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Showing posts with label nature. Show all posts
Showing posts with label nature. Show all posts

Color

Color

“Mere color, unspoiled by meaning, and unallied with definite form, can speak to the soul in a thousand different ways.” 

- Oscar Wilde

Generated using AI

For a normally sighted person, color is everywhere. Colors can be pleasantly subdued, enhancing relaxation, or loud and calling to us from advertising billboards or magazines. Color entices us to eat, consume, or at least buy. Color likely has helped us to survive as a species. Our (known) contacts with the world and the universe are by way of our five senses. Persons with a normally functioning visual system obtain what is probably the largest amount of information about the world surrounding them from vision, and color experiences are an important outcome of this flow of information. In the past several thousand years, color has blossomed into much more than just a survival and communications tool. We have learned to derive aesthetic pleasure from it by way of crafts, design, and art.

A fabric is dyed with red dye; when painting, we use various colored pigments or draw with various colored crayons or ink pens. The rainbow has four colors, or is it six or seven? In a mirror, we see the colors of objects appearing slightly duller and deeper than in the original. On a winter day toward evening, shadows look deeply blue. We are told that color illustrations in an art book are printed just with four pigments and that all colors on a display screen are “made” from red, blue, and green light-emitting phosphor compounds. To cope with these confusingly varied sources of color, we just disregard them in our everyday languages. An apple is red, the traffic light is red, the rose as seen reflected in a mirror is red, the bar in the bar graph on a tablet display is red, and the paint on the brush is red. All of these varied experiences have something in common: redness. We simply attach the perceived phenomenon to the object without bothering about the source or thinking about the nature of color.

We normally experience color as a result of the interaction between light, materials, and our visual apparatus, eye, and brain. However, there are also means of having color experiences in the dark like pressing against the eyeballs or hitting the temples moderately hard. There are two sets of facts that complicate understanding of the phenomenon of color firstly, many different stimuli can result in an essentially identical color experience and secondly a particular stimulus can result in many different color experiences, usually as the result of changes in illumination and/or surrounding stimuli. The same situation applies to vision in general.



The best definition of color that we can have is " Color: Attribute of visual perception consisting of any combination of chromatic and achromatic content. This attribute can be described by chromatic color names such as yellow or brown, red, pink, green, blue, purple, etc., or by achromatic color names such as white, gray, black, etc., and qualified by bright, dim, light, dark, etc., or by combinations of such names."


Understanding Light

Light consists of a certain range of electromagnetic radiation, which is a convenient name for the as-yet not fully explained phenomenon of energy transport through space. Electromagnetic radiation, depending on its energy content, has different names: X-rays capable of passing through our bodies and, on prolonged exposure, causing serious harm, ultraviolet (UV) radiation that can tan or burn our skin, light that we employ to gain visual information about the world around us, infrared radiation that we experience on our skin as warmth or heat, information transmission waves for radio and television, or electricity transmitted and used as a convenient source of energy. Electromagnetic radiation travels at high speed (the speed of light, about 300,000 km/s). The human eye, our visual sensory organ, is sensitive to a narrow band of electromagnetic radiation, the visible spectrum.

The Electromagnetic Spectrum. (a) This diagram shows the wavelength and frequency ranges of electromagnetic radiation. The visible portion of the electromagnetic spectrum is the narrow region with wavelengths between about 400 and 700 nm. (b) When white light is passed through a prism, it is split into light of different wavelengths, whose colors correspond to the visible spectrum.
https://chem.libretexts.org/ 


Ways of producing light 

Incandescence 

Light is normally produced by a glowing body in a process called incandescence; for example, the sun, a burning wax candle, or an electrically heated tungsten metal coil in a light bulb, but there are other modes of generation. Incandescence is the shedding of electromagnetic radiation by a very hot material, resulting in light that can give rise to color experiences. Our dominant example of an incandescent body is the sun, where the energy is produced by what is known as nuclear fusion. The nature of incandescence as produced on Earth is most easily observed in the work of a blacksmith. An iron rod, placed in an intense coal fire, as it heats up when it reaches about 525°C will begin to give off a dull reddish glow. When viewing it in the dark, we recognize it as the source of reddish light. As the temperature of the metal increases so does the intensity of the emitted light and its energy content. Simultaneously, reddishness diminishes and the object becomes “white hot.” With further increase in temperature, it eventually assumes a bluish-white appearance. Energy is absorbed by the the iron rod from the fire and emitted in visible form by the glowing metal. The imparted energy can have many sources: thermonuclear in case of the sun; electrical in case of a light bulb; and chemical in case of burning coal. All elements can, in proper conditions, be made to show incandescence, as can many inorganic molecules. Organic molecules (those containing carbon), are usually destroyed before they show incandescence, with incandescence produced by their decomposition products (say, in case of candle wax). The nature of the emitted energy depends on the form of the incandescent material: gaseous substances and many chemical elements emit energy in one or more distinct bands; incandescent liquids and solids tend to emit energy across broad spectrum bands.

