Look into the spectrum - Spectroscopy

 Look into the spectrum

through spectroscopy

"What we are nowadays hearing of the language of spectra is a true 'music of the spheres' in order and harmony that becomes ever more perfect despite the manifold variety. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei."

- Arnold Sommerfeld, Atombau und Spektrallinien

Imagine you have a magical pair of glasses that allow you to see things in a whole new light—literally! Spectroscopy is like those glasses but for scientists. Instead of helping you see hidden worlds, spectroscopy helps scientists see hidden details about the stuff around us by using light beyond the power of our naked eye to comprehend. You know how when you look at a rainbow, you see all those different colors? Well, light is made up of lots of different colors (wavelength), and each color has its own special "fingerprint" that can tell us about what it's made of. Spectroscopy is like taking a close look at those fingerprints to figure out what's in the things around us. Together, they form a symphony of energy, each wavelength playing its part in the cosmic melody of existence. Within the Electromagnetic Spectrum lies the key to understanding the universe and unlocking its infinite wonders.

1. A picture of sunlight at a particular (random) angle. Due to the angle and some imperfections in the mobile camera, the sunlight splits into different colors which is the essence of spectroscopy.

2. Splitting of light in a diffracting grating which splits the light in a more organized manner. The diffracting grating is an important tool in spectroscopy. Which gives us a goos spectrum of white light. 

3.  The sunlight is reflected by a diamond-like crystal which produces a unique color. This is not essentially a useful way to understand spectroscopy but understanding the physics behind it is useful to understand spectroscopy. 

(Images taken by John and are not edited or color corrected)

A spectrum refers to a range or continuum of something, typically ordered by some characteristic quality. In physics, the electromagnetic spectrum encompasses the range of all possible frequencies of electromagnetic radiation, including visible light, radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays. The visible light spectrum, for instance, includes all the colors of light that can be seen by the human eye, from red to violet.

The nature of the electromagnetic spectrum is that it is always in a state of interaction with matter. Actually, we can confirm the presence of spectrum only through interaction with matter. We can use this interacting nature of the electromagnetic spectrum to look out for what is around us and understand nature. This technique which is used to study the spectrum is called Spectroscopy. Through spectroscopic techniques, people can analyze how light is absorbed, emitted, or scattered by substances, allowing them to infer characteristics such as composition, structure, and behavior.

Figure elucidating the interaction of the electromagnetic wave with the matter in a technical way

Click the image to view better

Source: http://hyperphysics.phy-astr.gsu.edu/hbase/mod4.html 

Spectroscopy enables us to explore and understand the spectrum by examining how different materials interact with electromagnetic radiation. By analyzing the patterns and characteristics of the spectrum, spectroscopy provides valuable insights into the nature of matter and its interactions with light. Thus, spectroscopy and spectrum are intimately linked, with spectroscopy serving as the primary tool for studying and interpreting the spectrum

Note on spectrum

The concept of the electromagnetic spectrum has evolved over centuries, beginning with Isaac Newton's experiments on visible light in the 17th century and progressing through subsequent discoveries by scientists such as Thomas Young and Augustin-Jean Fresnel, who revealed light's wave nature. James Clerk Maxwell's equations in the 19th century provided a theoretical framework for understanding electromagnetic radiation, while the study of spectroscopy, pioneered by Joseph von Fraunhofer and Gustav Kirchhoff, shed light on the interaction between light and matter. The 20th and 21st centuries saw advancements in technology enabling the exploration of regions beyond the visible spectrum, leading to the discovery and utilization of radio waves, microwaves, infrared radiation, ultraviolet radiation, X-rays, and gamma rays. Today, the electromagnetic spectrum encompasses a wide range of frequencies or wavelengths, each playing a crucial role in scientific research, technology development, and everyday applications, driving innovation and deepening our understanding of the universe.

The theoretical framework of spectra

The theoretical framework of the electromagnetic spectrum is based on the principles of electromagnetism and quantum mechanics. Electromagnetism provides a fundamental understanding of how electric and magnetic fields interact and propagate through space. These equations describe how electromagnetic waves, including light, propagate at the speed of light and carry energy and momentum. Quantum mechanics further refined our understanding of the electromagnetic spectrum by introducing the concept of quantized energy levels. According to quantum mechanics, energy is not continuously distributed but exists in discrete packets or quanta. This concept explains phenomena such as the discrete spectral lines observed in spectroscopy, where atoms and molecules absorb or emit light at specific frequencies corresponding to the energy differences between their quantized energy levels.

How the electromagnetic spectrum is produced?

