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A specific reality aids in developing consciousness for allowing more precisely sensing characteristics of cerebral activities and the world surrounding us. Making attempts to find out what such a reality is must be continued for enjoying the civilization involving various cultures. Then, one of the most important factors determining what kinds of situations correspond to happiness is consciousness; the consciousness encourages the brain to perform cerebral activities depending on the consciousness. For this reason, it is difficult to expect that the consciousness widens windows for the consciousness without contributions of at least science and arts, and it is difficult to expect that the consciousness widens also variations on such windows without contributions of at least science and arts. Arts stimulating the right hemisphere have great potentialities for developing consciousness that can moderate activities of the amygdala. However, the responsibility for continuing to make the above attempts belongs to at least science, which must contribute to being aware of realities of things that cannot be seen for being too much smaller and also must contribute to being aware of realities of things that cannot be seen for being too much larger. An awareness of realities of molecules is one example that might have opened windows toward a specific portion of happiness. For example, a portion of benefit, a portion of convenience, and a portion of comfort are obtained from manipulating molecules chemically or molecular-biologically. Then, the aim of technology is to concentrate our consciousness on a specific expectation that inventing new materials and products with the use of scientific knowledge always yields more benefit, more convenience, and more comfort. Happiness involves both a specific portion depending on convenience and another specific portion depending on comfort. Moreover, the happiness may involve a specific portion depending on benefit. These situations can accompany an increase in the entropy of which the physical meaning has become clear from the fact that substances have been able to be recognized as ensembles of atoms or molecules. Today, a strong desire for the above three portions of happiness has the potential for resulting in a risk to the happiness because of discouraging the reality of Earth and the limit of the potential of the environment from being recalled. Opportunities to feel the reality of the Planet and to imagine its meanings can be fortunately obtained from observations for various astronomical objects.
Picture Album: A Giant Hubble Mosaic of the Crab Nebula
The Crab Nebula is a supernova remnant, all that remains of a tremendous stellar explosion. Observers in China and Japan recorded the supernova nearly 1,000 years ago, in 1054.
Credit: NASA, ESA, J. Hester and A. Loll (Arizona State University)
The Crab Nebula is one of beautiful nebulae. Consistently connecting a piece of knowledge with another piece of knowledge decreases information entropy; consistently connecting between the two results in precious information. Information entropy associated with its beauty can be decreased if the pieces of information carried by pulsars, supernovae, neutron-stars, and general relativity are consistently considered with the beauty. According to Claude Elwood Shannon, the concept of information entropy can characterize treatments of pieces of information such as their propagation, their association, and their modification, and it aids in analyzing roles played by pieces of information.
In 1054, a specific brightness similar to the Jupiter appeared as a sufficiently small contrast with the normality. If the night sky is clear, a lot of bright stars are found normally. According to an interpretation on a diary written by an ancient Japanese poet Teiji Fujiwara, the brightness appeared at 2:00 AM on 19 June in the direction where Zeta Tauri is located, and it was able to be seen until the day on 28 June. It was a supernova. A Dutch astronomer Jan Hendrik Oort and co-workers identified the remainder of this supernova as the Crab Nebula in 1942. Having connected the historical information with the observed information allowed the value of the observed information to rise.
Oxygen, which is one of atomic constituents forming water, can be found with carbon, nitrogen, silicon, iron, and so on as one of atomic constituents forming dust and gas ejected by the explosion, which caused the above supernova. The hydrogen atoms bonded to the oxygen atom of each water molecule consist of protons and electrons that were synthesized in the expansion process due to the big bang 13.8 billion years before. A proton forming each hydrogen atom with an electron is 1836 times as heavy as an electron, since each proton is composed of two u-quarks and one d-quark. However, it is sufficiently light for moving in comparison with the other nuclei. Each proton belonging to a water molecule can readily move from the oxygen atom of the molecule to the oxygen atom of an adjacent water molecule via a specific bridge formed by electron clouds jutting out from the oxygen atom of the adjacent water molecule. The proton’s capability to move from an oxygen atom to another via electron clouds strengthens the attractive forces between water molecules. Water molecules can form more stable clusters than other molecules interacting with each other through the van der Waals force. The motion of protons from an atom to another via electron clouds can be found even in a biomolecule such as a protein molecule, DNA, RNA, etc. Effects from the motion of protons significantly contribute to forming specific structure of each biomolecule, and also contribute to making molecular biological reactions such as various enzyme reactions proceed for maintaining activities of the living things.
