4,500 years, the abacus was humanity's main counting tool and is still used in parts of Asia. However, it has its limitations; it is unable to multiply and divide as efficiently as it adds and subtracts.
In 1617, Scottish mathematician John Napier published a document entitled Rabdology (calculation with rods) describing a device that came to be known as Napier's bones. The 'bones' are thin rods, inscribed with multiplication tables. The user calculates the sum by adjusting the rods' vertical alignment, and then reads off the multiplication totals horizontally. With a few hours of study, the average person can use a set to solve large multiplication and division problems. Experts can even use them for difficult calculations such as extracting square roots from fairly large numbers. However, these manually operated devices were not calculators; although the simplification of the sums had been achieved, a human operator still had to perform them mentally.
In 1642, Blaise Pascal invented the Pascal calculator, a device truly capable of performing mathematical calculations by means of a clockwork-type mechanism. It was ingenious, attempting arithmetic functions previously thought impossible and it eventually performed all four arithmetic operations without relying on intelligence. It could add and subtract two numbers directly, and multiply and divide by repetition, but the machine was never a commercial success. This was due to the fact that the techniques for producing the interior parts were expensive to implement. In truth, the Pascal calculator did not replace Napier's bones or the abacus in many accountants' offices.
Thomas de Colmar, a French inventor and entrepreneur, invented and produced the first mechanical calculator robust enough for everyday use. It was known as the Arithmometer. Manufactured in 1851, this invention saw the rapid rise of faster calculating machines that could add, subtract, multiply and divide large numbers with greater accuracy. It became the first commercially successful unit. However, its biggest disadvantage was its size; it often filled a desktop and weighed 15 kilograms or more.
Another leading figure in the development of the calculator was Curt Herzstark. Born in Vienna, Austria, in 1902 into a family that produced calculators and other office machines, he regularly travelled through the former Austro-Hungarian Empire selling mechanical calculators to banks and other businesses and it was on these travels that he heard the same complaints from his customers. The impracticalities of the mechanical calculators in use was hindering them. They were large and heavy.
For 10 years, Herzstark thought about the problem of how to make calculators significantly smaller, but it was far from a simple task. His answer was to forget about the inside of his tiny calculator and concentrate first on designing the outside. Then in 1937, he had a breakthrough and began work on a calculator that was portable so it could be transported easily. The unit was approximately 10 centimetres high and only five centimetres in diameter with a cylindrical body. A year later, Herzstark had a finished design that achieved everything he wanted. In 1945, he took his plans to Vienna and was able to convince the Prince of Liechtenstein to provide financial backing for his Curta calculator.
His invention was a work of staggering ingenuity. From a distance, it resembles a short, stocky pepper grinder, yet it contains more than 600 precision parts, allowing the operator to add, subtract, multiply and perform long division with a mere turn of the crank. Advanced users could even calculate natural logs and square roots. Approximately 150,000 Curta calculators were made between 1948 and 1970, but by the early 1970s electronic pocket calculators ended the manufacture of mechanical calculators. However, the Curta still remains popular and people buy them to add to their collections. No truly mechanical calculators have been invented since; the Curta was the best and the last of its kind.
Memory in Plants
In the study of the plant kingdom, a slow revolution is underway. Scientists are beginning to understand that plants have abilities that were previously unnoticed and unimagined
A Monica Gagliano is an evolutionary ecologist at the University of Western Australia in Perth. In her first experiments with plant behavior, learning and memory, Gagliano decided to test her new subjects the same way she would animals. She started with habituation, the simplest form of learning. If the plants encountered the same unharmful experience over and over again, would their response to it change? At the center of the experiment was the plant Mimosa pudica, which has an unusual protective response to unfamiliar motion or touch: its leaves fold closed and so it takes on a different shape. Gagliano introduced these plants to a new experience: she dropped them. At first the mimosa plants responded by shutting their leaves tight, but as Gagliano repeated the action – seven sets of 60 drops each, all in one day – the plants' response changed. Soon, when they were dropped, they stopped responding – their leaves no longer folded closed. However, when she prompted them with a light shake, they still shut their leaves tight. It was as if they had learned that being dropped was nothing to be worried about.
