What Can SV Teach an Sorcerer in the Mesolithic?

[X] [Solstice] Make a false stone on a nearby hill

[X] [Blight] Brick up the opening

[Theroriparian] [X] [Theroriparian] Send the Heroine to deal with it

[X] [Bog Iron] Give mortals half the iron from what they bring

Greetings, this is Destroyer.

LoserThree said:

This is the counting by twos again, yes?

I would like to hear more about it. But I don't think I'll do much with counting until I can do it with the glyphs.

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LoserThree said:

Hm.

That may be something.

Tell me how to count to seven gross and one dozen and four on my fingers.

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Bianca, I would implore you to count in sixteens instead of dozens. I will be dedicating my communication to this purpose, due to its immense importance for the future.

The greatest reason for doing this is that the prime factors (as was described by another voice) of sixteen are exclusively twos. Sixteen is 2 multiplied by 2, multiplied by another 2, and multiplied again by 2. This is so important because it makes translation between base 16 (hexadeximal) and base 2 (binary) extremely simple.

This lets you use a number system that is similarly convenient to counting in dozens, that is extremely easy to translate into counting in 2s. This is desirable because binary is the greatest number system for doing written calculations with, in simplicity and speed, among other future benefits.

However, Binary is also the most cumbersome number system for day to day counting with fingers and the speaking of numbers as words, as it consists of long sequences of ones and nothings.

For everyday use, counting in sixteens is just as, if not more, convenient and easy as counting in dozens.

For your original question of counting with your hands, you can represent one through sixteen by touching your thumb to the fingertips and inside of the three knuckles of each finger in sequence. One would be your thumb touching the tip of the first finger closest to your thumb, two would be the tip of the middle finger, four would be the little finger tip, five would be the outermost third knuckle of the first finger, and twelve would be the second knuckle on your little finger. Thirteen would be the base knuckle of your first finger and sixteen would be the base knuckle of your little finger.

Sixteen would be called one 'hex'.

So, you can count ones on one hand and count how many hexes on your second hand. Seventeen would be one on the ones hand, and one on the hex hand, to represent 'one hex and one.' When you count past thirty-two, you again start over at one on your ones hand and now have two on the hex hand. Three dozen would be two hexes and four, for example.

This lets you easily count all the way up to sixteen hexes and sixeen, or a gross, eleven dozen and four, with just your hands.

You can't really count beyond that with your hands without using finger binary, and even then finger binary, with all ten fingers and thumbs representing a sequence of ones and nothings, can only count to exactly seven gross, one dozen and three, which is an unfortunate if humorous coincidence.

A hex of hexes, or sixteen sixteens added together, is called a byte. In dozenal, this is one gross and ten dozen.

Seven gross, one dozen and four is exactly four bytes.

A hex of bytes is a hexabyte, and a byte of bytes is a block. A hex of blocks is a hexablock, a byte of blocks is a bytablock, a hexabyte of blocks is a hexabytablock, and a block of blocks is a blockablock. Any numbers greater than a blockablock (which is a huge number you won't run into for a very long time) are described by using the smaller number names to say how many blockablocks there are.

A gross of grosses would be five hexabyte and one byte.

For reference, a blockablock is close to a great gross of great grosses of great grosses. The (roughly estimated) total number of grains of sand in the entire world is close to a blockablock of blockablocks of sand grains, which gives you an idea of how easily massively large numbers can be represented like this.

Of course, I can already hear the 'but what about multiplying and dividing by three!' There are some very recognizable patterns in base sixteen that correspond to multiples of three, but there are also useful patterns of five in base sixteen as well, which dozenal doesn't do well at all.

I have hopefully established how counting in hexadecimal is as good as or better than dozenal for everyday purposes and finger counting, and a way of speaking very large numbers easily. I will now move on to its use in relation to binary and written calculations, and why such a thing is vastly preferable to performing written calculations in dozenal.

Firstly, I must explain powers of a number. A number taken to the power of a second number is the first number multiplied by itself over and over again, by the second number of times. I will represent powers as 2^2 and 2^3 for 2 to the power of 2 and 2 to the power of 3, respectively, for brevity. Any number to the power of one is itself, and any number to the power of zero is one.

2^2 is two twos multiplied together, which two groups of two added together is four.

2^3 is three twos multiplied together, which is two groups of two which are four, and then two groups of four which is eight.

2^4 is four twos multiplied together, which is the same as 2^3 multiplied by 2, and two groups of eight make sixteen.

3^2 is nine, as three groups of three add up to nine.

3^3 is one hex and eleven, or two dozen and three, as it is 3^2 multiplied by three again, and three groups of nine add up together to make this number.

A dozen to the power of 2 is a gross, a dozen^3 is a great gross, and a dozen^4 is a dozen great gross, and so on.

Hex^2 is is a byte, hex^3 is a hexabyte, and hex^4 is a block, hex^5 is a hexablock, hex^6 is a bytablock, hex^7 is a hexabytablock, and hex^8 is a blockablock.

The important part for binary is understanding the powers of 2. 16 is a power of 2, which is why it is so easily translated to binary.

In dozenal or hex, when writing with numerals, you have 12 or 16 symbols to choose from, representing nothing through eleven and fifteen, respectively. In the ones place you have how many ones, up to the max for a single digit, and any more than that is represented by a second digit in the next place value next to the ones digit saying how many dozens or hexes are added to the ones.

This is very much like the hand counting system I described, with each digit representing zero through eleven or fifteen. You can only count up to eleven or fifteen of dozens or hexes, and eleven or fifteen ones added, before you need another place value digit next to the dozens or hex place to represent how many gross or bytes are added. Then another digit to represent how many great gross or hexabytes, then another next to that that represents how many dozen great gross or blocks, and so on, until you have enough digits to fully represent the value of your number.

Each place value represents how many of a specific power of the base number are added to the value. The ones place is how many hex^0 there are, the hex place is how many hex^1 there are, etc.

Binary is the smallest base, with only 2 digits: one and zero. Each digit works the same way as other bases, as each digit represents how many of a power of 2 are added to the value, but each digit can only be one or zero, each digit only represents whether that power of 2 is added to the value. Each binary digit of zero or one is called a bit.

So, twelve would be 1100, as twelve is one eight (2^3), one four (2^2), no twos (2^1) or ones (2^0)

Binary, as each digit only represents a presence or absence, can use much simpler numeral symbols. The best way to do this is with long and short lines, where each long line is one and short is zero, stacked sideways next to each other. This lets you write them closer together than can be done with larger bases. But, with long numbers this becomes hard to read, so you break up the binary number into groups of four bits with horizontal lines drawn beneath the groups of four bits to make it easy to read.

The important part here is that each group of four bits represents a value of zero through fifteen, and is mathematically identical to a hexadecimal digit in its place. This only works for powers of two as a base, it also works for base 8.

So, all you need to write numbers in binary from hexadecimal, is to write down the binary for each hexadecimal digit one after the other, in the same order. This is impossible in any base that isn't a power of 2.

For reference,

zero is ....

one is ...l

two is ..l.

three is ..ll

four is .l..

five is .l.l

six is .ll.

seven is .lll

eight is l...

nine is l..l

ten is l.l.

eleven is l.ll

a dozen is ll..

thirteen is ll.l

fourteen is lll.

fifteen is llll

and sixteen is l ....

The pattern becomes obvious now. If you do forget what a hex digit is in binary, you can just ask yourself: is the digit greater or equal to than eight, if yes the eights place is a one. If the digit is greater or equal to than the previous bit's value added to four, then the fours bit is a one. If the digit is greater or equal than the previous bits' values added to two, then the twos bit is a one, and the same for the ones bit as well.

For example, to find ten, it is more than eight (l...), less than eight and four (l...), and is equal to eight and two (l.l.) without a one added. So ten is l.l. and eleven is ten with one added: l.ll

Now you have an easily learned and teachable way to write numbers. You simply read and write hexadecimal as groups of four bits.

I can't elaborate much on WHY binary is the best for written calculations, due to the length limits of this message, but take time to think about why digits of only one or nothing would make the mathematics described by Junction much simpler. Try it out.

LoserThree said:

When would this be necessary?

And while I do understand what you mean, I will need to make glyph-work before I can be sure.

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For each digit, the only additions you need to know for this is how to count to three (a one in both numbers, and the carry one).

LoserThree said:

That is a debt. How is a debt a count of denial? Denying debts is, well, it can be useful. But surely denial of debts should not be the expected thing. Everyone wants debts to themselves to be redeemed, don't they? I do.

I don't know when I would need to work like this with numbers so large I need to put them in glyphs to do the work.

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If you have a number of fruits, and eat a number of them, subtraction lets you find how many you have left. This is useful with large stores of food, with many bytes of items to keep count of.

LoserThree said:

Eugh.

This time I do not think I follow what you mean. I may revisit this if I make glyphs work for me

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This is easier in binary. The process described is done that way because multiplication is really just repeated additions, and you can break up the multiplication into a sequence of much smaller single digit multiplications, and adding together the products of those single digit multiplications.

In binary, single digit multiplications are with only one or zero, so you add the multiplicand (number being multiplied) once for each one in the multiplier, with extra zeros at the smaller end based on the place value of the 1. Any number multiplied by zero is zero (zero groups of any number is nothing) and any number multiplied by one is itself (one group of the number).