Water molecules decrease their kinetic energies if temperature of water is decreased. When temperature reaches the freezing point, water is transformed from the liquid state having the large entropy to a crystal state having the small entropy. In contrast, an increase in temperature increases kinetic energies of water molecules. When temperature reaches the boiling point, their kinetic energies prevent the water from maintaining the liquid state, and then, the kinetic energies transform the water from the liquid state to the gas state having the larger entropy. The phase transitions of water can be linked with kinetic energies of water molecules on the basis of a general concept that substances are recognized as ensembles of atoms or molecules.
1. Awareness of random movements of molecules
In 1827, the Brownian motion of colloidal particles was already discovered under the microscope by the botanist Robert Brown as the irregular motion of the colloidal particles. However, consciousness that is not oriented toward an interest in an essential cause of the irregular motion did not allow people including even Brown to be aware of the importance of connecting between the irregular motion and a particular evidence for the existence of molecules.
A colloidal particle distributed in a colloidal suspension is irregularly vibrating around itself. However, the colloidal particle sometimes repeats a small shift in an irregular direction. Then, if extremely small things having considered as an imaginary things are recalled, it is not difficult to become aware of realities corresponding to the existence of molecules and their movements. However, consciousness cultivated by daily experiences encourages the brain to reject the existence of extremely small things that cannot be seen. Accepting the reality of the extremely small things may not be easy for the brain controlled by consciousness cultivated by awareness resulting from daily experiences. Then, the questions corresponding to asking how the above irregular motion of the colloidal particle should be analyzed and to asking what should be considered through analyzing the random motion are questions that are asked us. Trying to reply these questions has made the brain think that observing irregular motions of colloidal particles is equivalent to obtaining the evidence of existence of molecules being invisible. Ultimately, trying to reply the questions has made the brain succeed in linking the irregular motions with an idea about the random movements of molecules, and has allowed our understanding to reach the fact that the number of molecules is estimated from the success. The estimation of Avogadro’s number corresponding to information of the number of molecules has been achieved. Having linked observed information with a hypothetical idea has revealed that the hypothetical idea is real.
Collisions with molecules make colloidal particles vibrate and shift irregularly. By considering that this phenomenon is made to accompany the effect of the gravitation of Earth, a new evidence for the existence of molecules can be obtained. The Brownian motion allows colloidal particles to continue to be distributed in a liquid against the gravitation of Earth. Collisions of the colloidal particles with a huge number of molecules allow them to be distributed against the gravitation. However, no matter how frequently the collisions occur, the colloidal particles cannot be raised freely at higher positions in the liquid. If a colloidal particle moves at a higher position against the gravitation, then the colloidal particle has a larger potential energy. An increase in the potential energy of the colloidal particle cannot freely occur even if collisions of the colloidal particle with molecules frequently occur. In other words, colloidal particles cannot homogeneously be distributed from a lower area to an upper area even in a layer of the liquid that has a thickness of 0.1mm. In fact, the density n(z) of colloidal particles more decreases at larger z being a higher position in a hollow slide. The random movements of molecules making the collision occur exist. Therefore, molecules exist even if they cannot be seen and their existence cannot be felt.
Similarly, the density n(z) of the air also becomes lower at larger z being higher altitude. The relation between the number of molecules consisting of the air and the potential energy of each molecule is similar to that found from a colloidal suspension.
Certainly, even extremely small objects being invisible such as molecules receive attractive forces due to the gravitation of Earth. This fact is confirmed even from the relation between an ensemble of molecules and the entropy of its system. The relation can be readily estimated from the use of statistical mechanics. Assuming that N molecules confined in a cylinder having a length L and a cross section πR２ behave as an ideal gas at temperature T, the free energy F of the system is given by
F = F0 – NkBT loge [(1/V)∫exp(–mgz/kBT) dV],
where F0= –NkBT loge [(eπR2L/N)( 2πmkBT/h2)3/2] and V=πR2L. Moreover, mg is a force caused by a uniform gravitational field for each molecule; the z axis is vertical and parallel with the axis of the cylinder; kB is the Boltzmann constant
(kB=1.380658×10-23J/K); F0 is the free energy when mg = 0.
The free energy allows the entropy S to be given by S = – ∂F/∂T. Therefore,
S = S0 + Sg ,
where
S0 = – ∂F0/∂T
Sg = NkB {∫n(z)/n0 dV loge [(1/V)∫n(z)/n0 dV]
–∫n(z)/n0 loge [n(z)/n0] dV } [∫n(z)/n0 dV]–1.