Energy absorption and incandescence are explained using the atomic model of matter. Atoms consist of protons and neutrons in the nucleus, surrounded by electrons in shells. When an atom absorbs energy, its outermost electrons get excited to higher energy levels. These excited electrons eventually fall back to lower levels, releasing energy as electromagnetic radiation. If the emitted energy has a wavelength between 400 and 700 nm, it is visible light. Significant radiation emission, or incandescence, occurs when an object's temperature reaches about 525°C.

https://www.shrufg.top/


Blackbody radiation

A blackbody is an idealized material that is a perfect absorber and emitter of energy across all wavelengths. It absorbs all incident radiation, regardless of frequency or angle of incidence, and re-emits energy perfectly based on its temperature. The theoretical emission spectrum of a blackbody can be calculated using Planck's law, which describes the intensity of radiation emitted by a blackbody as a function of wavelength for a given temperature.

Real materials often exhibit emission spectra similar to a blackbody, and this similarity allows scientists to use the concept of blackbody temperature, expressed in Kelvin, to describe the emission behavior of light sources. Even if a light source’s emission spectrum is not exactly like that of a blackbody, its color temperature can still be correlated to the temperature of a blackbody that emits light of a similar color. This is known as the correlated color temperature (CCT).

In practical terms, consider the example of a blacksmith heating an iron rod. As the rod heats up in a coal fire, it begins to glow red at around 525°C (798 K). This reddish glow intensifies and changes color as the temperature increases, moving towards white and eventually bluish-white as it reaches higher temperatures. This color change corresponds to the shifting emission spectrum of the iron, which approximates that of a blackbody at different temperatures.

Low-burning coal, with a blackbody-like spectrum at around 1800 K, emits primarily in the reddish-orange part of the visible spectrum. Incandescent light bulbs, typically operating at about 2500 K, have an emission spectrum that is also close to that of a blackbody. However, these bulbs are inefficient because most of their emitted energy is in the infrared region, which we perceive as heat rather than visible light. This inefficiency is why incandescent bulbs become very hot during operation.

In contrast, fluorescent lamps are more energy-efficient. They emit most of their energy in the visible spectrum, resulting in less wasted heat. The most energy-efficient fluorescent lamps, known as triband lamps, emit light in three specific bands around 440 nm (blue), 540 nm (green), and 610 nm (red). These wavelengths align with the peak sensitivities of the human visual system, making these lamps more efficient in terms of visible light output compared to other types of fluorescent lamps that emit across a broader spectrum.

The appearance of certain materials can change significantly depending on the spectral power distribution of the light under which they are viewed. For example, a material might look different under incandescent lighting compared to daylight. Blackbodies at temperatures of 2500 K and higher emit light that, to the human eye, appears colorless or "white" due to our adaptation to daylight. This neutral white light is perceived when objects with high reflectance functions are illuminated, making them appear white. Various light sources with different spectral power distributions can still result in light that appears white, as long as the light has a similar effect on our visual perception as daylight.

Thus, the concept of a blackbody provides a foundational understanding of how different materials emit and absorb energy. It also helps explain the color changes observed in heated objects and the efficiency differences between various types of light sources.

https://www.nuclear-power.com/


Luminescence

Light can be created by processes not based on the absorption of energy, known as luminescence. There are three main types of luminescence:

  1. Electroluminescence: This occurs when electrons, influenced by an electric field, collide with particles of matter, resulting in the emission of light. Examples include sparks, arcs of light, lightning, certain lasers, and gas discharges.                                                      


  2. Chemiluminescence: This is the production of light from chemical reactions, typically oxidations, at low temperatures. Natural chemiluminescence, also called bioluminescence, is seen in glowworms, fireflies, some deep-sea fish, decaying wood, and putrefying meat. Commercial examples include glowing liquid-filled plastic tubes.           


      

  3. Photoluminescence: This appears in two forms, fluorescence and phosphorescence.

    • Fluorescence: Certain molecules absorb near-UV or visible light and re-emit it as visible light of a higher wavelength. Fluorescent whitening agents in detergents, for example, absorb UV radiation (300-380 nm) and emit visible light (400-480 nm), giving materials a very white appearance. Fluorescent dyes absorb and emit visible light, such as a fluorescent red dye that absorbs light from 450-550 nm and emits it at 600-700 nm. Fluorescent minerals and light tubes are also examples of fluorescence. Fluorescent light tubes have an interior coating of fluorescing phosphor compounds and contain a small amount of mercury. When excited by an electric field, mercury emits near-UV energy, which is absorbed by the phosphor compounds and re-emitted as visible light. Fluorescence stops when the energy source is interrupted.
    • Phosphorescence: Some substances can store absorbed energy and continue to emit light for some time after the exciting energy is stopped. This is different from fluorescence, where light emission stops immediately once the energy source is removed, like Glow-in-the-dark materials that continue to emit light after being "charged" by exposure to light.                                                                              

These luminescence processes provide diverse ways to produce light, each with unique applications and properties.


