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Before the twentieth century, classical physics offered a clear and reassuring picture of the world. Within the framework of Newtonian mechanics, the universe appeared deterministic, consistent, and composed of particles whose properties were well defined at all times. Physical laws contained no ambiguities or dualities, and measurement revealed pre-existing properties. This assumption of objective realism began to fracture with the birth of quantum mechanics. Fig. 1 . Artistic representation of wave–particle duality. Source: Shutterstock From classical certainty to quantum duality In classical physics, particles and waves belong to distinctly different physical categories. A particle is characterised as existing at a specific point in space; its interaction with another particle occurs at a specific location, much like collisions between billiard balls. In contrast, a wave is described as spreading across a spatial region, and its interaction with another wave leads to a superposition, with regions where the waves reinforce each other followed by regions where they cancel out. A familiar example includes water waves. Classical waves transfer energy through a medium by passing it from one molecule to the next. Before the emergence of quantum mechanics, light was also considered a classical wave. Although electromagnetic waves don't require a medium to propagate, they still possess classical wave characteristics such as frequency, wavelength, and amplitude. As such, they superimpose, creating a typical interference pattern with areas of reinforcement and cancellation. These wave-like properties of light were demonstrated by Thomas Young in his two-slit experiment in  1801 ( Fig. 3 ). Fig.2 . The interference pattern produced by light passing through two narrow slits. The bright fringes form where the crests of two waves reinforce each other. The dark bands result from the waves cancelling each other out. The belief that nature respects our categories was shattered in 1905 when Albert Einstein proposed that light can exhibit a particle behaviour. The photoelectric effect demonstrated that light is not a continuous flow of energy, as previously thought, but is made up of discrete energy packets , later named photons. The realization that something as fundamental as light can exhibit wave properties in one experiment and particle behavior in the other shocked the scientific community. This finding challenged the classical views that had guided physics for centuries, paving the way for quantum theory. Arrival of the Schrödinger equation The sentiment was growing that wave-particle duality may be a fundamental feature of physical reality at the microscopic scale. If light, previously known as a wave, can exhibit particle behaviour, then particles can possess the wave characteristics. In 1924, Louis de Broglie  made the first step toward laying the foundations for quantum mechanics by proposing a formula that connected the fundamental property of waves, their wavelength λ, to the fundamental property of material particles, their mass m . Fig. 2 . The de Broglie wavelength equation, where λ = wavelength of a particle, h = Planck’s constant, p = momentum, m = mass of the particle, and v = velocity. The crucial link between particles and associated waves was found. Motivated by this idea, Erwin Schrödinger applied the known physics of waves to the physics of matter and formulated the equation that became a cornerstone of the emerging quantum theory ( Fig. 2 ). Its role in quantum mechanics is comparable to that of Newton's formula F = ma in classical mechanics. The wavefunctions ( ψ ) governed by this equation can provide a complete description of quantum states. Fig. 3 . The time-dependent Schrödinger equation, where i = imaginary unit, ħ = reduced Planck constant, ψ = wavefunction, t = time, Ĥ = Hamiltonian operator (total energy operator), The classical foundations used by Schrödinger in deriving his equation raised the expectations that quantum waves should possess physical properties comparable to those of electromagnetic waves. In that case, the double-slit experiment with electrons should exhibit an interference pattern similar to the one observed with light in Young's experiment ( Fig. 3 ). The pattern should appear as a smooth transition between bright and dark bands, without any dots indicating particle-like behavior. Fig. 4 . Double-slit interference pattern produced by red light. Image: Jordgette, Wikimedia Commons, CC BY-SA 3.0. Cropped from original. The double-slit experiment with electrons could not be conducted at the time due to technological constraints. According to the de Broglie equation, an electron has a wavelength much smaller than that of visible light, given the electron's mass and the speed required for the experiment. To produce an interference pattern, the slits and the distance between them must be extremely small, which was beyond the capabilities of the technology of that time. Max Born and the birth of quantum probability During that period, Max Born was working on a related problem, analyzing collisions between electrons and atoms. Previously, the double-slit experiment was interpreted from a classical standpoint. However, if we zoom in on the slits, they become a quantum system, represented by the atoms they are made of. As electrons pass through the slits, they interact with the atoms and are deflected. Born wanted to see if there was a connection between the deflection angles and the interference pattern predicted by the Schrödinger equation . Born found that the angles align perfectly with the predictions of Schrödinger's equation. This led to the conclusion that quantum waves are not physical phenomena, but rather mathematical abstractions. A wavefunction encodes all the information about a particle and evolves alongside the particle through space and time. As such, it can statistically predict a physical outcome when a particle is measured. The wavefunction  ψ ( x ), which describes a particle's evolution through space, can predict the probability of that particle hitting the screen at a given point x . If we directed a stream of electrons through two slits, they would create an interference pattern due to the statistical distribution. The bright bands would highlight regions of  high probability, while the dark bands would correspond to regions of low probability. This perspective marked the rise of the probabilistic interpretation of quantum mechanics. While classical mechanics predicts exact results, quantum mechanics can only predict probabilities, demonstrating a radical shift from classical certainty to quantum uncertainty. The  Born rule  ( Fig. 5 ) cemented this idea by utilising Schrödinger's wavefunction  ψ ( x ) to determine the statistical distribution of measurement outcomes in quantum mechanics, expressed as the probability density P ( x ). Fig. 5 . According to the Born rule , the probability of finding a particle at position x  is given by the square of its wavefunction ψ ( x ). Interestingly, Heisenberg presented his uncertainty principle a year later. Although he used a different method, his uncertainty principle can be derived from the Born rule. Indeed, if the quantum w avefunctions can only yield probabilities instead of definite results, uncertainties must be inherently embedded in their structure.  Copenhagen Interpretation The statistical interpretation of the interference pattern sparked heated debates about the physical nature of quantum waves. Schrödinger never accepted the notion that quantum waves are merely mathematical abstractions . In 1927, when electrons were scattered by a crystal lattice, a diffraction pattern emerged, analogous to that of light. Diffraction patterns are more easily observed than interference patterns because the gaps through which electrons must pass can be wider. Nevertheless, even with the diffraction pattern , electron impacts were registered by the detector as single events. The alignment of the crystal lattice gaps with the electron's wavelength, as predicted by  de Broglie,  validated his wave-particle  duality hypothesis. However, what are these waves exactly? On the one hand, their wavefunction is essential for predicting interference and difraction patterns. On the other hand, the crystal lattice experiment observed impacts as individual events. This paradox demanded timely resolution. The Copenhagen interpretation, led by Niels Bohr and Werner Heisenberg, remains the most widely accepted. Born rule dominated the views, shifting the physical description of reality from deterministic to fundamentally probabilistic. Quantum waves are not directly observable; they are not physical waves like water or sound waves. But their wavefunctions accurately describe their evolution and predict measurable outcomes within the realm of probability. Consensus was that quantum systems are inherently indeterministic, lacking well-defined properties until measurement provides a definite result. Uncertainty is ingrained in the structures of the microscopic world, which is why physicists have a theory that behaves like a wave but yields a single localised outcome in experiment. When particles arrive one at a time Several decades later, with further technological advances, the probabilistic interpretation gained clear experimental support. When a beam of electrons was sent through two extremely narrow slits toward a detector screen, the screen registered electrons as single localised events. They appeared not as an energy wave spreading across a spatial region but as individual dots. However, over time, these dots gradually accumulated to form an interference pattern that corresponded to the Born rule ( Fig. 6 ). Fig. 6 . Gradual build-up of a double-slit interference pattern. Each dot represents a single particle (electron or photon) detected on the screen. Credit :   Bach et al. (2013), New Journal of Physics . Via Wikimedia Commons, CC BY 3.0. Furthermore, when technology allowed a single photon to be emitted one at a time, remarkably similar behaviour was observed. Instead of a continuous flow of energy, the detector recorded the same single-photon events. The photons appeared as dots, gradually building up the familiar interference pattern. If photons and electrons behaved purely as classical particles, they would produce two clusters on the screen corresponding to the two slits through which they passed. If they behaved purely as classical waves, they would produce smooth bands of varying energy density. Instead, what emerges is something different: bands of high and low probability density , exactly as predicted by the Born rule. This result captures the essence of quantum mechanics. Quantum objects propagate through space according to their wavefunctions, which determine the probability distribution of where they may be detected. Yet when they interact with the detector screen, they always appear as localized particles. The apparent tension between these two descriptions lies at the heart of quantum theory. A mathematical structure that evolves like a wave ultimately produces individual particle-like events in measurement. More than a century after its discovery, quantum mechanics continues to challenge our intuitions about the nature of reality. In many ways, our exploration of the quantum world is still in its early stages. As experiments probe ever-smaller scales and higher levels of precision, the foundations of this strange yet remarkably successful theory remain an active and fascinating area of scientific inquiry.