Here, n(z)/n0 is given by n(z)/n0 = exp(–mgz/kBT), and the relation 0 < n(z)/n0 ≦1 is satisfied. If n(z)/n0=exp(–mgz/kBT) with n0=(Nmg/πR2kBT) [1–exp(–mgL/kBT)] is considered, Sg can be a priori evaluated. n(z)/n0 can be obtained from measurements of pressure of a gas, so that it is possible to even a posteriori evaluate Sg for the distribution of molecules. The above equations also are applicable to the distribution of colloidal particles in a colloidal suspension, and then, mg is a force caused by a uniform gravitational field for each colloidal particle.
In addition, Earth does not have the strength of gravitation that allow n(z)/n0 to approach a small value near zero at finite temperature. In the universe, it is possible to find astronomical objects having the strength of gravitation that allow n(z)/n0 to approach a small value being sufficiently close to zero at finite temperature.
The form of equation representing Sg is similar to that of equation representing the concept of information entropy for analyzing information. This means that the behavior of S and the behavior of information entropy can be mathematically similar. Generally, information entropy founded by Shannon is similar to the entropy of a thermodynamic system with respect to a mathematical form. Despite this, analyzing uncertainty accompanied by pieces of information concerning the daily life must be helped by the concept of information entropy. If an increase in the amount of information occurs without considering relations between pieces of the information, the increase allows an increase in the information entropy. On the contrary, if a relation is formed between pieces of the accumulated information, the information entropy is allowed to decrease. This means that making attempts to decrease situations where pieces of the accumulated information exist independently is important.
The dependence of the density n(z) of the air on altitude is a portion of realities that the daily life allows us to feel. The random movements of molecules are a reality that is not seen with the naked eye, and also a reality that allows a concrete physical meaning to be given to the entropy. Despite this fact, a trace of the reality concerning their random movements corresponds to the dependence of n(z) on altitude. Thus, a portion of realities that do not allow us to feel can coexist with us in the daily life. Such realities result also from astronomical observations. One of the realities is dark energy, and our bodies and Earth are immersed in the space filled with the dark energy. Another one of the realities shows that our bodies and Earth are immersed in the atmosphere of dark matter, which is surrounding the Milky Way. According to current observations, dark matter exists in inhomogeneity. Moreover, a number of neutrinos always penetrate our bodies and Earth. Naturally, these are realities that cannot contribute to an increase in the entropy of today’s global system.
The consciousness cultivated by comfort, convenience, and benefit may encourage the brain to accept the existence of molecules for more happiness. In this epoch, it is difficult to find a situation where the existence of small objects being invisible such as molecules is simply rejected. However, this does not simply mean that the brain subjected by the consciousness accepts the fact that a specific portion of thermodynamic features of a system being an ensemble of molecules is characterized by the entropy of the system. The brain has a tendency to reject the meaning of an increase in the entropy of the global system.
CO2 molecules can efficiently absorb infrared radiation in a 2.5-3μm band and infrared radiation in a 4-5μm band. The CO2 molecules in the atmosphere can return a portion of infrared radiation emitted from the surface of Earth. Emitting more CO2 gas increases the entropy of the global system. If more emission of CO2 and more heat generation are accompanied by the use of energy for acquiring more benefit and for achieving more convenience and more comfort, the entropy of the global system must be increased.
2. Contrast with astronomical objects
Consciousness being concentrated on acquiring more benefit and on achieving more convenience and more comfort can encourage the brain to forget the fact that Earth is only one planet providing the normally habitable environment for all the living things. Continuing to recall the fact that happiness can be formed on this habitable planet is important for continuing to enjoy the civilization. Experiences in the daily life cannot efficiently contribute to forming images of Earth. The contrast between Earth and astronomical objects should aid in give Earth images that cannot be formed through the daily life.
(1) Gravitational accelerations
On the surface of Earth, a particle having mass m receives the force mg. g is the gravitational acceleration, and is given as 9.798m/s2 because Earth has the mass of 5.9736×1024 kg. Then, Sg is approximately estimated as Sg = –NkB[mgL/kBT]2 since the magnitude of n(z)/n0 is close to 1. For the gravitation, the entropy of the system in the cylinder is slightly decreased. In addition, at an altitude 1000m, g is given as 9.795 m/s2, and at an altitude 400 km (the altitude of the International Space Station) as 8.67 m/s2 because g = G×[Mass of Object]÷[Distance from Center of Object]2 with G = 6.67259×10–11 m3/(kg s2).
On the moon having the mass of 7.3477×1022 kg, g is estimated as1.622 m/s2. On the Mars having the mass of 6.4185×1023 kg, g is estimated as 3.711 m/s². On the Neptune having the extremely thick layer of ice and the mass of 1.0243×1026 kg, g is estimated as 11.15 m/s2.