B Three days after this training, Gagliano tested the same plants again and they still did not respond to being dropped. The experiment was repeated six days later and one month later with the same results – their leaves stayed open. Gagliano had not predicted that the plants would retain the training three days later. Whereas in studies of bees, for example, a memory that remains for 24 hours is considered long-term. Therefore, according to the rules that behavioral scientists routinely apply, Gagliano noted that the mimosa plants had demonstrated that they could learn from experience.
C One of the most well-understood forms of plant memory is vernalization, in which plants retain an impression of a long period of cold, which helps them determine the right time to produce flowers. These plants grow tall through the fall, brace themselves during winter, and bloom in the longer days of spring – but only if they have a memory of having gone through that winter. This idea goes back to the 1920s when Trofim Lysenko, a Soviet Union scientist, discovered early in his career that by chilling seeds he could turn winter varieties of grains into spring varieties. These seeds that were normally planted in the fall and harvested in the spring could now be both planted and harvested in the same season. Although this was not described as plant memory at the time, Lysenko was, in essence, implanting a false memory of winter in plants that need a cold signal to grow.
D It was not until the 1980s that scientists started talking explicitly about plant memory. A French team led by Mordecai Jaffe, for example, happened upon a type of memory in which a plant recalled a history of damage to a leaf on one side of its stem, and therefore dedicated its energy to growing in the other direction. Since then, scientists have found that certain plants can remember a range of experiences (like exposure to cold and heat or excess light) and modify their responses. For example when plants experience drought and dehydration, they might retain more water when faced with the same stress again. We now know that plants are capable of much more than they're given credit for. They can 'sense' vibrations, which might help them to recognize insect attacks. They share information by broadcasting chemicals through the air or from their roots. In the study of the memories they form, the next step has been to understand how they do it.
E In recent years, plant scientists have started using the insights of molecular genetics and, in particular, epigenetics, the mechanisms that switch particular genes on and off. Richard Amasino, a professor of biochemistry at the University of Wisconsin-Madison, US, has studied the complex memory mechanism that controls vernalization and flowering in Arabidopsis thaliana, or thale cress, a plant that is a popular tool in laboratories for understanding many plant traits. This plant has a set of genes that create the proteins that cause flowers to form. Amasino explains that before vernalization, the cells are full of a second protein, named FLC, that represses those key, flower-promoting genes. But when the plant is exposed to cold, its cells slow the production of FLC until it stops, and the balance of protein power then changes. The cells start producing more and more flower-promoting proteins, until the thale cress plant is ready to burst into bloom.
F Since the early experiments with vernalization, biologists have worked to show that certain plants in certain situations can store information about their experiences and use that information to guide them about when to bloom, and how to grow, develop, or behave. Functionally, at least, these plants appear to be creating memories. Interestingly, a group of plant scientists based in Australia and led by Peter Crisp, recently argued in the journal Science Advances that for plants, forgetting (or not forming memories at all) may be a more powerful tool for survival than memory, and that 'memory, in particular epigenetic memory, is likely a relatively rare event.' Crisp, the lead author of the paper, now at the University of Minnesota, US, points out that plants have incredible abilities to rebound from stressful conditions. Crisp argues that 'having a memory, keeping track molecularly of signals that you've received in the past from your environment, does have a cost'. A plant that remembers too much might sacrifice healthy growth to be constantly on guard against extreme weather conditions, salt, and insects. Perhaps it is beneficial for plants to let those types of negative experiences go, instead of always preparing for the worst.
The facility for verbal language
Apes may learn to communicate with humans, but what are the differences between this and true human speech?