The electromagnetic spectrum is produced by the emission, absorption, and scattering of electromagnetic radiation by matter, ranging from subatomic particles to astronomical objects.

Emission: Atoms, molecules, and other particles can emit electromagnetic radiation when they undergo transitions between energy levels. For example, when an electron in an atom moves from a higher energy level to a lower one, it emits a photon of electromagnetic radiation. The frequency (or wavelength) of the emitted radiation depends on the energy difference between the initial and final energy levels, according to the equation  ΔE=hν, where  ΔE is energy, ℎ h is Planck's constant, and ν is frequency. This emitted radiation contributes to the electromagnetic spectrum.

Different ways of obtaining electromagnetic spectra in a lab. 

Source: https://ciet.nic.in/moocspdf/Chemistry01/kech_10202_eText.pdf

Absorption: Conversely, matter can absorb electromagnetic radiation when it interacts with photons. If the energy of a photon matches the energy needed to promote an electron from a lower energy level to a higher one, the photon will be absorbed, and the electron will transition to a higher energy level. The absorbed radiation is typically in specific frequency ranges corresponding to the energy differences between the atomic or molecular energy levels involved. This absorption leads to dark absorption lines in the electromagnetic spectrum, where certain frequencies of light are missing due to absorption by specific substances.

Scattering: When electromagnetic radiation interacts with particles or surfaces, it can be scattered in different directions. The scattered radiation contributes to the overall electromagnetic spectrum, often with no distinct pattern. However, certain types of scattering, such as Rayleigh scattering, are wavelength-dependent and can result in phenomena like the blue color of the sky.

Synchrotron Radiation: In some cases, highly energetic particles moving through magnetic fields, such as those in synchrotron accelerators or astrophysical environments, can emit synchrotron radiation. This radiation spans a wide range of frequencies and contributes to the electromagnetic spectrum.

These processes result in a continuous range of frequencies or wavelengths, from radio waves to gamma rays, that make up the electromagnetic spectrum.

Emission spectra of various elements in the periodic table in the visible region.  This means that these elements when heated produce a light that contains this spectrum. If you see the emission spectra of Tungsten (W) and Neon (Ne) you can see the presence of a complete spectrum i.e. all the visible colors are visible, This is the reason these materials are used in lighting applications.  

Source : THE Elements A Visual Exploration of Every Known Atom in the Universe. Photographs by Theodore Gray and Nick Mann

What is spectroscopy?

Spectroscopy is a scientific technique used to study the interaction between matter and electromagnetic radiation. It involves analyzing how materials absorb, emit, or scatter light at different wavelengths or frequencies. By examining the unique patterns of light absorbed or emitted by a substance, spectroscopy provides valuable information about its composition, structure, and properties. Some common spectroscopic methods include infrared spectroscopy, ultraviolet-visible spectroscopy, nuclear magnetic resonance spectroscopy, and mass spectrometry. 

In spectroscopy, several fundamental equations are essential for describing the interaction between electromagnetic radiation and matter. 

• The Beer-Lambert Law establishes a relationship between the absorbance of light by a sample and the concentration of the absorbing species, defined by the molar absorptivity, concentration, and path length of the sample. 
• The Planck-Einstein Relation relates the energy of a photon to its frequency or wavelength, providing a basis for understanding the quantized nature of electromagnetic radiation. 
• The Rydberg Formula describes the wavelengths of spectral lines emitted or absorbed by hydrogen-like atoms, aiding in the analysis of atomic spectra.

Additionally, the Schrödinger Equation in quantum mechanics is crucial for determining the allowed energy levels and wavefunctions of electrons in atoms and molecules, providing a theoretical framework for interpreting spectroscopic transitions.

Let's become a spectroscopist

First, Using a CD as a diffraction grating to split white light and analyze it is a simple yet effective way to demonstrate spectroscopy. CDs, with their closely spaced tracks of pits and lands, act as diffraction gratings when illuminated with white light. When white light is directed onto the surface of a CD, the grooves on the CD surface diffract the light, causing it to spread out into its component colors. This process is similar to how a prism splits white light into a rainbow of colors. Each color in the spectrum corresponds to a specific wavelength of light. By observing the pattern of colors produced by the diffracted light from the CD, one can analyze the spectrum of the light source. This spectrum reveals information about the composition of the light source, as different materials emit or absorb light at specific wavelengths.

1. The spectrum of white light was obtained using the above-mentioned way. 

2. The spectrum of green led. As you can see green LED is partially composed of red and blue lights other than green light which is evident by comparing the spectra with the graph in 7.

3. The spectra of red LED. As you can see it is partially composed of yellow light i.e. the red light for the LED splits into red and yellow-orange colors. 