Picture Album: Springtime on Neptune — 1998 Image of Neptune
Image 228 of 1207
Credit: NASA, L. Sromovsky, and P. Fry (University of Wisconsin-Madison)
Moreover, we can find a large gravitational acceleration on the surface of a specific astronomical object called a white dwarf. Sirius perceived by the naked eye as a single star being the brightest in the night sky is a binary star system, consisting of a white main sequence star, termed Sirius A, and a faint white dwarf companion, termed Sirius B. Although Sirius A is 25.4 times more luminous than the Sun, Sirius B known as a white dwarf is only 0.026 times more luminous than the Sun. Sirius A is 2.02 times more massive than the Sun and Sirius A’s radius is 1.711 times larger than the Sun’s. The surface temperature of Sirius A, is 9,940 K, and the surface temperature of Sirius B is 25,200 K. The Sirius system belongs to Canis Major, which is one of the 88 modern constellations, and is one of the neighbors of Orion being one of the most conspicuous constellations. Sirius A and Sirius B move around the center of gravity in a period of 49.9 years, and the distance separating Sirius A from Sirius B varies between 8.1 and 31.5 AU (1AU=150,000,000 km being nearly equal to the mean distance between Earth and Sun). The Sirius system is one of Earth's near neighbors and is located at a distance of 8.6 light years.
Picture Album: The Dog Star, Sirius, and its Tiny Companion
Image 187 of 1207
The big star at the center is Sirius A. A small point in the left and down side of Sirius A is Sirius B.
Credit: NASA, H.E. Bond and E. Nelan (Space Telescope Science Institute, Baltimore, Md.); M. Barstow and M. Burleigh (University of Leicester, U.K.); and J.B. Holberg (University of Arizona)
In 2005, using the Hubble Space Telescope, astronomers determined that Sirius B known as a white dwarf has a radius 0.0084 ± 3% of Sun (6,000 kilometers being nearly equal to Earth 's) and a mass 97.8% of Sun. Sun’s Equatorial radius is given as 6.955×105km and Sun’s Mass is 1.9891×1030kg. Thus, the gravitational acceleration reaches g = 374,000,0 m/s² on the surface of the white dwarf. The gravitation on Sirius B is 370 thousand times as strong as that on Earth. Then, n(z)/n0 becomes a extremely small value near zero. Then, Sg is approximately estimated as Sg=NkB[1-loge(mgL/kBT)], and it has a large negative value since mgL/kBT is large. This means that the entropy of the system in the cylinder is apparently decreased for the gravitation. In addition, the gravitation on the surface of a neutron star having a radius on the order of 10 km is 500 thousand times stronger than that on the above white dwarf.
The compression of these stars due to the gravitation makes us ask how the stars keep their sizes. Answering the question of why the white dwarf can keep its size and the other question of why the neutron star can keep its size is equivalent to answering the question why an atom can keep its size. Recognizing the existence of atoms allows an awareness of the Pauli exclusion principle. Ultimately, accepting the existence of atoms being invisible enables us to explain the reason why Earth keeps its size.
(2) Seeking realities of atoms and molecules
The existence of atoms and the movements of atoms were refused in the beginning of 20th century. Knowing of atoms is not equivalent to understanding the existence of atoms. Consciousness cultivated in daily life encourages the brain to conclude that extremely small things being no able to be seen are equivalent to nothing. Things that cannot be sensed by sensory organs can become equivalent to the evidences that they do not exist. Phenomena that cannot be sensed by sensory organs can become equivalent to the evidences that they do not occur. Paying attention to such phenomena and establishing a relation between pieces of information, doing these are necessary for aiding in widening awareness.
The reality of the existence of atoms deduces the necessity of considering the stability of each atom having the structure formed by electrons and a nucleus. Without considering that each atom has a nucleus, activities of stars could not be understood. Without recognizing the structure of atom, imagining the reaction between a nucleus of beryllium and an alpha particle could not be allowed.
Collisions between beryllium and very fast alpha particles emitted from polonium generate radiation, and exposure of paraffin to the radiation causes the ejection of protons from the paraffin, which is a hydrogen-rich compound. This fact was shown by experiments done by Irène Joliot-Curie and Frédéric Joliot in 1932, and was confirmed by somewhat advanced experiments done by James Chadwick in 1932. Suggestion given from their experiments enables us to understand the fact that each nucleus consists of protons and neutrons. Experiments for which electrons having extremely high speed are made to collide with protons enable us to understand the fact that a proton consists of one down quark with charge −1⁄3 e and two up quarks with charge +2⁄3 e. In addition, this allows us to understand the fact that a neutron consists of two down quarks with charge −1⁄3 e and one up quark with charge +2⁄3 e. If the existence of atoms were rejected from the reason that they are invisible, establishing the current understanding would be impossible.
