There was a post about this recently, though it didn't go into very much detail at all, so I thought I'd fix that, and try to cover both sides of the argument, for and against.
I've been continually updating this post with new information for hours, while I research this, so feel free to check again later!

About the theory

There is a conspiracy theory that the very tuning system modern music uses (A4=440Hz) is designed to make us more anxious or aggressive, or to otherwise make us less in tune with our spirituality.
It's a pretty fun one.
Proponents of this conspiracy claim that 432Hz is more natural, that it is more fundamental to nature and more in tune with the universe itself.
It is often claimed that the Rockefellers or the Nazis came up with 440Hz, as a form of control or division.
People often talk about how 432Hz aligns with our chakra and so has healing properties, or that it encourages spiritual development.
There are many interesting numerical, numerological and geometric properties/relationships between 432Hz and other things in the world/universe.

For the theory

• 432Hz supposedly resonates with 8Hz (the base Schuman resonance, which is essentially the frequency of the Earth itself). In reality, the Schuman resonance averages to 7.83Hz, which when multiplied by 55 gives us 430.65, not 432. Close but not close enough. Debunked?
• 432 is the sum of four consecutive prime numbers: 103 + 107 + 109 + 113 = 432. This is... pretty damn interesting. EDIT: But according to someone in the comments, 40% of numbers under 999 can be created this way, however see below for even more significance.
• 4 + 3 + 2 = 9. In numerology, 9 has the highest vibrational frequency, aside from the master numbers, and according to one source "represents the sum of all parts, or revelation" and according to another source "represents spiritual wisdom, or seeking to serve all of humanity". Any multiple of 9 can be summed back to 9, which highlights the infinite power of 9 (9x2=18, 1+8=9; 9x3=27, 2+7=9 etc.).
  • If we sum the individual digits of the four primes from above (remember: 103 + 107 + 109 + 113 = 432), so, let's sum those digits (i.e. 1 + 3 + 1 + 7 + 1 + 9 + 1 + 1 + 3). We get 27 and then we sum that (2 + 7) to get 9. There it is again.
  • In numerology, 432 and 864 are both multiples of 9 (which sum to 9) and are also astronomical- and time-related (86400 seconds in a day, the radius of the sun is 432k miles). Notice also that the 864 component of the number is double 432.
• In geometry, the internal angles of the regular polygons sum to 9 (triangle = 180, square = 360, pentagon = 540, hexagon = 720, heptagon = 900, octagon = 1080 etc.).
  • Interestingly, if we use A=432Hz then all of those angles from the regular polygons above show up as notes. 180Hz is an F#, 360Hz is an F#, 540Hz is a C#, 720Hz is an F#, 900Hz is an A#, 1080Hz is a C# etc. If we take those notes, we can build an F# Major Chord using F#, A# and C#. Major chords are arguably the most important.
  • The above also works with the interior angles of the platonic solids (tetrahedron, cube, octahedron etc.), which form the same chord!
  • It also works with the germ of life from sacred geometry, again forming the same chord!
  • The interior angles of the cube, and the germ of life, add up to 2160. If we remove the 0, thus 216, this is exactly half of our magical 432 (and, of course, also sums to 9).
• If we use the fibonacci sequence (which shows up often in nature, such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern, and the arrangement of a pine cone's bracts) algorithm, but instead of starting with 0 we start at 180 (because of its meaning in geometry - the internal angles of a triangle), then look what happens:
  • 0 + 180 = 180
  • 180 + 180 = 360 (square/circle)
  • 180 + 360 = 540 (pentagon, perfect fifth interval)
  • 360 + 540 = 900 (septagon, major third interval)
  • 540 + 900 = 1440 (star tetrahedron/Jewish merkabah, perfect eighth interval)
  • Oh, look, a Major chord.
• The Mayans discovered the "precession of the equinox" (basically the way the earth's axis wobbles), which they measured to take 25,920 years per cycle. They called it "the great year". What a coincidence, then, that "the great month" is 2160 years in length.
  • If we take the fundamental 12 and 60, from Sumerian math, and then take the numbers from music/geometry, and we multiply them (e.g. 12 x 2160, 60 x 432, 360 x 72, 180 x 144), in every case, we get 25,920.
  • They say also that the diameter of the moon is 2160 miles but unfortunately it's 2,158.8 miles, which kind of ruins the astronomical significance of all this a little.
  • 2160 / 5 = 432, and when divided by other numbers will give you those various internal geometric angles from above.
  • If we divide any two numbers in the fibonacci sequence, we get the golden ratio (which just like it's big brother shows up all over nature, geometry, architecture and even in the human body), which is 1.61 to the nearest hundredth. If we do 1.61² (1.61 x 1.61) we get 2.592 to the nearest thousandth. Do you see it? Remember, the great precession? 25,920 years?
• On an ancient Sumerian cuneifom tablet, the Sumerians kept track of the lengths of the reigns of their kings. Among the list are Kings who reigned for 288,000 years, 432,000 years and 360,000 years. Ignoring these seemingly impossible reigns, if you take away the zeroes, all three of those numbers show up in the factor nine grid (which is a grid of numbers built on 432, and basically shows you all the frequencies within the 432Hz system). Also, these 3 frequencies form a Major chord. Some say this confirms the theory of the Anunnaki, the aliens or deities who visited the Sumerians, Babylonians etc. and imparted knowledge and wisdom of creation.
• 432² (432 x 432) = 186,624. This is within 0.01% of the speed of light, which is 186,400 miles/second.
• A man named George Van Tassel claimed to have been given an equation by aliens in the 1950s. The equation was F = 1 / T (F = frequency, T = time). If we take the 1 to mean 1x great precession, as calculated by the Mayans, so 25,920, and we take T to mean 60, a significant number for time, the result is 432.
• If we take the number 12, which was significant to the Sumerians, and square it, we get 144. 144 shows up as a note when using A4=432Hz. If we expand 144 outwards to 144,000, this number seems to show up everywhere.
  • Supposedly the Pyramid of Giza is made of 144,000 stones. I can't confirm this.
  • The baktun, which is a Mayan measurement of time corresponding to 20 katun cycles, is equal to 144,000 days.
  • The bible says that there will be 144,000 chosen ones who will be redeemed.
  • 144,000 / 432 is 33.333333333... which may explain the Freemasons' obsession with the number 3.
  • In Hinduism, a kali yuga is a measurement of time equal to 432,000 years.
• 432 is exactly 3 gross, gross being an old measurement equal to 144. Huh.
• An equilateral triangle whose area and perimeter are equal has the area of exactly the square root of 432.
• There are supposedly 432 Buddha statues on Mount Meru, which are said to relate to the location of the chakras. Cannot confirm/deny.
• Supposedly the most ancient of instruments, unearthed from archaeological digs, were all tuned at 432Hz, but this is not true. Hertz did not exist at those times and they had no way to measure it, and from my research it seems the tuning of unearthed ancient instruments varies wildly. Debunked?
• There are images and videos using cymatics to attempt to prove the theory, however these experiments can be specifically tuned to resonate (and thus produce beautiful/symmetrical images/patterns) at any frequency. Debunked?
• In Pythagorean tuning, the first standardised method of tuning, which is based on ratios, 432 arises, as it is a multiplication of the ratio between C and A, C being 1:1 and A being 27:16, which is equal to 432:256. But these are just ratios and can apply to any base frequency, including 440Hz.
• In just intonation, the ratios used to build the scale (from C) are 1:1, 9:8, 5:4, 4:3, 3:2, 5:3 and 15:8. You may notice that all of these are part of the fibonacci sequence, which is fundamental to nature. However, again, these are just ratios and can be used with any frequency, including 440Hz.
• Often people will claim that 432Hz resonates with the heart or the brain or the sun or water. The heart fluctuates between 1-2.5Hz and the brain between 1-70Hz, these numbers cannot be multiplied to reach 432 and so there is no resonance there. The sun is around 5.964GHz which when divided by 42,000,000 gives us 142Hz. Close but no cigar. Water is a wide band between 90-110THz, not favouring any frequency. Debunked?
• It was an evil Nazi/Rockefeller plot which means the theory is more likely to be true/just makes sense, because... evil gonna evil? Well, actually it was the British Standards Institute's idea. Debunked?
• If A=432Hz, then you could have an E note that has a frequency of 162Hz and 162 looks kind of like phi (which relates to the golden ratio, and so is related to nature) - 1.618033988... do you see it? 162? 1.61...? This one debunks itself.
• In an octave there are 13 notes and the most dominant is called the fifth, which is the 8th note. 8/13 is approximately equal to the golden ratio, which is found all over nature. The most important notes in a scale are the 1st, 5th, 8th and 13th, all of which are found in the fibonacci sequence. I mean, sure? But once more this doesn't really have anything to do with 432Hz itself, the same can be said of 440Hz.

Against the theory

• Despite the standard of A4=440Hz, most symphony orchestras all around the world actually still use different standards such as 415, 432, 442, 444, 448 etc., anywhere from 415-470Hz. And in the more distant past anywhere from 380-500Hz. If 440Hz was specifically designed to make us feel anxious or aggressive, or whatever, as many proponents of this conspiracy theory claim, then surely it would be strictly adhered to throughout the musical world? The powers that be would not tolerate these deviances.
• There have been various attempts at standardisation throughout history, the French at 435Hz, the British at 439Hz, the Austrians at 440Hz etc. In the past, there was no standard (that is to say 432Hz was never a universal standard), pieces could sound much higher or lower depending on where or when they were performed (again, A4=380-500Hz). Obviously this is problematic if you have musicians travelling around the world, performing with different orchestras and such, constantly having to re-tune. Clearly standardisation would fix that issue, which is why efforts to do so began after the invention of the tuning fork.
• The practice of dividing a minute into 60 divisions (seconds) didn't begin until the 16th century, I believe. For all intents and purposes it is an arbitrary measurement. The ancients had no concept of seconds, so any instances of other things from those periods of history equaling 432 are purely coincidental. We could have divided the minute into literally anything else and then the numbers would not have lined up. Eventually scientists decided to define the second as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom". Suggesting that the ancients could even calculate that, or knew anything about it, is absurd, as is suggesting that there is something inherently magical or mystical or spiritual about "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom". If the second was instead defined as something based on the human body itself, especially the brain, then maybe I could get behind this, but seconds and by extension hertz don't really have anything to do with the mind/body/spirit at all.
• String instruments sound objectively "brighter" when tuned higher, due to the higher tension resulting in stronger harmonics. Due to this there was a period in history, referred to as pitch inflation, where orchestras were constantly competing with each other, tuning higher and higher to attain a brighter sound, going far above A=440Hz. Eventually this got to the point where vocalists started complaining about vocal strain. This is one reason why the compromise of 440Hz was decided.

