Friday, 26 April 2024 ------------------------ Hello. All is well. Continuing with chapter five, we discuss vision, hearing, and the other senses. Light waves pass the cornea into the eye through the pupil. Depending on the light level and emotional state, pupils dilate or constrict by muscles connected to the iris. The light hits the lens, a curved transparent structure, focusing the light, then hitting the retina in the back, where photoreceptor cells are located. In the fovea, cones produce high spatial resolution with colors. In the rest of the retina, you have rods that produce low spatial resolution and are responsible for noticing movement in our peripheral vision. Optic nerves, in parallel streams, pass the sensory information to the visual cortex in the occipital lobe. In the trichromatic theory of color vision, all color is produced from three photoreceptor cells, each sensitive to one of three primary colors: red, green, and blue. If you stare at a bright light and then look at something dark, you'll notice an afterimage of the bright light. This is explained by opponent-process theory, which says we process colors in pairs, such as black and white, where our eye inhibits the opposite color, causing the negative afterimage. Depth perception, our ability to view space in 3d, is achieved by monocular and binocular cues. For example, with two eyes, you get two images that, when used together, add a sense of depth. With hearing, we convert pressure waves to sounds. Our ear consists of three main parts: the outer, middle, and inner. The outer ear is the pinna, the part of the ear we can see, the auditory canal, and the eardrum (tympanic membrane). In the middle ear, we have three bones called ossicles: Malleus (hammer), incus (anvil), and stapes (stirrup). In the inner ear, the cochlea is a snail-like structure filled with fluid containing hair cells (the auditory sensory receptors). First, pressure waves hit our pinna. The shape of our pinna changes the wave depending on where it hits it, helping us localize where the sound comes from. The waves then hit the eardrum, causing it to vibrate, causing the ossicles to move, causing the fluid in the cochlea to vibrate, stimulating the hair cells. The signal produced is sent to the thalamus, then to the auditory cortex in the temporal lobe. The inner ear also has semicircular canal structures responsible for the vestibular sense (balance and movement). For pitch perception, there's a temporal theory, which states a difference in pitch is produced by the rate of neural firing, and place theory, which states that hair cells have different sensitivity, some sensitive to lower or higher pitches. Apart from pinna structure, for sound localization, we have binaural cues, both interaural level differences (pressure difference between ears) and interaural timing differences (timing difference between ears). Deafness is partial or complete hearing loss. It can be congenital deafness (born deafness) or conductive hearing loss, which have many factors that could cause hearing loss. Our taste (gustation) and smell (olfaction) senses are chemical. For taste, we have taste buds, receptors that bind to the food molecules dissolved by saliva. We have five taste senses: sweet, salty, sour, bitter, and umami (savory). There may be a sixth, a sense of tasting fat. For smell, we have receptors at the top of the nose, the mucous membrane. Many species send chemical messages by smell for reproductive status signaling, known as pheromones. We have receptors throughout the skin for touch (somatosensation), temperature (thermoception), and pain (nociception). We have different senses of touch receptors to detect different pressures and vibration frequencies. For temperature and pain, we have free nerve endings. We have two general types of pain: inflammatory pain due to tissue damage and neuropathic pain due to neural damage. Some are born without the ability to sense pain, known as congenital analgesia, resulting in shorter lifespans due to injuries. The vestibular sense, proprioception, and kinesthesia receive information from the sensory organs in the inner ear (utricle, saccule, and the three semicircular canals) and from the stretch and tension of muscles, joints, tendons, and skin. Time for some math. Continuing with chapter one, we learn about the Cartesian product. The multiplication of sets. With two sets, `A` and `B`, we notate the cartesian product as `A xx B`, and define it with set-builder notation as `A xx B = {(a,b) : a in A, b in B}`. The notation `(a,b)` is an ordered pair. An ordered pair is a list of two objects. The order matters so `(a,b) != (b,a)`. Let's say `A = {1,2,3}` and `B = {a,b)` In roster notation, it'd be `A xx B = {(1,a), (1,b), (2,a), (2,b), (3,a), (3,b)}`. The cardinality of a cartesian product is the product of all sets's cardinality, like `|A xx B| = |A| * |B| = 3 * 2 = 6` Interestingly, we can define the cartesian plane as `RR xx RR = {(x,y) : x,y in RR}`. Here, we have a cartesian power of 2, the cartesian square. We can define the cartesian power `X^n` as `X^n = X xx X xx ... X = {(x_1,x_2,...x_n) : x_1,x_2,...,x_n in X}`. For example, `X^3` gives us a three-dimensional space, like `RR xx RR xx RR = {(x,y,z) : x,y,z in RR}`. The notation `(x,y,z)` is an ordered triple, containing 3 ordered elements.