Picture Album: Gas Pillars in the Eagle Nebula (M16): Pillars of Creation in a Star-Forming Region Image 12 of 1207
Credit: NASA, ESA, STScI, J. Hester and P. Scowen (Arizona State University)
The existence of early stages in which molecules are being formed is confirmed by observing electromagnetic waves coming from nebulae such as Eagle Nebula, Orion Nebula, a dark nebula, etc. The electromagnetic waves coming from these nebulae can include microwaves, sub-millimeter waves, millimeter waves, and so on. Light also comes from the nebulae.
Moreover, the first stage in which nuclear fusion reactions occur can be confirmed in the nebulae. The nuclear fusion reactions occur in formed stars, and they allow each nucleus being heavier than a proton being a nucleus of hydrogen to be formed with the generation of brightness. The final stage is a situation where nuclei being heavier than a proton are ejected from old stars. The occurrence of a supernova being explosion induced by a heavy old star allows the ejection of many kinds of nuclei being heavier than a proton to be ejected toward the interstellar space. The ejection of a huge amount of heavy nuclei including gold and platinum occurs from a binary neutron star merger. On 17 August 2017, gravitational waves emanating from a binary neutron star merger (GW170817) were detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO). For this binary neutron star merger, it is estimated that heavy nuclei was ejected in huge amount such as an average total mass being 0.03 – 0.06 times as heavy as the mass of Sun.
Starbirth
This picture, an assembly of individual images taken by NASA's Hubble Space Telescope, shows young stars at the center the Orion nebula.
The most massive clouds have formed the brightest stars near the center. These stars have formed from condensing clouds of interstellar gas within the last million years, and the stars illuminate the gas left behind after the period of star formation was complete. Although the more numerous faint stars are still in the process of condensing clouds under their own gravity, the center of the faint stars have become hot enough to emit light.
Credit: NASA, C.R. O'Dell and S.K. Wong (Rice University)
Nuclei ejected into the interstellar space capture electrons having negative charge, and then, atoms are generated. Finally, atoms are bound with each other, and then, molecules are generated. Then, electromagnetic waves of specific wavelengths are emitted from the molecules, and can be observed by the use of radio telescopes. Ultimately, finding the origin of the electromagnetic waves of specific wavelengths in a specific direction is equivalent to identifying a specific region called a molecular cloud where the formation of molecules proceeds. Moreover, measuring the strengths of the electromagnetic waves allows the amounts of products to be estimated.
Picture Album: Hubble Captures View of 'Mystic Mountain'
Image 3 of 1209
This image shows a three-light-year tall pillar of dust and gas rising within the Carina Nebula being a stellar nursery, located 7,500 light-years away in the southern constellation Carina. A pair of jets of gas can be seen shooting in opposite directions at the top of the image. Another pair of jets is seen at another peak near the center of the image. These jets are landmarks linked to new star birth. The colors in this image correspond to the glow of oxygen (blue), hydrogen and nitrogen (green), and sulfur (red).
Credit: NASA, ESA, and M. Livio and the Hubble 20th Anniversary Team (STScI)
In a region identified as a molecular cloud, hydrogen molecules exist in the largest quantity. Helium atoms exist in the second largest quantity. Moreover, various molecules are contained in the molecular cloud, although their amounts are small.
In order to form a molecular cloud, molecules must be synthesized. The formation of a hydrogen molecule H2 starts from the stage in which a proton H+ moving in the interstellar space captures an electron e−. Then, a hydrogen atom H is formed. An effective formation of hydrogen molecules H2 proceeds while being mediated by protons and electrons. At a temperature near 1000K, the principal process of the formation of H2 is composed of two stages. In the first stage, a hydrogen atom H bonds with protons H+ and then the formation of H2+ and the emission of light occur. In the second stage, the reaction of H2+ with H produces H2 with H+.
In a molecular cloud, even water molecules are found. An oxygen atom O that is formed by an oxygen nucleus having captured electrons must bond to two hydrogen atoms. A principal process of the formation of a water molecule H2O is represented as a chain reaction given as
H2+＋H2→H3+＋H, H3+＋O→OH+＋H2,
OH+＋H2→OH2+＋H, OH2+＋H2→OH3+＋H,
OH3+＋e−→H2O＋H.
This is the origin of water in the universe, and also, it is the origin of the water that Earth holds.
An ion OH+ being found in the above chain reaction captures an electron e− and then a formed OH molecule emits light, namely,
OH+＋e−→OH＋light.
OH molecules are specific molecules that can emit coherent electromagnetic waves through an emission mechanism called MASER. Water molecules and methanol molecules also can emit coherent electromagnetic waves. In fact, the use of radio telescopes allows coherent electromagnetic waves to be observed.