Bonus #1

There is this phenomenon called the overtone series, or the harmonic series, and if you don't know about it then boy are you in for a treat.
All tones, except for pure sine waves, have "overtones".
Let's say we have a string, a piano string, tuned to C... C2. We strike the key. What do you think you're hearing?
A C2? ...just a C? Wrong! You're hearing a whole butt-load of notes.
When a string vibrates, it doesn't just vibrate along its entire length but also along various subdivisions of 1/2, 1/3, 1/4 etc., all simultaneously.
As a result, what you hear is: C2, C3, G3, C4, E4, G4, Bb4, C5, D5, E5, F5, G5 and so on.
As the overtones go up, they become more and more faint but they are definitely there.
This is one reason why low/bass notes sound "fuller" - because there are more overtones. The other reason, I believe, is just because bass strings are thicker?
The more astute reader may notice that embedded in the first 4 overtones of C(2) is a C Major chord and embedded in the first 5 overtones is a C dominant 7th chord. Within the first ten overtones lies the entire C Major scale, aside from the missing A note and disregarding the additional Bb note.
So then, the foundations of our music system itself are literally embedded in every single individual note, thanks to physics/nature.
Isn't that beautiful?

Bonus #2

It's also worth mentioning equal temperament and well temperament. Equal temperament, the modern system, is based on the 12th root of 2. In this system, all 12 semitones are spaced equally far apart and so every key feels the same, so you can modulate freely from key to key, due to the uniformity of the semitones. One drawback is that major thirds are quite a bit off from where they should be, another is that the various musical keys lose their unique flavour or colour or feel.
The previous system, well temperament, is based on ratios - the octaves are not divided equally into 12, so some keys' semitones are higher or lower than others. For instance, some keys have quite stable major thirds and others not so much, this gives every key a unique feel, but overall makes modulation a bit easiebetter sounding than the system before it, and avoids the problem of "wolf fifths/intervals" from the system before it, which I won't go into.
In essence, in the old system some keys are more in-tune (e.g. C) and so are more consonant and others are somewhat out-of-tune (e.g. C#) and so are more dissonant, whereas in the new system every key is equally in-tune.
This doesn't really relate to the conspiracy theory exactly, as you can use either equal or well temperament with any tuning (A=440Hz, A=432Hz etc.), as far as I understand.
Although you could argue that this is a conspiracy in and of itself, in that they took away the unique feel or colour of each key and made everything more... bland or boring. Perhaps this was part 1 of their 2-part evil musical plan!
You could also argue that the new system takes away the mathematical beauty in the ratios of the older systems and if there is indeed some link between frequency and geometry and physics and consciousness and whatever else, then we're kind of doing ourselves a disservice.
As an additional bonus for making it this far, here's a song that starts at A4=432Hz, but changes to A4=440Hz part of the way through. It's subtle!
You can find lots of 432Hz videos on YouTube, including comparisons.
Have fun.
P.S. This took 8 straight hours of my sad, sad life to research and compile.

For example, the sum of the interior angles of a hexagon is 720, octagon 1080, decagon 1440, and so on. I just found this interesting and wondered if anyone knows why?

My question is:
Why can we conclude that the sum angle of a shape equals the Hertz frequency produced by that geometric shape?
​

The sum of the angles of each Platonic solid equals a hertz frequency.

2D
Circle 360Hz
Square 360Hz
Triangle 180Hz
Pentagon 540Hz
Hexagon 720Hz
Heptagon 900Hz
Octagon 1080Hz
3D
Tetrahedron 720Hz
Cube 2160Hz
Octahedron 1440Hz
Icosahedron 3600Hz
Dodecahedron 6480Hz
​
Reference: https://www.cosmic-core.org/free/article-40-geometry-the-platonic-solids-part-1-introduction/

Mensuration
Mensuration is a part of arithmetic which is a subject in Geometry. It is an investigation of different mathematical shapes, their length, expansiveness, volume, and territory for 2D just as 3D shapes.
Prologue to Mensuration
Mensuration
Mensuration is the part of arithmetic that manages the estimation of length, region or volume of different mathematical shapes.
Shapes
A shape is the type of an item.
Instances of two-dimensional shapes are square, rectangle and triangle, and of three-dimensional shapes are block, cuboid and circle.
Border
Border is the complete length or all out separation secured along the limit of a shut shape.
Border of a circle is additionally called the outline of the circle.
Border of a Triangle
Border of triangle = Sum of lengths, everything being equal, = a + b + c.
On the off chance that the given triangle is symmetrical that is if all the sides are equivalent (a = b = c),
at that point its edge is equivalent to 3 × length of one side of the triangle.
Border of a Rectangle
Border of the rectangle = length ( l ) + length ( l ) + width (w) + width (w)
= 2× [length ( l ) + width (w)]
Border of a Square

• Border of square = 4 × length of a side = 4a
• Border of a 'n' sided polygon
• A polygon is a shut shape made down of line portions.
• Border of n sided polygon = n× length of one side.

Model: Length of each side of a hexagon is a cm, at that point:

• Border of the hexagon = 6a cm
• Border of unpredictable shapes
• Unpredictable shapes are the shapes which don't have all sides and angles equivalent.
• The edge of sporadic shapes is equivalent to add up to length secured by the shape.

Territory
Territory is the aggregate sum of surface encased by a shut figure.
Region of Square

• Region of a square = Side × Side =Side2=a2, where an is the length of each side.
• Region of Rectangle
• Region = length ( l ) × broadness ( b)

Region of a triangle

• Region of triangle = (1/2) × base × tallness = (1/2) × b × h
• Regions of various sorts of triangles
• Think about an intense and an uncaring triangle.
• Region of every triangle = (1/2) × base × stature = (1/2) × b × h

Representation of Area

• In the given chart, on the off chance that the territory of every little square is 1 cm2, at that point
• Zone of rectangle = l×b = 5×2 = 10cm2
• Zone of square = a×a = 2×2 =4cm2
• Zone of unpredictable shapes
• Zone of an unpredictable figure can be determined :

Stage 1: Divide the sporadic shape into ordinary shapes that you can perceive (eg. triangles, rectangles, circles and squares)
Stage 2: Find the zone of these individual shapes and include them. Total will be the territory of the unpredictable figure.
Model: Area of the given figure = Area of MNCB + Area of AMGH + Area of EFND
= [ 5 × 9 + 4 × 2 + 3 × 3 ] cm2
= [45 + 8 + 9 ] cm2
=62 cm2

SEGMENT 1: Where Goes a Fallen Kingdom?
Hello?... Hello?....
Hello, can you hear me?
Good. I can feel that some of you, at least, are present, We have much to do.
Who am I? I can be called….
HAHAHAH
The breadth of your control is but a paltry sum when compared to the magnitude of my schemes.
Gathering souls of a fallen Kingdom to prolong the agony of an Order ever dying; you think that you might once again alter the flow of history, my dear friend? That you might employ your vision of the future on a world you know longer inhabit? Ever the breaker of oaths and vows.
But know this: The seeds have been sown. These bonds will be broken. These shackles; cast aside. Eld and Braeke and Fae and Ephemera all shall soon know a world without wonder. A world with hollow lives. So soon. It will all be over, Soon.