The video in Fig. 1 offers a perfect opportunity to explain how real rainbows behave and how editing can manipulate the laws of physics. At first glance, the image appears to show a spectacular display of multiple rainbows. The rainbow on the left looks physically consistent and sets the expectation of realism. However, a closer examination of the intersecting arcs raises strong suspicions. Is this video authentic? Let’s apply basic optics to find out Fig. 1 . A viral video appears to show multiple overlapping rainbows, but does the geometry reflect real atmospheric optics? Click to watch this video on Facebook When rainbows behave as nature intended Rainbows appear under specific conditions: the Sun must be behind the observer, with raindrops in front. Sunlight enters each raindrop, refracts at the surface, reflects internally, and refracts again as it exits. These optical processes produce several recognizable features. Rays undergoing a single internal reflection form the primary rainbow ( Fig. 2 , left). Its colour order is fixed: red on the outside and violet on the inside. The rays undergoing two internal reflections form the secondary rainbow ( Fig. 2 , right). The additional reflection reverses the color order, with red inside and violet outside, and reduces color brightness. Fig. 2 . Geometry of primary and secondary rainbow. Light undergoing one internal reflection produces the primary rainbow (left), while two internal reflections produce the fainter secondary rainbow (right) with reversed colour order. Adapted from ISTA ( ista.ac.at ), with additional elements added. Thus, the primary arc appears brighter, and the secondary arc above the primary is either fainter or not visible at all. The laws of optics also expect the inner section of the primary arc to be lighter than the sky around it ( Fig. 3 ), whereas the sector above, known as Alexander’s band, appears darker. The left rainbow in the video aligns well with these expectations: correct colour sequence, realistic brightness, and a weaker secondary arc. So far, everything related to that particular rainbow checks out. Fig. 3 . The double rainbow. The brighter primary arc shows red on the outside, and the fainter secondary arc above with reversed colours. The region between them is the darker Alexander’s band. The sky inside the primary bow is brighter. Credit: Alexis Dworsky - Own work, CC BY 2.0 de, https://commons.wikimedia.org/w/index.php?curid=15646431 The "extra rainbow" that makes no sense Look at the three arcs on the right side of the video, which intersect the arcs of the main rainbow. This is where physics begins to raise an eyebrow. In principle, the presence of a second rainbow beside the main one is possible. This rare atmospheric phenomenon, called a reflection rainbow  ( Fig. 4 ), occurs when sunlight reflected from a wet surface, such as a road or nearby reservoir, acts as a secondary light source, effectively creating a “virtual Sun” that produces its own rainbow. However, because the “virtual Sun” has a different location, the resulting bow would not appear as a simple duplicate of the main rainbow, nor would it produce perfectly symmetric intersection patterns. Fig. 4 . AI-generated illustration of a reflection rainbow whose primary and secondary arcs intersect those of the direct-sunlight rainbow near the horizon. Let us ignore, for the moment, the third, lower arc in the video, which should not be present at all because it violates the angular geometry governing rainbow formation, specifically, the ~42° radius characteristic of the primary bow. Focusing instead on the two upper arcs of the “extra rainbow,” we find that they closely resemble a shifted copy of the genuine rainbow on the left. To understand why this is suspicious, we need to consider the angular geometry of rainbows. Every rainbow is centred on its own antisolar point, which is the point directly opposite the light source as seen by an observer ( Fig. 5 ). A conventional rainbow is centred opposite the real Sun, whereas a reflection rainbow would be centred opposite the virtual Sun created by reflection in water. Because the real and virtual Suns occupy different positions, the corresponding rainbows must have different centres and therefore different orientations and curvature, as shown in Fig. 4 . Fig. 5 . Rainbow geometry is defined by the observer’s position. Sunlight entering raindrops produces a circular arc centred on the antisolar point, which is the point directly opposite the Sun relative to the observer. AI-generated illustration. This has an important consequence: the second rainbow cannot appear as a parallel duplicate of the first. Instead, its arc must diverge geometrically, reflecting the different directions of the incoming rays. When two bows appear geometrically identical, maintaining constant spacing and forming symmetric shapes where they overlap, this suggests that they share the same centre, which would only occur if one were a duplicated image rather than an independent optical phenomenon. For an observer to see two genuine bows simultaneously, the light rays responsible for each must arrive from different directions and converge at the eye. Identical geometry implies identical viewing directions, which is inconsistent with two separate light sources. A rainbow is not a physical object fixed at a particular location in the sky, but a viewing geometry defined by the observer’s position. Each observer sees their own rainbow, centred on their own antisolar point. A rainbow geometrically identical to yours could only be seen by someone standing very close to you, not by you as an additional, independent bow. The geometric symmetry of the second rainbow clearly shows that the principles of perspective have been violated. Rather than exhibiting two physically independent bows formed by different light sources, the extra arcs behave like a shifted replica of the original. This second "rainbow" cannot be the result of an independent atmospheric phenomenon. The duplication effect results from either a reflection in the windshield or the superimposition of one image over another during editing.

