The teeth of a tiny mollusk (Patella vulgata), which is a species of sea snails, have been found to be some of the strongest biomaterials in the world. Also known as limpets, these mollusks are a very small crustacean, often around 0.05-2 cm in size with a large cone shell and possess an incredibly complex system of teeth that dazzles the mind.

Research has revealed that the tensile strength of the sea snail’s teeth is higher than that of spider silk and is comparable to only the strongest commercial carbon fibers. It was found that the teeth of sea snails scraping algae off of rocks showed a tensile strength between 3 and 6.5 GPa (gigapascals). Spider silk roughly reaches a tensile strength of about only 1.3 Gpa. Scientists say that the snail’s teeth can even withstand the pressure that turns carbon into diamonds. Studies have determined that, to our current knowledge, there is no other material of this size (roughly 100 μm micrometers) with as much strength and durability.

This exceptional durability has led scientists to do research on the structure and functioning of these teeth, and the studies showed fascinating results.

The role of teeth in nutrition

Sea snails have a special tongue, called a radula, which they use to scrape off food from rocks. The most important feature of the radula is that it contains more than 100 rows of iron-mineral teeth. However, those used for food intake consist of only 10 rows on the outermost part of the teeth. During eating, a tremendous mechanism operates: the teeth are constantly repositioned according to their conditions of maturation and wear. Worn teeth are replaced by newly matured teeth over the course of 12 to 48 hours to ensure that fresh, sharp teeth are used instead of dulled ones.

This wonderful displacement system operates in a similar way to the movement mechanism on a conveyor belt where the teeth begin to grow primarily in the posterior part of the radula. Meanwhile, they are strengthened and matured by iron mineralization. When this mineralization is complete, they are moved towards the front of the radula. In this way, completely matured teeth are permanently retained at the far-front scraping area. During the scraping process, the matured teeth wear out at a rate equal to the growth rate. In the meantime, a new set of teeth begins to grow. By means of this magnificent cycle, new teeth are constantly created and matured so that there are no disruptions in nutrition.

Biomineralization

The structure of the sea snail’s teeth is also a masterpiece of material science. The dazzling durability of its structure provides optimum strength when scraping food off of rock surfaces.

Although the exact process of biomineralization of the teeth is not known, it is believed that it involves reactions of dissolution and re-precipitation. When the non-mineralized matrix is examined, well-arranged and densely packed chitin fibers are observed that are only a few nanometers apart. The matrix is a structure which keeps the reinforcing material together in layers that are composed of different materials. This organic matrix serves as a framework for crystallization in the structure of the teeth. In the mineralization system, the basic macromolecule α-chitin component is created first. The first mineral that then precipitates is the “goethite,” i.e. the aqueous iron-oxide mineral, which crystallizes parallel to the chitin fibers. These crystals are nucleated on the chitin fibers and formed between them by pushing and pulling the fibers. This way, crystals placed in order cause biomineralization of the structure.

It was found that 80% of the overall volume of the structure is composed of these crystals. The gap between the crystals and the chitin matrix is filled with amorphous silica (SiO₂). The iron contained in the aqueous iron-oxide mineral is the metal that constitutes the largest proportion of the composition. Other metals such as sodium, potassium, calcium, and copper are present in different proportions depending on the sea snail’s exact geographic location.

Critical factors in durability

The most important reason that the sea snail’s teeth have such high durability is because the fibers of the aqueous iron-oxide minerals in the teeth are nano-scale. This is due to the fact that materials of this size are not affected by the conditions that reduce strength.

Another critical durability factor is the small length of critical fibers. Critical fiber length is a parameter that defines the length of a material required to transfer strain from the matrix to the fibers at the time of external pressure. To achieve maximum strain, the length must be greater than the critical length. Materials with a large critical fiber length can hardly reinforce the matrix because most of the strain is not transferred to the fibers and remains on the matrix. On the contrary, materials with smaller critical lengths can transfer the strain on the matrix to the fibers. Therefore, they serve as an effective reinforcement for the matrix.

Fibers of aqueous iron-oxide minerals are of a critical length of 420 to 800 nanometers. This is much smaller than the length of the fibers in the teeth of about 3.1 µm (micrometers). This shows that nanofibers are an effective reinforcer for the matrix and contribute greatly to the ability of the teeth to bear loads.