In a molecular cloud, carbon monoxide molecules CO are molecules having the second largest amount although the amount of CO molecules is 0.0001 times as large as the amount of H2 molecules. In order to form a CO molecule, a carbon atom C that is formed by a carbon nucleus having captured electrons must bond to one oxygen atom. A principal process of the formation of CO is represented by each reaction given as
C＋OH→CO＋H,
CH＋O→CO＋H.
In a molecular cloud, various reactions proceed simultaneously, and various species of molecules are formed. Observing the strength of a specific electromagnetic wave, which has the wavelength of 2.6 millimeters, allows us to confirm whether CO molecules are formed or not. Continuing such observations enables us to follow the situation where the formation of CO molecules proceeds in specific areas in a molecular cloud.
Observations allow hydrogen molecules, water molecules, and carbon monoxide molecules to be found in molecular clouds, with other various molecules such as carbon dioxide molecules, ammonium molecules, formic acid molecules, hydrogen cyanide molecules, ethylene molecules, methanol molecules, methylamine molecules, etc. These molecules might contribute to the formation of amino acid molecules being the parts of proteins and the formation of nucleotide base molecules being the parts of DNA and RNA. Amino acid molecules and nucleotide base molecules are biological molecules being essential for life. We cannot simply deny that amino acid molecules and nucleotide base molecules may exist in grains of ice in molecular clouds.
Molecular clouds can become cold and the temperature of molecular clouds can reach even 10K. At the temperature, liquid hydrogen freezes. In molecular clouds, hydrogen can, however, not freeze, because the density of the molecular clouds is too low to freeze, and it is on the average 10²–10³ molecules per cubic centimeter. The density of hydrogen molecules that make a balloon swell up is about 1019 molecules per cubic centimeter. In comparison with this, the molecular clouds keep extremely low densities. However, the amount of hydrogen contained by a molecular cloud is extremely huge, because its size is more than several light years. Giant molecular clouds can become tens of light years in radius and have masses being 104–106 times as large as the mass of Sun.
Picture Album: Hubble's Sharpest View of the Orion Nebula Image 32 of 1207
The Orion nebula is located along our spiral arm of the Milky Way. The Orion nebula is found in the middle of the sword region of the constellation Orion the Hunter. Some of stars forming in the cloud of gas and dust have never been seen in visible light.
Credit: NASA,ESA, M. Robberto (Space Telescope Science Institute/ESA) and the Hubble Space Telescope Orion Treasury Project Team
In fact, observations make us realize that many molecular clouds are fields where new stars are formed. The Orion Nebula is an example of a stellar nursery where new stars are being born, and it is the specific star-forming region being the nearest to Earth. This nebula is one of the brightest nebulae and it is located at a distance of 1,344 ± 20 light years. The nebula is estimated to be 24 light years across. From the use of the Hubble Space Telescope, observations of the nebula revealed more than 150 of protoplanetary disks which are considered to be systems in the earliest stages of solar system formation. The origin of planets is exemplified there. Thus, stars seen in the Orion are young. The youngest and brightest stars may be less than 300,000 years old, and even the brightest stars being only 10,000 years in age may exist. Observations of the nebula reveal the existence of various stages concerning star formation. The detailed image of the nebula, which was obtained from the Advanced Camera for Surveys instrument of the Hubble Space Telescope in 2005, captured more than 3,000 stars of various sizes, including the Trapezium, infant brown dwarfs, and possible brown dwarf binary stars. This persuades us to understand that molecules exist as molecular clouds in extremely huge amount, and a molecular cloud can correspond to a molecular nursery as well as a stellar nursery. The origin of molecules located outside the territory of consciousness supported by awareness cultivated by daily experiences continues to be revealed by precise observations.
3. Analyzing Happiness on the Planet
A portion of molecular biological phenomena in living cells and on their surfaces is supported by the random movements of molecules. A portion of meteorological phenomena depends on the random movements of molecules in the atmosphere. Atmospheric circulations are driven by the random movements of molecules in the atmosphere. The accumulation of CO2 in the atmosphere can activate the random movements of molecules. The accumulation of CO2 in the atmosphere can drive unusual atmospheric circulations, and consequently, extreme weather depending on the circulation raises the potential for shrinking our happiness. Certainly, recognizing the existence of atoms allows molecular biological technology, medical technology and material technology to be developed for supporting a specific portion of happiness. Even for continuing to maintain such a portion, it is important to make efforts to recall the fact that maintaining our happiness is linked to the random movements of molecules and the fact that their random movements should continue to be moderated.