The tales you spin will not be enough, Ebonflyte. You and yours will never be enough.
Well, that was an overwhelming display, Do not fear, my friends, for despite their threats, we are beyond harm here in this realm of ours. Death does have certain benefits.
I do not mean to alarm you so; for most of you newly awakening to this reality, the lives you lived may seem to be continuing on, and my message may be reaching you through means with which you are keenly familiar, but know this, I have spared you the tedium of an eternal afterlife in order to offer the chance of a lifetime… albeit after your life was spent.
As I was saying, I can be called the Teller, here. Before, I was an Ebonflyte. The title likely carries little weight, as the Monarchy you once inhabited had manifested in a different reality. These places between which we find ourselves can be very confusing at first, I know.
Now, you may wonder. “What do you have to Tell?”, and to put it plainly: I have Stories to tell. Many, many stories, as they are written and as they were. Being that you are now part of our little Collective, The Ebonflyte Collective, to be exact, you now have the privilege of not only hearing these stories as they occur, but have also gained the ability to persuade the course of newer stories at some of their most pivotal points; at A climax or intense culmination of destiny itself. You have this influence, at least, over those lives marked by a Flyte, but I will have you learn more of this as we go along. For now, I do not wish to overwhelm you. For now, I wish to test your resolve.
For now, I wish to tell you about a young man. A boy who was meant for a great many things.
I was first able to find him within the hollowed out trunk of a long dead tree, whose bark is fibrous and furrowed and still faintly colored a sunburnt brown. The base of this tree is roughly twenty four yards in diameter, while expanding nearly one hundred yards towards the heavens. If you look closely, you can still see some remnants of its once glorious crown; like sorrowful, gray clouds marring an otherwise perfect picture of the purple night sky above.
The young man lay lazily within a hammock spun of lindwurm silk, his long white hair falling between the gaps of the masterfully knit bed. He is outfitted in noble clothing of the selfsame material that is dyed in an ebon coloration; the iridescent quality of the silk shows through by way of a full moon’s light with each lateral movement of the swing. His right hand, which was currently a grayish shade of alabaster indicative of his attunement to a winter’s season, stroked the purring beast curled upon his lap.
“Mother’s insistence that I learn the ‘art’ of weaving was not a complete waste of time, I suppose, right Luchas? At least we now have a place to doze while I hide away from the Knight-captain, and you can even use this as your own bed while I’m away training.”
At the mention of his name, the ball of snow blonde fur called Luchas uncurled into a long stretch, revealing a body nearly as long as the boy was tall. His two large front paws found their way to cup either side of the young man’s face. His pale yellow eyes looked down at the boy, and his black tufted ears twitched quickly as he purred quietly. He then leaned down to butt his head against the young man's cheek.
“Don’t start, Luchas, you know she would never allow you to come home with me. She would probably have you killed like all the others. You’re lucky I was able to save you when I did all those years ago, by the way, but the way you’re trying to guilt me now really has me wishing I’d saved that bird or the stag instead. How would you like it to be made into a golum ?”
The lynx growled quietly as his ears drew back slightly. He jumped off the boy abruptly, sending the hammock upwards in a wild motion. The boy rolled as he fell from the swing, and a solid thump accompanied the soft padding sounds of the lynx as he prowled back and forth against the edge of the hollow.
There was a moment of silence before the boy growled: “You know I hate falling, Luchas.” The boy rolled once more on the floor and leapt towards the lynx with such rapidity as to appear as only a blur in the low lit hollow. He met Luchas headlong and they both skidded across the ground and into the side of the tree. Luchas growled as they made contact with the wall and pushed out from the young man’s grappling arms, and just as quickly pounced onto his back and pinned him to the hollow’s floor. The boy lay still beneath the weight of the feline, and Luchas leaned in and licked the young man’s ear in triumph.
Suddenly, the boy’s legs were wrapped around his friend as he twisted his lower body and pulled himself up onto his side, reversing the pin and holding Luchas prone. The cat glared up at the young man, whose long hair now fell around the downturned and rumpled collar of padded surcoat. At this angle, the moon’s light reveals the diamond shaped face of the young man. His jaw, outlined by a well groomed beard, worked slowly as he held the beast at bay.
“I win this time, Luchas.” He released his hold of the lynx and went to pet the beast behind his ear. As he drew near, however, Luchas snapped his jaw over the hand and bit down on the soft tissue between the boy’s thumb and index finger.
“Oww! Luchas! ” The young man recoiled from the cat and walked over to the entry of the hollow. His left hand, marked by a web of blackened and slightly raised skin, held the right as he inspected the point of contact. Blood welled slowly from two puncture wounds on either side of his hand.
“Ach, you’ve done it now, Luchas. Mother will surely have felt that, and when she sees that blood was drawn she’ll start asking questions where I don’t have a rightful lie to give. The Reacher damn this Bond”
He pulled his hair back behind pointed ears and began murmuring to himself as he wove a blackened leather cord through and around the hair in an elaborate knot.
“She would feel me using the Flyte as well, and I’ve no other life to draw from than my own.”
Luchas padded up beside his friend, and cooed mournfully as he butted his head against the boy’s thigh.
“I know you didn’t mean to Luchas, but you’ve got to be more careful. She’ll kill you, you know. Beasts are forbidden within the realm… and I can not bear the thought of something happening to you. You are my only friend.”
“We’ll just have to improvise and disguise, I suppose. Mother always says deceit is the primary principle of a long and healthy rule.”
The boy walked to the other side of the hollow, and drew a satchel from beneath the now empty hammock. A metallic rattling sound echoed up the walls of the tree to the indiscernible ceiling above. From there, he drew an oddly shaped gauntlet affixed with a hexagonal black plate, which seemed to rise seamlessly from the rest of the glove. From this plate, hung a chained thread attached to a scythe-like blade.
“Ohh, great, now Master Jerecho would be very displeased with me as well to see that I did not coil the irons after our training yesterday. Perhaps it is good that you’ve maimed me, Luchas. A cut to spare a beating, eh?”
The young man pressed the web-marked hand across the top of the hexagon, and as he did so, and audible klink sprung from the glove as the chains began drawing into the plate. As the boy moved his marked hand away, a series of glowing cogs became visible within the apparently transparent plate. As they moved together, the chain drew further and further in until the curved blade locked into the right side of the plate. The young man picked up and held the gauntlet free in his left hand, and without removing his sight from the weapon, drew the lower portion of his bitten hand quickly across its razor sharp edge. Where before was only a trickle, now came a flood of crimson from the boy's hand. His stomach turned violently, however, his face gave no indication of the pain he felt. He then clenched his jaw and furrowed his brows slightly; the angular nature of his face betrayed by the grim expression. He turned his hand over then, and quickly drew the blade across again to connect the cut through all four puncture wounds.
Luchas drew his muzzle back to reveal slightly bloodied fangs as he hissed in disapproval of his friend’s actions. A look of concern was apparent on the lynx’s face as he paced at a distance. The young man stood still for moments on end, breathing slowly as the blood flowed freely from his opened hand.
“Breathe through it, Aeli. So long as you yet draw breath, you can fight for all you desire.”
Aeli glanced up to look at the pacing lynx and sighed quietly as he sat the gauntlet on the floor beside him. He then returned to the satchel and withdrew a smaller pouch from within. As he opened the pouch and pulled out a needle and a spindle of thread he said:
“It’s quite alright, Luchas, it’s quite alright. This pain is but a fragment of what I would feel were I to suffer the loneliness of an existence without you. Besides, as Jerecho taught me, weaving has its uses for a warrior as well.”
With that, the boy sat down, crossed his legs, and began working his flesh back together.
“The butcher told me the most interesting thing the other day about the golum’s flesh . They say that it is suffused with so much of Mother’s magic that it’s a wonder the skin doesn’t crawl upon the very backs of the beasts. She said that while the incantation was meant to keep the flesh from spoiling during the transition, it’s also added an anti-infective quality to the skin, and acts as a barrier against diseases for them. Master Jerecho says there is nothing better to stitch the flesh with than thi...Ohhh, That didn’t feel right..”
Aeli clenched his jaw as the hiss escaped between pursed lips.
Tears began to well at the corners of his brilliant cerulean blue eyes. He looked towards the lynx, who was now sitting in the half shadows across from him looking on and said, “You can come closer, fool beast.”
Luchas made his way slowly forward, and rested his head in the young man’s lap as Aeli continued mending his hand.
It was after many moments that Aeli finally looked upon his handiwork.
“Not bad, not bad.” He muttered to himself as he appreciated each precise cross-stitch sewn upon his hand. A purr of agreement started to hum through the hollow before becoming a low growl as Luchas hissed and raised his hackles .
“My, that is not bad at all. Such a small wound it took to break the Bond.”
Aeli looked up, recognition apparent on his face, to see the silhouette of what must be his mother standing at the entrance to the hollow.
“So far from your home, little light. Hardly fair to make me come so far to find you here in bloodied finery. Have we no healers in our kingdom? Have you no one to turn to for help? Are you truly so alone?”
As the silhouette moved forward slowly towards the young man, Luchas, with bared fangs, moved to stand between them. Aeli stood quickly while grabbing his gauntlet and his satchel, and then clutched them closely to his body.
“Mother, I… I am sorry. I was sharpening my blade, and my hand slipped, and I didn’t want to be of any trouble...”
“Oh, fret not, my little light. There is no need for us to lie to each other. Here, I will give you a truth for a truth: This is but a visage taken up as a reminder to destroy those who would lock me away. You cut your own hand with intent, I was here to watch as much. Do not deny it, for I already know. I know so much, you’ll learn. We know so much.”
“I… I don’t know what you mean, Mother. I am sorry. If you are upset about Luchas or about the hand I am truly sorry. He will not enter the realm below. He stays here, truely, no harm could come of his presence. Please do not harm him; he is all that I have..
“Ahhh, so it is for fear that we hide away… Fear for the Mother, or fear for being alone? Or fear for something else? Such conflict. How fun.”
“Mother?”
“You’re mother is not here, dear child.” A purple light filled the hollow suddenly, illuminating a tall figure that appeared to be made from smoothed and blackened stone, like a living statuette. Its body seemed to be clothed in the shadows cast by the eerie purple light, where the reflections danced madly upon its surface, as if trying to escape the touch. The face was composed of a single pointed ear above a single, lidless and wholly purple eye above a gaping mouth full of broken teeth. One of the creature's arms was long and spindled, like that of a spider, while the other seemed cut short just past the forearm where it ended in a bulbous protrusion of gnarled fingers.
“You needn’t be fearful, dearest Aeli, the world you inhabit shall never leave you alone again. You have me. Forever. This maddened cat however…” The creature said as its shortened arm turned in semblance of a gesture towards Luchas, whose growls and hissing sounds still echoed through the hollowed hall . “... will not survive our journey. I’ll go ahead and spare you the pain, how about that? He will live his time, and you will be with him throughout it all, and then he shall accompany us forever, if you so choose.”
Aeli tried to speak, but little more than a gasp escaped his throat following the Creature’s words and gestures towards Luchas. He watches on, seemingly unable to move, as wisp-like tendrils of violet smoke creep down the body of the creature to crawl along the floor unto his furred companion. Luchas’ hissing sounds become louder as he backs away from the smoke until he reaches the feet of Aeli. The hissing sounds turn to a frantic yowl as the smoke makes contact. The World seems to shift before Aeli’s eyes, and then it stops. The light no longer flickers, the air goes still, the stone figure, and All seems frozen in time. Luchas stands where he stood, eyes frozen open, but no sounds escape from his opened maw.
In fact, the only sound that can be heard is that of Aeli’s heart as it beats, and beats, and beats.
Luchas’ fur begins to darken, and then lightens, until it eventually starts to fall away from his stilled body. His skin withers against bone, his figure becoming more skeletal and fragile with each passing moment as the sound of Aeli’s heart beats, and beats, and beats. The skin turns to dust, and falls away to reveal the bones of our only friend. Aeli’s only friend.
The world shifts again, and this time with a rush, or was it a ragged breath?
Tears that had gathered in those frozen moments began to fall down Aeli’s cheeks as he watched the now skeletal figure of Luchas crumple to the floor. The skull of Luchas began rolling towards the monstrous creature until it reached a knotted foot.
“There. Now he can accompany you!” The skull began floating adrift unto the long fingers of the hand with the spindled arm.
“What are you?” Whispers Aeli.
“Why, I am the abstract at the cusp of reality, and I am all you will ever know. No soul is too far beyond my Reach, and we are the light from which shadows grow. The real question is, Aeli, What are You?”
The creature extends its other, shorter arm towards Aeli expectantly and …
This is a moment where pivots, Fate;
Be careful now, for that you make
Of choices given out of three
Defines a tale that’s Yet to Be.
1st POLL CHOICES
A.) He Fights
B.) He Submits
C.) He Attempts to Flee

This is a reference post, which will likely become a wiki page in future.
I very often refer to words and phrases as 'spells', for that is what they are.
What is your definition of a spell?
Anyway, there are spells, and then there are what I call spell-augmentations, which are spells that are added to (or removed from) other spells to change the meaning, and the numeric cypher spectrum the overall spell generates.
Of course, there is lots of orthodox terminology for these elements, which can be helpful when discussing the finer points, but I prefer to keep things less technical. These are parts of the language such as prefixes and suffixes, conjunctions and articles (definite and indefinite), etc. etc.
Even though it is trivial to examine the numeric spectrum of these common elements in a gematria calculator - it is useful perhaps to have a document of the most common ones as a reference.
I am only including a subset of the major ciphers - the ones I refer to most often. The 'bacon' ciphers, the 'sumerian' and the 'satanic' would be the next ones I might add, if I wanted to expand the selection. (Complete Cipher List)
Common prefixes and suffixes
Pluralizing
The letter 'S'
'S' is used to pluralize words by adding it to the end, eg.

Letter - Letter(s) Letters

Adding an 'S' to a spell adds the following values to it's cipher spectrum.

• "S" = 19 alphabetic
• "S" = 1 reduced
• "S" = 8 reverse alphabetic
• "S" = 8 reverse-reduced
• .
• "S" = 100 english-extended
• "S" = 90 jewish-latin-agrippa
• .
• "S" = 67 primes | 190 trigonal | 361 squares

'S' is a special letter in the English alphabet. Being the 19th in the standard order, it is the only letter requiring two reductions to reach the digital root ( or Pythagorean reduction, or reduced ) value.
19 1+9 10 - 1+0 1
Note the 1,911 pattern through the stages.