Absorption, reflection, scattering, and transmission

Light undergoes numerous transformations from creation to oblivion. When photons interact with atoms or molecules, they lose energy and are re-emitted at lower energy levels, often as infrared radiation, resulting in a loss of visible light and an increase in perceived heat. An ideal blackbody is the most efficient absorber and emitter of energy across a wide range, but real objects absorb selectively, reflecting or scattering some photons. Reflection occurs when photons bounce off a smooth surface at the same angle, while scattering happens when photons hit rough surfaces or fine particles, spreading light in many directions.

Scattering is common in natural phenomena and materials like textile fibers, water droplets in clouds, fog, smog, dust, milk, and bird feathers. The blue sky results from the scattering of shorter light wavelengths by small atmospheric particles, while clouds appear white due to the equal scattering of all wavelengths. Near sunset, the sky turns red as particles scatter shorter wavelengths, leaving longer wavelengths to dominate.

No material perfectly reflects or scatters light, but some, like pure barium sulfate and metallic mirrors, come close. Most colors we see result from a combination of wavelength-specific absorption and scattering, known as object colors, depicted by spectral reflectance curves.

Transmission is the passage of light through a transparent material, like water. If the material lacks absorbing substances, the transmitted light's spectral distribution remains unchanged. When absorbing materials like dyes are present, some light is absorbed, and the rest is transmitted, with the amount depending on the material and layer thickness. The Beer-Lambert-Bouguer law describes the absorption and transmission of light by dissolved substances.



Refraction 

Refraction denotes the change in direction of light as it passes from one medium to another, such as from air to water or glass. This occurs because light changes speed when entering a different medium, bending according to the laws of refraction. Refraction is fundamental to phenomena like rainbows and image formation in cameras and eyes. In both, lenses control the refraction to focus light and form clear images. The degree of refraction depends on the optical densities of the media and the energy level (wavelength) of the photons, with higher energy photons bending more sharply.

A practical application of refraction is the use of glass prisms to separate light into its component wavelengths. When a beam of white light passes through a prism, it disperses into a spectrum of colors, visible when projected onto a white surface. Each color corresponds to a specific wavelength: blue (400-490 nm), green (490-570 nm), yellow (570-590 nm), orange (590-630 nm), and red (630-700 nm). This separation of colors can be reversed to recombine the light into white light.

The most dramatic natural example of refraction is a rainbow, where sunlight is refracted and dispersed by water droplets in the atmosphere. Refraction also causes the sparkling "fire" seen in cut crystals, diamonds, and other gemstones. However, refraction in lenses can lead to chromatic aberration, a problem where different wavelengths focus at different points, causing blurred or colored edges in images. Lenses must be corrected for this to achieve clear focus across all colors.


Interference 

Puddles of water with bright multicolored bands near car repair shops or gas stations after rain, as well as the shimmering colors on butterfly wings or peacock feathers, are examples of iridescence. Unlike the scattering effect seen in blue jays, iridescent colors change in hue and intensity based on the viewing angle due to a phenomenon called interference.

Interference occurs when light waves split into separate parts that later recombine. Think of it as two synchronized swimmers: if they move perfectly together (in phase), their splash is bigger; if they move oppositely (out of phase), their splash cancels out. Similarly, light waves in phase amplify the light, while out-of-phase waves reduce the light. A common source of interference is a thin transparent film, such as oil on water or a soap bubble. The thickness of the film determines whether the reflected light waves are in or out of phase. When in phase, light of different wavelengths reflects at corresponding angles, producing pure, strong colors that change with the viewing angle. In thin films with varying thickness, like oil on water, multiple colors appear due to varying path lengths of the reflected light.

This phenomenon also occurs in nature. The wings of butterflies and feathers of birds like peacocks and hummingbirds have microscopic structures that create thin-film interference. These structures split and reflect light at different angles, resulting in vibrant, shimmering colors that change as the light or observer's position changes. Iridescence in these structures is often due to layers of chitin or keratin, creating multiple thin films that produce striking visual effects. Interference is also seen in everyday life. The colors in soap bubbles are due to thin-film interference. The varying thickness of the soap film creates a spectrum of colors that shift as the bubble moves. Similarly, anti-reflective coatings on glasses and camera lenses use destructive interference to reduce glare by causing specific wavelengths of light to cancel each other out.



Diffraction

Diffraction is a phenomenon that combines scattering and interference of light waves. When a light wave encounters the edge of a solid object, such as a razor blade, its behavior depends on the sharpness of the edge and the wavelength of the light. The wave might pass unimpeded, get scattered, or be absorbed, reflected, or refracted by the material at the edge. When there are multiple edges, like fine lines etched into a glass or metal plate, the scattered waves can interfere with each other—waves in phase will reinforce, while out-of-phase waves will cancel each other out.

To understand diffraction, think of it like water waves encountering a barrier with multiple gaps. As the water waves pass through the gaps, they spread out and interact with each other. Where the peaks of the waves meet, they reinforce each other, creating larger waves; where the peaks meet the troughs, they cancel each other out. This creates a pattern of waves that can be seen in the water, similar to how light waves create patterns of light and dark bands when they diffract.

