As is the case in many scientific arenas, the first studies in the field of algorithms were conducted by Muslim scientists. The concept of algorithm was used for the first time by the worldwide renowned Muslim scientist Al-Khwarizmi, who lived between 780–850 AD in Baghdad. Al Khwarizmi put his name to historic studies in the fields of mathematics, astronomy, and geography. His work entitled Hisāb al-jabr wa-l-muqābala (Calculation by Completion and Balancing) constitutes the first collection of algorithms. The Latin translation attracted great attention in Europe. The Europeans used the term algoritmi, rendered from “Khwarizmi,” to refer to rules for solving arithmetical problems by using Arabic numerals.

Having first developed as a branch of mathematics, algorithms have been described as a sequence of instructions that is used to solve a certain problem. These finite number of steps,begin at a certain point and come to an end with a result. But, today when we talk about algorithms, what comes to mind are the methods pursued in the operations of sequencing in computer programming; though algorithms are used in many fields, including physics, chemistry, biology, and music.

When different algorithms are used for solving the same problem, this enables us to reach the same solution through different means. There are, for instance, a great number of sorting algorithms (selection sorting, merge sorting, quick sorting) that have been developed for the purpose of incrementally sorting a given set of numbers. The same also applies to the search algorithms which find a given number in a set of numbers. What does this imply for us? Different people can attempt to solve the same problem with different algorithms or approaches that are better, truer or more “beautiful”. Thus, it is always important not to reject an idea without a prior examination or understanding, to welcome proposals of different opinions and to try to benefit from better alternatives or solutions. Thus, we can understand from an algorithmic approach that establishing dialogue and showing mutual respect are essential moral virtues in transforming differences into wealth.

Computer algorithms solve certain problems according to pre-defined parameters. Thus, we should never forget that computers cannot carry out a spontaneous operation, but can only carry out functions that have previously been programmed into them by human beings. Although some researchers, by relying too much on recent developments in computer sciences, and particularly in fields like artificial intelligence, attribute human characteristics to computers. They even estimate that they can produce human-like things in the near future, which seems rather unfeasible when we consider countless physical and spiritual features of humans. What does this imply for us? Pursuing a systematic method when solving problems in both computer sciences and daily life would considerably increase one’s success rate in solving any problems encountered. The most critical stages in problem solving are obviously a correct diagnosis and full description of the problem. The algorithms are developed and the most coherent and suitable are then chosen.

After an algorithm is designed in a flowchart, it is translated into software and tested against verifiable data prior to its usage in real operations. This test is necessary to prevent probable flaws in the software. What does this imply for us? By utilizing all the talents and especially the intelligence granted to us, human beings are always able to find what is better or truer. Research has been conducted in scientific studies by keeping in mind that there is always a next step in any development that has been achieved; the experience of the history of mankind demonstrates that a method that has been developed today might prove to be inadequate tomorrow.

When analyzing a number of different algorithms that are used to solve the same problem, the cost is assessed, with the least costly and most suitable one being selected. The cost of an algorithm is determined according to the number of operations carried out in solving any problem. An algorithm which solves the same problem with a greater number of steps has a lesser efficiency and a lesser performance.

Sorting algorithm by insertion

Sorting algorithms are one of the most frequently used algorithms in computers. As sorted data is more easily processed and used, data are usually sorted first with a sorting algorithm before it is processed within more costly operations.

In insertion sort (i.e., sorting by insertion), numbers to be sorted are inserted into a new “sorted” set. The new sorted set is empty at the beginning, and the numbers are inserted one by one into the right position of this set. During each insertion, the number at hand is compared to the numbers of the new set from the smallest to the largest. During a comparison, if the term (number) at hand is smaller than the term in the new sorted set, then the term is inserted right before the term in the sorted set. As each term is generally compared with all the terms which precede it, sorting of n numbers is done by about n2 comparisons. Thus, the cost of such a sorting algorithm is O(n2).

The quick-sort algorithm

This algorithm is used to find the shortest way between two points. Let us suppose that we have a limited number of points, some of which are inter-related. During this type of calculation, the shortest way is systematically found by checking all the combinations that have been able to be established among given points. The web sources that are provided for planning routes and mapping services with PNDs (Portable Navigation Devices) for travelers can be given as examples; here the minutest details of every highway and road have been recorded to the virtual media. In accordance with certain criteria, by taking into consideration all the probable routes between the two addresses provided by the user, the optimum driving route, including road and street names, is suggested.