Besides the structure and composition of the snail’s teeth, its morphological shape is also important in providing strength. It ensures that the strain is evenly distributed all over the tooth.

Modeling of biomaterials

All these studies indicate the presence of high-strength composites, which is when a material obtained by combining two or more materials with different physical characteristics, in nature.

Sea snail teeth, which have been created as a highly resistant and strong biomaterial, act as an inspiration for engineering and material science. Their characteristics, such as content and design, are expected to be modeled in areas that require durability and rigidity.

These marvelous systems found in the natural world, sometimes in creatures as tiny as a snail or mollusk, serve as a reminder that nature is filled with wonders for us to explore.

References

· Barber, Asa H., Dun Lu ve Nicola M. Pugno, Extreme Strength Observed in Limpet Teeth,  Journal of The Royal Society Interface, April 2015, DOI: 10.1098/rsif.2014.1326, PubMed.

· World’s Strongest Natural Material Discovered, How It Works, Imagine Publishing, No. 71, p. 11.

· en.wikipedia.org/wiki/Limpet
www.iflscience.com/plants-and-animals/worlds-strongest-natural-material-limpet-teeth/

· www.newworldencyclopedia.org/entry/Limpet

· Barber Asa H., Lu Dun and Pugno Nicola M. “Extreme strength observed in limpet teeth.” 12. J.R. Soc. Interface. http://doi.org/10.1098/rsif.2014.1326

The scene depicts an ordinary day in a metropolitan city. People are crossing the streets, perhaps going to work. There are traffic lights and so on. However, it is just a simulation program; all the actions of the people and all the events in the environment were predetermined. We can imagine questions popping into Neo’s mind: “Is the universe really a kind of simulation? Does God interfere with the universe or does it operate like a machine?” and followed by “Is it possible to compute someone’s fate? Does free will exist?”

Neo would neither be the first nor the last to ask similar questions. Until the 1930s, the answers to these questions were sometimes influenced by the idea of scientific determinism which considered the universe like the one in The Matrix. A paradigm shift took place in 1930s when two brilliant scientists proposed their ground breaking studies on non-determinism. Gödel’s Incompleteness Theorem and Heisenberg’s Uncertainty Principle considered the phenomenal aspects of non-determinism in the universe. First, we will have a short journey through the idea of scientific determinism. Then, we will investigate non-determinism and its consequences.

The idea of scientific determinism

The term ‘scientific determinism’ is defined to be the computability of future states, given the current state and a computer that has sufficiently large computation capacity. Suppose we take a snapshot of the universe at a particular time, or press the pause key and freeze the universe such as the example from The Matrix. What scientific determinism says briefly in simple terms is that by looking at that entire picture of the moment, the picture of the next second can be calculated using the laws and formulas of physics. On a large scale and in the long term, this idea leads to an exact computation of a moment of the universe given the initial conditions and its governing laws at the time of its creation. This is the key point for some scientific determinists who exclude the Divine work in the universe; if God exists, He only sets the initial conditions and the physical laws of the universe. Then the universe works on its own like a machine.

The first modern idea of scientific determinism was articulated by Newton in 18th century. Newton believed that all the laws governing the universe could be deduced from formulas, and these formulas could be derived by following the scientific method. First of all, science requires consistency among all known formulas and theories. This led the German mathematician David Hilbert to tackle the problem of proving the consistency of arithmetic in 1900s. One way of showing the consistency of arithmetic was to prove or disprove infinite number of statements in arithmetic, which was practically impossible! Instead, a clever idea was to develop a methodology that will generate the proof or disproof of a given arbitrary statement in arithmetic. If that methodology existed and was shown to be correct, that would be the happy ending of the story. Motivated by this problem in 1913, Alfred Whitehead and Bertrand Russell wrote their work, Principia Mathematica, a three-volume work on the foundations of mathematics. It was an attempt to derive all mathematical truths without the requirement of human intuition. They utilized symbolic logic, since it has a profound methodology for proving statements.

Later, this work would have played a fundamental role for proving the correctness / incorrectness of any statement in the universe. As an ultimate goal, by deducing all the information that belongs to a certain time of the universe, it would have been possible to compute the exact situation of the universe at an arbitrary time, which we mentioned before.