There is also a clever trick called booth multiplication that can multiply any unbroken string of ones into one addition and subtraction, which results in binary multiplications usually needing less additions than dozenal, while also needing no carry multiplications.


If you can still hear me now, Bianca, then I shall continue in more detail as to how binary is greater than other systems of numbers for written calculations.


The common reason for this is that with all of the operations that Junction described, they achieve what they do with very large numbers by breaking apart those numbers into their digits, and doing calculations with sets of single digits in specific ways that are then combined back into larger numbers.


There is no simpler set of digits than binary.


For example, with carry addition, each set of digits can only ever add up to two, or three if there is a carried one from the previous digits. Anyone, even the slowest of children, can count to three. The tradeoff is that there are more operations, as there are more digits needed for the same value, but each operation is so much simpler and easier that the calculation ends up being faster, as you barely need to think at all for each operation, and you can do each operation in your head basically just as fast as you can write down each digit of the answer. Since you grouped the bits into fours, you can just read out the hexadecimal value of the answer.


Subtraction is similarly easy: if you need to borrow from the next bit, and the next bits of both the numbers are zero, or both one, the answer is one in that bit of the answer, and you borrow from the next bit over. If the next bits of the first number and the subtractor number are one and zero, the answer is zero and you stop borrowing and move to the next bits. If they are zero and one, then the answer is zero, but you keep borrowing. If you keep those rules in your head, you can subtract two numbers just as fast as you can add them.


Both of these can be done just as fast as you can write the numbers down once you have practiced them, as the individual operations are so simple you barely need to think about them.


But, both of those pale in comparison to how much easier multiplication is in binary, when compared to dozenal.


Firstly, to define some terms: The multiplicand is the first number being multiplied, and the multiplier is the second number that the first number is being multiplied by.


When you are doing the carry multiplications for each digit in the multiplier in dozenal, you need to do a one digit multiplication of the entire multiplicand, for each digit of the multiplier, and add all of those products together. This requires a complex carry multiplication of nines, sevens, fours, elevens or whatever the digits may be, one after the other, for the entire multiplicand, and do that process all over again for each digit of the multiplier.


You must also keep in mind that each digit of the multiplier has a place value, meaning that if you are multiplying some multiplicand by the four in four gross three dozen and two, you are actually multiplying it by four gross, not four, and why the result has two zeros in front of it. This is why you need to shift the starting bit over by the place value of the digit in the multiplier you are using.


By contrast, in binary, there are only two values each digit can represent: one and zero. So each digit of the multiplier multiplies the multiplicand by either one or zero, and any number multiplied by one or zero is either itself or zero.


So, you skip the complex carry multiplication in its entirety, and just add the multiplicand to the products below for each one in the multiplier, after adding the right number of zeros at the front to match the place value of the one. Then you add the products together with binary addition, and you have your answer. As you can see, this is MUCH simpler than it is in dozenal.


The downside of this is that there is an addition for every one in the multiplier, which for something like fifteen hex fifteen would be a lot of additions. Most of the time this is still easier than the alternative due to completely skipping the carry multiplications, but there is a trick I mentioned earlier that fixes this problem called booth multiplication.


Booth multiplication relies on a simple fact about binary subtraction: that a one followed by a lot of zeros, with smaller one subtracted from it, will result in a long string of ones whose largest one is one place less than the original one, and with the littlest one being in the same place value as the one that was subtracted.


I will give an example: eight hex with four subtracted from it is seven hex twelve.


In binary, that is

l... .... minus .... .l.. is .lll ll..


As you can see, a subtraction of a single bit from a lesser place value from a single bit of a higher place value with nothing but zeros in between, results in an unbroken string of ones starting at the smaller one and ending just before the place the bigger one used to be.


So, in multiplication, if the multiplier was seven hex twelve, you would normally need to add it once for each of the ones in that number. You can instead subtract it once at the place value of the smallest one in that unbroken string of ones, and add it once at the place value of the first zero following the largest one in that string, and get the same number, as they are mathematically equal to each other.


So, when multiplying binary numbers, multipliers with the longest unbroken strings of ones are actually the easiest to multiply, because any unbroken string of ones can be multiplied with only one subtraction followed by one addition.


This trick usually results in the same number or even less additions and subtractions than there would be additions in dozenal, and each addition and subtraction is easier in binary than the additions are in dozenal, and you don't need any carry multiplications.


So even in the absolute worst case of the multiplier being nothing but alternating ones and zeros where booth multiplication can't be used, it still ends up being faster and easier than dozenal, because there is no complex carry multiplications needed for the products that get added together.



Long division is not as greatly simplified by binary as multiplication, outside of the subtractions that are a part of long division being simpler and easier, but the part of long division that requires you to test hoe many times the divisor fits into a part of the dividend is made irrelevant, as it can only fit or not fit once, as the quotient produced is in binary, but it is otherwise the same process.




I will now speak on the subject of geometry and the various ways we have of precisely defining shapes with numbers.

The first thing that must be made understood is the concept of a unit of measurement.

A unit of measurement is a precisely defined measure of a property of a physical object or substance, that is used as a reference to measure the difference between itself and the object or substance being measured.

For example, a unit of measurement for length in our world, the meter, is defined as the distance needed to draw a circle around the earth (a consistent and constant value to all people living on our world) divided by exactly two bytablock, six hexablock, two block, five hexabyte, and ten byte. This number makes a great deal more sense when using a base ten number system, as it is exactly four times ten thousand thousand. For scale, a fully grown man is usually between one and a half and two meters tall, with the average height being somewhere between one and two thirds and one and three quarters meters tall.

Everything to do with length or size can be measured as a certain number of meters or parts of meters, and as everyone in the world agrees on the exact length of a meter, when someone says to a craftsman "I want a spear shaft exactly two meters long" the craftsman can make them a spear shaft of exactly the length they wanted, without needing to do any pointing or gestures to demonstrate the size. In fact, this can be done without the people even meeting in the first place, and the request for a spear shaft is given by written message.

This is important, because the making of certain tools and devices requires parts to be made a very specific size and shape, and if they are not the tool or device will not work. These sizes can no longer be measured or described by finger widths and hand spans, as the difference in size between different people will make the sizes wrong.


The actual unit of measure you use for the purpose of measuring lengths doesn't really matter, so long as everyone using it agrees on what the exact length of that unit is. For the purposes of teaching you geometry, I am not going to use any specific unit at all, I will just call it a 'unit' or 'unit of length.' At a later time I will dive into greater detail on the lore of measurement and what the best measures for you to use would be. I will still give lengths, as relative differences between lengths are a core part of geometry, but the units those lengths are in are irrelevant to the methods of calculation.


For the purposes of measuring things, and using these shape calculations for practical purposes, you just need to measure with a consistent measuring unit, such as the length of your foot or arm, and divisions of that length. You won't need anything more precise than that for some time, and I will explain what is needed then, as I have already said.


The other unit that I will define here is that of angles. Angles are a precise measure of rotation, and we will need much more precise terms than "a quarter turn" if I am to describe the lore of geometry to you.


There are two common measures of angle that our people use, that of degrees, and of radians. Radians are difficult to explain, and not very useful unless you are already very deep into the lore of geometry, so I will only describe degrees here.


A degree is one part in one byte, six hex and eight (or two gross and six dozen) of a complete rotation. This particular division was chosen because it divided evenly in a great many ways. So, a full rotation is one byte six hex eight degrees, a half rotation would be eleven hex four degrees, and a quarter rotation would be five hex ten degrees, and an eighth of a rotation would be two hex thirteen degrees. A quarter rotation is called a 'right angle,' and is the angle something that is pointing straight up makes with flat and level ground.




A third of a rotation would be seven hex eight degrees, one sixth would be three hex twelve, and one twelfth would be one hex fourteen degrees. One fifth of a rotation would be four hex eight, and one tenth of a rotation would be two hex four degrees.


A dividing circle is a circle used to measure angles, with divisions marked around its edge and a defined center point to rotate angles around.


In the world of pure geometry, there are no inaccuracies, there are no forces or friction or indeed even time. Those worldly concerns are irrelevant to the mathematics of how shapes are defined with numbers. There are only absolute truths and axioms, and their derivative conclusions, to guide our knowledge here.


Let us begin with the definition of a point. A point, is a precise location in space, with no size or any dimension at all other than its own perfectly precise position.


Lines are infinitely long threads that are perfectly straight, and whose position is defined as a line that passes through two points. Their true essence is actually as a collection of all infinitely many points that are on that same line.


A plane is an infinitely thin, perfectly flat surface that extends forever in every direction, whose position is defined by three points it passes through which are not on the same line. If they were on the same line, the plane could freely rotate relative to that line as an axle, and its position could not be known. A plane's true essence is that of all infinitely many points that are on that same plane.


A line segment is a part of a line that is constrained in length by two endpoints.


A curve is sort of like a line, in that it is defined by a set of points and a relationship between those points, and that the essence of a curve is that it is all infinitely many points that are on that curve, but the path a curve takes through space is defined by the particular mathematical relationships that define the curve, of which there are countless kinds of curves.