This effect is particularly noticeable with a grating, an assembly of many fine edges. When daylight strikes a grating, the interference of scattered waves produces a display of spectral colors viewed from different angles. A common example is the surface of a compact disk, which shows colors due to the diffraction of light by the tiny grooves on its surface, although the effect is imperfect due to irregularities and curvature.

Diffraction gratings are widely used in optical equipment to separate polychromatic light into its individual components. Certain natural structures also cause diffraction. For instance, the wings of some insects have microstructures that act as diffraction gratings, creating vibrant colors. Liquid crystal molecules can also act as diffraction gratings; their arrangement depends on temperature, making them useful in temperature indicators. The vivid colors of opal gemstones are another example of diffraction effects in nature, resulting from the microscopic arrangement of silica spheres within the stone.


Molecular Orbitals

So far, we've discussed physical sources of color stimuli like refraction and interference, and the behavior of excited electrons in atoms and molecules. Electrons in atoms are arranged in orbits around the nucleus, and when electrons from two atoms pair up, they form a chemical bond, creating a molecule. In some molecules, electrons move freely across larger areas, giving rise to color.

For example, sapphire is mainly aluminum oxide. Pure aluminum oxide, or corundum, is colorless, but sapphires contain impurities like iron and titanium. An electron transfer between these impurities results in electron excitation under absorbed energy from visible photons (550 to 700 nm). The energy is then released in the infrared range, making the sapphire appear deep blue by reflecting light from 400 to 550 nm.

Dyes and organic pigments also show this behavior. These molecules have alternating single and double bonds, known as conjugated bonds, which absorb visible light, making the substances appear colored. These molecules are called chromophores. Auxochromes are side groups that can accept or donate electrons, enhancing the color.

Natural substances like blood and chlorophyll get their color from conjugated bond systems, and most modern colorants are synthetic, with around 8,000 having commercial significance. Fluorescent colorants absorb near-UV or short-wave visible light and emit visible energy, making them both absorbers and emitters of visible light.


Electrical conductors and semiconductor 

In conductors and semiconductors, electrons can travel throughout the material. In copper wire, for instance, electrons can move from one end to the other, creating an electric current when an electric field is applied. Metals have a plasma frequency; wavelengths higher than this frequency are reflected, while lower frequencies pass through, making some metals like chrome good reflectors of visible light. Copper, with a plasma frequency in the visible range, appears reddish.

Semiconductors like silicon, boron, arsenic, and indium have a gap in their energy absorption behavior, leading to the absorption of specific energy bands and the generation of color. Cinnabar (mercury sulfide) and cadmium sulfide are examples of colored semiconductors. Doping semiconductors with impurities can produce color in devices like LEDs.

The understanding of color stimuli is extensive but not fundamental due to limitations in quantum theory. However, this knowledge allows for creating synthetic substances with specific absorption and emission behaviors, such as lasers. Lasers, which produce coherent light beams, were first made using ruby. Now, lasers of any visible wavelength can be created, with applications in manufacturing, medicine, measurement, and entertainment.

Despite the complexities, the causes of most color phenomena are well understood. All color perceptions result from photons of specific wavelengths reaching our eyes, where their energy is transformed into responses by our brain and body.




Hope this article inspires you. 

Contact me through my blog or https://www.instagram.com/phy.sci/?hl=en.

Music, Enrtropy, Neurons and Information


Music, Enrtropy, Neurons, and Information

“I would teach children music, physics, and philosophy; but most importantly music, for the patterns in music and all the arts, are the keys to learning” 
― Plato 


Music is something that we listen to every day in many forms. Entropy and Neurons are yet to be understood by the people who work on them but they provide interesting insights about things around us. It is really interesting how we are moved by music and with that feeling, we can understand ourselves in a scientific way.  To understand it we need to know something about each word in the topic and interpret it in our own way. This will be a long read but will be fascinating once you understand it in your own way.  

Brain, neurons, music sheet, disorder

NOTE: The audio and the video will take a few seconds to load. wait till it load or open it in a new tab. 

Click the play button and wait for a few seconds.

If the video and audio is not playing. Refresh the page. 

Music

Music can be academically defined as an arrangement of sounds. There are some technical terms that one should be familiar with. When the sound gives a pleasant and harmonious sensation it is called consonant, if the sound gives an inharmonious feeling then it is called as dissonant. 

The sound of a trained singer singing a song, the sound of a temple or a church bell, when a student plays piano we get a consonant. When a normal person sings a song, the sound of hitting metal utensils, when a cat walks on a piano we get a dissonant. One can easily recognize this, whether he knows music or not. Sometimes in nature, we get these sounds like birds, cows, and fish make consonants (not always), whereas bugs, bees, and donkeys made dissonant. 

The first audio is the ringing of the tuned bell the second is the hitting of metal utensils. Now you can find the difference between consonant and dissonant.
REFRESH THE PAGE IF THE AUDIO SHOWES AN ERROR,

From a musician's point of view, jass is mostly dissonant but gives a feel that depends on the player (not mocking jass, just a fact), metal and rock music is not pleasant but harmonic so it depends on the listener. Other than that all are consonant. Generally, consonants are predictable sounds.