Earth is the largest of the rocky planets in the solar system. However, its size pales in comparison to the gaseous giant Jupiter, which could fit about 1,321 Earths inside it. This stark difference in size raised a profound question among astronomers: why are gaseous planets so much larger than rocky ones? The answer can be traced back to the origins of our universe and the creation of matter. In a universe of giants, small worlds can be extraordinary. The Big Bang left the young universe filled with primordial gas composed of the lightest elements: hydrogen and helium. These two elements still dominate the universe, accounting for about 98% of all visible matter. Our Sun is no exception, being composed largely of these elements, and so are the gaseous planets: Neptune, Uranus, Saturn, and Jupiter. In other words, the universe provides far more raw material for gas giants to grow from. The heavy elements required for rocky planets like Earth took much longer to appear. They formed under the extreme conditions inside stars that began to emerge roughly 200 million years after the Big Bang. Thermonuclear reactions in stellar cores gradually transformed some of the primordial hydrogen and helium into heavier elements such as silicon and iron. However, this process was demanding and slow, becoming increasingly difficult as the element's atomic number increased. Periodic table of the chemical elements . Source: Type Calendar. The creation of the heaviest elements required an even more dramatic event: supernova explosions. When massive stars reached the end of their lives, they exploded and scattered their interiors across space, enriching the universe with newly forged elements. Only after generations of stars lived and died did enough heavy material accumulate for rocky planets to form. Yet even after billions of years of stellar evolution, the universe remains dominated by its simplest ingredients. Hydrogen and helium still vastly outnumber the heavier elements produced in stars. This cosmic imbalance explains why planets like Jupiter can grow so large. Gas is abundant, rock is rare. During the formation of a solar system, there was far more gas available than the elements needed to build solid worlds. Jupiter’s enormous size is not unique to our solar system; it is a direct result of the universe's beginnings when the Big Bang filled the cosmos with light gases long before the existence of our Sun. This proves the adage that good things come in small packages. Planets like Earth are made from some of the rarest and most complex elements the universe can produce. Life takes this complexity even further, assembling those elements into extraordinary structures such as DNA. From them emerged a tiny species  of human beings capable of looking back across billions of years and discovering that their story began with the Big Bang.

The phrase "We are made of stars" was commonly used as a poetic metaphor to highlight the beauty of the human spirit. It was never anticipated to hold any scientific value, let alone accurately describe our physical makeup. However, this view changed in the 1980s when American astrophysicist Carl Sagan famously stated that the atoms composing our bodies were created in the cores of ancient stars and dispersed across the Universe when the stars exploded as supernovae. These stars originated from primordial clouds formed after the Big Bang. Consequently, the entire history of the Universe, from its inception to the present, is encoded in the chemical composition of our bodies, implying that the Universe is within us, just as we are within the Universe. Fig. 1 . The Universe is within us, just as we are within it. Image: Shutterstock The history of humanity begins with the origin of everything: the Big Bang. This was a cataclysmic event marked by extremely high temperatures, densities, and fast transformations. The newly born space was saturated with energy, ready to convert into matter. Within a second, the rapidly expanding universe cooled to a temperature of 10^15 Kelvin, triggering the Higgs field to become active and allowing elementary particles, such as quarks and electrons, to acquire mass. At this stage, the universe resembled a soup of free particles, which would serve as the fundamental building blocks for the material world we inhabit today. As the universe continued to expand and cool, the elementary particles became less chaotic and began forming bonds. Quarks combined to form protons and neutrons, and the protons and neutrons combined to form nuclei. The positive nuclei attracted negative electrons, leading to the formation of atoms. Hydrogen (H) was the first chemical element to emerge due to its simple atomic structure, consisting of one proton and one electron ( Fig. 2 ). The second element, helium (He), with two protons in its nucleus, required a far more complex process of fusion. The third element, lithium (Li), with three protons in its nucleus, faced even greater challenges. Consequently, this phase, known as Big Bang Nucleosynthesis, concluded with the universe being composed of 75% hydrogen, 25% helium, and traces of lithium. Fig. 2 Atomic structure of the first four elements in the periodic table. While the Big Bang Nucleosynthesis lasted only minutes, the next stage, the formation of heavier elements with more protons in their nuclei, took about a billion years to complete. The number of protons in the atom determines the identity and chemical properties of the element. Each element in the Periodic Table, Fig. 3 , differs from the previous element by one extra proton in its nucleus. Since protons are positively charged and repel each other, binding them together becomes increasingly difficult as more protons are added. This explains why the heavier elements with more protons in their atoms require prolonged periods of extremely high pressure and temperature, conditions that the expanding and cooling Universe could not provide. These conditions could only be met inside the massive stars that had yet to emerge. Fig. 3   Periodic table of the chemical elements . Source: Type Calendar. Before the emergence of the stars, the Universe was a dark place filled with thick clouds of hydrogen and helium. This period is known as the Cosmic Dark Ages. Over time, clouds separated into clumps, which grew in size with their cores becoming denser and hotter. When the temperature inside them reached 10 million Kelvin, hydrogen fusion commenced, and the first stars lit up the early Universe. These primordial stars were massive, substantially larger than our Sun. They served as giant cosmic crucibles, fusing new, heavier elements in their cores through a process known as Stellar Nucleosynthesis. The video in Fig. 4 , showcasing the 1954 hydrogen bomb test by the United States, provides insight into how the first primordial stars were ignited through the hydrogen fusion process. Fig. 4   The hydrogen bomb test conducted in the US, 1954. Source: Wikipedia The extreme temperature maintained inside these stars enabled complex fusion reactions,  resulting in the formation of heavier chemical elements, such as oxygen (8 protons) and calcium (20 protons), which are found in our bodies . However, the stars kept these elements to themselves, locked in their cores. It was only when they began fusing iron (26 protons in its nucleus) that they reached the end of their life cycle and exploded as supernovae, dispersing new elements into the surrounding interstellar space. During these explosions, the temperatures reached the highest levels known in the Universe since the Big Bang, allowing the final elements, as heavy as silver (47 protons) and gold (79 protons) to emerge through a process known as Supernova Nucleosynthesis. The remnants of these stars, enriched with new elements, served as the building material for the next generation of stars known as Population II. These stars underwent similar nucleosynthesis processes, converting more hydrogen and helium into heavier elements, thereby increasing their presence in the Universe. Still, even today, the Universe is predominantly composed of the most basic elements formed during the Big Bang, hydrogen and helium, with only 2% left for the elements with more complex nuclear structures. This observation remains the most compelling evidence in favor of the Big Bang theory. Our Sun belongs to the most recent category of Population I stars. Due to its relatively small size, it can't sustain the conditions needed to create heavy elements and primarily fuses hydrogen into helium. The heavy elements that constitute our bodies, such as oxygen and carbon , came from a nebula, the gas and dust cloud left behind after the explosion of a Population II star, which our solar system used during its formation. That star had recycled chemical elements created by its predecessor, a primordial Population III star, which formed from the hydrogen and helium clouds of the Big Bang. The human body consists of about 60% water (H2O), which includes hydrogen atoms in its molecules. This hydrogen links us to the Big Bang, while other atoms connect us to the stars that enriched the Universe with additional elements. Fig. 4   Carl Sagan was a renowned scientist and a profound thinker. Therefore, based on observations with powerful telescopes and laboratory experiments, we can conclude that we are composed of stardust, except for hydrogen, which was formed during the Big Bang. Every atom in our bodies was once part of a primordial cloud or a star that died to let us live. On early Earth, high-energy events like lightning and volcanic activity facilitated the formation of organic matter, beginning with simple molecules and ultimately leading to the emergence of DNA. The discovery of DNA marked the start of a new era, an evolution from primitive, single-celled organisms to intellectually advanced humans capable of inquiring about their origins and discovering the answers.