A flat surface is a section of a plane that is constrained by lines and/or curves to a finite shape.


With those definitions established, I will define some simple relationships between these things.


When a point is collinear with a line segment, it means that that point falls on the line that line segment is a part of.


When a point or line or flat surface is coplanar with a flat surface, that means it is on the same plane that flat surface is a part of.


Lines and planes intersect when they are not collinear or coplanar, but there are points (or a line in the case of two planes intersecting) that are collinear or coplanar with both of them. Essentially, two lines that cross at a point, or a line crossing through a plane, or two planes crossing each other. The point of intersection (or line of intersection in the case of two planes), is the point or line that is collinear or coplanar to both the intersecting lines or planes. Angles between intersecting lines or planes are taken with the point or line of intersection as the center or rotation of that angle. In the case of two lines, the imaginary dividing circle measuring their angles is coplanar with an imaginary plane that both lines are coplanar with. In the case of a line intersecting a plane, the imaginary dividing circle is coplanar with a plane that is perpendicular (this is defined later) to the plane being intersected, and also coplanar with the line intersecting the plane, and the dividing circle is centered at the point of intersection. In the case of two planes intersecting, the dividing circle is centered on the line of intersection, and is perpendicular to the line of intersection (again, this is defined later).


The complementary angle is the angle which is adjacent to the angle you are measuring on two intersecting lines, and adds up with the angle you are measuring to eleven hex four degrees, or a straight line.


When two lines or planes are parallel, that means they will never intersect each other. All points contained within them will remain the exact same distance from the closest point on the other plane or line. When line segments or flat surfaces are parallel, that means the lines or planes they are a part of are parallel. Essentially, they are pointing in exactly the same direction with an angle of zero degrees between them, but they are not collinear or coplanar.


Two lines or planes that are perpendicular, intersect and are at right angles to each other. Line segments or flat surfaces that are perpendicular are so if the planes or lines they are a part of are perpendicular. A line can be perpendicular to a plane, as a line can be at right angles to a plane if it sticks straight out of it like a perfectly straight stick that is pointing perfectly straight up from perfectly flat and level ground. A plane is perpendicular to a stick in the same way.



With those definitions established, I will now begin defining the simple flat shapes. Assume they are constrained to a single plane, and all points and lines and curves are coplanar within each shape.


I will define the components of shapes.


An edge: An edge is one of the lines or curves that make up the boundaries of a shape.


A corner is a point where two edges intersect at their endpoint.


The inside of the shape is the area constrained by the edges of the shape, with a finite size.


The outside of the shape is the area unconstrained by the edges of the shape, with infinite size unless constrained by another, larger shape.


Now onto the shapes themselves.


Firstly, the circle. The circle is made by a curve of all points that are the same distance from the center point of the circle, that are on the same plane as the center point. The radius of a circle is the line segment that has one endpoint as the centerpoint of the circle, and the other endpoint is on the edge curve of the circle. The diameter of the circle is the line segment that has both endpoints on the curve of the circle, and also contains the centerpoint of the circle. It cuts the circle exactly in half, essentially. The tangent of a circle is the line which is collinear with one of the endpoints of the diameter, or the edge endpoint of the radius, that is perpendicular to the diameter or radius. For example, a perfect circle rolling on perfectly flat ground (not necessarily level, but flat. The ground could be tilted this way or that, so long as it isn't curved) would have the ground be tangent to the circle.


Next, polygons, or sided shapes.


A triangle is a three sided shape made up of three line segments with three corners where those line segments intersect at their endpoints. The three angles of the inside of the edges on a triangle will always add up to eleven hex four degrees, or a half turn. This is true no matter the proportions of the triangle. A triangle is actually completely defined in shape by the length of its three sides, or by any two of its corner angles, as finding the third is as easy as subtracting them from eleven hex four. This is why making structures made from sticks attached at their ends are strongest when the shapes the sticks make are triangles, as the joints between the sticks don't have to resist rotation, as the fixed lengths of the sticks will resist rotation of the corners.


A quadrilateral is a four sided shape with four corners. The four angles of the inside of the edges of a quadrilateral will always add up to one byte six hex and eight degrees, or a full turn of rotation, no matter the proportions of the quadrilateral.


Any irregular polygons have total internal angles of their number of sides, minus two, multiplied by half a turn, or eleven hex four degrees. For example, a pentagon, or five sided shape, has five sides, subtract two and you have three, and three times eleven hex four degrees, makes two byte, one hex and twelve degrees of total internal angle.


As irregular polygons beyond triangles and subsets of quadrilaterals are difficult to predict and calculate, I will stop here with them and move onto regular polygons.


Regular polygons are polygons with sides of all the same length, and equal angles at all of their corners.


An equilateral triangle is a triangle with three equal sides and angles. The angle of all three corners is three hex twelve degrees.


A square is a quadrilateral with four equal sides and angles. The angles of its corners are all right angles, and as a result all of its sides are either parallel or perpendicular to each other.


Higher sided regular polygons don't really have any additional properties that matter to you for the moment.


I will now speak of the various types of partially irregular quadrilaterals and of the properties of right angle triangles, which have more practical applications in the real world.


Firstly, the rectangle. The rectangle is essentially just a square if the sides were no longer all equal, but the four right angles at the corners remained. The sides are still all parallel or perpendicular with each other.


Next, the rhombus. A rhombus is essentially a square with no defined angles at its corners, but its edges are still parallel with their opposites, and are all of the same length. Angles that are opposite corners from each other are the same angle, and angles which are not opposite each other are complementary angles.


Next, the parallelogram. The parallelogram, as the name would suggest, is a quadrilateral with parallel sides like the rectangle, but without the right angles in the corners. The angles follow the same rules of equal and complementary angles as a rhombus.


Finally, the trapezoid. The trapezoid is a quadrilateral with only one pair of parallel sides, and no other limits on its proportions.


Next, we have the right triangle. The right triangle is a triangle where one of the corners is a right angle. This type of triangle has some special properties, in particular that knowing the lengths of any two sides is enough information to define the triangle using what is called the pythagorean theorem: for the two smaller sides that end at the right angle corner, when each side is multiplied with itself and added to the other side that was also multiplied with itself, the resulting number will be equal to the third side opposite the right angle corner multiplied with itself. To actually calculate the third side, you need to find the square root of the resulting sum or subtraction, which is why being able to do square roots is useful. One can use right triangles to calculate distances between distant objects if you can measure the angles between them and one of the sides of the triangle. There is an entire field of geometry called trigonometry that focuses on the study of right triangles and the various calculations that can be done with them, of which there are many practical uses for.


Now, I will begin defining terms that will be things you may want to calculate about the various shapes I have described, in particular the perimeter and the area.


The perimeter of a shape is the total length of all its edges, whether they are curves or lines. For polygons, measure the length of all their sides and add them up. For circles this is more complicated, but I will describe that later.


The area of a shape is somewhat more complicated to explain. Imagine a square with a side length of one unit. This is called a unit square. It has an area of one square unit. The area of any shape is how many square units and parts of square units can fit into that shape. This becomes a very important question when you are trying to measure the size of a field of crops. Other voices have mentioned 'acres' as a unit of measuring how much land there is to plant with crops. An acre is one such unit of area. Though usually area is measured in terms of a length unit 'squared'. Such as, feet squared. A square foot would be the area of a square with the side length of one foot.


This is why taking a number to the power of two is often called 'squaring' the number, as to calculate the area of a square, you multiply the side length by itself.


The area of a rectangle is its length multiplied by its width, or the length of two perpendicular sides multiplied together. You may notice that if the rectangle had equal sides like a square, that its length and width would be the same and would multiply one side length with itself.


The area of a triangle is the length of one side, multiplied by the length of an imaginary line that intersects the opposite corner to the side we are measuring, which is also perpendicular to the side we are measuring, and divide the product in half. The easy way to visualize that is imagine you are standing the triangle up with one side on the ground. You multiply the length of the side that is on the ground, with the height of the top corner, and divide the result in half to get the area. The easy way to remember it is one half of the base times the height.


The area of all other polygons amounts to various ways of cutting up the polygon into sections of rectangles and triangles that you calculate the area of and add all those areas up. But there are some compressed versions of these area calculations for common polygons I will tell you.


Firstly, the parallelogram and rhombus. They essentially use the base times height formula of a triangle, but without the halving. You measure the length of one side, and the length of an imaginary line segment perpendicular to that side which ends at a point collinear with the opposite side, and multiply them together.


Next, the trapezoid. Any trapezoid has the same area as any other trapezoid with the same lengths of their parallel sides, and the distance between those parallel sides. So let us call the longer of the parallel sides the base, and the shorter parallel side the top. The height is the length of an imaginary line segment which is perpendicular to the parallel sides, whose endpoints are collinear with each parallel side. The calculation of a trapezoid's area is the height multiplied by the top, added to the product of the top subtracted from the base, multiplied by half the height. For this, remember that any trapezoid with the same length base and top and height has the same area. So all of them have equal area to a trapezoid with one side perpendicular to the parallel sides. Such a trapezoid is essentially a rectangle with the area of the top times the height, with a right triangle of the same height but with a base that is the difference between the top and base of the trapezoid stuck to one side. Hence why you calculate the area of a triangle with a base of the trapezoid's top subtracted from its base and the same height as the trapezoid, added to the area of a rectangle with the length and width of the top and height of the trapezoid.