4. The spectrum of blue LED. As you can see the blue LED spectra split into indigo and violet. 

5. The clear spectrum of which light.

6. The graph showing the composition of different LEDs and compare it with white light and a distant astronomical object (DOI:10.3762/bjoc.12.170)

(1-5 are taken using a mobile camera and they are un-edited images)

Second, In this experiment, various concentrations of a colored liquid are prepared, with each solution having a different level of light absorption due to the presence of colored molecules. To perform the experiment, a light source, such as a smartphone flashlight, is directed through each solution. The color picker app is then used to measure the intensity of light transmitted through the liquid. By comparing the intensity of the transmitted light for each concentration, one can determine the absorbance of the liquid at specific wavelengths. According to the Beer-Lambert Law, absorbance is directly proportional to the concentration of the absorbing species and the path length of the sample. Therefore, as the concentration of the colored molecules in the liquid increases, so does the absorbance of the solution. By plotting the absorbance values against the concentration of the colored liquid, a linear relationship should be observed, confirming the validity of the Beer-Lambert Law.

UV/VIS absorbance spectrum of sucrose solutions over 10 mm path length. As you can see for higher conc. the absorption is high. It is because there are more number of molecules when the concentration is higher so the incident light will interact with more molecules hence the absorption is greater. 

Source: doi: 10.3390/s8010010 Cantilever Micro-rheometer for the Characterization of Sugar Solutions

Beginner course in analyzing spectra

UV spectroscopy, also known as ultraviolet-visible (UV-Vis) spectroscopy, is a technique used to measure the absorption of ultraviolet and visible light by molecules in solution. UV-Vis spectroscopy relies on the fact that molecules absorb light at specific wavelengths corresponding to transitions of electrons between different energy levels. The absorption of light causes the electrons to move to higher energy levels, which results in a decrease in the intensity of the transmitted light. The absorption spectrum obtained shows peaks and troughs corresponding to the wavelengths at which the molecule absorbs light.

The raw UV spectra of tea samples in the wavelength range of 400–2498 nm are plotted in Figure.   

Visible and near-infrared spectra of tea samples. 

(From the article "Nondestructive monitoring of polyphenols and caffeine during green tea processing using UVVis-NIR spectroscopy")

Source: DOI:10.1002/fsn3.1861

The absorption peaks at 480 nm and 670 nm were located in the visible region of the spectra (400–800 nm). It proved that the tea leaves mostly absorb light in the visible spectral range (blue-violet (455–492 nm) and red (622–770 nm)) while green light absorption (500–560 nm) is too low, so this is the reason the tea leaves look green.

The absorption spectra of water showers that the water doesn't have any absorption peaks in the visible light region so the water is transparent to visible light.

Absorption spectra of Water for a wide range of incident electromagnetic waves.

Source: https://wiki.pathfinderdigital.com/wiki/fso-underwater/  

Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful technique for studying molecule structure and dynamics. It exploits the magnetic properties of atomic nuclei, revealing details about their arrangement and chemical environment. By subjecting samples to radiofrequency radiation in a strong magnetic field, NMR spectroscopy generates spectra with peaks corresponding to specific nuclei types. This information aids in identifying compounds and understanding molecular interactions.

When peanuts are used as adulterants, there is an additional risk of potential health hazard to consumers due to allergy-induced anaphylaxis. Peanuts can be used as an adulterant in powdered hazelnuts, almonds, and walnuts. The close inspection of NMR spectra of various powders can reveal the peanut as an adulterant in these products.  

H NMR spectra obtained by the two polar solvents (A: deuterated phosphate buffer/methanol-d4, B: methanol-d4) show an individual marker signal (Extraction A: singlet at 3.05 ppm, extraction B: singlet at 3.02 ppm), which could indicate the admixture of peanut. The highlighted region showed the difference between peanuts and other nuts. 

Source: Detection of Peanut Adulteration in Food Samples by NMR Spectroscopy. J. Agric. Food Chem.,• DOI: 10.1021/acs.jafc.0c01999

The above figure shows the variation of the peak at 3 ppm (Parts per million calibrated based on the frequency difference between the resonance of the sample and the reference compound) from which we can find this type of adulteration. 

The IR (Infrared) specifically Mid-infrared (MIR) spectra are informative fingerprints of molecular vibrations and rotations within compounds. This spectral region typically ranges from approximately 4000 to 400 cm^-1. In MIR spectroscopy, molecules absorb radiation in the mid-infrared range, causing characteristic peaks in the spectrum corresponding to specific functional groups and chemical bonds. These peaks provide valuable information about molecular structure, composition, and interactions.