The fall of scientific determinism

At that time, Principia Mathematica left two questions open:

• Could a contradiction be derived from the Principia’s axioms (the question of inconsistency)?

• Does a mathematical statement which could neither be proved nor disproved in the system (the question of completeness) exist?

These questions were the heart of the discussion, and they had to be both answered as ‘no’ by Principia Mathematica to be deterministic. We have already explained the necessity of consistency before. On the other hand, some states cannot be calculated in an incomplete system which violates the determinism.

In 1931, Gödel published his famous article “On formally undecidable propositions of Principia Mathematica and related systems.” This work claims to refute the claims of scientific determinists about deriving all mathematical truths from logical systems. In his article, Gödel’s first incompleteness theorem showed that sufficiently complex systems (such as the ones described in Principia Mathematica and the physical laws of the universe) could not be complete and consistent at the same time. Gödel proved his theorem using a genius idea, which was by showing that a similar statement to “This statement cannot be proved” can be expressed in any sufficiently complex logical systems. Hence, one who proves it will create an inconsistency in the formal system, or it will be considered as improvable, violating the completeness rule of the formal system.

Another stroke to scientific determinism came from Heisenberg in 1927 with his famous Uncertainty Principle. Heisenberg asserted that both the velocity and the position of a particle cannot be accurately measured at the same time. Measurement requires interfering with the particle in terms of position or velocity. Observation becomes a part of the outcome which is in fact not known to be the real outcome. In short, uncertainty principle implies that the particle positions can only be calculated as a probability distribution.

One can object that this effect may be a result of our lack of the knowledge needed to find out the facts about particle position and velocity. However, Copenhagen’s interpretation of Quantum mechanics is commonly accepted, and it states that the problem of uncertainty is not epistemological but ontological; i.e., the problem is not due to the limits of scientific knowledge but depends on the constitution of the universe . From a mathematical aspect, Gödel’s theorem strongly asserts the same fact.

Consequences of non-determinism

Non-determinism in the Universe brought back earlier concepts categorized as meta-physical, such as ‘fate’ and ‘free will,’ into the debate about scientific knowledge for further investigation, and made a phenomenal change in the perspectives on the existence of God.

In The Matrix, remember the scene wherein Neo says “Deja vu” after he sees the black cat for the second time at the stairs of the apartment. Then Trinity tells him that it happened due to a change in the Matrix. The free will of Neo and his friends causes the failure of the deterministic nature of the Matrix; the Matrix cannot make exact calculation of their actions and foresee the future. Instead, it alters the simulation program based on their actions. Now, the concept of fate is not a predetermined destiny in the Matrix; it involves the human free will, hence nobody knows what will happen in the future, including the Matrix itself.

Free will requires the ability to make choices independent from deterministic constraints. A friend of yours offers you to take one of two identical apples, and you take one of them. If it was possible to rewind time and get back to the moment of the offer, this time you might choose the other apple. Note that the states are precisely the same; the entire history of the events in the universe is exactly the same as the one in previous scenario. This is the key point: in two equivalent states of the universe; i.e., all conditions are exactly the same, free will allows you to choose different options in these two states. This situation contrasts with a deterministic universe however well suits to a non-deterministic one.

Another major consequence is about the Creator’s role in the universe. As mentioned before, scientific determinism can reduce the concept of ‘God’ into the following statement [4, 6]:

• If there is a God, He created the universe, set the initial conditions and the laws, and left it the way it works. He doesn’t interfere with its execution.

By non-determinism, this statement can no longer be regarded as the absolute truth. Instead of clearly determined outcomes in the future time frames, Quantum mechanics introduced the notion of probabilities. In each decision point (i.e., quantum time frames or every single moment), there are many possible outcomes. That means either there is an entire ‘randomness’ or there is a Decision Maker that decides at these decision points and controls the flow of all actions in the universe. In case of randomness, it is always possible to reach a ‘failure state’. However, the universe has never failed for billions of years. Here, the failure state is not the ending of the universe or Armageddon, because these states are internally consistent. Failure state means to get the ‘blue screen’ as in Windows; suddenly everything stops or perishes. ‘Failure’ can be described as an unexpected error that leads unrecoverable / unhandled error which crushes the operating system. At this point, the universe needs to restart in order to start everything from the beginning. The idea of randomness in the course of actions is strongly opposed by Einstein as stated in his famous saying “God doesn’t play dice.”