No reputable psychic would finish a session without reading your aura. They will tell you that  your body radiates energy in colors specific to your personality traits. For instance, if your aura is blue, you are reflective and peaceful; if it is red, you are fiery and dominant. T he color may differ from one psychic to another, but they will blame it on your emotional state and the pressures of modern life. They will even let you choose your color. After all, why settle for one when the rainbow has loads? However, if you ask about a link between energy and color, they will diverge into the murky waters of chakras and higher dimensions. And you will leave none the wiser. So, what energy do our bodies emit, and how is it related to color? Fig. 1 Aura imitation. Credit: Radiant Human, Art photography by Christina Lonsdale. Our bodies generate various forms of energy, but the only kind we can perceive visually is light. Light is a form of electromagnetic radiation, encompassing six additional bands that are not visible to the human eye ( Fig. 2 ). Each band is defined by its wavelengths. Since wavelengths are not intuitive, I will substitute them for the more familiar concept of temperature. Fig. 2    Full electromagnetic spectrum, from radio waves to gamma rays. Source: BBC Bitesize According to Wien's displacement law, there is a strong correlation between a body's temperature and the color of the light it emits. For instance, to emit blue light, a body must reach an extremely high temperature of approximately 18,000°F (10,000°C). This is the temperature of blue Sirius, the brightest star in our night sky ( Fig. 3 ). As the body's temperature decreases, the emitted radiation shifts towards the red end of the visible spectrum. An example of a red star is Betelgeuse, which at 5800°F (3200°C) is significantly cooler than Sirius. Fig. 3 Blue Sirius and red Betelgeuse. Credit: Hubble European Space Agency , As the temperature continues to drop, the red glow weakens and eventually fades into nonexistence. The photo in Fig. 4 shows the eruption of Arenal Volcano in Costa Rica in 2006 . The dark background is ideal for viewing the colors predicted by Wien's law. Lava appears orange when it is hotter and turns red as it cools. When the lava cools to around 1000°F (500°C), it transitions from visible red to the invisible infrared zone . Faint red specks are visible between the two main flows, disappearing into darkness where the lava has cooled further. Fig. 4 Eruption of Arenal Volcano, Costa Rica. Photo by Matthew.landry (Wikimedia Commons, CC BY-SA 3.0) . As the temperature cools further, we move deeper into the infrared spectrum. At 160°F (70°C), home radiators release energy we can only perceive as heat. At 100°F (37°C), our bodies emit wavelengths that are neither visible nor tangible. We can't be seen in the dark because our glow can only be captured by the infrared camera. Therefore, if psychics wish to see our auras, they should develop an organ capable of detecting the infrared range, similar to what pit vipers possess. Pit vipers have pits on their heads, located between the eyes and nostrils ( Fig. 5 ). These pits contain membranes that detect infrared wavelengths emitted by their prey, such as mice and birds, which have body temperatures similar to humans. The viper's brain converts this data into images. It is unclear if the images are in color. However, if they were, the colors would not match those seen by a viper's eyes, as the brain has already allocated these to the visible spectrum. Fig. 5 Salazar's pit viper. Photo courtesy of Zeeshan A. Mirza You may argue that roses are red and violets are blue, although they lack inherent star qualities. The flowers don't own these colors; they borrow them from the Sun. A t  10,000°F (5,500°C), our Sun sits in the middle of the visible spectrum ( Fig. 2 ), emitting green wavelengths alongside other colors, displayed in rainbows when sunlight refracts through raindrops. Roses appear red because they reflect red wavelengths of sunlight while absorbing all others, while violets reflect blue wavelengths. When the Sun disappears from the sky, it takes these colors with it, which is why flower beds lose their colors at night. Colors can evoke emotions, and we often use them to convey our feelings. We can say we see red or feel blue, but we don't mean it literally. The colors psychics claim to see are figments of their imagination, and science doesn't deal with the imaginary world; that's left to poetry. If you want to believe you are beautiful like a rainbow, you don't need to pay a psychic to tell you that. We measure beauty in good deeds, not in wavelengths. There is simply no connection between character traits and visual colors.

We need light to see; in total darkness, we can see nothing. Yet, even in broad daylight, most of the electromagnetic radiation emitted by the Sun remains invisible to us. For example, we can't detect the infrared part of the electromagnetic spectrum because the photoreceptors in our eyes are not sensitive to it. This leads to a natural question: if we can't perceive infrared wavelengths during the day, when they are abundant, how do infrared (IR) goggles allow us to sense them at night, when the Sun, their primary source, has disappeared? The answer lies in the design of the goggles ( Fig. 1 ) and in the fundamental ways light interacts with matter. Fig. 1 . Infrared goggles used for thermal imaging. Light beyond human vision The electromagnetic spectrum spans a vast range of wavelengths ( Fig. 2 ), most of which are invisible to the human eye. The Sun emits radiation primarily in the visible, infrared, and ultraviolet regions of the spectrum. Although beyond our visual perception, infrared and ultraviolet radiation behave like visible light in many respects: they propagate through space, carry energy, and interact with matter. When sunlight reaches an object, three main interactions can occur: Reflection . Some wavelengths are reflected. The portion reflected in the visible range determines the colours we see. Transmission.  Some light passes through the material. This interaction, called transmission, typically occurs in optically transparent substances such as glass. Absorption.  Some radiation is absorbed, transferring electromagnetic energy to the material and converting it into heat. Fig. 2    Full electromagnetic spectrum, from radio waves to gamma rays. Source: BBC Bitesize The first two interactions require a continuous flow of radiation from an external source. If the source disappears, there is no light, visible or invisible, for the objects to reflect or transit. Absorption, on the other hand, follows different rules. The absorbed radiation does not immediately return to the surroundings.  Rather, it remains within the material, where it makes atoms and molecules vibrate more vigorously. These microscopic vibrations manifest as thermal energy, which we perceive as heat.  An object that has absorbed energy becomes a source of its own thermal radiation. It continues to emit electromagnetic waves even in complete darkness, although not necessarily in the visible range. Thermal radiation is so named because its wavelengths depend primarily on the object's temperature. As the temperature rises, the peak emission shifts toward shorter wavelengths. For an emission to move from the invisible infrared to visible red light, temperatures must reach hundreds or even thousands of degrees. Erupted lava, for example, glows red when extremely hot ( Fig. 3 . But as it cools, its emission shifts back into the invisible infrared. Fig. 3 Eruption of Arenal Volcano, Costa Rica. Photo by Matthew.landry (Wikimedia Commons, CC BY-SA 3.0) . The Earth's surface does not typically reach temperatures high enough to emit visible light, nor does it cool to the extremely low temperatures found in interstellar space, where microwave radiation dominates. Consequently, objects around us emit primarily infrared radiation. During the day, we rely mainly on reflected visible light to see. But at night, this persistent infrared emission becomes especially important, allowing infrared goggles to provide a different kind of vision. How infrared goggles work Even in complete darkness, objects continue to emit infrared radiation, with an intensity that correlates with their temperature. This radiation fills the surroundings with invisible information, a thermal landscape that some nocturnal animals can sense naturally, and that humans access through night-vision devices. The design of infrared goggles begins with a crucial detail: ordinary glass absorbs much of the infrared spectrum, which is one reason windows help retain heat indoors. For this reason, infrared lenses are made from specialised materials that allow infrared radiation to pass through and be focused onto a sensor. The sensor consists of tiny elements, or pixels, capable of detecting extremely small differences in infrared intensity. These differences are converted into electrical signals. Because the intensity of emitted infrared radiation depends on temperature, these signals can be used to generate a detailed thermal map of the scene. To create a visible image, the goggles assign brightness levels or colours to the regions of different temperatures. Warmer regions may appear brighter or tinted red, while cooler areas may appear darker or tinted blue. In this way, heat patterns are transformed into images that our eyes and brains can understand. In essence, with night-vision devices, we perceive objects by their heat rather than by the light they reflect. The key insight is that objects continually exchange information through energy. Infrared technology gives us a new way to access this information, extending our senses beyond their natural limits and unveiling a hidden layer of reality that has been there all along.