Music is evolved through the ages among that classical music is the most ordered and has strict rules about music and the free-going type is jass, yet people like both the music. It is a question of why people like music? (Think it yourself)

This is a classical music sheet. See how the notes(the black dots on and in between the line) are ordered and simple. (when the dots go higher and higher the pitch increases) 
This is a Jass music sheet. This piece of music is one of the famous compositions. Even though it is good to hear it trumpet players see it as a difficult piece to master. See how the notes are organized it looks more complex than earlier sheet music.   

Technically a piece of music has rhythm, harmony, and melody. We normally combine them to produce music. We can sense them easily. 


The sense of rhythm

The best example of rhythm is our heartbeat or a ticking analog clock. It produces a sound in equal intervals of time or it is silent in a particular interval of time. 1,2,3,4:1,2,3,4;1,2,3,4;1,2,3,4... now if you count this pattern in your mind and repeat it the make a sound in everyone or in any pattern when which you wish you are producing rhythm ( technically a 4/4 rhythm pattern). 

By nature, we have a sense of rhythm, we tap our legs, nod our heads or clap our hands while listening to a song which is nothing but our sense of rhythm. From nature, we can grasp the rhythm from The rustling of leaves, the sound of rain, the sound of water flowing, the sound of waves on the beach, the song of birds, etc. 

Some of the rhythmic sounds. The first two are computer generated. The first is used in music and the second is the dile tone in a telephone. The last two mimics the natural world. like a heartbeat and walking on a hard floor. 

The sense of harmony

In a very general meaning harmony is the existence of things together. So in music, it is the existence of different sounds together. The sets example is the "gooood mooorrrninggg" of kids in school. Is harmony sounds as a single sound but has various tones in it. Another example is the audience singing a song in a concert or a group of people in a choir. We as social beings sense and produce hormones in our daily life but we do know how. 

The sense of melody 

In general, a melody is a tone that produces a consonant. A bird singing is a melody, our random hummings are a melody. It has a certain pitch to be filled and follows a rhythm. The " Happy birthday song" is a good melody. So a melody is a set of notes which make a consonant. 

Bobby McFerrin Demonstrates the Power of the Pentatonic Scale at the world science festival. The audience are singing harmony and Bobby is singing melody. 


The walking humans - music producers

As physicists approximate a cow as a cylinder (not a joke it is real check it here), we can approximate a walking human as a simple pendulum. As we walk we exhibit a harmonic motion i.e., an up-down motion, back-and-forth motion, extension, and compression. 

The walking human represents a simple harmonic motion similar to a pendulum.
A pendulum produces a sine wave similar to the movement of human feet and hands. 
NOTE: Click the video and wait of few seconds to load. Then again click the play button.  

All this is associated with a sound like a taping of feet, swinging of hands, and breathing. So a walking human can produce a piece of music.

When a group of people walk we can create a good random consonant. From this, we can obtain a predictable sound. By doing this we have different predictable sounds in harmony and when we can synchronize them we get spaces of silence that have two adaptations.  we can filter our unwanted predictable sounds, and we can effectively find a tempo (time frame of a rhythm) and follow it and form a convincing melody or a beat. 

The amplified sound when a human walks. You find a rhythm in it and a jass melody too.  

So our natural activity can produce a piece of good music so people get inspiration from themself and from nature. Different cultures have different types of sounds and music but the feeling that they convey are universally understood? Which is again a question that we have to think about. I also have another question about this we humans do not need music to exist ( Like a human can exist without pizza) then why do we need music? (Think about these questions by yourself).


Basics of harmony 

To understand the pattern of harmony in a physical and a mathematical way I encourage you to do a small activity. Make something as shown in the figure. Frequency ratios, Now take a model that was proposed by Pythagoras, in the following arrangement the white border is a slider so it can dived the string into two different parts and creates different sound when it is moved differently. 

Now when the slider is kept in such a way that the ratio of their lengths or the frequency is a simple integer we will get a consonant (like 1:2, 1:2, 2:3, etc). Other frequencies like 1:13, 3:19, etc are normally dissonant. You can check it by yourself by making such an apparatus. These sets of notes are in different frequencies form chords and all the major and minor chords are composed of the simple frequency ratio. 


The first three sounds are in simple integer ratio as in the figure so they make consonants (Which are the basic chords as mentioned earlier). The last two sounds are in a higher integer ratio so they are not consonant. ##

We generally like chords with lower integer ratios. The question here is why do we like chords with lower integer ratios?


The auditory system - The place where neurons play their game.

Once Sound reaches your ear it vibrates your eardrum which in turn vibrates the three bones that pass these vibrations along to your cochlea, inside the cochlea is the basilar membrane and which is a strip of tissue that runs along the length of the cochlea the basilar membrane is designed so that the stiffness and other properties vary along its length so different parts of it resonate at different frequencies near the base of the cochlea responds best to high frequencies and at the tip it responds best to low frequencies all along the basilar membrane are these sensors called hair cells because they're each in a different position on the membrane they each respond best to a different frequency so effectively the cochlea performs a Fourier transform it separates audio signals into different frequencies each connected to a neuron which sends a signal to the brain saying that it heard this frequency neurons communicate primarily through electrical signals. 