So the question is “how can the concepts ‘God’, ‘fate’ and ‘free will’ be related to each other?” Now, we may say the following statements about fate: it is not computable, it is not random (due to the definition of fate), and free will is possible. In this case, we have two options:

• there is no free will – God controls all the events and free will is not involved in it,

• there is free will – God incorporates free will in his creation of the upcoming states

According to the second idea, we have been given the right to choose among limited amount of options and then God creates the chosen option. For instance, I would like to move my arm and show the tendency to move it. So, God creates necessary conditions such as the pulse from the brain that orders the arm to move, and the arm moves. Of course, He always preserves the right not to create the things according to my will. In that case, the arm doesn’t move – I might have a stroke or might not have sufficient strength or something else might happen.

Consequently, in case of free will, fate becomes all the outcomes of God’s will by including free will in the universe. But “God knows everything, everything that will be in the future. Then, doesn’t that mean the universe is deterministic?” As we mentioned above, determinism requires the computation of future states. However the Creator knows the fate with His infinite knowledge by overseeing the entire system but not computing. Here, computation and knowledge are two different concepts; knowledge may not be acquired by computation. If somebody shows us the result of a multiplication of two numbers, we learn the result by seeing it but not computing it.

Non-determinism in the universe might be considered as the beginning of a re-marriage between science and meta-physics. Non-determinism implies that it is not reasonable to absolutely reject Divine work in the operation of the universe and the idea of free will. The concepts that are considered to be currently meta-physical such as fate and free will need further investigation in the physical sciences.

Fatih Gelgi has a PhD in computer science. He is currently the computer coordinator of Accord AMSP team in Los Angeles.

References

[1] K. Devlin. “Kurt Gödel – Separating Truth from Proof in Mathematics,” Science, 298: 1899-2000, 2002.

[2] F. Gelgi. “Implications of Gödel’s Incompleteness Theorem on Artificial Intelligence vs. Mind,” The Fountain Magazine, 46, 2004.

[3] K. Gödel. “Uber formal unentscheidbare Satze der Principia Mathematica und verwandter Systeme I,” Monatshefte für Mathematik und Physik, 38: 173-98, 1931.

[4] S. Hawking. Brief History of Time, Bantam Dell Publishing, Ed. 10, 1988.

[5] E. Nagel, J. R. Newman. Gödel’s Proof, New York University Press, 2001.

[6] C. Taslaman. Kuantum Teorisi Felsefe ve Tanri, Istanbul Yayinevi, 2008.

[7] Wikipedia, “Principia Mathematica,” retrieved on Feb 27, 2010 from http://en.wikipedia.org/wiki/Principia_Mathematica.

Notes

1. Interested reader may refer to [5] for the detailed and understandable explanation of Gödel’s proof.
2. For details see “Chapter 4: Uncertainty Principle” in [4].
3. Different interpretations of Quantum physics can be found in [6] or at: http://kuantum.gen.tr.

– Moive Review

Science Fiction/Fantasy and Action/Adventure

Rated R for sci-fi violence and language

Starring: Keanu Reeves, Laurence Fishburne, Carrie-Anne Moss, Hugo Weaving, Joe Pantoliano

Directed by: The Wachowsky Brothers

Produced by: Andrew Mason and Joel Silver

Written by: Andy Wachowski and Larry Wachowski

Distributor: Warner Brothers

In the year 1999. To be more precise, people believe it is the Year 1999. In facts we are well into the middle of the twenty-first century. In addition, this is not the only reality concealed from us. The “creators” of artificial intelligence were caught unprepared while they were drunk on the extent of their accomplishments. There has been a great revolution-machine revolted against humanity and conquered life. Now we do not even have a system about whose corruptness and shortcomings we can complain. Yet we continue to work from 8 a.m. to 5 p.m. in our daily shifts, eat hamburgers while watching television, and attend parties. Children are still being born, and the sun still rises and sets.