Finally, the perimeter of a circle. This is somewhat complicated by the fact that the edge of a circle is a curve. However, we have found an exact constant called pi. Pi is a number that when multiplied by the length of the diameter of the circle, will result in the circumference of the circle, which is what the perimeter of a circle is called.


Pi is a very, VERY long number (which is actually infinite in length) that is between three and one eighth and three and one quarter, and is what is called an irrational number. Irrational numbers are numbers that are not whole numbers, but are also not the result of the division of whole numbers. They keep adding more and more digits forever after the less than one point (called the radix point, when not referring to a specific number base) that was previously mentioned by the other voice that explained written division, but there are no repeating digits. Pi can only ever be very closely approximated, and never precisely calculated as a result. A reasonable approximation is three and one seventh, or one hex six divided by seven. In the case of representing one seventh by radix point, that would be approximately (as one seventh in hex is a repeating heximal) three and two sixteenths or hexths, four byths, and nine hexabyths. Spoken more quickly, three point two four nine.


The more accurately calculated version of pi itself and not a close fraction, which is a worthy thing to try to remember, is three point two four three fifteen six ten eight eight eight five ten three zero eight. At least, try to remember up to the three eights in a row, as they are easy to remember. That number, three point two four three fifteen six ten eight eight eight, is far more accurate than anything your people will need for many many generations, and for all practical purposes is closer than you could ever need to the actual value of pi. Any more digits than that is more of a curiosity than anything else.


However, it is generally much easier to simply multiply by one hex six and divide by seven than it is to do the full radix multiplication with pi, which I now realize we have not described any means to do so, so the one hex six divided by seven option is the best available to you.


I shall now teach you how to calculate the area of a circle. This is somewhat more complicated than polygons, as in order to calculate the area of a circle you need pi, but outside of that it is just like finding the area of a square. To find the area of a circle, square the length of the radius, and then multiply that by pi. The area of a half circle or quarter circle is just the area of a circle divided by two or four, or by whatever fraction of a circle you are finding the area of.

The area of a rectangular doorway with an arch at the top, would be the area of a reactangle with the width of the door, and the height of the arch subtracted from the height of the doorway as the length of the reactangle, with the area of the half circle of the arch added.

For circular curves that have corners on the shape, simply calculate the slice of the circle that would be required for that outer or inner curve, and then calculate the area of the rest of the attached polygon as if it had a big triangle taken out of it. For inward circular curves, imagine the slice of the circle needed for it, then add an imaginary triangle to the now irregular polygon to fit that slice of the circle in, and calculate the area, and then subtract the area of that slice of a circle.

Essentially, if you have an irregular shape with many inward and outward curves and sides, create imaginary circle slices either added or subtracted from the shape to turn the shape into a polygon, and calculate the area of that polygon, and subtract or add those slices to that area to find the area of the actual shape.



I will end this communication here, and leave the description of the volumes of three dimensional shapes (meaning shapes that are more than just lines on a plane, like cubes and balls and the like) for next time, as I feel our time is growing short, and the volume of shapes is no simple thing to describe with the rigor deserved of such a thing.

On the matter of boats, the pontoon may be a simple improvement that is easily available.
That is, take a boat - perhaps a hollowed log, perhaps a raft - and then attach, some distance away, on opposite sides, smaller hollowed logs or other boatlike things. That way, if the boat tips, it would push the log down into the water, forcing it back up and keeping it from tipping, making it much more stable.

This works best, of course, if those pontoons are hollow but sealed - hollowing a log then capping the hole by which it was hollowed, though it can also work if they're simply open to the top, or otherwise something that naturally floats.

Virian said:

I don't see why not? The heroine gets an action, the people are told how to act with the bog iron, the Plunder is a single big action that might take a few days tops and the syphoning of power is the one that probably takes the longest.

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"Bolded options will take up so much of Bianca's time that she won't have time for another bolded option. If the bolded option wins more than one category, only the bolded directive with the most votes will be followed. If no bolded options are chosen, Bianca will put more time into the player advice that most interests her."

liberty90 said:

"Bolded options will take up so much of Bianca's time that she won't have time for another bolded option. If the bolded option wins more than one category, only the bolded directive with the most votes will be followed. If no bolded options are chosen, Bianca will put more time into the player advice that most interests her."

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I'm fine with it then

devilgirl666 said:

By telling stories, spreading messages, carving symbols and stories onto wood and stones, and setting an example, you can influence the thoughts and actions of the people. This will help you build a strong and united empire where most works together for the common good, and for Bianca, under supreme leader Bianca.

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Once again putting the horse before the cart except horses have not been domesticated and carts not invented. Hell, they might not even have the wheel.


[X] [Solstice] Make a false stone on a nearby hill
[X] [Blight] Just kill the monsters
[X] [Theroriparian] Send the Heroine to deal with it
[X] [Bog Iron] Give mortals half the iron from what they bring

Can bianca kill the monsters and brick up the opening?

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Greetings Bianca, this is Destroyer.

I have come to tell you of a means of moving water uphill from a river, without any effort of your people after the device is built, and secondly of a simple device of measuring changes in air pressure. I will also provide a note on why certain things float and others do not, and a description of Archimedes' principle.


There is a pump system that Bianca's people could use called a hydraulic ram pump, one that uses almost no moving parts, just two one way flapper valves like there are on blow-bags. This system requires no extra effort or mechanisms in order to pump, so long as there is an available stream it will endlessly pump water uphill through a clay pipe using the flowing motion of the stream as the source of power needed to pump the water.






I will now explain the principle of operation. So, firstly, everything that has mass, meaning everything with weight, which obviously includes water, has a property called inertia. Inertia is the property of mass that means it takes effort to make the mass move, and it also takes effort to make the mass stop moving once it starts moving. The effort needed to bring a running man to a stop can be applied by either his legs or by the ground if he trips and falls. When a man falls while running on soft dirt, he leaves behind a furrow of dirt where he slid to a stop on the ground. Digging up and moving this dirt out of his way required effort, effort that the motion of his body provided until his body ran out of motion and stopped.

The hydraulic ram pump takes advantage of the fact that moving water has inertia, and thus it has effort stored in its motion that takes time and external force to stop.

By cleverly using two one-way flapper valves in a pipe with moving water, we can take some of the energy in the motion in the water and turn it into hieght of water pumped uphill.

You need to pick a good spot on or near the river, specifically a place where there is a relatively fast drop in the height of the water, at least one man high, preferably two, over a distance of five or six men laying down end to end. A short waterfall would be ideal, but not needed. Then, make a long tube five or six man-height long and place one end in the river upstream to provide the inlet of the water. If you are using a waterfall this can be much shorter, the requirement here is to get the difference in height at the outlet end. Run this pipe next to the river downstream to the spot you picked. Water should be rushing out of this pipe constantly.

A note: all clay pipes and pots and such used in this should be glazed for waterproofing.

Next, we can begin constructing the ram pump. First, we make a large, tall pot to act as the air spring and water tank. This pot is meant to be upside down, with its openings near the bottom, with no openings near the top.

There are two openings here, one in the center of the bottom, and one on the side near the bottom, this one is where the water gets pumped out of. Make a flapper valve like what is used on blow-bags to fit the center bottom hole, to only allow water into the bottom of the pot. It would be wise to use tanned hide on the sealing surface of this flapper.

Next, we make another smaller pot with one hole in the side that fits the pipe coming from the river, one hole in the top that is meant to be fit to the bottom hole on the upside down pot, and one more hole in the other side from the pipe input hole, this one gets fit with the second flapper valve, and this one flaps into the pot so water can't get out of the pot from this valve, but can come in.

Now, seal the bottom hole of the top pot to the top hole of the bottom pot with clay, and then take the upstream end of the pipe out of the water until water stops flowing out of the pipe. then, seal the end of the pipe to the side-hole in the bottom pot that doesn't have a flapper with clay and let dry. Then connect another pipe to the side hole in the top pot, and make that pipe go to where the water is needed elsewhere.

Then, build a fire to fire all of this to seal it and make it sturdy, and place the end of the inlet pipe back in the river. The water will rush in through the pipe, and when it meets the side flapper in the bottom pot it will be stopped, and rush up through the upper flapper into the top pot. Once the water in the top pot rises above the level of the hole in its side, the air trapped in the top pot is sealed. The more water is pushed in, the more the air compresses, until the rushing of the water can no longer push any more, and the air pushes the water back down. The water is pushed back down through the bottom pot and back up the inlet pipe some, and its motion opens the flapper in the lower pot. with that flapper open the water then rushes out the side hole in the bottom pot until that flapper closes, but now the water has forward inertia again, and so with nowhere else to go it rushes up into the top pot again, and the process repeats indefinitely.

This can pump water hundreds of paces uphill and away. This makes for a very convenient and useful way of irrigating fields that are uphill and away from the river.

A note: you should not use the bad water with no frogs for irrigation, as the poison might be taken up by the plants you are growing.

Note 2: if the pump stops cycling for some reason, or needs to be restarted, simply pushing in the lower side valve that water spills back into the river out of with your hand or a stick for a few breaths and then releasing it will restart the cycle.