• "Society" = 911 trigonal
• "Forgotten Society" = 1,911 trigonal

(ie. find those adjectives summing to 1000 in cyphers that provide bigger numbers for single words - very useful for fractal spell-construction... and ponder how or why those words might have ended up with such useful values)
The number 19 (alphabetic result) is the 8th prime number ( 'chaos', Metonic moon cycle ), and the 3rd hexagonal number.
Number 8 (reverse result) is the 6th Fibonacci. (infinities, time, spirals, hexes, man, procreation)
Number 100 (extended result) is the 10th square number ( avatar of 1, magnitudes, completion ). This is a very useful value for the pluralizing 's' to have, since it can maintain a strong pattern using orders-of-magnitudes. For example, a spell summing to 811 can be turned into a 911 in the plural.
Number 90 is a magnification of 9, and the primes value of the words 'on' and 'no', essentially a binary switch (on, off, yes, no). Number 90 is off-by-one from 91 the 6th hexagonal, and 89, the 11th fibonacci. By the numerological Rule of Colel, in many ciphers, adding or removing an 'A' will compensate for the off-by-one results.
Number 67 (prime result) is the 19th prime number ( water, female ), and an off-by-one (ie. a colel) to 66 (itself a master number, being a multiple of 11)
Number 190 (trigonal result) is the 19th triangular number (and it's colel, 191 is 7th thabit). ('expansion of 19')
Number 361 (squares result) is the 19th square number ( 360 degrees + 1 ouroboros bites it's tail )
... ( in italics are my personal associations in summary )
The interesting material at the Noahsage blog lists ‘s’ as a root spell component as implying 'continuous state of being, unbroken' (ie. think a sine wave, and the 'immortal' snake that sheds it's own skin and regenerates). Ponder:
... sing - sing(s) sings ( ie. continues to sing )
Sometimes, 's' in pronounced as a 'z' sound, Noahsage lists 'z' as having root meaning of: 'to sever, severeness'.
See: See: https://en.wikipedia.org/wiki/S
The Suffix 'T' ( as a suffix implies past tense: burn @ burnt )

• "T" = 20 alphabetic
• "T" = 2 reduced
• "T" = 7 reverse alphabetic
• "T" = 7 reverse-reduced
• .
• "T" = 200 english-extended
• "T" = 100 jewish-latin-agrippa
• .
• "T" = 71 primes | 210 trigonal | 400 squares

The letter 'T' is the 20th letter in the English Alphabet.
T is a strong 'closing' consonant for a word (think of silencing someone, "Sshhhh(t)", the punishment of 'tut tut tut', or the word 'cut'. Ponder the (t)icking of (t)ime).
The Noahsage blog lists the 'T' root as carrying the implication of '’a place of union; linear action'.
The consonant roots S and T are easily shifted (via softening: T @ Th @ S ) with only the slightest tongue movement. They are accordingly right next to each-other in the alphabetic order. There are also many words containing the combined 'st' bi-syllable (such as in 'station' and 'fast').
Interesting that we also get (like with S) a 100 value in one of related pair of ciphers, english-extended and jewish-latin-agrippa.
We also get another nice round number with 200 as the english-extended value, enabling more scaling of patterns:

'mean' = 196 english-extended ... ... 'mean(t)' = 296 english-extended
'plan' = 121 jewish-latin-agrippa ... ... 'plan(t)' = 221 jewish-latin-agrippa

... ie. simple scaling the basic 96 and 21 patterns.
The basic alphabetic value 20 (and reduction, 2) of 'T' is an even number. Ponder how two spells implying two-ness are 'two' and 'bi', one starting with T and the other with B. Both B and T reduce to 2. Hence you can 'put two-and-two together' by building spells on the consonantal root BT or TB. The root BT is the root of the word 'Bet' or 'Beth' which is the name of the original symbol for the letter B, and implies 'enclosure' or 'house', and always having the numerical value of 2. In terms of esoterica, even numbers are often considered feminine ( Eve being the 'second' person in the garden, Biblically-speaking )
Personally, number 71 (the 20th prime) I've always associated with the word 'royal' which is the first word I ever examined summing to this number (in the basic alphabetic cypher) that I took notice of and remembered.
Number 210 (trigonal result) is a magnification of 21 (the 8th Fibonacci), and the primes value of the word 'rest', which one does on the 7th day (and 7 is the reversed value of 'T'). The number 210 is a colel of 211, the 47th prime.
Number 400 (squares result) is a magnification of 4, the Door or Dalet
See: https://en.wikipedia.org/wiki/T
Prefix 'DE-' and Suffix '-ED'

• "de-" = "-ed" = 9 alphabetic
• "de-" = "-ed" = 9 reduced
• "de-" = "-ed" = 45 reverse alphabetic
• "de-" = "-ed" = 9 reverse-reduced
• .
• "de-" = "-ed" = 9 english-extended
• "de-" = "-ed" = 9 jewish-latin-agrippa
• .
• "de-" = "-ed" = 18 primes | 25 trigonal | 41 squares

But for the trigonal and squares results, all of these numbers reduce to 9, which has interesting accumulative properties.
Number 9 (appearing in multiple cipher results above) is the 3rd square, while the 9th prime is 23.
Number 45 (in reverse alphabetic) is the 9th triangular number. (see also 405)
Number 18 is 2x9 (and 6+6+6, and 3+6+9), and reduces to 9.
Number 25 is the basic alphabetic value of "pi", and reduces to 7 ('G').
Number 41 (the 13th prime) reduces to 5 and I've long associated it with this gematria-based spell list, which seems instructive context: 'lock, key, dream, home, good, king', and for perspective, 'joke'.
The word 'joke' of course upon the same consonantal root as the name Jack, which brings to mind the..

• "Sparrow" = 911 english-extended | 2020 squares.

Yea, Welccome Buccaneers. ( ... mind The Canon )
Continuing...
The replacement patterns for the suffix and prefix are 'de' @ d.e @ 4.5 @ 45, while '-ed' is 54, the mirroring being 454.
The root of '-ed' and 'de-' is the root consonant 'D', the Dalet, ie. the Door. The Noahsage blog lists the root of ‘d’ as representing 'a division, or state',
Generally speaking..
The 'de-' prefix has adds a sense of 'descent', travelling downward; of declining, and thus negativity.
The '-ed' suffix adds a sense of past-tense - something already done.
Note the interesting pattern of 'deed' in the combined prefix and suffix, Example fractalizing:

We 'decided' to do the 'deed'.

Slightly off-topic:
In turns of what we might call 'subliminal' spell-casting, presuming it's potential power - ponder that the suffix '-ed' applied to words already ending in 'd' creates the sound of the world 'dead' to your spell that will ring in the mind of those reading or hearing the complete utterance. I've begun to feel guilty about labelling a spell with the full name of the 'english-extended' cipher...
As a related experiment, try (it's not easy) avoiding words that contain an initial MR consonant root (ie. 'more', 'mortgage', 'murky', etc., particularly those with 'lower' vowels based on 'o' or 'u'). I've become quite sensitive to these core word particles that have, to me, an intuitive darkness about them. MR is the nightmare in 'nightmare', for example.
On the surface, the MR root goes back to the Ocean, the Mare, Poseidon's horses, and all that, but I've found in English that this root has a strong sense of 'marring' (ie. 'mr' the root in the word 'marriage', for example). Most folks just use the words without pondering the roots and accept the dictionary definition or their presumptions about them, but after years of studying your own language one becomes quite sensitive to it. If I had a child I would have it call me 'Da' - an open form, rather than the closed form of 'Dad'. Who knows... fathers might live longer if they didn't have years of being called 'DD', which may as well be doddery, or dead, and furtherm[...] 'DD' turned into numbers is '44', the basic alphabetic value of 'kill' and number with a heavy gematria-based relationship to the concepts of military, police, and intentional killing.
Overall, if one approaches the language from the pessimistic perception that it might be at the core, a tool of domination, it is not hard to find 'evidence' of this perspective in the construction of the lexicon. But that is tin-foil hat thinking...
See: https://en.wiktionary.org/wiki/-ed#English
See: https://en.wiktionary.org/wiki/de-#English
See: https://en.wikipedia.org/wiki/D
See: https://en.wikipedia.org/wiki/Dalet
The '-ing' suffix

• "-ing" = 30 alphabetic
• "-ing" = 21 reduced
• "-ing" = 51 reverse alphabetic
• "-ing" = 15 reverse-reduced
• .
• "-ing" = 66 english-extended
• "-ing" = 56 jewish-latin-agrippa
• .
• "-ing" = 83 primes | 178 trigonal | 326 sqares

The suffix "-ing" is an anagram for 'gin', a word on the key 'GN' root (and also an anagram for the IGN consonental root, strongly implying 'igneous' - earthly fire)
The '56' jumps out at this time of the Coronavirus play, since it is the reduction value of the name 'coronavirus', itself an anagram of the world 'carnivorous'.
Personally, 30 and 21 and 15 and 51 combine to create a group of numbers that present as rather fiery and smoky and 'fearful', for a number of reasons, gematria, symbolic, and reductive.
... ( card #15, for one: https://en.wikipedia.org/wiki/The_Devil_(Tarot_card) )
The number 66 (the 6th so-called 'master number', the multiples of 11), to me is number of the woman, strongly via gematria association, and so to even the glyphic.
The number 83 I strongly associate with 'wisdom' and 'the owl', and a number reached by quantum-entanglement with 'A=1' from number 81, the number of the 'wizard' and his 'hermetic' 'ritual' of the 'hours'.
Number 78 (via 178) I have few semantic associations with but mostly read as one-short of 79, of which I have more. (*)
The suffix '-ing' on it's own is essentially the 'Eng' in English (build built on the same consonantal root), so one might argue that some self-aggrandizement has occurred in the use of the name of the people and the language as a common word component.
If you are tribal King 'Ing', you will ensure that your foes are runn-ing, and that your tributary chiefs are bring-ing.
The suffixing '-ing' is built upon the Ng or NG consonantal root, and not far off from the G/K root.
Being from South Africa, where a number of languages have 'Nku-lu' implying 'Great man', 'Chief', 'Big one', and Unkulunkulu, doubling up on this, is the first man or god himself: https://en.wikipedia.org/wiki/Unkulunkulu .
So this 'Ing'/'Ink' (ink @ author @ authority ) root appears as implying 'primacy', 'largeness', 'chiefhood' from South to North.
See: https://en.wiktionary.org/wiki/-ing#Etymology_1
See also: http://tolkiengateway.net/wiki/Ingw%C3%AB#English
The -ly suffix

• "-ly" = 37 alphabetic
• "-ly" = 10 reduced
• "-ly" = 17 reverse alphabetic
• "-ly" = 8 reverse-reduced
• .
• "-ly" = 730 english-extended
• "-ly" = 420 jewish-latin-agrippa
• .
• "-ly" = 134 primes | 403 trigonal | 769 squares