However, none of this really exists, for only the “Matrix” exists. This “Matrix” is the name of a dream from which we cannot awake. It also is a three-dimensional curtain pulled between reality and humanity. With your fork-actually your fork does not exist either-you can still feel the taste of a nonexistent slice of meat. Tiredness, disappointment, and sorrow are all possible, along with the signals they send to your brain, most of which they already own.

Unless you believe “ignorance is a virtue,” like someone who realizes the difficulty of “knowing” does after he or she has known, you would like to learn. Yet, you also realize immediately that knowing this particular truth does not exalt you. This is neither an auto-criticism nor a suggested solution, but rather a knowledge that you will not be able to relate to others with extravagant praise or mention in every meeting or social gathering.

In fact, you would prefer not to know it at all: Matrix is the name of a computer program that is animated as if it is “life.” In reality, our bodies are connected to metal basins, and cables of various sizes are plugged into us. Our life lasts only as long as (the lifetime of the “battery.” We are planted on electronic fields, harvested and fed “until we exhaust” the battery. We are walking around with large plap-ins,which provide our connection with the machine, located at the back of our heads. Only those few who were born naturally have seen the world in which real parents exist, known in the movie as “Zion,” and do not have plug-ins. Zion is the only place that the electronic barbarians cannot enter, which is why the ruthless guards of the Matrix are trying so hard to find its coordinates.

THE CHOSEN MAN

Thomas Anderson is a computer geek who works for a software company during the day and spends his nights as a computer hacker known as “Neo.” There is a truth that he has been trying to find for a long time: Is his life somehow being controlled? He is after “Morpheus,” whose name is usually uttered as if he were a terrorist. Neo feels that this man is somehow connected to his problems and can provide him some answers. Morpheus gets in touch with Neo through his assistant “Trinity.”

When they finally meet, Morpheus promises to show Neo “the truth,” of which even minute parts are invaluable. Now, faith is the power that reality cannot deny. Neglecting humanity’s fragile nature, men and women built the Machine and will defeat it to the extent that they can free their thoughts from it. Is Neo the awaited savior? If so, what will he promise to humanity? Unless they are killed at the instant they “awaken,” will he promise the underground breakfasts consisting of mossy oats at best? In place of a joyful but unreal world, can he promise a dark but real world?

ELECTRONIC SCIENCE FICTION

Finally, a science fiction movie that can be viewed with enjoyment and suspense, one that is graded “A” despite its shortcomings. In The Matrix, the dose of excitement, long and technical dialogues, and contrasts are properly blended. The fighting scenes, modeled after Asian action movies and modernized in a computer environment, have been transformed into a public demonstration by the aesthetic style of the Wachowsky brothers. They do not hesitate to use such scenes, for they know that even viewers who do not like such action and fighting scenes will appreciate the results. With cameras that can shoot 12,000 clips per second, with actors seemingly almost independent of gravity, these fighting scenes seem like dances conforming to the movie’s theme, rather than brutal fights.

The movie moves smoothly between prologue and awakening, development and meeting, result and struggle, and conclusion. Among the cool, black-clad men and women with sunglasses, Reeves, Fishburne, and Moss have peculiar facial expressions. But the movie itself has a power beyond its individual components. One example of this is how the camera approaches objects: In one scene, the camera is located right under the helicopter and window from which a gun is being fired. Both action areas can be seen, yet the focus is on cartridges seemingly suspended in the air and then gradually gliding to the ground

As a matter of fact, the question: “Seeing that this electronic mechanism fools man and condemns him to a virtual life, to a dream from which awakening is impossible, could not man be deceived by a better view of 1999 rather than the present one?” is answered before long. Agent Smith accidentally lets the cat out of the bag when he has cornered Morpheus: “We wished a better world for man, but man defines his essence with such misery and sorrow that these designs were rejected by human conscious in the experiments.”