Now, to describe the construction of a barometer:

First, make a tube with an inner width of roughly the length of your little finger, about as long as your arm, and straight as possible. At one end of the tube, make some finger width notches (press your finger in the edges of the tube end in three or four places) in the end of the tube.

Second, make a pot about two hand lengths tall and wide, tapering to a hole at the top that is a finger width wider than the outside of the tube, so that the tube can be easily sealed to it with clay.

Next, insert the tube into the hole of the pot, and have the tube go all the way down to the bottom of the pot, with the notch-end first. The idea here is so that water has to go all the way down the tube and through the notches to flow into the pot. Next, seal the hole of the pot to the tube with clay, and fire the thing.

All parts of it should be glazed for waterproofing.

Next, the float indicator.

The purpose of this device is to fill it partway with water, so there is trapped air behind the water, and the expansion and contraction of air as pressure changes will be shown by the water level in the tube rising and falling.

In order to more easily see the changes in water level, we need a float with a long, thin stick, just a bit longer than the tube is. A small block of wood that fits easily in the tube would work, as would a hollow bulb of glazed pottery that is sealed around the stick.

The float has the stick attached to it, so you measure how far the stick pokes out of the tube to measure the water level.

To aid this measurement, add notches to the stick, about a little finger width apart, all the way up the stick. This lets you just count how many notches are out of the tube to measure the water level. Make a thicker notch every four notches to make it easier to count.

Then, fill the tube most of the way with water, then put your mouth on the end and suck. This will pull the water up the tube, and the water in the pot down through the notches at the bottom of the tube, until air starts being sucked under the notches. This will reduce the amount of air trapped in the pot to a more useful level.

When you stop sucking, the water level should be lower than before.

Drop the float with attached notch-stick into the tube, and record how many notches are sticking out of the tube.

Then come back several times during the day, and every morning and evening, and write down the number of notches. My previously described binary writing of numbers is very good for this.

If the number of notches has decreased, air pressure has risen and pushed down the water. If the number of notches has increased, then air pressure has decreased and the trapped air has pushed up the water.

If the air pressure drops quickly over the course of a day or so, you have a storm coming.

Air in the open can expand and contract and move about as it wills, but the trapped air is held inside the pot by the water. It will still expand and contract, but water doesn't. So the water is pushed up and down the tube as the pressure changes.


Next, I will describe why things float, and how this can relate to boat building.

Firstly, things float because water is heavy and wants to flow down. How does this push things up? This is simple. Water is incompressible, meaning it does not expand or contract outside of changes in temperature.

If you fill a pot with water, and push your hand into the water, the water level in the pot goes up. Your hand displaced the water, and in order to push the rest of the water up, you had to push your hand down with enough force for the water it displaced to be pushed up.

When something is lighter than the amount of water it displaces, its weight cannot push the rest of the water up all the way for it to go completely below the water, and so it displaces the amount of water that is equivalent to its own weight, and the rest of it floats above the water's surface.

A stone sinks because it is heavier than the amount of water it displaces.

The same is true of boats. You can, in fact, make boats out of stone or metal, so long as there is enough air inside the boat to make the whole boat lighter than its displacement. So long as the boat is water tight, and water is kept out of the inside, it will float. Most of the boats our people use are metal, especially the largest ones are always made of metal. But, if there is a leak in the hull of the boat, and too much water gets in, the amount of air inside the boat isn't enough to keep the boat afloat and the boat will sink.

Much of the buoyancy of your new canoes is not from the wood, but from the air inside the canoe being lighter than water. Wood floats because it has lots of little air pockets inside of it that lower its density (which is a measure of how heavy a certain volume of material is, higher densities being heavier for the same displacement).

So, to make better boats, increase the volume of air inside of them relative to their weight.

I hope this assists you in your endeavors, Bianca.

@LoserThree

Hail Bianca!

I, Rafin return to answer questions you posed to me.

Farming, when done correctly and using technology, creates surplus food enough that some people need not busy themselves with food collection at all. They have time to learn and create many things instead. Also, as people defeat disease and hunger and keep animals and enemies at bay, their lives become longer. It's in such a situation that reading and writing become truly worth utilizing. You already don't busy yourself with feeding yourself and you already discover novel things and pursue ambitious goals. So writing already has use to you.


If the sorrows of mortals are truly unimportant to you, why does their wailing feel like a heavy burden? Enduring it and faking empathy is a skill like any other. Also, if any mortals grow to love you like a parent or grandparent, they will teach this love to their own children. If they think you will love and protect their children and their children's children then they might even gladly lay down their lives for you, knowing that it will enable you to look after coming generations better, just like a childless person might sacrifice themselves for the family of their siblings.




"Sharpener" is not a good translation for the word I used. In our language the root of the meaning is more akin to "sour-source". This is because when the substance was first discovered it was known as a component of all known acids. Only later did it become known that it is more generally the fuel for fire and life. To explain where it comes from and where it goes I will have to explain the basics of substance-composition lore.

All tangible non-magical substance is made out of basic building blocks of which over two hundred are known to us. These building blocks can connect and fuse in varying ways under varying conditions forming new substances with wildly differing properties. These combination substances can be further combined or break apart in other conditions. But the basic building blocks themselves are the smallest things that still hold distinct properties as tangible substances and breaking them apart is very very difficult and very very destructive. On the whole world the amount of each of these remains mostly the same. Only little rains down from the void beyond the air in the sky and only few of these break down and decay over a long long time. We call the basic building blocks "elements".

Oxygen ("sour-source") is one of these elements, the sixteenth as we have decided to count them. It does not get consumed, neither by fire nor by life. Instead it gets combined with other elements, often with heat and sometimes with light as a byproduct.

A very common combination is with carbon, the sixth element, most visibly encountered as coal. Carbon is the most abundant building block of life, a major component of every part of every plant and every animal. The air carries plenty of carbon particles combined each with two oxygen pieces. When something containing carbon, like a piece of wood for instance, is sufficiently heated or subjected to a first spark or ongoing flame, the carbon combines with the free oxygen in the air. This produces more heat and light, thus making more carbon nearby combine with more oxygen. This is the most common form of fire.

Another common combination of oxygen is with hydrogen (meaning "water-source" in our language). Hydrogen is the first element. It is the smallest and lightest of all the elements. The combination of two parts hydrogen and one part oxygen is known as water. This is how pure water is made. Water is found in a lot of places, both inside and outside of living things. Hydrogen burns very easily, but is rarely found freely in nature. Even if one were to find it, pure hydrogen is invisible and lighter than anything else in the air. Still, when hydrogen burns, water vapor is the result.

Carbon and hydrogen often bond in many complex ways. Fats, oils, sugars, starch and fibers all are complicated combinations of mostly carbon and hydrogen. As are those airs that come from the earth and are flammable. As are farts. You can set fire to farts. It is a silly and risky game.

When a living thing breathes in air, the lungs draw oxygen from it, which the blood then carries to all the parts of the body that need power (be it heat or movement) to work. There it gets combined with carbon-hydrogen substances (and sometimes with other things) that the body gets through food and burned in miniscule fires to power everything the body does. Carbon-oxygen is a waste product. It gets carried back to the lungs by the blood and then expelled as the living thing exhales.

Plants do not eat carbon-hydrogen things. Instead, the green parts (and sometimes other colorful parts) of a plant take carbon-oxygen (the waste air from breathing) and hydrogen-oxygen (water) and combine them into carbon-hydrogen (sugars) to store and distribute as food for the whole plant and all its functions. The excess oxygen then gets expelled. This process does not produce heat and is not self-sustaining. Plants use the light and heat of the sun in order to forge the sugar they need.

So as long as there are enough plants in the world there is enough free oxygen so that breathing is possible.


Stain too is a combination of carbon, oxygen and hydrogen. When you talk of making it stronger, you are actually separating it from parts of the water it is mixed with, thus getting liquids containing more and more stain and less and less other things (like water).

Separating oxygen from the rest of the air is a very difficult procedure. In our world one way it is done is with a device so cold that it makes the substances of air become liquid the way water vapor becomes liquid when cooled. All the substances of the air become liquid at different temperatures of cold, so by catching one liquid after the other and locking it in airtight containers, you get fairly pure concentrations of each separate substance of the air. I would not know how to make such a freezing device with the tools you have at hand. Not for a long time. Maybe there is an easier way not known to me.

We Just Write said:

This can be avoided if much of the top levels of government are decided by votes of the state's people, instead of being directly chosen by you. To avoid problems of coerced voting getting scumbags into power, votes should be conducted such that who voted for what person is not known by any except the voter in question. Though counting the number of voters and making sure it matches the total number of votes is still a good idea.

It is also good that those voted in only hold their position for a set number of years, needing to be voted again in order to keep their position of power.

We will also introduce a related concept: federalism. The farther away from the center of government, the harder it is for the government to directly govern a given place. This problem can be mitigated by having local governments that only govern specific regions within the state as a whole, having their own voted officials while remaining answerable to the central government. These places with local government can then also vote representatives that they send to the central government every few years, participating in its affairs.

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With my final words I, Rafin, wish to express disagreement with Junction.