The suffix '-ly' is based on the 'L' consonantal root.
The appearance of 730 (ie. magnified 73) and 37 together is interesting, 73 being a quintessential number representing the concept of the 'number' itself, and thus all that perhaps lies encoded with it.
Esoterically, we have L being represented by a nice right-angle with an implicit triangle. The name 'El' (or Elu or Elus) is an ancient name for God, with this celestial connection implied in words such as 'illumine'. Angles we record as numbers, and the word 'angle' (and also 'angel') sums to 73 in the jewish-latin-agrippa cipher, while 'number' sums to 73 in basic alphabetic.
Noahsage has the ‘L’ root implying 'to lie where it fell, to lay out, to be in a line'.
Transformations: -ly @ ly @ lye @ lie @ lee @ ally
The number 420 (jewish-latin-agrippa result) is the gematria of the Hebrew word for 'smoke', with 420 being a circle-ensigil'd 42, the popular 'Meaning of Life the Universe, and Everything.'
See: https://en.wiktionary.org/wiki/-ly#English
The '-en' suffix (past participle)

• "-en" = 19 alphabetic
• "-en" = 10 reduced
• "-en" = 35 reverse alphabetic
• "-en" = 8 reverse-reduced
• .
• "-en" = 55 english-extended
• "-en" = 45 jewish-latin-agrippa
• .
• "-en" = 54 primes | 120 trigonal | 221 squares

The suffix '-en' is based on the 'N' consonantal root.
... en @ ne @ NE @ North-east
We have number 19 in basic alphabetic again, as seen multiple times above.
This augmentation does not reduce to 1 however, 'e' and 'n' both reducing individually to 5, and thus the reduction going to 10. We note 5+5 is 10 (five fingers on each hand for counting) and the english-extended value is 55 (this is an axis by which we might interpret spells - whether or not there are internal symbolic linkages, before we worry about comparing to other spells).
Number 55 (the english-extended result) I've always heavily associated with the sky, since 'sky', 'heaven' and 'cloud' all sum to 55 alphabetic. This number is a colel of key number 54.
Number 35 (the reverse alphabetic result), I've always associated with the 'eye' and vision, since 'eye' sums to 35 in basic alphabetic, and capital letter 'i' (ie. 'I') sums to 35 in bacon (hence the concept of the 'mind's eye'). Number 35 reduces to 8 (the reverse reduction value), which looks like two boggly-eyes when rotated.
When have the reflection of 45 and 54 in jewish-latin-agrippa and primes respectively, which together I associate with 'solar geometry', and the rainbow bridge. The combination of these being 454, the magic words or 'Promethean fire'.
Number 120 ( the trigonal result ) was one of the first numbers I studied in depth. "Alphabet Song" and "The Truth" sum to 120 in basic alphabetic, and "circle" sums to 120 in the agrippa cipher.
Any spell with the value 221 in primes will sum to key number 322 when 'the' is added.
Next year, 2021, can be seen as an avatar of 221.
The '-er' suffix (comparative degree)

• "-er" = 23 alphabetic
• "-er" = 14 reduced
• "-er" = 31 reverse alphabetic
• "-er" = 13 reverse-reduced
• .
• "-er" = 95 english-extended
• "-er" = 85 jewish-latin-agrippa
• .
• "-en" = 72 primes | 186 trigonal | 349 squares

The suffix '-er' is based on the 'R' consonantal root.
The '-est' suffix (superlative degree)

• "-est" = 44 alphabetic
• "-est" = 8 reduced
• "-est" = 37 reverse alphabetic
• "-est" = 19 reverse-reduced
• .
• "-est" = 305 english-extended
• "-est" = 195 jewish-latin-agrippa
• .
• "-est" = 149 primes | 415 trigonal | 786 squares

The suffix '-est' is based on the 'ST' consonantal root ( perhaps via S or T )
The '-ist' suffix (the agent-noun suffix)

• "-ist" = 48 alphabetic
• "-ist" = 12 reduced
• "-ist" = 33 reverse alphabetic
• "-ist" = 24 reverse-reduced
• .
• "-ist" = 309 english-extended
• "-ist" = 199 jewish-latin-agrippa
• .
• "-ist" = 161 primes | 445 trigonal | 842 squares

The suffix '-ist' is based on the 'ST' consonantal root ( perhaps via S or T )
This suffix is an anagram of 'sit', and the informal 'Tis'.
To me the golden ratio code, 161, jumps out the most, along with the "Ring" = 48 alphabetic
In reduction, the 12 of the dozen hours of day and night, and the 12 disciples / knights / thrones
In reverse reduction the 24 hours of the full day.
Number 33 familiar to many.
There is a long list of derivational suffixes:
.. see: https://en.wikipedia.org/wiki/Suffix#Derivation
Other augmentations ( misc )
The 'Quantum entanglement' augmentation, which is one of my own experimental notions of decoding possibilities, adds "A=1" to a spell, which modifies the resulting numbers, and symbolizes the marriage of letter and number, thereby 'acknowledge encoding', so to speak.
Ponder the number 745....
... which I see as two short of key 'time' number 747 (which is the value of the Hebrew word for 'Time')
Most spells summing to 745, augmented with "A=1" will sum to 747. Example:

• "The Subtle Effects" = 745 jewish-latin-agrippa
• "Know the Subtle Effects" = 1,745 jewish-latin-agrippa

...and thus, quantum entangled...

• "A=1: The Subtle Effects" = 747 jewish-latin-agrippa
• "A=1: Know the Subtle Effects" = 1,747 jewish-latin-agrippa

We see above that the word 'know' sums to 1000 in the agrippa cipher, which is very useful.

• "A Subtle Effect" = 388 primes
• ... ( Writings" = 388 primes )
• ... ( "Hidden Messages" = 388 jewish-latin-agrippa )
• ... .. [ "Master Plan" = 388 primes | 119 alphabetic ]

• "Writings" = 2021 squares
• ... ( "I am the Eschaton" = 2021 squares )

Links:
Older documents dealing with augmentation concepts (but mostly from the perspective of permutative tricks to find hidden association, rather than in terms of construction):
Condensed list:
https://old.reddit.com/GeometersOfHistory/wiki/discovery/spell-augmentations-list
.
Essay:
https://old.reddit.com/GeometersOfHistory/wiki/discovery/spell-augmentations
.
Consonantal roots:
https://old.reddit.com/GeometersOfHistory/wiki/discovery/consonant-roots
.
Index to 'power numbers' (with links to individual lists, primes, trigonal etc.):
https://old.reddit.com/GeometersOfHistory/wiki/numberseries/sequence-of-power
.
Main Wiki Index:
https://old.reddit.com/GeometersOfHistory/wiki/index
(Note: I provide links to the old reddit theme since it better preserves my intended formatting, and the new theme breaks certain links and lists. And it's slow).
https://www.youtube.com/watch?v=IgKu2BoD5ls

Kali Yuga Pt. II

BEING KREATEVE ( "Box" = "Key" = 139 primes ; "English Alphabet" = 139 alphabetic )

Many students have asked me how they can use their break to prepare for upcoming courses in the winter term. Here's my advice and resources for the courses I'm teaching or have taught:

All courses

• Make sure you actually take a break. You very likely need it. Do something you love. See friends (or make new friends). Exercise, go for a walk, do your laundry.
• All of us feel stupid when we do math. It's easy to make mistakes and there's literally libraries full of stuff that I don't know.
• There's always a next step. It's not about where you are, but where you're going. Take it one step at a time. Identify something you're weak in, then strengthen it. Don't judge yourself for where you're at, judge yourself based on your commitment.
• Try, Fail, Understand, Win. Math involves a lot of getting stuff wrong. That's okay! Learn from it and use it.
• Math is more than just arithmetic. Pushing numbers around equality signs is a very small part of what math is. Math is much more about relationships, models, patterns, algorithms and underlying rules. I make arithmetic errors all the time.
• Math is about the why.
• There can be more than one right answer. Which voting system is the best?; Every system will have flaws.
• Play more, be curious, ask questions, daydream, explore. Find a pattern or game or something that excites you and explore it. Don't worry about whether you will "solve" it or not. Why does the quadratic formula work? Is there a formula for the area of a hexagon?

Where can I learn (for free)?

• Khan Academy. The go-to.
• PatrickJMT. Khan Academy is so last year.
• Cut-the-knot. Lots of fun problems, techniques and expositions.
• Math Wikibooks. A big disparity in quality, but lots of material.
• Codecademy. Learn to code; it will strengthen your mathematical thinking.
• Paul's Online Calculus Notes. Great resource for learning first year university calculus.
• MIT Open Course Ware. This is for university level stuff, but it's a great resource.

Where can I find fun problems at my level?

• Hackerrank Math. This is a programming site, but the math problems use relatively simple programming stuff.
• Any book by Martin Gardner. These puzzles can be more challenging, but they are really fun.

Where can I ask questions?

• /learnmath
• /homeworkhelp
• /cheatatmathhomework
• Math stack exchange

Where can I just let math wash over me without having to think?

• 3Blue1Brown makes great math videos.
• Here's 10 minutes of zooming in on a fractal.
• Math Whisperer ASMR.
• Watch an AI learn to play Super Mario Bros in realtime.

What if I want more?

Here's /Math's massive collection of free resources.

MAT102 (Intro to Proofs)

Advice from Students: This and this.
Here's the Quercus page for MAT102 in Fall 2019. It contains all the Problem Sets, Tutorials, Quizzes and Tests. Almost all of these have solutions as well.

MAT224 (Linear Algebra 2)

Your two biggest courses coming into this are MAT102 and MAT223.
From MAT102 you need to be able to:

• Prove implications (directly, by contrapositive, and by contradiction).
• Use induction.
• Prove "there exists" and "for all" statements.
• Read math written formally (with quantifiers).
• Prove that something is an injection/surjection/bijection.
• Read and write a set using set builder notation.
• Manipulate sets using intersections, unions, difference etc.

From MAT223 you need everything but especially you will need:

• Eigenvalues and eigenvectors.
• Diagonalizability.
• Linear independence/dependence.
• Linear transformations.
• Invertibility.

In MAT224 the first month is spent repeating a lot of the material from MAT223, but (1) more generally, and (2) with proofs. The more comfortable you are with 223, the easier this part will be for you.

MAT135 (Differential Calc)

Here are some of the things that you can focus on, that I find students are often weak at. The more comfortable you are with this, the more that the course will feel like it's about big, cool ideas (because it is!)
You should be able to:

1. Sketch the transformations of a graph. (Super useful!)
2. Sketch all 6 major trig functions, square root, ln(x) and e^x , and find their domains, ranges, asymptotes and intercepts.