Use of algorithm in medicine

Any research or inquiry used in the diagnosis and treatment/curing of a disease is defined as a medical algorithm. The logic of a decision tree is used in diagnosing, curing and following up diseases with these algorithms. Guiding algorithms, for example, “if symptoms A, B, C are observed in patient, then, the patient is probably suffering from the disease D, so, use the treatment E” are used in medical expert systems. The purpose of such algorithms is to standardize the medical services provided and thus minimize potential uncertainties and errors that likely to arise. Moreover, such algorithms are also used for educational and training purposes and as a guide to approaching the patients, diagnosing and curing diseases and towards solving their problems with greater ease. A great number of medical information that has been published has been transformed into numerous algorithms, ranging from those that use simple calculations to those that make highly complicated decisions. For instance, in the algorithm that was developed to measure the Body Mass Index (BMI), age, sex, height and weight are among the questions that are asked of the patient. The data obtained from the patient is later applied to a formula developed from the experiences of medical science, and the said index can thus be calculated. However, doctors should compare the results obtained from such algorithms with their existing knowledge, for even such simple algorithms as BMI become undependable in different cases, for example an athlete or an expectant mother. Algorithms only provide guidance for physicians, but the final decision should be taken by the physician after having individually assessed the status of each and every patient.

Algorithms and music

The algorithmic composition has been used in music for centuries to produce music with a methodological approach. Canon, for example, is a form of music produced with an algorithm in which a melody is replicated by one or more imitations of it played after a given duration.

Human brain, nature, and algorithms

Although the secrets of brain have not yet been fully explained, vital information has been compiled about its biological structure and functioning, thus proving that different sections of the brain fulfill different roles. Such sophisticated tasks as controlling the bodily organs, mental discernment, functions corresponding to the use of tongue and other sensory activities, the perception of colors, calculation of actions and the perception of physical conditions, are all carried out by use of brain mechanisms and faculties. All these tasks are accomplished by algorithmic processes which have not yet been fully explained. The issue of the unification of the data or images received by the eyes is, for instance, one of the matters that scientists do not yet fully understand. Although many have tried to imitate the human brain, such simple cerebral functions as walking and communicating have, to date, not been convincingly imitated.

What algorithms imply for us

As science and technology develop more and more, new inventions are being made, algorithms are being proposed for unsolved problems, while algorithms of already solved problems are being further developed. For example, many ciphers, which in the 1970s were believed to be unsolvable within an acceptable span of time, are being easily solved today thanks to the algorithms that have been developed and the ever-increasing operational power of computers. Consequently, developments in algorithms suggest to us that we should always search for that which is better and more effective; also we should remember that there are a number of different ways that lead to the very same target. Thus, we should always be open to the ideas of others and willing to consult with them before making a decision about any subject.

Ahmet Isik has a PhD in mathematics and is a freelance writer.

References

• Cormen, T. H., C. E. Leiserson, R. L. Rivest, Clifford Stein. Introduction to Algorithms, MIT Press, 24th Edition, 2000.
• http://www.nist.gov/dads/termsType.html#P

The brain is probably the most complex organized biological structure in existence. We think, learn, compute, memorize, feel, show emotion, and love. The brain is the center of all these activities, and of many other mental and physical functions as well. Each human being has a unique personality, and each individual behaves in a certain way. Our behavior reflects how our brain thinks.

Throughout one’s life, a person’s brain constantly learns. Each input, such as events that affect us, leaves its traces in the brain. We recollect these events later. But how do we learn? How do we remember things? What is the physical dimension of learning, feeling, and remembering? What is the physical significance of brain dynamics? Some of these questions are probably the most difficult questions for neuroscientists and other interdisciplinary brain researchers to answer.

Studies of the brain are as old as the practice of medicine. Although advancements in medicine, with the help of engineering and computer technologies, have been significant in recent years, brain research progresses much slower. Brain research has been a focus of such interdisciplinary sciences as neuroscience, biomedical engineering, electrical engineering, medicine, artificial intelligence, and psychology. However, an exact and detailed understanding of the brain’s dynamics and associating its neuronal activities with certain physical phenomenon remains largely beyond our grasp. The fact that the human brain cannot be used for experimental purposes is another factor in brain research.

THE BRAIN’S STRUCTURE

The brain is considered the human body’s central commanding unit. Along with the spinal cord, it forms the human being’s central nervous system. It poses a modular structure, each module of which is known to be responsible for certain functions, and possesses its own respective complexity. Readers wanting to know more about the brain’s structures should check the literature produced by specialists in the field of neuroanatomy.

Figure 1 illustrates the brain’s structure. The cerebral cortex, essentially a biological sheet of tissue covering the brain, is about 0.08 inches (2 mm) to 0.24 inches (6 mm) thick, and gives a geometrical representation of the brain’s shape. The brain’s stem (not shown) is the area between the thalamus and the spinal cord. It is the center of the most of the brain’s basic functions, such as breathing and the heart rate. The area behind the brain stem is the cerebellum. Located at the brain’s base is the hypothalamus, which, among other things, controls the body’s temperature. It reacts to hot and cold temperatures by sending out signals to adjust the body’s temperature. The thalamus serves as a sink for sensory information, and communicates the received information to the cerebral cortex. Although not proven in human beings, the thalamus serves as the center of sleep spindles, sinusoidal signals emitted by animals while they sleep.