When a neuron receives chemicals called neurotransmitters from a sensory cell or from another neuron those trigger ions which move positively charged potassium and sodium ions inside and outside of the neuron so there's a flow of current into the neuron at the same time all the charges that are accumulating on the inside and outside of the neuron are only separated by the thin cell membrane so this forms a capacitor on the edge of the neuron and the current source is charging up this capacitor (of course the cell membrane isn't perfect at holding back the ions so some of the calculus is going to leak through this means that the membrane acts as a resistor so now we've turned our neuron into an RC circuit) and we can analyze it just like we would in a physics class, the key value that we are interested in is the voltage across the membrane. The reason that we're interested in that is that once this reaches a certain threshold it will trigger voltage-gated ion channels to discharge the neuron and then it'll send neurotransmitters to the next neuron and repeat the whole process so here's the equation for our neuron the input current which again depends on the other neurons and sensory cells that our neuron is connected to equals the leakage current plus the charging and both of these depend on the voltage which is what we want to solve.


Let's say you're listening to a chord with three notes and they're both frequencies that means that two of your hair cells are being triggered and each one of those sends a signal to one sensory neuron we'll say these two sensory neurons hook up to one interneuron which takes a signal to your brain what we're going to do is we'll take our neuron equation and apply it to these three neurons the hope is that once we solve it we'll be able to plug in different frequencies for different chords and hopefully we'll see some difference in the signal that goes to your brain between good chords and bad chords so we'll start with neuron number one since it's connected to a hair cell the input is just a sine wave, at whatever frequency the node is but there's also a lot of noise in our brains there's so many random factors that could change the input current so we'll also add a term here that represents random noise neuron number two is exactly the same but with a different frequency for a different note neuron number three gets its input from the first two neurons and again the way it works is the input neurons will normally send close to zero current until they fire then they'll instantaneously send the pulse of current so we'll use a Dirac Delta function to model this it's a function that's zero everywhere except at the moment the neurons fire of course we'll have to solve for neurons one and two to figure out those times this system of equations can be and has been solved and the solution is obtained as follows. 



I don't think it's particularly enlightening (If it is enlightening do read about it) so instead of solving it let me walk you through what typically happens and I say typically because that noise that we included makes the solution slightly random the current signal coming from the hair cell is generally not high enough to trigger the sensory neurons on its own so it takes the addition of our noise to actually fire during the first cycle of the sound wave that we're listening to the neuron is charging up so the moment that it's most likely to fire first is at the peak of the sine wave when the current input is highest if it didn't happen to fire at that time then the next most likely cancer is going to be at the next Peak so if we make a probability distribution of the sensory neurons firing times it'll look something like this a high peak after one cycle of the sound wave and then they get smaller after that on round number three the input from a single sensory neuron is also generally not high enough to trigger it and because of the resistor or charges leaking across the cell membrane if there's no constant current input then it'll eventually discharge so in order for neuron number three to fire it needs to receive a signal from one neuron and then really soon after receive a signal from the other neuron this needs to happen before it has time to discharge so the more often the signals from neuron 1 and neuron 2 line up the more often neuron 3 will fire and send a signal to your brain we can use this to make a probability distribution of neuron number three's firing times but of course it depends on the relationship between the two frequencies that you're hearing.



Entropy and Information

Entropy and information are big words in the modern academic world because we don't understand it to a full extent but the basic definition and insight will provide us a good understanding of the thing that we are dealing with. 

Entropy is the measure of disorder. A well-arranged room has lower entropy because the thing that room is already stable to our senses and we don't do anything about it. whereas a messy room has more entropy because things can be arranged in more ways, so the things in a messy room can be arranged in different ways, unlike a well-arranged room.  


Information is knowledge of facts. Facts are something we know, so we can know something by seeing, hearing, feeling, reading, writing, practicing, etc. Now when we take the above room case we have information from both rooms, It is easy to get detailed information from a well-arranged room because we can easily navigate things and understand them. A messy room will have information but not in the way we like, normally in a very short time we will say a well-arranged room gives more information than a messy room. It is true and false depending upon some factors. 


Music, Entropy, and Information

So here are some probability distributions for small integer chords you can see that they're pretty regular the signal that your brain gets is organized and predictable but here are some probability distributions for large integer chords as you can see they're much fuzzier it's not predictable when that neuron is going to fire we actually have a way of measuring this fuzziness it's called information entropy or Shannon entropy (after its inventor to introduce it let me show you this picture this is the Arecibo message).

https://upload.wikimedia.org/wikipedia/commons/thumb/5/55/Arecibo_message.svg/150px-Arecibo_message.svg.png
Arecibo message


In 1974 we sent this picture through radio waves into the cosmos I guess as an attempt to introduce ourselves to whatever aliens might find it but pretend that you're an alien and your job is to watch the data from a radio telescope and notify someone.