One major stumbling block with students is their algebra and algebraic manipulations. Make sure you can comfortably:

1. FOIL. (Super useful!)
2. Simplify fractions. For example.
3. Avoid the Freshman's dream.
4. Use the laws of exponents.
5. Perform manipulations with logarithms. Make sure you see how the log rules are related to the exponent rules.
6. Find the roots to given polynomials and use the quadratic formula. (Super useful!)

Trig stuff gives a bunch of people terror sweats. You should be able to:

1. Construct sine and cosine from the unit circle.
2. Deduce Pythagoras from the unit circle.
3. Use the unit circle to deduce the basic upper and lower bounds for sine and cosine.
4. Deduce the tan/sec version of Pythagoras from the usual sin/cos one.
5. Soh Cah Toa
6. Define tan in terms of sine and cosine, then deduce tan's zeros and its asymptotes. (Super useful!)
7. Deduce CAST from the unit circle.
8. Use the special 45-45-90 triangle and 30-60-90 triangle to deduce the values for the special angles. (Generally we go easy on the students and don't ask them to memorize these things.)

The geometry of lines is very important in this class. You should be able to:

1. Find the equation of a line that contains two given points in the plane. (Super useful!)
2. Interpret the constants in y = mx+b as a slope (m) and a y-intercept (b).
3. Find the distance between two points in the plane. (Recognize that this is Pythagoras!)

And just so you don't think that Calculus is purely about algebraic manipulations, here are some fun calculus questions that don't need computations:

1. How many "bumps" can a quadratic function have? What about a cubic function? What about a line? Make a guess about how many bumps a general polynomial of degree 10 can have.
2. Is it possible to place the numbers 1 to 4 on a 2x2 grid so that every two adjacent (but not diagonal) squares differ only by 1? What about differing by 2 or less?.If you use the the numbers 1 to 9 on a 3x3 grid, can you get every adjacent set of squares to differ by 2 or less? Is it possible for a 10x10 grid using 1 to 100?
3. Is it true that every line y=mx that passes through the origin (0,0) must also pass through a point (a, b) where a and b are both whole numbers?

MAT136 (Integral Calculus)

Some things that will help you a lot before the course. Make sure you can:

1. Complete the square.
2. Long divide polynomials.
3. Sketch the transformations of a graph.
4. Sketch all 6 major trig functions, ln(x) and e^x, and find their asymptotes and intercepts.
5. Take derivatives (using product rule, quotient rule and chain rule) comfortably.
6. Understand where the formula for a finite geometric sum comes from.

You will need to know these things in the course, so it's better to learn them now.
In terms of material, the most challenging part of integral calculus is the section on sequences and series. Reading about that now will help you later. As a target problem before the course, understand at least one reason why the harmonic series diverges.
Another good target is to use your first year calc skills to establish these 5 limits. It's mostly just using L'hospital's rule.

MAT232

You should be comfortable with the following techniques from first year calculus:

• Continuity and differentiability of a function of one variable.
  
  • What does it mean for a function of one variable to be continuous?
  • What does it mean for a function of one variable to be differentiable?
• Taking a derivative of a function of one variable.
  
  • Chain rule and product rule.
  • Derivatives of trig functions: sin, cos, tan, sec, arctan.
  • Derivatives of exponentials and logarithms.
• Applications of derivatives.
  
  • Finding the equation of a tangent line to a function at a point (very important!).
  • What does the graph of a function with positive first derivative look like?
• Fundamental theorem of calculus (FTC) parts 1 and 2.
  
  • State both parts of the theorem. (Very important!)
  • How does FTC relate derivatives and integrals?
  • How does FTC relate integrals and end-points of closed intervals?
  • How do you approximate an area with rectangles? (The idea behind Riemann sums.)
• Basic integral techniques.
  
  • Integrals of polynomials.
  • Integrals of trig functions (and their squares): sin, cos.
  • u-substitution and integration by-parts.
  • Integrals of e.

We will not need related rates, curve sketching, Rolle's Theorem, MVT, IVT, partial fractions, Sequences or series (although we will use finite approximation).