NEURONS

Neurons, the brain’s building blocks, are the only cells that do not renew themselves (all other cells die and are replaced). Each human being is born with approximately 100 billion neurons in his or her brain. Thus, a certain neuron in the brain of a newborn human being is the same neuron when he or she is old. A normal brain loses 3 to 5 neurons each second. Stress, drug and alcohol consumption, and aging may cause more neurons to be lost. For an ordinary human being, however, the total number of neurons lost during an average lifetime is very negligible.

Neurons are probably the most complex and intelligent communication networking ever created. The brain contains billions of cells, each one of which is connected to another. All of them share and transmit and, more importantly, process the information. This feature introduces the intelligence of neurons, the nature of which is not yet completely known to scientists, who remain fascinated by the engineering behind this intelligent networking.

To better understand neurons’ functionality, imagine yourself cruising in your convertible on a two-lane road. As you start to pass the car in front of you, you suddenly notice a car coming toward you. You have no more than 2 or 3 seconds to evaluate the options and respond accordingly: you either accelerate and complete the pass, or slow down and get behind the car you were passing. In either case, you have to consider the speed of the oncoming car, its distance, and some other safety parameters. You eventually evaluate your options and reach the safest decision in less than 2 seconds.

What is the big deal? This is just another ordinary event that we are used to experiencing every day. Behind this seemingly ordinary event, however, a tremendous amount of communication and computation is taking place among the neurons. Stimuli invoked by visual information (the oncoming car) observed by the eyes make their way through the central nervous system to the brain. Neurons receive the stimuli, evaluate them, and pass their response to nearby neurons by electrochemical polarization. Billions of neurons are involved in the process.

This information flow among neurons depends on learning (one’s driving experience). The response, the final decision of neuronal computation combined with learning and consciousness, is delivered to central nervous system so that it can act. The nature of consciousness and how it is linked to neuronal computation remain unknown.

These processes are so automated that we do not consciously realize that each physical, mental, and emotional function is governed by our brain, which, in turn, is governed by its tiny component neurons. These neurons enable us to make such judgments every day, and to communicate with the surrounding environment through sound, sight, touch, smell, taste, emotion, feeling, thinking, and so on.

THE HUMAN BRAIN AND COMPUTERS

The human brain and computers are two different things. One is a living, thinking, learning, feeling, crying, and loving organism. Happiness and sadness, in the form of marginal emotions, are reactions of the brain. Such terminology makes no sense to computers. In that sense, it might be misleading to compare the human brain and computers. However, there are some common functionalities that make such a comparison logical.

Both the human brain and computers have memory. Memory in human brains is defined as “stronger synaptic connections,” whereas computer memories are formed by semiconductor chips. Both can adapt and learn. The human brain can learn easier and faster than a computer, which can only “learn” certain tasks by being programmed with special algorithms. The nature of such “learning” is very limited.

On the other hand, computers can perform many complex tasks much faster than human brains. For example, try multiplying two numbers, dividing the result by 7, and then subtracting 9 from that result. The computational speed of a human brain is much slower than that of a computer.

Due to their high speed, computers perform parallel jobs relatively faster. The human brain also can perform parallel tasks at the same time. For example, it controls the heart rate and blood pressure while performing computational tasks. In addition, the human brain is better at interfacing with the outside world and coming up with new ideas; computers only do what they are instructed to do, regardless of the task’s simplicity or complexity. The human brain distinguishes itself from computers by its extraordinary capability in the areas of imagination and innovation.

Another common functionality is that both transmit information. Computers use semiconductor switches that are either on or off. Everything inside of a computer is represented by either a one (1) or a zero (0). Although neurons in the human brain are either on or off, meaning that they are or are not firing an action potential at a particular point in time, an accumulated charge that activates neurons gives the human brain more flexibility. Neurons are more than just on or off, for their excitability is always changing as they constantly receive information from other cells through synaptic contacts. As stated earlier, this information is carried through electrochemical polarization. Although this electrochemical process does not always result in an action potential, it may alter the chance that an action potential will be produced by raising or lowering the neuron’s threshold.

Another important distinction between computers and the human brain is that the human brain never rests, while computers do after they have been turned off. Even during sleep, the human brain continues to work dynamically. Indeed, it produces distinct signals, called sleep spindles, that may be observed externally while the person is asleep. While an individual’s body rests during sleep, his or her brain recollectively refreshes itself.