If you see a signal that looks like it's from Aliens most days you'll just see something like this random noise.

Then one day you see one of these signals gives you more information clearly.  It is so organized that it must be an intelligent message, see you already have an intuition (Even if we don't know the meaning of the signal we can grasp this from the analogy of the messy room earlier.) For entropy, a signal that appears more organized is more likely to contain information a high entropy signal like this is probably just noise but a low entropy signal like this tells us something if you were just shown each of these signals then the low entropy one carries more information.

Now here's the counter-intuitive part let's say that you know that both of these signals are from Aliens they're both intentional, now which one gives you more information this one does the one with higher entropy see the low entropy organized signal follows simple rules you could recreate it by only knowing a few things but to recreate the high entropy signal you would need to know each bit so you actually gain more information by understanding the messy signal is ambiguous but decoding It ultimately gives you more information.



The entropy of neural signals reaching your brain is low for consonant low integer chords it's high for dissonant High integer chords and this makes sense in a lot of ways. I mean if you hear a C major chord on a piano then of course it was intentional it carries a simple message and it's unlikely to happen by chance somebody is probably reading music and playing it.  On the other hand, if you hear three adjacent chromatic notes then it could just be that something fell on the piano on the surface you might not gain information from it but if somebody was reading music that directed them to do that then it would carry a profound amount of information because there are hundreds of bad chords and only a few good chords.

When it's less organized you have more to work with nevertheless our brain prefers the unambiguous case and that's why we like certain chords and we will easily have to connect to the musical and what feel it is delivering. Like a C major: Innocence, happiness with a spiritual feeling; Cm: Innocence, sadness, heartbroken and evokes yearning (Search them meaning in Google); D major: Triumphant and victorious. Feels like war marches or holiday songs; Dm: serious and melancholic. Brings on feelings of concern and contemplation; Em: Restless love, grief, and mournfulness; F chord: Optimism and the will to explode, etc.



When we hear a melody, we still need to think and figure out what the musician wants to say and that's the definition of high entropy. It is not a coincidence that according to our analysis of neural firing times, this is a high entropy interval. It is easy when we have low integer frequency chords that form consonants and are predictable & ambiguous to us. 

When Claude Shannon introduced the concept of information entropy, he called it that way because the disorganization of information is clearly analogous to the disorganization of matter which we call entropy and thermodynamics and statistical mechanics but maybe there is another similarity between the two. 

In matter entropy always increases on a global scale and this is just a result of statistics. If you drop food dye into the water there is only one state where all the dye molecules form a particular shape but there are trillions of states where the molecules look random so over time they'll tend to look random, This is the second law of Thermodynamics. 

https://vinacanete.files.wordpress.com/2013/01/coolwater.gif


Maybe human culture follows a second law of information, I mean modern films, music, visual art, and literature all of it depend on ambiguities that are left up to us to understand them. A single spoken sentence can contain so many layers of information that are completely absent from something like a computer programming language even day-to-day functions like determining whether somebody is lying or if they understand you. 

All (sound made by a human) is difficult to process because human speech has such high entropy but listening to music might be our way of training our brain for that. So, jazz music and indigenous drumming really aren't that different they both train us to process difficult information that might be the best benefit that music gives us. Of course, you can't listen to Hard music all the time because it might be white noise which has a very high entropy that we can not comprehend. 


This is a connection to model theory (click here)

NOTE:

## Audio is made by John Paul J

  • The rest of the audio is taken from "Sound Effect from <href="https://pixabay.com/?utm_source=linkattribution&utm_medium=referral&utm_campaign=music&utm_content=29388">Pixabay</a>"
  • The pictures and equations are made by  GIMP and "a paper" mobile application by John Paul J. The equations are not exact and are referred from the following. 

  • https://pubmed.ncbi.nlm.nih.gov/21981535/
  • https://pubmed.ncbi.nlm.nih.gov/20481757/
  • https://pubmed.ncbi.nlm.nih.gov/27134038/

  

Hope this article was useful and I hope you learned something from it.

If you have any theories or questions regarding this you are free to express them in comments or you can chat with me on my Instagram page https://www.instagram.com/phy.sci/?hl=en.





IF ANY DOUBTS AND CLARIFICATION YOU CAN COMMENT HERE.
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Pressure around us

 PRESSURE AROUND US 

Courage is grace under pressure. 

-Ernest Hemingway  


Here I am going to mention a pressure that is experienced by all living entities and even plays an important role in their life. It is " Air pressure". 



What is air?

Air is a mixture of many gases and tiny dust particles. Air can only exist inside a closed boundary like a bottle, cylinder, atmosphere, etc for life forms to exist. Surprisingly air is a perfect mixture of all the gases i.e air is homogeneous even though it is made out of different gases. So air can be considered a single entity.  

How do we interact with air? Without air we can't breathe, plants can't survive, we can't have a stable temperature, we can't fly, and many other interactions that we see, experience, and study it. 


What is pressure?