We’re all used to seeing the Moon, our natural satellite, shining brightly in the night sky. But have you ever spotted an artificial one gliding silently overhead? These man-made objects, orbiting Earth, appear as steady, moving points of light — they don’t twinkle like stars or flash like airplanes. You can often see them shortly after sunset or just before sunrise, when the sky is dark, but the satellite is still high enough to catch sunlight, reflecting it down to your eyes. The brightest among them is the International Space Station (ISS), which can even outshine Venus. Fig. 1 . The ISS orbiting Earth. Image generated with assistance from ChatGPT (OpenAI) Long before the satellite era, people wondered why the Moon remains in the sky while everything on Earth falls to the ground. Sir Isaac Newton answered this question in Principia Mathematica  (1687), explaining that celestial bodies maintain stable orbits thanks to a delicate balance between gravity and motion . In essence, the Moon is constantly “falling” toward Earth, but its sideways velocity keeps shifting it away just enough to trace a curved path around our planet rather than crashing into it. Motion Without Gravity . The best way to understand why this balance works is to separate the two effects, motion and gravity, and then combine them. Let’s start by imagining a simplified world where gravity doesn’t exist ( Fig. 2 , left). Picture the Earth replaced by a massless dot C in space. Now send a satellite flying at the speed V past it. With no gravitational pull to alter its course, the satellite will continue moving forever in a straight line, following Newton’s first law of motion: an object in motion stays in motion unless acted upon by an external force. It won’t bend toward the dot or slow down. Instead, it will simply pass by and continue moving away at the constant speed, increasing its distance from the dot with each passing second. Fig. 2 . Without Earth, the satellite would move in a straight line. With Earth present but zero velocity, the satellite would fall radially toward Earth. A stable orbit occurs when gravitational acceleration continually deflects the satellite’s velocity from straight-line motion, producing a closed trajectory. Gravity without motion . Now let’s position the Earth in place of the dot, erase the satellite’s velocity, and let it go ( Fig. 2 , center). Without any horizontal motion, the satellite will be pulled toward the Earth, accelerating along the line connecting their centers. This is pure free fall. The satellite doesn’t orbit. It simply plunges straight down along the gravitational vector, de creasing its distance from Earth with each passing second. Motion plus gravity . We combine these two effects, keeping gravity active and imparting the satellite with lateral velocity (F ig. 2 , right). As the satellite's velocity attempts to propel it in a straight line away from Earth, gravity constantly pulls it toward Earth, deflecting its straight path into a curved trajectory. If the satellite's speed is too high, gravity won't curve it enough, and the satellite will spiral away from Earth into space. If the speed is too slow, gravity will curve the path too much, causing the satellite to crash into Earth. When the speed is right, gravity curves the satellite's trajectory just enough to maintain a stable orbit. Higher Orbits, Lower Speeds . As altitude increases, gravity weakens, reducing the inward pull. To stay balanced, the orbital velocity must decrease accordingly. This is why satellites in higher orbits move more slowly than those in lower orbits. For example, geostationary satellites, which synchronize their rotation with Earth's 24-hour period, must orbit at a high altitude of 35,786 km, requiring a speed of 3.1 km/s. In contrast, the low-orbit satellites, such as the ISS, orbiting Earth at approximately 400 kilometers (≈ 250 miles), must travel much faster, at about 7.7 km/s, to avoid crashing into Earth . This delicate balance — stronger gravity necessitates higher speed, while weaker gravity allows for lower speed — governs all orbital motion, from satellites to the Moon.   No air, no friction, no fuel . Satellites orbit far above Earth's atmosphere, where the air is so thin that it exerts virtually no drag. Without air resistance, there’s no energy loss and no slowdown, allowing the satellite's motion to continue indefinitely. This is why the Moon doesn't require engines to sustain its graceful dance around our planet, illuminating our nights with its majestic presence. The Moon's perfectly balanced speed will continue to counteract the Earth's gravity until the Sun burns its fuel and the solar system finishes its natural cycle. In low Earth orbit, where a trace of atmosphere remains, drag slowly degrades satellites' energy, which is why the ISS requires occasional engine burns to maintain its altitude. However, once you are high enough, beyond the reach of air molecules, you can truly fall forever without actually falling. This is the essence of orbital motion: a continuous compromise between the straight line of the sideways velocity and the gravity curving it inward. Newton imagined firing a cannon from a tall mountain; with enough speed, the cannonball would fall toward Earth but never reach it, tracing a circle around the globe. That same idea powers every spacecraft in orbit today, from the ISS to communication satellites to the Moon itself. Next time you spot a silent light moving above the horizon, remember: what you are seeing is an object falling toward Earth… but always missing .