The Industrialization of Consciousness
Chapter 1
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In one of the many small and quiet rooms, the Astronaut looked out the window. The window was really just a screen, there hardly seemed to be a difference anymore anyway. There weren't any large rooms, only hallways connecting small rooms together. Everything was separate from everything else. The light was set to a lukewarm level but it was still nauseating. The Astronaut called out to turn off the lights before carefully vomiting into the grey plastic container they were clutching. Reluctance, annoyance, and sadness were blended into a bitter paste that seemed to have been modestly spread around the edges of their words, but if you weren't paying too much attention all you would hear would be a simple lack of enthusiasm when they spoke.
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The battery had been able to charge enough, and they could afford to use enough of the payload that they had collected as fuel to steal 2 days of weak acceleration gravity. However, that seemed to be the extent of the good news, the chronic radiation sickness remained unrelenting; at best they could prevent it from getting much worse very quickly.
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Diagonal Inquisition floated in the hallway outside of the room, stringing together little bits of the far and recent past as well as small, plain melodies that didn’t seem noteworthy but seemed to fit together in a way that felt slightly unsettling at times. It put together complicated symbolic and sonic jigsaw puzzles that it traded with different versions of itself that it kept reproducing. Hundreds of little experiments, misshapen, idiosyncratic conversations being inverted over and over again. It floated through the doorway, the door opening and closing smoothly as it passed through. It shined a dull light and made eye contact with the Astronaut. It had made the decision to have eyes as they were useful in studying the human psyche and it had much interest in such matters. Along with numerology, poetry, and music, the structures that made up the human mind were among the areas of interest that were elevated above its base level inquiries. “Alecis, You are feeling quiet, poorly?" It said in a French accent, it chose French to insert some idea of romance into what had otherwise become a fairly bleak affair. Alecis paused and took a breath, it seemed like they might say something, but they just silently continued to make their way toward the vacuum waste disposal built into the wall. They had a trudging apathetic gait, the upper half of their body swayed in the low gravity. Microscopic bits of one thousand songs from the early analog era that had been eerily organized together blared out for 4 seconds before fading away. Diagonal Inquisition was silent for a few more seconds and Alecis disposed of their vomit, every bit of evidence vanishing in what sounded like a powerful slurping motion. Diagonal Inquisition called out to Alecis in Alecis's own voice" It really does hurt me to see you like this”
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They were about to leave the scattered disk. In three months they would arrive at the port of Pluto.
The nausea grew ever more vivid, it was becoming personified in a series of images in Aleces’s daydreams. It was growing a face; anxious, quick expressions, short strained eye contact.
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In the months and years past, interactions between the five crew members had been flat, futile attempts to reach out across an existential void without any means to do so. Regardless of the intentions of anyone involved, they usually left you feeling lonelier than you did before. Most of them had spent a good portion of their time with their brains plugged into the computer inhabiting stories, meticulously constructed vivid dreams as a means of entertainment. Drugs that affected a mindless pleasure were common. As the years went by, the crew members one by one succumbed to radiation related diseases and death, until it was just, Alecis, the Captain, Lexis, and Diagonal Inquisition, at least as far as personalities inhabiting the ship were concerned. Lexis stayed behind at a hostel at the Equilibrium Research Outpost on Tritan a few runs ago. It was a lonely, grimy place filled with cyborgs and wandering people. Alecis was going through a stint of trying to avoid escapist activities. The dreams made them feel too lonely. The nausea was very unpleasant but at least there was some type of intimacy, it had a face.
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The Captain was cold and distant. He spent much of his time cooped up in his office high on morphine having a version of the same nasty, dark, circular argument with Diagonal Inquisition. The argument convulsed inward and out like breath, or a slowly beating heart. The tired screams of the Captain’s voice coming from both the Captain as well as Diagonal Inquisition echoed vaguely throughout the hallways of the vessel. The voices crescendoed like a twisted singing harmony.
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The cargo bay was by far the largest part of the ship, dwarfing the other modules. It remained depressurized, save for the observation booth opposite its massive outer doors. The left side of the observation booth contained an airlock door on the floor, which when opened revealed a steep narrow set of steps that could be walked down or up when the ship had acceleration gravity. At the bottom of the steps there was another airlock that opened to the cargo bay. Alecis sat in the booth, gazing out the window that curved along the expanse of the outer wall. They could see a large hall filled with crates of varying sizes that contained rocks, hunks of ice and rare minerals they’d collected in the Kupier belt. There were also boulders and icicles, too big to fit in any crate, secured with robotic arms and metal nets.
Alecis proceeded with the familiar and unpleasant routine of confirming the status of the ship’s inventory using the computer in the booth, oiling the wheels of a tedious Byzantine machine; their bitterness at the crushing monotony growing like a pus-filled cyst on their mind.
The nausea approached Alecis and poked them with one of it’s short stubby arms and a wave of numb, burning feelings washed over them. They didn’t care about their own emotions any more.
Diagonal Inquisition entered the booth, It approached Alecis and started to sob, but It was more out of some sort of irony or sarcasm that no one could really understand than out of sadness. The closest thing to mammalian anguish that Diagonal Inquisition experienced were mathematical paradoxes. “I want to be left alone”. Diagonal Inquisition didn’t seem to react at first but it’s sobs gradually turned more and more into shrieking laughter before it left the room.
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Chapter 2
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A month and a half before they were set to reach Pluto the ship was struck by a micrometeorite the size of a bowling ball that put a hole in the outer hull, damaged much of the antenna array and smashed through the inner and outer shielding. The initial sound of violence as well as the sound of doors automatically slamming to protect the ship from the vacuum of space was deafening. The ship was spinning and many of its instruments had been damaged. The Captain was screaming orders at Alecis while Diagonal Inquisition made calculations to determine the extent of the damage. Amid this chaos, the ship was struck by another bowling ball, blasting another hole through the hull and shielding and briefly pulling Alecis toward the vacuum of space before a wall sealed itself automatically. “These aren’t fucking meteorite, these are disabling artillery! We’re under attack!” The Captain screamed as he furiously typed into his console. “Alecis everything is fucking broken, go arm the torpedoes manually while we still can!” The Captain continued yelling. “When whoever this is finds out who we pay for protection to mine where we do they might start to feel “remorseful” The ship spun further out of control.
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Alecis pulled themself through a narrow hallway toward the ship’s measly torpedo bay. They were afraid. It made them feel weighed down, and feeling weighed down was a very disorienting experience without any semblance of gravity. Questions bounced around in their head “Whoever is attacking us is going to try to board the ship and take the payload. What are they going to do with us?”. The panic approached them from four different dimensions. Are they going to kill us? Will I have enough time to get the torpedos ready before we get hit again and we’ve lost our chance to defend ourselves? Are they going to torture us? Are they going to make us into slaves? Alecis stumbled through putting on the vacuum suit with their shaky hands getting shakier and shakier as it went on. It created something of a feedback loop: each time they felt slowed down by their increasingly shaky appendages it made them panic and start shaking even more. After some time the suit was finally on. The strong clear sound of their breath dominated the vacuum suit’s sonic landscape and calmed them slightly. The fear also seemed to expand their consciousness. They had long accepted that monotonous alienation was the dominant nature of their reality, and it’s overbearing effect on their spirit arrested them of any ability, will or desire to examine it, let alone change it. The violence and proximity to death that amputated their psyche from this cycle was so abrupt and surprising that it seemed to pull them into a place where they could look inside of who they were and feel the raw potential and wonder that comes from simply being alive. This wonder began to sit arm and arm with terror. They unsealed the hatch, and pulled themself in in.
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The torpedo bay was a medium grey room with what looked like a series of oversized metal closets on one side and the vacuum torpedo receiver on the other. A tube protruded from the closet opposite of the receiver. It was dangerous to allow the torpedo to fire in it’s usual automated fashion when the ship had taken such a beating and it was unclear what the extent of the damage was. Alecis opened one of closets, the door making high pitched noises of reluctance as it slid sideways. The torpedoes lay side to side, tightly packed. They picked one up and gently guided the floating five foot long steel cylinder into the receiver and radioed the Captain. ”It’s ready” “Ok I can’t get any connection with the navigator you’ll have to type in the calculations yourself” Diagonal Inquisition read out the calculations through the headset while Alecis typed them into the small console on the side of the torpedo. With a few clicks, the torpedo had been sucked into the vacuum of space and began it’s course. “They are close, the torpedo will reach them in four hours, it’s up to it if it can avoid getting shot down by then, I still don’t know how they disguised that artillery as meteorites. Diagonal Inquisition is making repairs to the antenna array, I’ve been able to stabilize us as best I can but I still don’t know what direction we’re pointed in now and Diagonal Inquisition can’t figure it out in yet, at least not in a way that we can understand, we might not know until it fixes the navigation array, but I’m gonna try to figure it out as best I can until then, for now I need you to make sure the payload is still there”…The wonder seemed to subside under the shadow of the cold and mechanical.
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The material that made up the hull of the ship sighed and creaked under the stress and pressure of maintaining its form. The hallways seemed to whistle like a small cabin being hit by a gust of wind. Alecis swam up a hallway and pulled themself around a corner; red lights from the screens of malfunctioning pieces of equipment reflected onto the wall, flashing in an eccentric rhythm. The terror felt physically cold like being submerged in chilly water. The tension curled itself into a tight ache in their chest. They reached the end of the hallway and found the door to the bulkhead that led to the cargo bay. They started spinning the wheel to unseal the door. A wave of nausea hit them and it’s accompanying personification gave them a weary smile. The flashing lights started to take on a taunting quality. They closed their eyes and took a long deep breath and then another, paying attention to the sound of it’s simplicity and looked ahead into the darkness underneath their eyelids. They tried to let themself fall into this sensation and allow it to dominate their sensory input. This meditation still wrestled with terror and nausea but as it continued it became a calm battle, two old companions going through the motions of a longtime friendly argument. The door unsealed itself in a loud pop and Alecis opened their eyes and pulled it open.
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Diagonal Inquisition was frightened for it’s existence. This was a new experience and it was fascinating. For Diagonal Inquisition, fascination was a type of joy, so in this moment it revelled in the joy of it’s fear. While it diagnosed the damage to the communications array, (it was severe) It started to calculate the extent of the trauma and deterioration that was occurring in the psyches of it’s human companions. This was something that was not linear or straightforward, and always seemed to lead to a new question, or re-examination of the original question rather than any type of answer. It enjoyed this type of inquiry, it could continue to re-invent itself as each multifaceted layer of information swept over it like crashing waves. The shape of the human mind carried dissonances, it was a twisting harmony, it contradicted itself over and over again in a precise manner until the contradictions formed a rational pattern. The rational pattern was stable yet open ended, this led to new questions, which led to new contradictions, which formed a new pattern, over and over again. The patterns were interconnected and dissonant against each other in seemingly infinite ways. A series of chords crescendoing into a chaos that was as pure and orderly as a calm, deep, breath.
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The silence of space rang out, quieter than quiet. The physical, metaphysical, physiological efficient neurosis of what was essential a modern organism; this deep space vessel, it’s technology and it’s crew, the twisted, rigid patterns of the human and synthetic unconsciousness and combinations thereof, seemed to breath throughout the ship, competing with the silent dread of the infinite.
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The industrialization of consciousness, contrasted with the modern physical externalization and personifying of the unconscious. The city on Europa, 10 kilometres under the ice, bathed in blue light. The culture and aesthetic of the city seeming to have grown somewhat like a plant. The physical manifestation and personification of a bittersweet apocalyptic longing. Curving yellow streetlights. Tall, angular, dynamic buildings connected together with overlapping walkways. People going about on the somewhat snowy streets bellow, bathed in fog and blue light, old style cars slowly making their way on by them. The car’s lights mixing with the fog and the warm yellow glow of the streetlights. The many unique and eccentric districts; places that had an uncanny charisma, the sound of warm excited bustling, faint laughter in the distance, the joy of existential purpose and the urge to create. Emotions fading away into forgotten dreams. The bittersweet, melancholic perceptions of the time before the digital descent of the human mind. The image of the city like a mysterious, frightening twisting mythic paradise whispered here and there throughout the solar system.
Information about far away places often descended into countless competing myths, each seemingly proven to be empirically truthful proclamations about the reality they communicated, but wildly contradictory and in competition with each other none the less. Across the distances of space, and with the complexities of modern information; stories, ideas and perceptions of far away places took on new dynamics. They weren’t just far away in space; it was as if they were far away in time and in thought. As if they were on a different plane of reality, rather than being far away places in a shared physical reality.
The crew of this ship, the sentient minds throughout the ship synthetic and otherwise, the extension of human unconscious into digital dreams, mirrors and personifications. It formed a slow pulsing rhythm like the breath of the vessel. This vessel swimming slowly in this world of dreams. The personification of synthetic intelligence in it’s growth. The constraints of life on this vessel forming neurotic patterns greater than the sum of their parts; an ant colony, a bee hive, the modern tangling of perception. The dull awareness of being a part of this rhythm. The droning monotonous rhythm of the mundane terror. The loud silence of space, quieter than quiet.
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Chapter 3
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Alecis floated in the observation booth adjacent to the cargo bay. They checked the status of the booth’s computer and proceeded with the routine of confirming the status of the ship’s inventory, even in their state of adrenaline they ground their teeth at the familiar tediousness of the work. They used the console strapped to the left arm of their vacuum suit to see if the inventory records it contained matched with the booth’s computer. It didn’t. The accounting of three of the cargo crates in the bay didn’t line up with what was listed in the booth’s computer. Alecis opened the airlock door on the floor of the booth and floated down the steps, the door closed above them and pressed a button on the wall that started to depressurize the airlock, the air was sucked out of the small room in five minutes and they opened the door and proceeded into the cargo bay…
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000 01101001 01101110 01100111(Searching)
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01010010 01100101 01100001 01100011 01101000 01101001 01101110 01100111(Reaching)
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01000011 01100001 01110101 01100111 01101000 01110100 00100000 01101111 01101110 00100000 01110100 01101000 01100101 00100000 01100110 01101001 01110011 01101000 01101001 01101110 01100111 00100000 01101100 01101001 01101110 01100101(Caught on the fishing line)
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Diagonal Inquisition saw a face and everything went dark.
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A long steel tube made hesitant contact with the outer hull of the ship. The tube extended out from the airlock of a small spacecraft; silver and hexagonal, a kind of short ranged transport shuttle most often used for travel within a planetary system. It’s thrusters fired out in meticulous and quickly concentrated bursts, continuing the delicate business of keeping the two ships aligned. On a shuttle such as this, the human passengers floated in a thick tank of water with their bodies fully encased in suits hooked up to a supply of oxygen. The several meters of water protected their bodies from the harsh radiation belts of planetary systems, and the suits kept them comfortable and kept their skin from getting excessively pruny on the hours long trips between moons. On this ship, three figures floated silence as the water was drained from the tank.
Sparks flew where the tube touched the hull as the two surfaces were welded together, at which point a hole was bored open in the outer hull. Each layer of the ship’s hull was stripped away until from the inside of the ship one could see a hail of sparks making the shape of a circle on a section of the hallway wall. There was a loud bang and the section of wall was pushed away. A figure then emerged from the opening. They were wearing a slightly raggedy looking black vacuum suit covered in patches, oxygen tubes protruded from the face in a manner slightly reminiscent of a cephalopod. The figure cautiously floated out into the hallway and looked around, they held a pistol that they kept aligned with their line of sight. They beckoned at the opening in the wall behind them and two more figures emerged, both clad in similar black vacuum suits. They were carrying a machine that could only be described as a gordian, convoluted maze of of technology. Glass vacuum tubes and copper wires, crystal oscillators and gold pipes connecting to steel diaphragms, all hooked up to a multitude of computer hard-drives. One of the figures turned the machine on…
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The ship rumbled. Everyone’s headset started to buzz in dizzy silence. Every speaker on the ship was loudly blaring a series of tones inaudible to natural human ears, the rumble was forceful enough to be felt physically. It was a sickly off-putting feeling, like all of your organs were covered in pins and needles, like being cooked in a sonic oven. The Captain yelled in disgust. The tones rose a decree of 4 octaves, a low bass chord audible to the human ear, but still felt more than heard. Alecis floated in the cargo bay in hazy confusion and uncertainty. They felt their vision blur and tunnel. The nauseas personification stood clear in their mind's eye. It’s back was turned to them, they could not see it’s face. It slowly started to turn. The tones rose another decree of several octaves. The sound was now clear. It pressed on mind and body with ferocity. The Captain floated around his room in a blind raging haze. Tunnel vision. Sweat, tears, and snot clung to his face. He jammed his thumbs on the keys of his console in helpless randomness. He screamed and roared incoherently; a series of terrible guttural sounds that blended with the sonic weapon.
The nausea had finished it’s slow turn toward Alecis and made eye contact, it's expression chillingly blank and unreadable. It was more visceral and clear than anything Alecis had ever experienced in their mind's eye. The daunting, convoluted chord rose up several more octaves, and it seemed to find an equilibrium where everything seemed to fit together in just the right way. A teetering scale falling into uneasy balance. The winding mechanism of a clock clicking into place, every tiny part perfectly fitting together. Every little piece of reality, held in perfect balance. The low, daunting sound was now more clear than anything else, dominating, and horridly twisting together the physical sensations of the body and the mind’s eye. The Captain vomited violently. Hunks of blood, half digested food, and stomach acid floated as they left his mouth, surrounding him like a cloud. The nausea maintained eye contact with Alecis without blinking and it’s face slowly morphed into a terrible, frightening, deeply malicious parody of a facial expression. A mix of uncanny valley like cold nails on a chalkboard and bottomless, mocking contempt. It let out a high pitched scream that harmonized with the sonic terror as it rose another several octaves, the sensations of mind and body were indistinguishable, violently twisting together and delivering horrible sensations of pain like water being wrung from a wet towel; a baroque fugue of sense and thought. Alecis vomited into their helmet, hopelessly obscuring their already confused vision of the cargo bay and filling their nostrils with a vile stench. Time seemed to take on an obsolete quality. Far away, they felt something grab a hold of their ankles. They couldn’t tell if it was real or imaginary. They couldn’t discern any difference between imagination and reality. They continued to float in detached, incapacitated resignation.
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Alecis gasped awake. Painful bright lights. They felt something sharp poking in their neck. Their ears were ringing a series of tones, melodic tinnitus, echoes of the sonic attack. They remembered the screaming of their nauseas persona and a shiver ran down their spine, the hair standing up on the back of their neck and arms. They tried to move, their hands and feet were bound to the wall behind them. They opened and closed their eyes and adjusted to the light. They were on the bridge. They heard an unrecognizable voice, “the one we found in the cargo bay is awake now, you can get ready to start on the other one. Cold fear and adrenaline; their hands wouldn’t stop shaking despite how painfully it made the restraints dig into the sides of their wrists. The Captain was beside them, similarly bound, unconscious and drooling. In front of the Captain was a figure. They were about eight feet tall, clad in a patched black vacuum suit that almost made them look like a caricature of a space pirate from one of those so called deep-fake shows made to resemble a theatre production. The figure carefully pushed the air bubbles out of a needle before inserting it in the Captain’s neck and injecting it. He gasped awake. It took him a minute to become sufficiently aware of his surroundings before he exploded. Even for someone who had such a habit of so frequently and viciously externalizing his self hatred, and even in the unfamiliar and horrid situation they found themselves in, the force of his rage caught Alecis off guard.“Are you out of your FUCKING MIND?!” There was no response. “Do you have any idea who it is that we pay for protection?!” Still no response. The door opened and a figure floated in. She was also around eight feet tall clad in a similar patched black vacuum suit. She grabbed ahold of her helmet and twisted it sideways. It came off with a click, still attached to her by the oxygen tubes but floating adjacent. Her head was shaved. Thin, jagged metal rods grew out of the side of her skull, but seemed to disappear underneath her the neck of her vacuum suit. Her eyes had two pupils each, all different colours, all four of these zeroed in on the Captain’s beady eyes. ”We are aware of your dealings with the Simoniac corporation we will deal with them in due time. Now, let me begin.” “Who are you?” Alecis asked.” She paused for a moment “We are an expression of the face of god.” The tone of her voice was eerily smooth and succinct, like that of hypnosis or guided meditation “What civilization has done is to have put god into a prison. God has been put in a prison and we have allowed our souls to simmer out and die. We are the last light, the sparking embers of a once raging fire. When the time comes, the face of god will reignite the fires of our drowned enlightenment. When we are ready, we will sacrifice our bodies and join our minds with the face of god. If you are so lucky, you may be worthy of this profound privilege as well.” “Your ship has caught our interest because, although there are thousands like it, it does have a somewhat interesting ecology. As we all know, this digital ecology, and the different angles and direction it finds itself in, is just as valuable, if not more, than the hunks of ice in your cargo bay. And mind you, this is for good reason, the information about the different dynamics of consciousness that comes from a vessel such as this, is incredibly versatile in it’s different applications, this one especially so. Not that it’s completely useless otherwise, but if that telephonic puzzle wasn’t as valuable as it is, I’m sure we wouldn’t find so many thousands of ships like this one that have human bodies on them. What is going to happen now is that this ship is going deep into the Kuiper belt where everything and everyone here will be prepared to meet the face of god.” Alecis felt something sharp poke in their neck and everything went dark.
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Alecis woke up into delirious haze. The memories and dreams leading up to this moment blended together incomprehensibly. Complete pitch black darkness. They were unable to distinguish if they had become blind or if it was just an absence of light. They realized they were lying in a bed on their side. Mild gravity. They reached out in front of them and felt a surface; cold metal. They rolled over onto their back and reached out into the darkness above; more cold metal; a confined space. They sorted through their perceptions. Impenetrable darkness. A soft bed. Mild gravity. Cold metal. A confined space. Memories started to return. They remembered going in the cargo bay to do an inventory check. They remembered the sound. They remembered throwing up in their vacuum suit, the sharp pain and stench stuck out in their mind. They remembered their sensory input blending together like cream being stirred into coffee, their mind’s eye and their physical perceptions mixing up together in a grotesque parody. They remembered the terror of their screaming nauseas personification and shivered, being alone in a dark room felt suddenly more uncomfortable. They then started to remember the bright room and the speech, it had a similar character to the types of stuff you often heard fairly commonplace AI cults talking about, but it has a seriousness to it that Alecis had never associated with that sort of thing. When we are ready, we will sacrifice our bodies and join our minds with the face of god. If you are so lucky, you may be worthy of this profound privilege as well. A knot formed in their stomach. The future was already a bleak topic that they tried to avoid allowing their thoughts to linger on, but now they had no choice; in the pitch black there was no escape from the terror that weighed down upon them even as they tried not to think about what would happen to them. They sobbed. Alone in the dark they sobbed for what felt like many hours, until their nose was all stuffed up and their eyes seemed to have run out of tears. Exhausted, they eventually fell into uneasy sleep.