The following figure shows the M-IR spectra of milk showing different nutrients and edible biological molecules present in it. If more water or any other chemical is added to it the resulting spectra will be different. 

Representative images of the mid-infrared spectrum of milk and the approximate putative region obtained with TQ Analyst software ver. 8.0 (Thermo Fisher Scientific, Madison, WI, USA).

Source: Recent Advances in the Determination of Milk Adulterants and Contaminants by Mid-Infrared Spectroscopy: Foods 2023, 12(15), 2917; https://doi.org/10.3390/foods12152917 

The famous and widely used diagnostic tool MRI in the medical field is also a type of spectroscopy. It reveals the inner structure of the human body. It is a non-invasive medical imaging technique used to visualize the anatomy and pathology. MRI relies on the interaction of hydrogen nuclei (protons) in water and fat molecules with a strong magnetic field and radiofrequency pulses. By measuring the signals emitted by these nuclei, detailed images of the spinal cord can be generated.

The following image shows the MRI image of a patient which shows the anatomy and pathology of the spine and its surrounding structures. 

Various orientations of spin were taken using an MRI.

Source: https://twitter.com/RadiologyEDU/status/1011287263983079424  

X-ray crystallography is a powerful technique used to determine the three-dimensional structure of crystalline materials at the atomic level. X-ray crystallography relies on the interaction of X-rays with the electron density of atoms within a crystal lattice. When X-rays strike a crystal, they are diffracted by the regularly spaced atoms, producing a diffraction pattern of spots on a detector.

The following figure shows the x-ray peak of  Maltose and Cocaine. As both of them are physically indistinguishable the XRD pattern of the compounds can be used to detect the presence of cocaine. The following shows the different peaks of the two compounds. 

Simulated diffraction patterns of cocaine and maltose are displayed along with the peak positions of the International Centre for Diffraction Data (ICDD) standard. Two mixtures, 50% cocaine / 50% maltose and 10% cocaine / 90% maltose, show the qualitative differences in the XRD pattern as the components are varied. Qualitative identification is based on the presence of the unique diffraction lines for each substance, the "X-ray fingerprint." In addition, a quantitative determination can be made for each component by measuring its peak intensity and comparing it to the intensities measured from one or more samples of known concentration.

Source: FORENSIC ANALYSIS BY X-RAY DIFFRACTION: https://www.rigaku.com/applications/bytes/xrd/miniflex/1060214993

Concluding remarks: 

Using a CD as a diffraction grating for spectroscopy is a fun and educational experiment that can be easily performed at home or in a classroom setting. It provides a hands-on way to explore the properties of light and learn about the principles of spectroscopy. Additionally, it highlights the versatility of everyday materials in scientific experimentation and encourages curiosity and exploration in the field of optics and spectroscopy.

In summary, understanding spectroscopy is crucial for advancing scientific knowledge, developing new technologies, improving healthcare outcomes, and addressing global challenges. It enriches our understanding of the natural world and empowers us to innovate and make informed decisions in both scientific and everyday contexts.

HOPE YOU LEARNT A NEW THING AND CHANGE THE WAY OF LOOKING AROUND YOU.

You can also comment on this page to discuss this topic.

If you have any questions regarding this you are free to express them in the comments or you can chat with me on my Instagram page to discuss this.  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.

See my previous posts 

Science of pencil

Empiricism and Rationalism

Water and life

Why do remotes work when we smack them?

Vibration - Eternal motion

Scientific values of water

IF ANY DOUBTS AND CLARIFICATION YOU CAN COMMENT HERE.

IF ANY INFORMATION IS INACCURATE I AM READY TO CORRECT IT

 

 

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.

See my previous posts 

Science of pencil

Empiricism and Rationalism

Water and life

Why do remotes work when we smack them?

Vibration - Eternal motion

For previous articles on this follow the following link

TAU1: https://jjohnpaul.blogspot.com/2021/04/mysteries-of-fountain-pen.html

TAU2 : https://jjohnpaul.blogspot.com/2021/06/tau2-egg-is-violating-physics.html

TAU3: https://jjohnpaul.blogspot.com/2021/07/tau-3-color-of-clouds.html

TAU4: https://jjohnpaul.blogspot.com/2021/07/tau-4-peace-be-with-elements.html

TAU 5: 

https://jjohnpaul.blogspot.com/2022/02/tau-5-why-do-remotes-work-when-we-smack.html

IF ANY DOUBTS AND CLARIFICATION YOU CAN COMMENT HERE.

IF ANY INFORMATION IS INACCURATE I AM READY TO CORRECT IT