When people talk about colonizing Mars, the phrase evokes a powerful image of thriving communities adopting a new, advanced way of living. Avangard buildings are equipped with state-of-the-art technologies, landscaped communal areas, and abundant greenery, including houseplants. This vision conveys the idea of building a new, better life on another planet, marking the first step in our quest to colonize the solar system and potentially establish human roots in the lifeless universe. Behind the vision of green domes lies a simple truth: Mars cannot sustain life. It can only host what Earth provides. After all, why not branch out to other planets and beyond? Let's give humanity a chance to seed the barren cosmos with life and knowledge! With the human population growing fast, we have nothing to lose and plenty to gain. However, before we become too absorbed in our ambitious goals, we must assess the real cost of bringing life to an alien world. Settling on another planet is not the same as expanding into new territories on Earth. Because the universe, as it seems, has no plans to accommodate our ambitions and much prefers to keep the human race confined to a single domicile. Mars would gain only what Earth loses Mars is not a happy place waiting for us to settle down. It is an alien, hostile environment incapable of sustaining even the most primitive forms of life, like bacteria. The Martian atmosphere has no oxygen for us to breathe. Without protective spacesuits, we would pass out within seconds and die within minutes. But the atmosphere is only the beginning of our problems. The plants would benefit from carbon dioxide, the main component of Martian air. But no export from Earth can withstand Martian radiation. Permanent protection would be required for every animal and plant, every insect, and even for every bacterium essential to maintaining a soil suitable for growth. All that Mars has is a barren rigolith. Everything that makes Earth alive does not belong there. Exported living organisms would have no chance to survive there and initiate their own cycle of reproduction. Every bit of life exported from Earth would require an extended support system to survive, which would also have to come from Earth: livestock to feed settlers, compost for growing crops, insects for pollination, and even bacteria to maintain a healthy soil. In essence, we would be moving Earth to Mars, one rocket at a time, at tremendous cost. This leads to an uncomfortable truth: what Mars gains, Earth loses. Colonization of a dead planet can never be considered expansion, but merely a redistribution of life resources from the planet where they belong to the planet that wants to kill them. Rather than colonization, we should focus on establishing isolated research outposts. Mars will not grow forests, oceans, or wildlife. Any presence there will be fragile, artificial, and heavily reliant on Earth's resources. The evolution argument is not realistic Some propose a different strategy: introduce microbes and wait for Mars to develop life of its own. However, this concept collapses under basic scientific timescales. Developing stable ecosystems takes millions to billions of years. During that time, Mars would require intensive environmental protection to prevent radiation damage, atmospheric loss, extreme temperatures, and biological collapse. Providing this level of life support on a planetary scale would require astronomical amounts of money and energy, with no guarantee of success. A single major failure, such as radiation exposure, contamination imbalance, or system malfunction, could undo centuries of progress in an instant. Earth protects life effortlessly. Our magnetic field, thick atmosphere, stable temperatures, liquid water, and gravity work together as a natural life-support system. Mars offers none of these advantages. The atmosphere is too thin to retain heat or oxygen, temperatures swing violently, dust storms can last for weeks, obstructing sunlight, and gravity is only about one-third of Earth's. On Earth, ecosystems recover from disasters. On Mars, recovery would rely solely on human intervention. Are We Solving the Right Problem? This raises a fundamental question: what is the purpose of moving life from a planet that naturally sustains it to one that actively tries to destroy it? If the motivation is survival insurance for humanity, it is worth asking whether strengthening Earth’s resilience would be far more efficient than building artificial life bubbles on Mars. Earth already has everything required for life to flourish. Mars requires everything to be manufactured, transported, and continuously maintained. Instead of exporting life into extreme danger, perhaps the real challenge is learning to protect the only planet that has proven capable of sustaining complex life, our own. Mars exploration has scientific value. Studying another planet helps us understand our own. But pretending that Mars is humanity’s next natural home creates dangerous illusions. Life belongs where it can thrive naturally. Right now, that place is Earth. Instead of dreaming about escaping our home planet, maybe the real frontier is learning how to take care of it. No other planet in the solar system can provide a natural habitat for the human species. Even beyond the solar system, the idea that we can simply move on to another Earth-like planet remains closer to science fiction than practical reality. The nearest star system, Proxima Centauri, lies over four light-years away, a distance so vast that even our fastest spacecraft would take tens of thousands of years to reach. We have yet to discover any Earth-like planet within realistic reach. And even if one exists, the technological, biological, and economic barriers to reaching and settling it would dwarf anything humanity has ever attempted. There is no backup planet waiting nearby, no cosmic lifeboat ready for boarding. Earth is not just our current home; it may be the only naturally habitable world we will ever access. The sooner we accept this reality, the sooner we can shift our priorities from escaping our planet to preserving it, and the safer our future will ultimately be.

Anyone who shares their home with a cat knows the fundamental rule of the feline universe: if it lies on the table, it must be pushed off. Whether it's glasses, pens, or phones, nothing is safe. This quirky behavior has earned cats media stardom and even placed them center stage in debates about the shape of the Earth. After all, who could resist the argument that if our planet were flat, cats would have already pushed everything off it? Yet if we take the subject seriously and apply real physics, we discover that gravity on a flat Earth would behave in ways that may surprise both sides. Fig. 1 . Artistic illustration of gravity on a flat Earth. Objects would not fall off the edge but would be pulled back to the planet, even when pushed off the rim. When we try to imagine gravity on an alternative Flat Earth model, we often stumble because our intuition is shaped entirely by life on a spherical planet. Limited to a single experience, we inevitably draw analogies from what we know, not realizing how much our lives would change on a planet with a different shape. Having said that, altering the shape would not alter the fundamental laws of gravity. These laws would still apply, allowing us to build a physically consistent model of this highly speculative scenario. What would remain unchanged? When we watch a cat knock a mug off a table, it is tempting to imagine a flat Earth as if it were simply a giant tabletop. However, it is not the table that pulls the mug downward; it is the planet beneath it. Even on a flat Earth, objects would still fall to the ground, responding to the inward gravitational pull exerted by Earth’s mass. Gravity is always radial, meaning it pulls objects toward a planet’s center of mass (COM), as illustrated in Fig. 2 . This remains true regardless of the planet’s shape. Fig. 2 . Radial gravity field of a spherical Earth.  Gravity vectors point toward Earth’s center of mass (COM), remaining perpendicular to the surface everywhere, which is why surface gravity feels uniform across the planet. As a result, objects on a flat Earth would continue to fall toward the ground, even near the edges. Pushing an object off the rim would not make it “fall into space” any more than tossing it up makes it escape Earth's gravity in our environment. Gravity would constantly draw the object back, forcing it to follow an inward path toward the planet's surface. In both scenarios, to break free from Earth's gravitational hold, the object would need a propulsive force far greater than even the most determined feline can provide. What would differ on a flat Earth? On a flat Earth, cups, glasses, and pens would still fall toward the floor, bound by the planet's gravity. Earth would still have the same total mass, and that mass would still generate a radial gravitational field. What would change significantly is how mass is distributed around the planet's center of mass. And that is where things become interesting. To visualize how gravity would behave on a flat Earth, imagine stretching the spherical planet into a flattened disk ( Fig. 3 ). This transformation redistributes mass, decreasing its amount vertically and increasing it across a horizontal plane. As a result, those near the center of two bases would have less mass beneath, and therefore experience weaker gravity than those closer to the edge. As there is more mass distributed sideways, gravity at the edge would be stronger than in the middle, an outcome that often surprises both supporters and critics of a flat-Earth model. Fig. 3 . Gravity on a flat Earth. Gravity vectors point toward the planet’s center of mass, causing surface