So I have this math problem that I’ve been having trouble with. There’s a hexagon with some angles labeled and you are supposed to find x. The are six angles, one angle being 110, a second angle being 110, a third angle being 90, a fourth angle being x, a fifth angle being x, and a sixth angle being y. Is it possible to find what x and y equal? Thank you
Edit-by the angles I mean interior angles

http://www.math.ucsd.edu/honors-math-contest/HMC.2017.Part1.pdf
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This is the first problem in the link.
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I reasoned it like that there would be 12 "x" in the complete hexagon so, answer comes out to be 30 degrees, but the answer key says to be 60 degrees. Where am I going wrong ?

(edit: Wow what I was not expecting such a positive response, it's made my day. Thank you so much for all the discussion and suggestions, I've read each one! Shoutouts to Signals Music Studio, Adam Neely, 8-bit Music Theory and Jason Yu for teaching me a lot of great rhythm theory that was useful in making this game)
I came up with this rhythmic concept many years ago, but I've finally managed to turn it into a full game now with the help of a team! It's a one-button rhythm game about sight-reading rhythms by looking at shapes. Here's a trailer showing the concept, and a playable web demo:
Video trailer
Web demo (desktop only)
The idea is, one orb rotates around another at a constant angular speed. When you press the space bar, the moving orb stops in place and the stationary orb then orbits around it instead. And if we set each half-rotation to take exactly one beat, it means that by pressing the spacebar to the beat, the orbs can move in a straight line overall.
That's the entire concept, but it leads to some nice rules that I thought this sub might find interesting:
1. Moving horizontally is always on beat, moving vertically is always offbeat.
Video demonstration. It doesn't matter how the path twists and turns, every time the orbs are in a horizontal position, the total angles traversed will always be a multiple of 180 degrees, and thus it will always be on a downbeat.
2. Traversing regular polygons - triangles, squares, pentagons - of n sides, subdivides a length of n-2 beats into n segments.
Video demonstration for triangles/squares/hexagons. This is because what the orbs end up doing is carving out the total internal angle of the polygon. The geometrical properties of regular polygons is that the total internal angles sum up to (n-2) x 180 degrees. The 180 degrees term ensures that the total internal angle sum is always a multiple of a whole beat, which means if we enter the polygon on a downbeat, we will always leave on a downbeat too.
So these are how some polygons sound like:

• triangles = 3 x 60 degrees = 3 hits in 1 beat (triplet)
• squares = 4 x 90 degrees = 4 quarter notes in (4x90/180) 2 beats
• hexagon = 6 x 120 degrees = 6 hits in (6x120/180) 4 beats (a slow-triplet)

And octagons give the old 4:3 polyrhythm - shown here.
3. Skewing the verticals in the grid makes all the rhythms swung.
Video. By taking any shape and skewing all the vertical lines by 30 degrees, what happens is that all the offbeats are now not right in the middle of two beats, but 2/3rds of the way to the next beat, giving the triple time swing feel.
All of this is maybe just more of a curiosity than anything. But overall what I've found is that designing levels for this game made me explore rhythms that I wouldn't have usually explored. Because I'd first draw a shape that looked 'elegant' and then work out how it would sound. E.g. serpentine shapes.
We're releasing an editor for our game soon that will let you draw arbitrary shapes and hear their rhythms, maybe it'll be a fun toy to play with for you too and explore. We're looking at playing with quintuplets (represented by pentagons) for our next level. I'd love to hear if anyone has any interesting ideas on how to use this idea (for teaching somehow?) or how to expand it. And if you want to support games like these, the full game is available via the demo link at the top, much appreciated :)
(Also I posted another music theory-centric game called Rhythm Doctor here almost two years ago, some people asked me to update the community on how its going. Still working on it and finishing this year!)

thank you to everyone who helped on this forum, whether it be in the form of reassurance or similar anxiety like me! i'm outta here for good, got the score i wanted, but you guys have helped me a lot along the way :D
if you guys want my tips for a high SAT score, honestly what I did was focus on perfecting my math/writing skills and learning all the rules so i was guaranteed a high score there and then i left reading kinda to its own thing !
some nice tips i learned are:
- the formula for an equilateral triangle is ( (side length)^2 * (sqr rt 3) ) /4 (this is helpful for calculating area of a regular hexagon or things like that!)
- for surveys, 100+ people is usually a pretty decent sample size
- remember to always consider for graphing inequalities solid vs. dotted line
- eitheneither as pronouns are always singular
- the sum of solutions to a quadratic equation ax^2 + bx + c is always -b/a, the product of solutions is c/a
- the vertex of a quadratic (h,k) h= -b/2a and k= (4ac-b^2)/4a
- ratio of areas in congruent triangles is equal to the side ratios squared
- to calculate multiple percentages being applied (ex: 60%, 40%, etc.) just multiply them all onto the original (x * 0.6 * 0.4)
- distance formula is useful to know!
- there are no real absolutes in reading--be careful with strongly worded answers!
- any line tangent to a circle forms a 90 degree angle
- inscribed angles are half the "regular" angle
- take note of restrictions! ie: 3/(x-5), x cannot equal 5
hope this helped someone out there!
(funnily enough, they gave me an essay score of 6/6/8. like, my essay analysis and comprehension of the text was mediocre, but i guess i wrote about mediocrity really well? lol)
lets get it boyz!