A Animal language works through rather limited vocabularies of calls, postures and sometimes scents that appear to convey concrete meanings. Konrad Lorenz, the great ethologist, has paraphrased the most universal animal signal as: 'I am here; where are you?' Animals clearly remember the past and sometimes plot elaborately to manipulate the behavior of others in their social group. Monkeys have been observed to give an alarm call, indicating that a predator is near when it is not, in order to distract other monkeys from a favorite food source. However, non-human animals apparently cannot discuss the distant past, the remote future, or abstract or hypothetical ideas.
B True or full language must include two specific categories of words, according to linguist Derek Bickerton. First there are those words that refer to concrete objects, perceptible attributes, and real actions – what linguists call 'lexical items'. At least some animals use lexical items in their language. In addition, true or full language includes a number of words that are primarily relational, numerical, referential, temporal, directional, and so on – which linguists call 'grammatical items'. It is the grammatical items that allow us to express complex thoughts in a single sentence without confusing our listeners; they eliminate ambiguities or, as linguists say, they 'disambiguate our utterances'.
C In contrast to full language users, individuals who have missed the opportunity to learn language normally, and indeed apes who have undergone considerable training, all use much simplified language. There is only one tense, the present tense. Moreover, grammatical items are rudimentary or often completely absent. This restricted or 'bare bones' language is what Bickerton calls proto-language. He believes it is the first means of verbal communication that we learn as children and is probably a fair approximation of the first means of verbal communication that we developed evolutionarily too. It is the form of language that we share with a few talented and trained apes. Bickerton suggests that proto-language is a robust if limited means of communication that survives even horrendous deprivation. It is the fallback rudimentary type of language also used by people fully adept in one language who are trying to express themselves in another; thus, proto-language lies at the root of pidgin language. Proto-language is the sort of language we can readily envision as developing by small increments from the extant oral and gestural utterances of many social species.
D Bickerton argues that proto-language and full language are two systems separated not only by their modes of expression but also by their genesis. In his view, proto-language and true language developed independently to serve different purposes, and they probably have different neurological bases. This is why proto-language does not become full language as the speaker matures or learns more. A trained ape, for example, does not suffer from arrested development of language; it is capable of fully developed proto-language but will never develop the other system that is full language. Under normal conditions, proto-language is supplemented and eventually supplanted by full language in humans.
E Why have apes failed to learn full language? It is not because they are physically ill-adapted for speech (which they are), nor is it because they cannot grasp the use of symbols. Experiments conducted by Allen and Beatrice Gardner, working with a chimpanzee called Washoe, by Penny Patterson with the gorilla Koko, and by Sue Savage-Rumbaugh with the pygmy chimp named Kanzi have all demonstrated that apes have an impressive ability to learn symbols. Savage-Rumbaugh's work with Kanzi has effectively demolished the criticism that ape language was a product of wishful thinking on the researchers' part. Clearly, apes exposed to appropriate language opportunities learn to combine symbols into multi-word utterances and to participate in meaningful dialogues. The problem, according to Bickerton, is that apes do not have the elaborate representational system that humans possess and so they never progress from proto-language to full language. There is an absolute limit to the complexities of their utterances, a limit that is both grammatical and conceptual.
F Bickerton hypothesizes that proto-language developed as a communication system, based on the neurological template that we share with apes. However, he believes that the neurological basis for full language evolved as a complex system for taking in sensory information about the environment, processing it, storing it, and perhaps evaluating it as a basis for future actions. The basis for full language, argues Bickerton, was a sort of mapping function, a means of representing the world internally. While all creatures map their world to some extent, humans have developed a stunningly intricate representational system that far exceeds that of other organisms in complexity and subtlety. In order to make a highly detailed and accurate map, one that changes minute by minute as new information is added, we interpose a tremendous amount of mental processing between the experience and our mental representation of it. This permits us to think about circumstances or events that are not occurring and may never occur. Without a detailed mental symbol that represents yourself, you cannot think about yourself in any complex way. Apes seem to have only a rudimentary sense of self and a limited degree of consciousness, and they lack the elaborate representational system that would enable them to develop truly complex thoughts and full language.