gravity to tilt inward everywhere except the central regions. As a result, most locations would feel sloped rather than flat. Flat shape, different gravitational landscape On a spherical planet, weight is constant everywhere because mass is uniformly distributed about its center. On a flat planet, we would be lighter at the center and heavier at the edge. The direction of gravity would also change, creating a new gravitational landscape beyond our imagination. The gravity would be perpendicular to the surface only at the center of both bases and along the midline of the lateral surface ( Fig. 3 ). In those locations, we would feel fairly normal, albeit lighter than on the spherical Earth. Elsewhere, gravity would be skewed; the more so, the closer we get to the rim. To adapt to the slanted gravity and avoid falling over, we would need to tilt. In our environment, tilting is required only on slopes, since gravity is otherwise perpendicular to the ground. On a Flat Earth, however, tilting would become a way of life, with the angle becoming steeper as we travel toward the edge. This would be a significant and unmistakable feature, constantly reminding us that we live on a flat planet. You can find more about this phenomenon in the post  Gravity on a Flat Earth: living in a skewed wonderland . Fig. 4 . Gravity Orientation on a Flat Earth Disk. On a flat Earth, gravity would be perpendicular to the surface only near the center of the base and near the midpoint of the rim. Everywhere else, gravity would tilt inward toward the planet’s center of mass (located inside the disk), forcing people and objects to lean to remain balanced. As a result, in most regions, we would feel like standing on a continuous slope rather than on flat ground. Due to the tilt, travelling from one edge to the other would feel like descending and ascending a slope. Starting from the edge, you would move along the gravitational vector ( Fig. 3 ), which would assist your movement, making it feel like you were walking downhill. As you approach the center, it would seem like the slope levels out, and in the central part, it would feel like walking on flat terrain. Once you pass the central part, you move against the gravity vector. Consequently, this segment of your journey would feel like climbing uphill, with the slope growing steeper. Comparing two incomparable worlds Traveling across a flat Earth would feel like descending a slope and then climbing back up again. This would give us the impression of traveling along a concave curve ( Fig. 5 ). Ironically, the more we flatten the Earth, the steeper this perceived curve would become. Flattening spreads mass farther from the center, therefore increasing the tilt experienced at the surface. This leads to a peculiar conclusion. The sensation of walking on a flat surface is only possible on a spherical planet. A flat Earth would destroy this sensation and create the illusion of moving over a curved terrain.  If Flat Earth proponents lived on a flat planet, they would probably claim it was curved. In this strange setting, you'll find yourself caught between two conflicting signals. Visually, the land would appear flat, yet your body would insist otherwise. This sensation of a skewed landscape arises from the gravitational force acting on your body. Although the land's curvature is an illusion, the force itself is real. It's the same force that makes you lean forward or backward when ascending or descending hills in our own environment. This sensation is so strong that visual cues are unnecessary; you can feel a slope with your body. On a flat Earth, you would have this feeling on level ground Fig. 5 . Bowl analogy for surface gravity variation. The curved shape illustrates how gravity strength would vary across a flat Earth, with weaker gravity near the center and stronger gravity toward the edges. The seeming curvature reflects the variation of surface gravity across the planetary disk. If we plotted surface gravity values along a cross-section, the resulting profile would resemble a bowl-shaped curve ( Fig. 5 ). Traveling from one edge of a flat Earth to the other through the center would therefore feel like walking from one rim of a bowl to the opposite rim, passing through the bottom. Gravity would be strongest near the edges, decrease toward the middle, level out near the center, and then rise again symmetrically on the far side. The bowl analogy provides a useful geometric approximation, but it has a problem. In our environment, if we were to walk inside a giant bowl, we would feel heavier at the bottom and lighter near the rim. This would be exactly the opposite of what would happen on a flat planet, where we would feel heavier and weigh more near the rim. Thus, in addition to sensing a gravitational slope, we would also experience continuous changes in weight as we traveled. Fig. 6 . Inverted arc analogy for gravity on a flat Earth. Walking inside this rainbow curve illustrates how gravity would be weakest at the center and strongest near the edges, while its inward tilt creates the sensation of moving along a curved gravitational path. We could invert the bowl to correct the weight gradient, but walking upside down hardly helps the imagination. For a better mental image, we could stretch the inverted curve across the sky like a rainbow and imagine walking inside the rainbow curve from one end to the other ( Fig. 6 ). This thought experiment would capture the full sensation of waking on a flat planet, with gravity being stronger at the rainbow ends and weaker at the center. Or we could just accept that this experience is beyond our imagination and trust in science. The laws of physics are consistent throughout the universe, allowing us to test any, even most brave hypotheses, successfully.

Physics is deeply rooted in equations. Every principle, from Newton's laws to Einstein's theory of relativity, is represented as a mathematical balance between the terms on the left and right sides. This balance involves not just numbers but also the relationships between physical quantities. For an equation to be valid, the way we measure these quantities must be consistent. This requirement is so fundamental that it is often taken for granted. Yet without expressing physical quantities in compatible units, physics would immediately collapse into nonsense. This is why unified systems of measurement are in place. Fig. 1 . Student: I followed the formula. Pythagoras: You followed it where it does not belong . Consistency in measurement units is essential in all exact sciences. In mathematics, we can't perform operations on fractions until we bring them to a common denominator. Similarly, in geometry, lengths must be converted to the same units, such as meters or feet, before meaningful comparisons can be made. The consequences of ignoring this principle are humorously illustrated in the popular meme shown in Fig. 1 . The Pythagorean theorem, which is widely used in physics and engineering, is effectively “broken” when one side of a right triangle is expressed as a real number and the other as an imaginary number. This numerical mismatch leads to an absurd result: the hypotenuse is reduced to zero, effectively collapsing a two-dimensional triangle into a one-dimensional line. The number i  represents the imaginary unit, defined as the square root of negative one: i =√−1 . If we remain within a consistent numerical domain, the absurdity immediately disappears. When both legs of the right triangle are expressed as real numbers, 1 and 1 , the Pythagorean theorem yields the meaningful result √2 , which Euclidean geometry predicts, and physical measurement confirms. Likewise, if we work consistently within the domain of imaginary numbers, the result is also perfectly coherent. If both legs are expressed in imaginary units, i and i , the Pythagorean relation produces a hypotenuse equal to i√2 . Although such a triangle does not correspond to a physical object in ordinary space, the mathematical structure remains internally consistent. The calculation does not break down because the underlying assumptions are respected. In the meme, the absurd result that a triangle is geometrically equivalent to a line arises from mixing incompatible mathematical frameworks. Just as mathematical operations must remain within compatible domains, physical quantities must share compatible units. In this sense, the meme highlights a fundamental principle: whether we manipulate numbers in mathematics, apply theorems in geometry, or solve physics equations, coherence in units is what keeps these disciplines connected to physical reality. There exist several unit systems. The most commonly used is the metric SI (International System of Units), which holds official status in almost every country worldwide ( Fig. 2 ). Choosing a particular system is largely a matter of convenience, since all properly defined systems yield correct results. The key requirement is consistency: all quantities must be expressed within the same framework so that comparisons and calculations remain meaningful. Fig. 2 . The seven SI base units that form the foundation of all physical measurements Consider a simple example. Suppose we want to compare the lengths of two rods. If one length is given in meters (SI) and the other in yards (Imperial system), we can't directly compare the numerical values. We must first convert both measurements to the same unit, whichever we prefer. Only then does the comparison become physically valid. Without this step, the numbers alone are misleading. The same principle applies to every equation in physics. Before plugging numbers into formulas, we must ensure that all quantities use compatible units. Otherwise, even a mathematically correct calculation can produce a physically incorrect result.