The only reason for Bianca to create a state is for her to get more of what she wants. The state's ultimate purpose would not be to better the lives of all its members. A system of voting in the people who hold power is not conductive to that. It makes the people think that they are the source of the power of government and that their needs are the highest good. But it is not so. Bianca is the fulcrum of all power. Any state she founds has her will as the final reason for its existence. Any system of governance must be constructed with that in mind.

Elections of representatives can still have value. But they can't be the bedrock of the government and they can't be the sole wielders of coercive power. If nothing else, it would be a lie. For if Bianca wishes to use coercion for some purpose, none should presume to stop her. And if Bianca falls in disfavor among elements of this government, attempts to enforce laws upon her are absurd. On the small chance that she creates a state that can actually resist or coerce her, she would have created the thing she hates most in this world. An entity that is over her, that she has to supplicate to survive.

Surely, Junction, you cannot want such a thing?

And with that, oh Bianca, I cannot promise that you will hear more of my words before the next summoning of the Cacophony. Such is the fraying of the mirror's channels. Farewell, and may your progress be glorious!

1941 + 59 = 2000 words.

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Junction speaking in reply to Rafin. We openly admit that our primary goal is to improve the lives of those in Bianca's world; most of the time, this also helps Bianca.

And you do have a point about possible issues of statecraft; we simply meant for the voted people to avoid the problem of yes-men and reduce resentment.

There are not enough people. We did this the last time too. This is an area of stuff we can't rush because societal complexity requires a surplus of people to be complex.

Honestly, it makes more sense to wait until people start forming their own complex systems and then improving those.

Yop

The Chicken can be found in southern, and eastern lands, where summers are long, and it rarely freezes. Look for Bamboo trees and forests, and your in the right part of the world. Bamboo is a very tall, but thin trees that are generally hollow on the inside. They grow in a cycle spending 5 years spreading their roots, then leap upwards 15 men high over the course of 90 days. If the local people report of the ground being covered by seeds dropped from bamboo once a generation, you will find chickens. More features of the chickens is that while birds they are poor flyers, spending their time on the ground looking for insects, and seeds to eat.

3ba

Rafin said:

@LoserThree

Spoiler: ooc

I have a question regarding the in character purpose of this chapter. The first part of the chapter represents what Bianca did during or right after listening to the cacophony. She replies to what we say and asks clarifying questions for the future. But it is the second part, the report of her actions over the last couple centuries, that trigger the sacrifice of choice.

So my question is this: What caused Bianca to contact us this time? Nothing in this second part is phrased as a question, let alone an important question that would make her seek our aid. So why did she summon us? It can't just have been because she finally wants answers to the clarification questions of the first part, or else why would she have waited ~200 years for that? I also don't believe it was to give us those actual four choices. She isn't indecisive normally and only leaves those up to us as fuel for our summoning. Does she just want something to do, some new hooks in her quest for power over substance? If yes, wouldn't she say so? As is, it seems more like someone calling to tell of all they accomplished. Is her relationship to us already warm enough that she would pay so dearly for a friendly call?

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This is Destroyer, once again. I come to speak of bows, and charred coals, and pulleys, and metal thread.

LoserThree said:

I took up bowyery, as Destroyer suggested. I did eventually make a bow longer than I am tall and which requires all my strength to pull. It was impressive and others have made useful bows of that size since then. With iron heads and feathered tails, their arrows can mortally wound large beasts. They only need to follow the beast until it drops. And, of course, they may still need to drive off their dying prey's companion beasts. But once the beast falls they have time to start a fire and prepare torches, which nearly all beasts flee from.

But my great bow did not last long. And I did little with it. I am good enough with a sling.

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The advantage of the bow over the sling is simple: when the archer is skilled enough, they can shoot three to five times with every breath. The bow, when properly mastered, is very, very fast.

I will not deny that a sling is a fearsome weapon, but for most purposes a highly skilled archer with a good bow is far more fearsome.

I described the technique for speed shooting, but the message was cut off partway through unfortunately.

Here is my second attempt.

To describe the technique, I will first define precise words for which finger is which. I will go from thumb to little finger, in order. First, the thumb, then forefinger or index finger or pointer finger, then the middle finger, then the ring finger, then the little or pinky finger. To describe which hand each finger is on, I will simply describe them as, for example, the left middle finger for the middle finger of the left hand, and the right pinky finger for the pinky finger of the right hand, etc.

The technique is reversible between hands, and I will refer to the hand holding the bow as the bow hand and the hand that pulls the string as the draw or drawing hand. This will replace 'left' and 'right' in the finger definitions above. I will refer to the inside and outside of respective hands, such that the inside of the bow hand, for example, is facing the palm of the bow hand, and the outside of the hand would be facing the back of the hand. I will refer to thumb side and pinky side as the side of the hand facing the thumb or pinky, respectively.

So, the essence of the technique is that of holding 3 or 4 arrows preloaded in the bow hand, on the outside of the bow hand held under the bow hand fingers curled over top of them to hold them very nearly in the shooting position, but with their nocks (the string end of the arrow) a few finger widths in front of the string at rest. Each arrow would have its own finger to itself or to a pair: for example, to hold 3 arrows would have had two arrows held under the bow hand middle and index fingers, with one arrow ready to shoot held under just the index finger. The two arrows in storage under the middle finger would be slightly tilted downwards towards the pinky side of the bow hand, but the ready arrow under the index finger would be mostly pointed directly forwards. Additional pair of arrows could be held under the ring finger at more of an angle for 5 arrows in the bow hand.

To shoot, they used a three finger pinch grip in their draw hand. They would pinch the ready arrow between the thumb and forefinger after reaching 'through' the bow string, such that when the arrow is gripped the thumb and forefinger are already around the bowstring. The middle and index fingers would curl around the bowstring to hold it, making the three finger pinch grip.

When shooting, they would shoot with the bow from a low, horizontal position, where the ends of the bowlimbs are pointing to the sides of the archer, with arrows preloaded in the bow hand. They would then pinch grip the ready arrow as described, and while pulling back their draw hand back to the side of their torso, while pushing the bow towards the target with their bow hand. They would release at the point of their choosing, and the exact draw length is not terribly important.

The secret of their accuracy is that they aimed the arrow using the same part of the mind that aims a thrown rock or spear, instead of aiming down the arrow with one eye. It is a trained reflex that takes advantage of inbuilt instincts in the human mind for throwing things.

Training it is as simple as trying to hit close targets while shooting the bow as described, particularly moving targets to take advantage of instinct as much as possible. At first you will miss a lot, but even by the end of the first day you will likely be able to hit hand sized moving targets at close range. Though, for the first familiarization with the bow start by shooting at stationary dirt targets to get the very first bits of body memory in place. In particular, try to train while jumping or moving if possible after the first bit of basic familiarization to further take advantage of instinct.

Keep trying to hit fast second and third shots at this time to familiarize yourself with speed shooting.

The thing yo always keep in mind is to not think about aiming to hit the target, simply look at the target and make the arrow hit it. If you try to think about it you will miss, this is an exercise in building an unconsious aiming reflex.

Keep training with smaller targets and at greater distances as you gain proficiency, and once you feel ready begin trying to hit birds in flight. Eventually you will be able to hit birds in flight, and at longer and longer distances, and be able to hit land animals at much longer ranges, even when evading. You should be able to hit large herd animals while they are running and you are running after them at this point.

You should be carrying at least 5 arrows in your bow hand at this time, and when shooting at a long distance of 150-200 paces should be able to shoot 3 arrows before the first hits the ground at that range. Shooting should be as easy as breathing.

At this point, it becomes a personal journey to true mastery that I have little advice for, as I do not possess such mastery myself.

To teach children is simple: make a game of it.

Teach them to throw handfuls of grass or dirt or small wood pieces in the air for other children to shoot at and take turns seeing who can hit the most targets, and then while running and jumping and hanging upside down from branches and the like. This should be done with a simple, small and weak bow fit for a child to learn with, and teach them how to make their own arrows, and then teach them the art of bowmaking a proper adult hunting and war bow and more complex arrow making. Making their own bow to use for hunting makes for a meaningful coming of age ceremony where they take more responsibility onto themselves for supporting their family and tribe.

Doing this for generations will result in a people of terrifying warriors of peerless skill, where even the women and children are a serious threat to enemy warriors, should they ever face them. What do your skill with axes and clubs matter when a child can put an arrow in your throat from thirty paces away?

This only really changes when faced with enemies that wear good armor of boiled leather or bone that are well covering enough to have only difficult to hit weakpoints in their armor. That obviously makes it much more difficult to kill them, as instead of simply needing to hit their chest with arrows, you need to carefully aim for gaps in armor on a quickly moving and dodging target.

The solution to this is generally closer ranges and more powerful bows shot by stronger archers to pierce the armor. This requires a good angle on the armor to penetrate, but it means directly hitting the chest is a good option again. There are also different tips for the arrows that can much better penetrate armor, and those are very sharp, long snd tapered points with less of a broad head. Thin iron or steel arrows (as in, the entire arrow shaft is metal) with a sharp point are even better at piercing armor.

The last thing, as a general corrolary to the training, is the training of endurance and stamina as a higher priority than raw strength or speed. Train them with training courses running through the woods and wilderness for long distances, and have them compete in races to see who can run the long courses the fastest while shooting at the painted targets along the way, and have obstacles that require climbing or jumping to get past to train in such things.