UNDERSTANDING THE BRAIN’S DYNAMICS

All activity inside the human brain is conducted through electrochemical polarization, a process that can be observed by placing electrodes on an individual’s scalp. The brain’s dynamics can be observed in the form of an electroencephalograph (EEG) or a magnetoencephalograph (MEG). An EEG, which is relatively less sophisticated than a MEG, maps the brain’s dynamics into electrically recorded brain waves. Multiple electrodes are systematically placed on the scalp, and potential differences are measured with respect to a reference point. In the case of a multichannel EEG, the number of electrodes may be as high as 64 or even 128. Figure 2 shows a single-channel recorded EEG. Potential differences measured through electrodes are sampled and stored in a computer for analysis.

The challenge presented to researchers is how to read multichannel EEGs and extract the information that really reflects neuronal activity. If the patient is epileptic, brain abnormalities may be easily distinguished in a multichannel EEG. From the location of electrodes, it may be possible to identify the general part of the brain giving rise to epileptic EEGs. In clinics, neurosurgeons usually open the patient’s scalp and measure the EEG directly by placing electrode grids over the cortical tissue. Even then, it is a real challenge to identify the defective region and proceed accordingly.

The EEGs of epileptic patients distinguish themselves from other brain activities by their relatively high amplitude. But what about other physical and mental tasks? Can we detect and identify those EEGs that reflect a certain mental task? Scientists from many disciplines are focusing on such questions. Many researchers are combining EEGs, MEGs, magnetic resonance imaging (MRI), and such engineering tools and algorithms as digital signal processing and spectral analysis to identify and understand the brain’s dynamics. The clinical need for such solutions are in high demand.

THE HUMAN BRAIN AND INTERDISCIPLINARY SCIENCE

The human brain has been a research focus of scientists from many disciplines. Scientists in medicine, neuroscience, engineering (electrical engineering and biomedical engineering), mathematics, physics, physiology, and computer science have been conducting either sole or interdisciplinary research for many years. The brain has so many dimensions that no single discipline can cover all of its aspects. Some of these disciplines are described below:

• Artificial intelligence attempts to build knowledge representation on the hypothesis that intelligent systems act intelligently. Hence, if the human brain’s intelligence were represented in a finite domain, this domain could be used by computers to mimic human intelligence. This approach faces a major challenge: human intelligence cannot be represented to the degree that artificial intelligence requires to mimic human intelligence.

• Computational intelligence, on the other hand, approaches the problem from the perspective of such engineering tools and algorithms as neural networks, fuzzy logic, and genetic algorithms. Neural networks and genetic algorithms can learn an underlying task to some degree, whereas fuzzy logic relaxes information representation by providing one more degree of freedom to the binary representation of information: a membership function concept. In this concept, the information has a probability of being a member of a certain class. The human brain’s electrochemical process may not always result in an action potential for a certain neuron(s). The binary concept cannot represent this phenomenon, whereas fuzzy logic may be helpful in modeling the chance of a neuron to produce action potential.

• Engineering provides technical tools and algorithms for conducting research on the human brain. Electrical engineering provides signal processing tools and algorithms for filtering and imaging, and other tools to process EEGs. Many scientists use these tools and algorithms to understand and localize EEGs. It would be very effective to localize human brain abnormalities with the help of engineering tools and algorithms.

Each science and method mentioned above has its own limitations. Combined interdisciplinary research provides more promising results for understanding the brain’s dynamics. Many other methods not mentioned in this article also are being used to study the human brain.

SOME FACTS

An average adult human brain weighs about 3 pounds (1.36 kilograms). A stegosaurus weighed about 3,528 pounds (1,600 kilograms) but had a brain that weighed only about 0.15 pounds (70 grams), or just 0.004 percent of its total body weight. In contrast, an adult human being weighs about 154 pounds (70 kilograms) and has a brain that weighs about 3.1 pounds (1.4 kilograms), or about 2 percent of his or her total body weight. That makes a human being’s brain-to-body ratio 500 times greater than that of the stegosaurus.

DISCUSSION

This is only a very brief description of the human brain and its functionality. As scientists and researchers learn more about the human brain, they realize that what they know is very small when compared with how much they still do not know. All scientific efforts undertaken thus far have opened only a small window on a large universe: our own galaxy, located inside our brain, with the neurons as its stars. Let each neuron be a moon. How much do we know about the moon compared with the universe in which it resides? The answer is the same for the following question: How much we know about the human brain’s neurons and the universe in which they reside?

REFERENCES

• Chudler, E. H., S. Pretel, and D. R. Kenshalo, Jr. “Distribution of GAD-like immunoreactive neurons in the first (SI) and second (SII) somatosensory cortex of the monkey.” Brain Research (1988) 456:57-63.
• Nunez, P. L. “Neurocortical Dynamics and Human EEG Rhythms.” New York: Oxford University Press, 1995.
• Figures 1 and 2 are courtesy of Eric H. Chudler, Research Associate Professor, University of Washington.