Showing posts with label Kimia dan Biologi. Show all posts
Fisikawan Menyelaraskan Diri dengan Neuron
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| Neuron dan transfer informasi |
Have you ever wondered why certain sets of musical notes sound perfectly melodious while others make you want to cover your ears? Now, physicists in Europe have developed a model that suggests that certain notes sound harmonious because of the consistent rhythmic firing of neurons in the auditory system. The researchers say that they have now quantified this effect by showing that the neural signals are regularly spaced for frequencies that are pleasant sounding, but are erratic for those that are not. They say that their model may also provide insights into other senses, such as vision, that employ similar neural processing systems.
Hitting the right notes
How humans and animals perceive sound has long fascinated scientists because of the brain's amazing ability to process auditory signals. "The auditory sensory system is the most investigated apparatus. But even simple sound signals – pairs of pure tones such as musical chords – are able to cause phenomena that can not be simply explained," says Bernardo Spagnolo of the University of Palermo, Italy, and one of the authors of the study published inPhysical Review Letters this month.
As examples, Spagnolo cites two things that musicians take for granted: the "pitch perception" and the "perception of consonance and dissonance". Simply put, perceiving pitch is simply being able to differentiate clear frequencies of sounds, while the perception of consonance and dissonance is being able to tell the difference between harmonious and inharmonious chords.
In their current research, the researchers focused on consonance and dissonance perception with the aim of identifying the location and quantity of the signals associated with harmony and disharmony in the brain.
On board the "spike trains"
Hearing involves the conversion of sounds into neural "spike trains". The researchers' model comprises three neural-like elements. Two of these elements represent sensory neurons and are driven by noise at two different frequencies. The outputs of two neurons, in the presence of a "noisy" environment, are synaptically connected with the third neuron, which represents an "interneuron". This is an internal neuron that connects a sensory neuron to other neurons in the brain. In reality there are more than two initial neurons, as the human ear can operate at frequencies of between 20 Hz and 20 kHz and can detect sounds over a range of 120 decibels.
The output spike train of the interneuron is the main focus of the study, which found that if an acoustic signal is transformed by the auditory system into spike trains with a regular distribution of inter-spike intervals, then the signal is perceived as harmonious. But when the inter-spike intervals are irregular, the signal is perceived as inharmonious. At the output of the interneuron, inharmonious input signals give rise to blurry spike trains, while the harmonious signals produce more regular, less "noisy" spike trains.
Senses and sensibility
The research team quantified the regularity of the interneuron output in terms of the entropy of the signal. "This regularity is linearly connected with informational entropy: harmonious chords give rise to high spike-train regularity and so low entropy; inharmonious chords give rise to low spike-train regularity and so high entropy."
Spagnolo points out that the model can investigate the role of external and internal "environmental noise" in the nervous system, with respect to the sensory phenomena of "recognition" and "permanence of information" contained in complex input signals in the brain. "Investigating this process can help to understand which types of input signals are able to survive in the noisy environment of the brain, reveal the mechanism of this process, and explain what it means from a perceptional and cognitive point of view," claims Spagnolo. He also says that studying and understanding the auditory system provides a basis for other less-studied sensory systems "that exhibit the analogous principles of conversion of environment stimuli into the neural spike trains".
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Proof
The word Proof comes from the Latin probare meaning "to test". Related modern words are the English "probe", "proboscis”, "probation", and "probability", the Spanish "probar" (to smell or taste, or (lesser use) touch or test),[3] Italian "provare" (to try), and the German "probieren" (to try). The early use of "probity" was in the presentation of legal evidence. A person of authority, such as a nobleman, was said to have probity, whereby the evidence was by his relative authority, which outweighed empirical testimony.[4]
Plausibility arguments using heuristic devices such as pictures and analogies preceded strict mathematical proof.[5] It is probable that the idea of demonstrating a conclusion first arose in connection with geometry, which originally meant the same as "land measurement".[6] The development of mathematical proof is primarily the product of ancient Greek mathematics, and one of its greatest achievements. Thales (624–546 BCE) proved some theorems in geometry. Eudoxus (408–355 BCE) and Theaetetus (417–369 BCE) formulated theorems but did not prove them. Aristotle (384–322 BCE) said definitions should describe the concept being defined in terms of other concepts already known. Mathematical proofs were revolutionized by Euclid (300 BCE), who introduced the axiomatic method still in use today, starting with undefined terms and axioms (propositions regarding the undefined terms assumed to be self-evidently true from the Greek “axios” meaning “something worthy”), and used these to prove theorems using deductive logic. His book, the Elements, was read by anyone who was considered educated in the West until the middle of the 20th century.[7] In addition to the familiar theorems of geometry, such as the Pythagorean theorem, the Elements includes a proof that the square root of two is irrational and that there are infinitely many prime numbers.
Further advances took place in medieval Islamic mathematics. While earlier Greek proofs were largely geometric demonstrations, the development of arithmetic and algebra by Islamic mathematicians allowed more general proofs that no longer depended on geometry. In the 10th century CE, the Iraqi mathematician Al-Hashimi provided general proofs for numbers (rather than geometric demonstrations) as he considered multiplication, division, etc. for ”lines.” He used this method to provide a proof of the existence of irrational numbers.[8] An inductive proof for arithmetic sequences was introduced in the Al-Fakhri (1000) by Al-Karaji, who used it to prove the binomial theorem and properties of Pascal's triangle. Alhazen also developed the method of proof by contradiction, as the first attempt at proving the Euclidean parallel postulate.[9]
Modern proof theory treats proofs as inductively defined data structures. There is no longer an assumption that axioms are "true" in any sense; this allows for parallel mathematical theories built on alternate sets of axioms (see Axiomatic set theory and Non-Euclidean geometry for examples).