I will teach you what I know of Parkour, later.

LoserThree said:

I attempted to make a bow with the string that runs from one arm, through a ring on the other, back through a ring on the first, and back to fasten at the other. I put bands around the place on the ring where the string rubs. And in a toy it could be seen to work.

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The wood the bow is made from should be a from a tree that has been split into quarters, and left to dry in the warm sun for months, and kept out of rain.

LoserThree said:

But whether on the ring bow or on real loads to be lifted, always the strings bind or swiftly wear down by rubbing. When it works, it is impressive. But when it works it never works for long enough.

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I did not elaborate enough on pulleys it seems.

A pulley is a wheel, that has a groove running around its entire edge for a rope to remain centered on the wheel. This is easiest to carve from wood.

On the part of the ring the string slips on, make that part of the ring straight. Then attach a small round wheel of wood on the straight part of the ring, using the straight part of the ring as an axle, so that the string can run in the groove of the wheel, as the wheel turns.

The string and pivot for the pulley should both be luvricated with fats and/or oils.

LoserThree said:

I would like better ways of making it. And burying it as you describe may work better than wrapping it in clay and cooking that.

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A much more convenient method is simply cooking it with a large pot with a lid with some small holes in the lid. The idea is to prevent oxygen in the air from reaching the wood that is charring, and the gases released by the wood will escape through the small holes and keep any oxygen from entering.

LoserThree said:

A voice told me to melt sand and other things to make something like pottery that isn't pottery. That voice should have told me that the stuff would burst like a pot dropped from great height, and that it would do so while I was trying to make it. Or while it was sitting, untouched and without prompting. The people think some kind of invisible force hates the stuff and breaks it when it can.

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You are not annealing the glass. That is the problem. The glass has to be cooled slowly in an oven over a whole day, not hot enough to melt, but hot enough to just barely glow the tiniest bit deep red. This lets the internal stresses of the glass as it hardens smooth out and not cause fractures. The oven should be left alone at the end of the day and not fed any more fuel overnight, and let cool until the glass can be taken out by hand.

LoserThree said:

I don't think any of you voices told me that the lightning lure needs to do more than just touch the ground. It needs to be driven into the ground, sometimes to depth of my whole arm or more. And if any part of the lure is not fast against another, they can burst apart and even start a fire. Also, every lightning strike on the lure adds damage to its head, even if it damages no where else.

I have tried to draw both unready iron and firm iron into fibers for lightning lures rather than casting the whole lure from head to root from one piece or similar. I have had no success in this. How can this be done?

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Mostly the act of drawing wire is of taking a rod of steel and hammering it thinner and thinner and longer and longer (while getting it to red heat between hammerings to soften it) until you get a flexible thread of iron or steel. There are ways to do it faster and easier, but those require precise drilling to use.

A good way to get a good electrical connection between metals is to melt some lead at the junction between the metals, which seals them very tightly together.

Gavinfoxx said:

We need to talk more about bread, I think she just has grain and veggie stew so far, and also figure out what part of the world she's in to determine the likely resources and domesticable! So there's river dolphins, a temperate climate, horses, crocodiles, rabbits, rats, mountains that have icecaps, and wild onions. She's somewhere in Europe or Asia maybe??

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From Rockeye. Drawing metal out into thin pieces makes it a thing called wire. The simplest way of making long thin wire is to hammer it and heat it, as has been said. You can also hammer it into thin ribbons and twist these into spirals that circle around and around as they go, as straight upward and evenly as possible, like the horns of some animals. Twisted ribbons of iron will tend to stay straight a little better than long ribbons of iron. This does not require especially much tools.

You can turn a large piece of metal into longer, thinner ones by building two big wheels that rest very close to each other, just far enough apart for something to be put between them. By heating the iron to make it soft and then putting it there and then turning the heavy wheels so the iron is pushed between them, it will be hammered on both sides by the heavy wheels and rolled into shape. Doing it again and again turns bricks or blobs into nice rods. This works best with softer metals and can get it down to maybe a finger's size or less. I think making the wheels is the hard part, they need to be very round and heavy, and also roll or spin well enough to squeeze metal between them. Wheel pressing metal might require gears to turn the big wheels. Or REALLY big and smooth rocks and helpers. Has anyone explained gears? Gears don't work really well when made out of rock and wood isn't much better, metal is best.

A much more difficult thing is the wire draw plate. This works best with a carefully made tool of good, hard iron that works on softer iron.

You might need a drill to make nice circular holes for the draw plate. A drill is just a hard sharp bit that spins really fast and presses hard into something else. It's for making circular holes in things faster, long and thin ones sometimes. An easy one to make is like this: A sharp hard tip attached to a wood rod about an arm long that has string run through a notch at the top of the rod. It helps if you also attach a wheel-ish with a hole in it to the stick near the bottom, something round and heavy that spins well. The string are tied to the top of the heavy stick, where the sharp bit and heavy disk are at the bottom. Also tied to both ends of another stick with a hole in it in the center. The new stick goes over the vertical pole sideways, like someone spreading their arms wide. It should move up and down freely, and the strings form a three-sided shape between the two ends of the cross stick and the top of the vertical stick.

You raise the cross stick up and wrap the strings around the vertical stick, then push it down very hard. When you push the sideways stick down, the strings pull on the vertical stick and make it spin. The drill starts spinning very fast and the string comes unwrapped. The heavy wheel near the sharp tip helps it spin better and also helps hold the drill onto what you want to make holes in. It's important to have it. The spinning keeps going because of the heavy wheel, and the spinning rod wraps the string up around it again and pulls the sideways stick up again. Then you can just push again to make it spin the other way. The whole drill then keeps spinning one way and then the other fast, just by pushing the bar down again and again. This also helps the sharp piece dig into what you are cutting. This whole contraption is called a pump drill. It's not the best but it's easier to make than other kinds.


Once you have a drill, take a small block or plate of very hard iron about half as wide as a finger and carefully drill a circular hole through it. The hole should be narrowest at one end and widen to about twice as wide at the other end. Make a lot of holes one after another like this, narrow at one end and a bit wider at the other. Each draw hole should be a little bit narrower than the last one. Then, hold the draw plate steady and secure with something like a big rock. Take the piece of metal you want to turn into wire. It needs to be mostly a smooth rod already. Scrape and shave one end a bit so the end is small enough to fit through the biggest draw hole. Cover the metal in grease or fat to make it slick, except the end. Stick it through so the small part is seen from the far side of one of the draw holes, and grab the end with something sturdy like pliers.

Pliers are a grabbing tool made of two long rods of metal with a hole in them near one end. Maybe as long as someone's foot or a bit less. The part where the two rods join should be about one in three down the length of the rod. Another metal rod or a wood one goes through the hole to hold them together, but still let them turn closer or further from each other. Then, you hold the long pieces in your hand and move them to open and close the short pieces that are on the other side of where they are joined. The small end will grab with a lot more force than you use on the big end. It works best if you make it so the pieces bend near where they join so the handle and grabby part line up together. Much like pulleys or levers, you turn a lot of distance and a little bit of force into a lot of force on a small amount of distance.

Once you grab with pliers, just pull the metal piece through the draw plate hole as fast as you can. It works best if the metal is hot or warm. Then, do the same thing with the next smallest hole. And the next and so on. It will get a little longer and thinner as it is forced through the hole in the hard iron. Sometimes you need to hit the far end of it with a hammer a bit to get it through the next hole. Keep adding grease or fat as needed. And keep using smaller and smaller holes until your metal rod is long and thin enough to be called wire instead.

Drawing rod into wire makes the iron harder and more likely to just break. You can anneal it by heating it very hot and letting it cool down very slow to make it soft again, so it can be drawn even thinner. Annealing also works on other shapes and kinds of metal, I think mostly, if you have problems where metal gets too hard and just starts breaking instead of being shaped when hammered.

Okay that was my big one for this cacophony. I return to the abyss...

[X] [Bog Iron] Give mortals half the iron from what they bring
[X] [Theroriparian] Find out what the magical river dolphin wants
[X] [Blight] Send the Heroine to deal with it
[X] [Solstice] Dig up the cover and reseal it

Hallo, mighty Bianca! I am Lump. I am eager to help you gain power! Accordingly, I will speak on two ideas: dolphin communication, and the elements that constitute the world.