Flat-Earthers often demand visual proof of Earth’s curvature, something you can only see clearly from space. But there’s a much simpler way to demonstrate that Earth can't be flat: gravity itself. The law of gravity is universal and remains consistent for all shapes and forms. Yet it would manifest differently if Earth were flat, continually reminding us that the world beneath our feet had been transformed. So, let's imagine walking on a flat Earth and experiencing a strange new world created by a touch of scientific imagination. Fig. 1 . If Earth were flat, gravity would cause an environment to tilt toward the ground, clearly revealing the planet's actual shape. Gravity is always radial, meaning it acts along the radial lines pointed toward the planet's center of mass. On the spherical Earth, these inward gravitational vectors are perpendicular to the planet's surface. This is because every point on the surface is already angled toward the center ( Fig. 2 , left). However, if Earth were a disk, the vector of the gravitational force would not be perpendicular to the surface. It would become more slanted as we travel away from the middle of the Earth to the edge ( Fig. 2 , right). This is why a flat-Earth model can't account for the gravitational conditions we experience on a spherical Earth and take for granted. Fig. 2 . On the spherical Earth, gravity keeps everyone upright. On a flat Earth, "upright" would become more slanted the closer we get to the edge. Every object and creature on a flat Earth would be affected by this shift in gravity. Have you noticed that when walking uphill, you tend to lean forward, and when walking downhill, you lean backward? This happens because your body adjusts to the gravitational vector to support your weight. You automatically adjust your posture and muscle tone depending on the surface you’re walking on. You do this subconsciously because if your spine were not aligned with the vector of gravity, you would lose balance and topple. A climber ( Fig. 3 , left) is positioned at a sharp angle to the hill. Yet, relative to the flat ground behind him, he remains upright. This illustrates that, despite the change in angle, he keeps his posture aligned with the gravitational vector regardless of his location. If he were holding a plumb line, it would indicate the direction of the gravitational vector and the posture that requires minimal muscle effort to maintain balance. Gravity always pulls the plumb line along the radial vector, showing a vertical orientation of minimal structural strain, whether in a living body or a building. Fig. 3 . Contrary to popular belief, vertical position is determined not by the angle with the ground, but by alignment with the gravitational vector. On a slope, both the climber and the house are still vertical. On a flat Earth, the upright posture, as well as the upright buildings, would only be possible at the center of the faces and the center of the edges, because only there the radial vector is perpendicular to the surface. The farther we move from those points to the edges, the more slanted the gravitational vectors become, and the more tilted our posture would have to be. Even on a level surface, we'd maintain a tilt as a natural adaptation to the radial lines upon which gravity acts on our body. In fact, everything would need to adapt, including soil, water, and atmosphere. Trees would lean toward the ground, much like they do on slopes now, and stilt foundations would be necessary to support houses, similar to those built on hills. The hills themselves would pose an unusual challenge for the angled climbers ( Fig. 4 ). Shaped like houses on stilts to bear their weight, they would make ascent feel much steeper than it looks. Conversely, descending would feel like a stroll in the park on our spherical Earth ( Fig. 4 ). This scenario would reverse when moving from the edge toward the center. In this case, climbing would feel surprisingly easy, whereas descending would become dangerous. This is because the plains on the flat Earth would no longer be level relative to gravity. Fig. 4 . On a flat Earth, the farther you move from the center, the more gravity pulls sideways, making every step feel like walking on a slope. Animals would also walk with their bodies angled to the ground, and even birds would need to keep the angle when flying in the sky, as gravitational vectors extend into space. In our world, when we drop an object from a window, it falls straight down, guided by the gravitational vector, which is perpendicular to the ground. On a flat Earth, the same vector would cause the object to fall diagonally. However, this path would appear normal in the skewed surroundings, as it would be consistent with the angled house. Even rain would pour diagonally, and its puddles would drain toward the Earth's center, similar to how they drain now from hills. Ultimately, everything in such a world: air, water, soil, and even the ground itself, would be pulled along those inward-pointing gravitational vectors. Over time, this constant pull would cause all loose material to migrate toward the center, smoothing out the tilted landscape. The atmosphere would settle into a uniform shell, water would pool symmetrically around the center, and the crust would gradually deform under its own weight. Instead of remaining flat, the surface would slowly reshape itself into the familiar, near-spherical Earth we live on today.

If you’ve ever wondered what “square seconds,” s², mean in the unit of acceleration (m/s²), you’re not alone. Square metres (m²) are easy to picture, since we use them in everyday situations, such as measuring the area of a room or a rug. And because space is three-dimensional, we can even cube the metre (m³) without much confusion. But squaring a one-dimensional quantity like time can definitely raise eyebrows. Why would we want to square time, and what does it mean? For instance, if a car accelerates at  a  =  2 m/s² , how much would its speed increase in 2 seconds? Do we square the seconds to find the answer? No, we don't literally square time to calculate acceleration. The s² can look strange at first, but it has a simple explanation. Measurement systems are designed to be compact, using as few base units as possible. With just metres and seconds, we can describe many important physical quantities, such as length, time, speed, and acceleration. As a result, units sometimes “stack,” as they do for acceleration, giving the slightly odd-looking m/s², which you can read as “metres per second per second.” Let’s take it step by step and see what this means in practical terms. Speed: how length changes over time Speed ( v ) tells us how fast the position changes with time. If a car moving at a constant speed covers a distance Δd = 30 meters in a time interval Δt = 3 seconds , we can calculate its speed as: i v = Δd ÷ Δt = 30 m ÷ 3 s = 10 m/s . Acceleration: how speed changes over time Acceleration ( a ) tells us how fast the speed changes with time. Our car, which was previously moving at a constant speed of  v  = 10 m/s , begins to accelerate and reaches 20 m/s in 5 seconds. We can determine its acceleration as: a = Δv ÷ Δt   = (20−10) m/s ÷ 5 s = 10 m/s ÷ 5 s =2 m/s/s = 2 m/s² As you can see, we didn’t use any square numbers; we divided speed by time. The squared term, s² , appears because speed already contains a time unit. In other words, the s x s=s² comes from two different roles of time: one second comes from measuring speed (m/s), and the other comes from measuring how that speed changes per second. Calculating a change in speed due to acceleration Let’s summarize what we’ve learned. Initially, our car was traveling at a constant speed of 10 m/s . It then began to accelerate at a = 2 m/s² . This means the car increases its speed by 2 m/s every second: After 1 second , the speed: v = 10 m/s + 2 m/s = 12 m/s After 2 seconds , the speed: v = 12 m/s +   2 m/s = 14 m/s After 3 seconds , the speed v : = 14 m/s +   2 m/s = 16 m/s Each second, the speed grows by 2 m/s . This repeated change per second is exactly what gives rise to the 'squared' time unit in acceleration.