Each molecule is an object that consciousness cannot allow the brain to recognize in daily life. Earth is an object that consciousness can hardly allow the brain to recognize in daily life. Knowing of molecules is not equivalent to understanding the meanings of the existence of molecules. Similarly, knowing of Earth is not equivalent to understanding the meanings of the existence of Earth. Making attempts to recall the reality of Earth should be continued. Earth is only one spacecraft for every living thing. Recalling real situations limited by the second law of thermodynamics is important for keeping the spacecraft. Moreover, attempts to avoid an increase in the entropy of the global system are important for maintaining happiness even if Earth is not a closed system. Inhibiting an increase that should be avoided in the entropy must be dependent on the intelligence of every person.
A specific Happiness Index is shown in the World Happiness Report published annually by the United Nations Sustainable Development Solutions Network. A positive meaning of life is caused from both the interior of mind and the exterior of mind. The World Happiness Report 2018 was published on 14 March 2018 by the UN. According to the Report, the Happiness Index suggests degrees of national happiness based on respondent ratings of their own lives and is given as degrees of happiness depending on six factors. These six factors comprise real GDP per capita A1, social support A2, healthy life expectancy A3, freedom to make life choices A4, generosity A5, perceptions of corruption (absence of corruption) A6. Data collected from people in 156 countries/regions are statistically analyzed and as a result, the 2018 Happiness Index is obtained. Thus, the degrees of happiness depend on 156 factors B1, B2, B3, … , B155, B156 corresponding to regional factors.
The Happiness Index allows us to estimate a rate P(Ai, Bj) at which the degree of a partial happiness specified by one of the six factors Ai and a regional factor Bj contributes to the total degree of happiness that appears on the Planet. P(Ai, Bj) (i=1,2,…, 6 and j=1,2,…, 156) are distributed depending on Ai and Bj. If P(Ai, Bj) is considered as a join distribution, the use of the conditional entropy HA(B) allows the Happiness Index to be analyzed through the concept of information entropy.
Then, the conditional entropy HA(B) is defined as
HA(B) ≡—Σi P(Ai) HAi(B),
where
HAi(B) ≡—Σj PAi(Bj)log2 PAi(Bj),
and
P(Ai)=Σ156j=1 P(Ai, Bj)
with
PAi(Bj) ≡P(Ai, Bj)/ P(Ai).
The Happiness Index means that P(Ai, Bj) satisfies the following relations:
P(A1)= 0.259, P(A2)= 0.352, P(A3)= 0.173, P(A4)= 0.132, P(A5)= 0.0524, P(A6)= 0.0323, and
0.00969≧ P(Bj) ≧0.00111 (j=1,2,…,156),
where P(Bj) =Σ6i=1 P(Ai, Bj).
This means that the inequality PAi(Bj)≠P(Bj) is satisfied. Moreover, PBj (Ai)≠P(Ai) is satisfied, when PBj (Ai) is defined as PBj (Ai)≡P(Ai, Bj)/ P(Bj).
The entropy H(B) that results from the distribution of degrees of happiness determined by only the regional factors is given by
H(B) ≡—Σj P(Bj)log2 P(Bj).
According to the Happiness Index, the distribution of degrees of happiness on the Planet yields H(B)= 7.22.
When the dependence of the six factors on the distribution of degrees of happiness is given as information, the entropy resulting from the distribution is given by the conditional entropy HA(B). According to the Happiness Index, P(Ai)HAi(B) (i=1,2,…, 6) are estimated as
P(A1)HA1(B)= 1.84, P(A2)HA2(B)= 2.54,
P(A3)HA3(B)= 1.24, P(A4)HA4(B)= 0.945,
P(A5)HA5(B)= 0.371, and P(A6)HA6(B)= 0.220.
Therefore,
HA(B)= 7.16.
In addition, the Happiness Index shows that the joint entropy H(A,B) is given as
H(A,B) = —Σi,j P(Ai, Bj)log2 P(Ai, Bj) = 9.40
Thus, the relation H(A,B) > H(B) > HA(B) is revealed. This means that considering additional pieces of information decreases the entropy. If the dependence of the regional factors Bj (j=1, 2,…, 156) on the distribution of degrees of happiness is considered as information, H(B) is given, and if the dependence of the six factors on the distribution is additionally considered as information, HA(B) is given.
Then, partial entropies HAi(B) (i=1,2..,6) contributing to HA(B) is given as
HA1(B)=7.12, HA2(B)=7.23, HA3(B)=7.14,
HA4(B)=7.17, HA5(B)=7.07, HA6(B)=6.83.
HA5(B) and HA6(B) both are smaller than the others.