1. Dolphin Training: As you discovered, dolphins are mischievous. They can and may cooperate. This dolphin may simply be bored, and making a game from your reactions. I suggest redirecting the dolphin's energy through mental and physical stimulation.
   1. Meet the dolphin's need for physical stimulation by feeding it fish. Dolphins usually spend lots of energy catching fish. If you consistently provide it with fish, simply by tossing a fish to it when you spot it, it will likely attach food-motivated value to you. It will also have energy to spare you its attention. You then can ask it for more positive-to-you behaviors.
   2. Meet the dolphin's need for mental stimulation. Dolphins enjoy learning new things and solving problems. That trait helps dolphins adapt to changes in their environment.
      1. In order to communicate with dolphins, you can teach them to understand and interpret cues like physical objects, symbols, hand signals, and sounds.
      2. Dolphins prefer positive reinforcements. Fish are a positive reinforcement, since they're something the dolphin desires. Food is a Primary Reinforcement.
      3. Once you've gained the dolphin's attention with Primary Reinforcements, it's time to bring in the mental stimulation of Secondary Reinforcements.
         1. Literally teaching a dolphin to communicate with you may be enjoyable to said dolphin. Fulfilling the role of teacher may redirect the dolphin's energy and help you establish a common vocabulary to determine what it ultimately wants. If it's magical, it may become a helpful earthforming tool. Dolphins can certainly employ violence against any creature within their range, and you may be able to direct that violence or earth-forming.
      4. Early ideas for regular dolphins:
         1. "Stationing" involves the dolphin approaching a predetermined spot consistently. You decide on the stationing signal. You might use an object or a handsign, along with a vocalization such as "Station."
         2. "Target-follow". If you have an object, such as a fired-clay disc, you may train the dolphin to touch the disc with its nose. A good vocalization could be simply "Target". If the dolphin successfully touches the target, it may be rewarded with food and praise, to cement the positive association.
         3. This will likely get you started. Dolphins can perform acrobatic feats and vocalizations. They can carry objects in their mouths. There are many advanced training behaviors, but I don't want to overwhelm, in case these early efforts aren't successful. The trainer and the dolphin can literally build a language together, and this may help you communicate.
      5. How to train your dolphin:
         1. Approach the dolphin with confident posture, and a positive "we are going to have a great time!" attitude. Much like humans try to interpret mood based on the body's stance and expression, dolphins are affected by their companion's mood.
         2. Begin and end each training session at consistent times.
         3. Time should be the only perfectly consistent element in training. It's ineffective to start and end sessions the same way.
         4. If the dolphin offers undesirable behavior, use nonreinforcement.
            1. Nonreinforcement is a lack of stimulus, either positive or negative. It can be described as "ignoring". Punishment tends to reinforce the negative behavior, since the dolphin received stimulus.
            2. If a session is not going well, you can always leave and come back another day. This teaches the dolphin that you respect your time, and there are consequences if it does not respect your time as well.
2. Elements and Chemical Notation
   1. So far, you have faced challenges including buildings collapsing, mortar crumbling, pollution from iron smelting, food growing and preservation, etc. You have also asked about how to adapt measures to different or changing environments. Since I and the Voices lack sight into your environment, I'd like to simplify our communication in order to maximize your control and power over your environment. I suggest doing this by expanding your library of glyphs to include Chemical Notation.
   2. Many voices have mentioned the invisible creatures that are sick-making. There are yet smaller entities that give these creatures their power. These tiny entities are the building blocks of every substance in the world. Because they are elemental, we term those entities "elements." You may find power and value in being able to predict, notate, and observe the interactions of these elements, because then you can begin to build systems to manipulate them. Naming them gives you power to speak to others about what you are doing in a unified, systemic way, empowering you to make records of successes and communicate about improving our approach.
      1. Voices have already named several elements: hydrogen, oxygen, nitrogen, potassium, and iron. They have suggested that you may call them what you wish: while this is true, we would lose the ease of communication. One can memorize the names of the elements, but one gains more power over them if one knows their glyphs. Like all good truenames, the glyphs describe an element's form, properties, and substance.
         1. So! Hydrogen! First among elements, being lightest in form. It is probably the most abundant element in the universe. Stars are made of it. It is in the air your human subjects breathe. Based on its composition, it reacts with the element oxygen to produce water. I would be happy to describe the relationship between hydrogen and oxygen using their elemental forms if you would like.
            1. We, the cacophony, describe Hydrogen with the glyph 1, and the symbol H. The symbol is helpful for brief, clear reference. The glyph describes the form of Hydrogen. It has one "proton."
            2. For now, it may be helpful to think of a proton as a dot, or a point. This matters because a solo hydrogen dot is lonely. It will typically seek a pairing. They do not fuck. They simply bond. Hydrogen usually appears in nature in a pair that we describe as H2. This pairing of elements is called a molecule. Hydrogen needs a friend. Two hydrogens are sort of content. The H2 molecule pairing is still hungry, and it seeks more elemental friends.
         2. Carbon! Carbon is vital to life on the planet. Carbon is described by 6 dots. We use the symbol "C".
            1. Impure carbon in the form of charcoal is part of the metal smelting process other voices have taught you.
            2. Carbon's proton dots love to reach out to the hydrogen pairing, and form a stable compound of 8 dots. The hydrogen / carbon pairing molecule is known as "hydrocarbons," which can be used as powerful fuels.
         3. Nitrogen! Nitrogen will be important in the farming discussion. It has 7 protons, or dots. We notate it as "N". Probably more on this later.
         4. Oxygen! The sharpener/sour source. We notate it as "O". Oxygen has 8 proton dots. Rafin described how oxygen is created by Plants, and how humans, in return, produce a molecule of carbon and oxygen. That's notated as CO2, because it's formed of one carbon bonding with two oxygen. CO2's a clear substance known as a "gas," that Rafin described. Plants and people are connected in this way.
         5. Calcium! This is needful for discussion of Lime, as you mentioned earlier. Calcium uses the symbol Ca, and the number 20, since it has 20 proton dots. It has a lot to do with bones: the bones of the world, and the bones of mortals. Also teeth. Calcium can be found in milk, and without enough of it, one's bones begin to crumble.
         6. Later I can draw you some glyphs that show the exact bonds between the atoms: how they work, and more on why that matters. I can teach you how to encourage their bonds, and give you ideas on how to break them. I can teach you more notation so that we can rapidly discuss exact recipes and proportions for making mortar and pressed earth dwellings and fuel and POWER.

I know that there are many places where my descriptions will be inadequate, but rather than add more detail, I will fall silent and await your requests for any clarification. I trust your mighty intelligence. I also trust that with your help, I will be understood.

I might know that rock. Is the stone itself sticky or is it just that you make sticky from it?

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• You make sticky from it. Here's how!
  • Lime is made of just two elements. Its glyph is CaO. That means you just need one Calcium and one Oxygen to make it. How do we get it? From limestone!
  • Limestone is a slightly more complicated compound. It adds a Carbon and an Oxygen pairing. We can roughly write part of it as CaCO3. The Calcium in this case often comes from the shells of long-dead creatures. That's why you can find it where there was or is now water-life. As the voices mentioned, you can use limestone in specific proportions to improve soil quality.
    • So! To extract the lime from limestone, your humans can put limestone in one of your heating towers. We'll call this kind a "kiln." You'll build this squat tower with a sloped pass-through tunnel, so your subjects can push the limestone into one side, and feed fire-fuel in to the other, lower side. I'll need to think more about the appropriate tool. Bare hands would be wasteful of your subjects. (May I suggest using layers of concrete sludge or mortar to help glue the bricks of the kiln together so it doesn't fall down. I can talk about some exact curing processes if you're interested.)
      • It's now time to add Heat as a change agent to break the bonds of the Limestone molecules, and separate them into two parts: Lime, and CO2, that gas that plants crave. So we heat the limestone reeeally hot by pushing it through the kiln, then out into a cooling zone.
      • Once it's cooled, you've got your "quicklime," the CaO stuff that you want for mortar.
    • Now we need a big pot, a subject with a strong arm and a stirring tool, and some sand to make mortar!
      • So we take that empty pot
      • Add 1 part sand
      • Mix in 1 part lime
      • Add 1.5 parts sand
      • Mix that dry for at least 5 minutes
      • After 5 minutes slowly add water until your subject gets the consistency they want. How will they decide? Learning through experimentation!
        • it is important to not flood the mixture by adding too much water--it thins out the sticky and makes it weaker
      • When your subject is happy with the consistency, mix for 20 minutes
• Theoretically, you should now have some lovely sticky stuff to glue all sorts of things together. You can put it between bricks, as I mentioned, or slather it over the surfaces as further support.

Bread! Adding heat and water to make grains more field-portable.

Get hulled grains, and a human with a smushing/grinding tool, even if it's just two flat rocks. Smush grains between the rocks until they break down into a dry, light substance called "flour."

Then stir in water to make a sticky dough. Too much water, and it'll be thin and won't bake. Too little, and it won't stick. Your subject should ball up the dough, and not see any streaks of flour.

Then they apply heat, but not too much. The ashes of a hearthfire can work! Your people can try various ovens.

They're looking for bread to be brown-colored on the outside, but not black. That's just carbon again, and it's not very edible in that form. The bread also shouldn't be wet on the inside. Your subjects can mess around with texture and heat to see what they like. Some bread lasts a few days; some can last much longer. If it turns black or blue or green, that's mold, which means bread is not really edible. Blue/green mold can be useful for medicine and other food. Black mold can sicken.

Later I can talk about how to harness the gas CO2 to make even nicer bread, if you're interested.

[X] [Bog Iron] Give mortals half the iron from what they bring
[X] [Solstice] Dig up the stone, guide the rite, steal the power (Community Management 4 + Distiller 1 + Empathy 1 = 6; Ob 4)
[X] [Blight] Plunder the Tomb of the Blight
[X] [Theropirapian] Send the Heroine to deal with it

@LoserThree
I have a question is writing like 100%doomed after 5 generations or is there a chanve to save it