The martial-art figures borrowed from Asia give the impression that this struggle to awaken humanity carries a deeper philosophy, yet only in the movie’s second half is this suspicion confirmed. But it is impossible not to notice the symbolic supports of the Bible and Greek mythology, which are layered one inside the other and pervade the movie’s life and imagery. The relationship of “Trinity” to the Bible is self-evident. Moreover, “Neo” (like his name, he also is “new”) ascends to his own “reality” under the protective wings of “Morpheus” (the Greek god of dreams), who heals the mental and physical harm caused by switching from one world to another. Trinity Morpheus, and Neo form a sacred trio who know the “truth” and partially own the mechanism to alter it. They are striving to benefit a humanity corrupted by its own faults, while at the same time being fully aware that they really do not have more than just their belief. Until he experiments with the limits of his powers to learn if he is the “Chosen One” or not, Neo continues to learn. A female soothsayer wants him to sacrifice himself. After all, is there any other savior for humanity, who became arrogant because of its accomplishments but lost the struggle against evil forces and was enslaved, other than a “Chosen One”?

A BROTHER TO LEM

I do not know how much of The Matrix is inspired by the science fiction work of Polish author Stanislaw Lem. But the theme of living in a fake world as if alive, which came to the public agenda with such books as Strangers by Day (by Vicki Malones, 1984) and movies as Dark City (written by Frank Lauria, 1998, the movie version released on February 27, 1998), or the theme of an existing dark reality contrary to the present make-believe world-in other words the theme of illusion-simulation-is not so new.

The Matrix’s story-line bears a considerable resemblance to a book written in the 1970s by Lem, who is considered to be the genius of science fiction. But rather than eulogies, Lem delicately criticizes science. He foresaw humanity’s misfortunes and degeneration years ago. He touches on the results of inventions and discoveries in his future tableaus, rather than becoming carelessly intoxicated by them, and analyzes our greed and inordinate desires via scientific diagnoses and terms. Lem fictionalizes a virtual world similar to The Matrix in his 1974 novel The Futurological Congress.

The story goes like this: After a space voyage, Ijon Tichy finds himself in an advanced twenty-first century civilization. He tries to understand the age in which he lives and what he missed while asleep in the shuttle. In this new age, people can assume any temperament they want via chemical stimulants, store in their brains any information they want to by means of drugs, torment those they hate in their virtual worlds, travel, and participate in any virtual fantasy. In this “democracy,” such serious social problems as prejudice and racial discrimination are solved by chemicals. Opportunities are endless. There are firms to decide things for you, fight your fights, even to satisfy your religious sentiments. In short, this society has an ultra-free market economy.

Ijon comes across a Professor Trottelreiner, whom he had known long ago and who was sent to sleep in a spaceship like himself. He shows Ijon more than he wants to know by giving him a bottle of fragrance to smell. The scent emitted from the bottle shows reality to Ijon. The eye-catching restaurant coated with Italian tile, and the palm trees are transformed into a coarse underground shelter. The pheasant they are eating is, in fact, a porridge that has a grayish-brown vomit-like color, because the last pheasant died 25 years ago. The palm tree is really the rubber underwear of the man living in the upper shelf, which in reality is too narrow. People inhabit an incredibly overcrowded world, and forks and knives are made of tin.

Worse than that, Ijon understands why people are always red and out of breath: There are no elevators, so people reach the ninth and tenth floors by climbing up elevator cords. The chemical empire has already started to transform them, for most people now have stained and discolored skins, longer ears, and scaly backs. All seen images and used chemicals conceal the already demolished system of the planet, on which more than 20 billion people live. The air we breathe is full of camouflage mascots, reality is hidden under layers of chemical products, and humanity is rescued superficially from the reality of poverty and misery!

The Matrix is a movie that should be seen more than once. The Wachowsky brothers took into consideration not only aesthetic styles, but also commercial worries by meeting the expectations of an average sci-fi viewer and then combining both issues on the same platform. After the Coen and Taviani brothers, it is possible to say that the Wachowsky brothers, who managed to attract interest with their previous movie Bound, have opened a respected room in the cinema for themselves with The Matrix. We can only hope that the sequels, already rumored to be coming soon, will be just as good.

The best side of the movie is the Matrix paranoia itself, which is even scary to say. The Matrix gains importance when the uncontrolled life is faced with the reality of existence, the purpose of which is almost forgotten. It gains importance by becoming the new name for alienation, enslavement, and enumeration. Everything is assigned a number, including people. Our identification and accomplishments, everything we do, is specified with statistics and numbers, which have more value than the individual in the twenty-first century.