Assuming that each fraction P(Ai, Bj)/P(Ai) becomes closer to 1 without depending on Bj (j=1,2,…,156), HAi(B) become closer to zero. This means that the approach of P(Ai, Bj)/P(Ai) toward the maximum without the dependence on Bj allows HAi(B) to become small. The fact that HA5(B) and HA6(B) both are smaller than the others HAi(B) (i=1,2,3,4) reveals that P(A5, Bj)/P(A5) and P(A6, Bj)/ P(A6) are closer to the maximum than the others and more weakly depend on Bj than the others. The Happiness Index shows that the two factors A5 and A6 contribute to the total degree of happiness on the Planet more independently of the regional factors Bj (j=1,2,…,156) than the other factors. We should be aware of this fact.
These two factors correspond to “Generosity” and “Perceptions (absence) of corruption”, and they are factors that reach the interior of mind of a person from the interior of mind of another person while causing the positive relationships between the people. One of the two, i.e., “Generosity” can be generated by sympathy, and the sympathy is caused by a specific activity of neuron networks that involves oxytocin being a neuropeptide produced in the hypothalamus. Furthermore, the sympathy itself can aide in producing oxytocin. The other, i.e., “Perceptions (absence) of corruption” encourages a particular activity of the amygdala to be inhibited or moderated. Inhibiting the activity of the amygdala can prevent a role of oxytocin from being stopped, and moreover can aid oxytocin in being produced. On the contrary, the activity of the amygdala inhibits the production of oxytocin. The two factors A5 and A6 can be related with a special activity of neuron networks that involves oxytocin being a neuropeptide produced in the hypothalamus. Continuing to aid in moderating the activity of the amygdala is important for improving the total degree of happiness on the Planet. No matter how advanced medical technology and material technology are, happiness can readily collapse without continuing to aid in moderating the activity of the amygdala.
Happiness is not a state that can be established by only an individual will and an individual hope. Happiness is a sate that can be established through the positive relationships between human beings aided in oxytocin and activities of the right hemisphere. Happiness can continue to be maintained through mutual contribution to happiness of the people. Activities of the right hemisphere can efficiently contribute to moderating the activity of amygdala although this effect is an empirical understanding. Artistic environments, artistic activities and the nature surrounding trees stimulate the right hemisphere in order to allow the brain to realize piece and a moderated atmosphere and to find human’s dignity. These things including music allow the brain to realize happiness. The happiness is characterized by comfort. Ultimately, features of happiness must depend on cultures. Cultures must depend on features of happiness that is hoped and maintained while moderating the activity of amygdala. Varieties situations can be produced as happiness while depending on cultures.
Knowing how to satisfy is an important criterion for allowing happiness to grow in mind. Inhibiting the activities of amygdala for the natural secretion of oxytocin can correspond to a situation where the brain feels happy. Fully activating the amygdala corresponds to leaving happiness. If we are asked what an aim of life is, reaching comfort is the aim. Benefit and convince are ways of establishing life. Comfort can allow people to recognize its limit. However, benefit and convince cannot allow people to recognize their limits in many cases. A specific portion of happiness depending on benefit and convince has a tendency to encourage people to forget the reality of Earth. Happiness obtained from knowing of a way to feel full of hope can prevent the current reality of Earth from becoming transient, while moderating the activity of amygdala. Preserving the current reality of Earth is to preserve happiness that future generations will have.
References:
1) C. E. Shannon, "A Mathematical Theory of Communication", Bell System Technical Journal, 27, 379–423 (1948).
2) About potentialities of the right hemisphere:
J. B. Taylor, “My Stroke of Insight”, (Hodder & Stoughton Ltd, 2009)
3) B. D. Marshall, “A resumed thermodynamic perturbation theory for positive and negative hydrogen bond cooperativity in water”, Journal of Physics: Condensed Matter 31, 184001 (2019).
4) J. Perrin, Brownian Movement and Molecular Reality, Translated by F.Soddy (Dover, 2005).
5) L. D. Landau and E. M. Lifshitz, Statistical Physics– Part 1 – Third Edition (Pergamon Press, 1980).
6) Neutron star merger detected on 17 August 2017 and called GW170817,
https://www.jpl.nasa.gov/news/news.php?feature=6975.
B. J. Shappee1 et al., Science 358, 1574-1578 (2017); M. R. Drout et al., Science 358, pp. 1570-1574 (2017); C. D. Kilpatrick et al., Science 358, pp. 1583-1587 (2017), Meng-Ru Wu et al., Physical Review Letters 122, 062701 (2019).
7) World Happiness Report https://worldhappiness.report/ed/2018/
8) T.M.Cover and J.A.Thomas, Elements of Information Theory Second Edition (Wiley India Pvt. Ltd., 2017).
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