Thursday, 25 April 2024
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Hello. All is well. In chapter five, we learn about sensations, perception, and waves.
Sensation occurs when a sensory receptor intercepts sensory information. As humans, we can pick up a few senses: vision, hearing (audition), smell (olfaction), taste, touch (somatosensation), balance (the vestibular sense), body position (proprioception), body movement (kinesthesia), temperature (thermoception), and pain (nociception).
The least amount of stimulus energy required for a sensory receptor to pick up a signal, at least 50% of the time, is known as the absolute threshold. Noticing a different stimulus in a given context is called difference threshold. For example, you may not notice your phone's torchlight is turned on if you're outside on a clear, sunny day, while it'll be quite obvious if it's in a dark room.
Before we perceive sensory information, it's converted from sensory stimulus energy to action potential (neurons firing). Sensation is not perception. We do not perceive the raw, sensory information. Our brain filters, organizes, and interprets sensations. We've got bottom-up processing and top-down processing. From my current understanding, I see bottom-up processing as the curation and top-down processing as the interpretation.
An example of curation is sensory adaptation, where our brain filters static background noise. An example is the background noise inside the cabin of a cruising airplane. It's the one I can relate the most to. Generally, I don't experience static lights or sounds fading out. That's not entirely true. I do have moments where I filter out background noise, possibly when I'm highly focused combined with stimulants. I have one memorable experience, meeting my parents in a restaurant, where apparently there'd been background music. After we left, they mentioned it to me, surprised I hadn't noticed it.
Attention is a significant factor in curating sensory information for our perception. When we're focused, we can easily miss exceptional information outside our focus, called inattentional blindness.
Motivation is a factor in our interpretation of the curated sensory information. Depending on what we expect, we'll interpret information differently. I think it's similar to the concept of priming we learned from the emotion book. However, this makes me question my model of curation and interpretation. Perhaps our curation (bottom-up processing) has various levels of adaptability, dependent on previous top-down processing, or am I confusingly mixing the two now.
Okay, that was sensation and perception. Waves. Our eyes can pick up a part of the electromagnetic spectrum called the visible spectrum. Light waves have two properties: amplitude and wavelength. Amplitude is the vertical length, the distance from the top (crest) to the bottom (trough). Wavelength is the horizontal length, the distance from peak to peak. You could say the wavelength is the frequency. A long wavelength is a short-frequency wave, while a short wavelength is a high-frequency wave. We measure wavelength in nanometers (nm). The visible spectrum range is 380-740 nm.
Sound waves are similar; they have a pitch (frequency) and loudness (amplitude). Pitch is measured in hertz (Hz), and loudness is measured in decibels (dB). Timbre, sound's purity, is the interplay of pitch, loudness, and timing of sound waves that allows variety in the sounds we perceive.
I've decided to switch my secondary book to "Book of Proof" by Richard Hammack. To preserve my brain, I think it'd be better to not only have fact-based reading but also more mathematical reading. The book I've picked is out of my depth, so I'll supplement it with information elsewhere when needed. I'll be using ASCII math notation.
This book is about understanding mathematical theorems rather than focusing solely on computation. A theorem is a proven statement in mathematics. They're the building blocks of mathematical theory.
In the first chapter, we begin with sets. A set is a collection of elements. An element can be any mathematical object. By roster notation, we define a set by listing elements between curly braces, for example, `A = {1,2,3}` This set has 3 elements, or the set has a cardinality of 3, written like `|A| = 3`. Order is not relevant when comparing two sets defined in roster notation, like `{1,2,3} = {3,1,2}`.
Depending on the context, if `A` was a number, it could also mean absolute value when written between two vertical bars. Absolute value is the distance from zero, regardless of direction.
Some sets have special symbols due to their significance, like natural numbers (`NN`), integers (`ZZ`), real numbers (`RR`), or an empty set (`O/`). In roster notation, we could define integers as `ZZ = {...,-3,-2,-1,0,1,2,3,...}`. The series of dots implies a continuation of the implicit pattern.
Set-builder notation is a way to express more complex sets. For example, `{2n : n in ZZ}` is a set with all numbers of the form `2n`, where `n` is an integer. This describes a set of all even integers. You can also write it like: `{n in ZZ : n is even}`. The first notation generates all even integers from integers by defining how they're constructed, whereas the second takes all integers and filters them by a condition. The syntax is `{expression : condition}`.
The expression defines the elements' form or type, like `x in NN`. The conditions define logical or relational conditions or rules for variables in the expression, like `7 > x > 5`, resulting in the set `{6}`, or `{x in NN : 7 > x > 5} = {6}`. A set with a single element is called a singleton. I'd prefer writing it as `{x : x in NN and 7 > x > 5}`. We can have multiple conditions.