Pressure is the force that is produced when something is pressed by you or something is pressing you. Force is pushing or pulling, in this case, we can consider force as pushing. In science pressure is a physical quantity that is very useful in many concepts like hydrostatic pressure, thermal pressure, fluid pressure, differential pressure, gauge pressure, vacuum pressure, atmospheric pressure, water pressure, etc. 


Fluids

Water and gases are called fluids because they exhibit similar behavior that is they can take the shape of a container, are loosely packed, have thermodynamic properties, and can flow. With physical observation, we can say that fluid is a medium in a space that occupies the space and life exist in the fluid or with the help of fluids.


Water and life 

As humans, we can't see our faces with our senses but can see others' faces and learn from them in a similar way we don't realize our surroundings. Now let's learn from the life form in water. Take a fish in a pond, a pond has a closed boundary and the fish can move inside it. Now the fish needs oxygen and it gets the oxygen from the resolved oxygen in the water. As we see the fish moves freely in the water without any resistance because the fish lives in that environment. we can see fish living near the surface of the water and fish that go deep as 10000 feet quite interesting right!

Now the water at a depth provides some pressure because some amount of substance is above it. (when a pile of pillows is on your chest we feel pressure in a similar way there is a pile of water above that point). Now lets us do a little calculation to understand what is happing.

Consider a cuboid pond of the following dimensions  

10×10×200            (Length×Width×Depth )

Its volume is then given as a 20000-meter cube 

Now consider a fish at 10 meters depth. So it has 10 meters high water above it. 

So, The volume of water above it is a 10000-meter cube which is 10000000 kg of water or 980 KPa of pressure, Now with a sound mind, we can see the fish should be crushed with that weight but it does not, (We don't usually think this in this way but it is really interesting). A pressure of around 100 KPa is enough to crush a soda can. Here the fish does not get crushed because it doesn't have air inside it and it is mostly fluid so it will balance its body pressure with the water pressure and move around.  


Humans, fish, and air

As land-living creatures, we move around the land in a medium filled with air which we don't notice because it is a part of us. 

We don’t even realize we are experiencing air pressure until we actually look for it. The things we don’t see at first, and take for granted, like gravity and air pressure, turn out to be among the most fascinating of all phenomena. It’s like the joke about two fish swimming along happily in a river. One fish turns to the other, a skeptical look on its face, and says, “What’s all this new talk about ‘water’?” from the lectures of Walter Lewin. 


We live at the bottom of the ocean 

From the above discussion, we should come to the idea that we live at the bottom of the ocean which is made up of air, which exerts a huge amount of pressure on us every second of every day. Suppose you hold your hand out in front of you, palm up. Now imagine a very long piece of square tubing that is 1 centimeter wide balanced on my hand and rising all the way to the top of the atmosphere. That’s more than 7000km (More precisely 10000km). The weight of the air alone in the tube (forget about the tubing just think of air or the jube is made up of air). That’s one way to measure air pressure: 1.03 kilograms per square centimeter of pressure which are called the standard atmosphere or 100Kpa. Which is huge. (From Walter Lewin Lectures and demonstrations)

Another way to calculate air pressure is with a fairly simple equation. Pressure is force divided by area: P = F⁄A. So, air pressure at sea level is about 1 kilogram per square centimeter. We know the relation between force, pressure, and area. The larger the area, the lower the pressure, and, conversely, the smaller the area, the larger the pressure. 

Now stretch out your hand (palm up) and think about the force exerted on your hand. The area of your hand is about 10 square centimeters, so there must be a 70-kilogram force, about 70 Kg, pushing down on it. Then why you are able to hold it up so easily?  Because the pressure exerted by air surrounds us on all sides, and there is also a force of 70 Kg upward on the back of your hand. Thus the net force on your hand is zero. Then why doesn’t your hand get crushed if so much force is pressing in on it? Clearly, the bones in your hand are more than strong enough not to get crushed. (From Walter Lewin Lectures and demonstrations)

How about my chest? It has an area of about 1,000 square centimeters. Thus the net force exerted on it due to air pressure is about 1,000 kilograms: 1 metric ton. The net force on my back would also be about 1 ton. Why don’t my lungs collapse? The reason is that inside my lungs the air pressure is also 1 atmosphere; thus, there is no pressure difference between the air inside my lungs and the outside air pushing down on my chest. That’s why I can breathe easily. Take a cardboard or wooden or metal box of similar dimensions as your chest. Close the box. The air inside the box is the air you breathe—1 atmosphere. The box does not get crushed for the same reason that your lungs will not collapse. Houses do not collapse under atmospheric pressure because the air pressure inside is the same as outside; we call this pressure equilibrium. (From Walter Lewin Lectures and demonstrations)

So it is really fascinating to think about the things around us. 


Hope this article was useful and I hope you learned something from it.

If you have any theories or questions regarding this you are free to express them in comments or you can chat with me on my Instagram page https://www.instagram.com/phy.sci/?hl=en.


For previous articles on this follow the following link
TAU 5: 



IF ANY DOUBTS AND CLARIFICATION YOU CAN COMMENT HERE.
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