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Who
Wrote the Bible? by Richard Elliott Friedman
“It appears that everybody but Moses wrote the Torah.”
Talmidah (Shira Halevi), The Life Story of Adam and Havah: A New
Targum of Genesis 1:26-5:5
Book Review: Who Wrote the Bible?
0. What is this book, anyway?
Who Wrote the Bible? , Second Edition, by Richard Elliott Friedman
The Torah, also known as the first five books of the Christian Bible and
the first five books of the Tanakh, are generally divvied up into
Genesis, Exodus, Leviticus, Numbers, and Deuteronomy. However, most
people who attended a big fancy university on the subject will tell you
that those books were not written in order, not written as
those books, and not written by remotely the same author.
I know, I know, tradition says that Moses wrote the Torah. You’ve
probably heard the jokes about how Numbers 12:3
makes that unlikely, and this book really gets into the
nitty-gritty of how exactly we can be sure that that isn’t the case; but
honestly, for me, what really cinched it was just reading the Torah
straight through, from “In the beginning” to “in the sight of all
Israel”. It’s clearly not the same guy! Not only is the writer working
from a bunch of different sources, but it’s not even the same writer!
It’s not just that each book is by a different writer - some
paragraphs switch writers.
But maybe you want to form an opinion on this without having to read
through six hundred and thirteen laws on not boiling a goat in its
mother’s milk. Better yet, you’d like to know who exactly wrote one of
the foundational texts of Western civilization. Well, the bad news is,
we don’t know exactly who. But we can actually make
some surprisingly educated guesses as to their backgrounds,
nationalities (...besides just “probably Israelite”), agendas, and - in
two cases - names! Enter Richard Elliott Friedman, who intends to
explain to us just that.
0.5. Who wrote this book, anyway?
Before believing anything anyone says with “Bible” and “history” in the
same sentence, paragraph, or day, it’s generally a good idea to see if
they have any formal academic qualifications whatsoever. (I realize this
is exactly the kind of credentialism we should be eschewing in our en
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Weightless
Arrow
Q. Assuming a zero-gravity environment with an atmosphere identical to
Earth’s, how long would it take the friction of air to stop an arrow
fired from a bow? Would it eventually come to a standstill and hover in
midair?—Mark Estano
A. It’s happened to all of us. You’re in the belly of a vast space
station and you’re trying to shoot someone with a bow and arrow.
Compared to a normal physics problem, this scenario is backward.
Usually, you consider gravity and neglect air resistance, not the other
way around.1
As you’d expect, air resistance would slow down an arrow, and eventually
it would stop . . . after flying very, very far.
Fortunately, for most of that flight, it wouldn’t be much of a danger to
anyone.
Let’s go over what would happen in more detail.
Say you fire the arrow at 85 meters per second. That’s about twice the
speed of a major-league fastball, and a little below the 100 m/s speed
of arrows from high-end compound bows.
The arrow would slow down quickly. Air resistance is proportional to
speed squared, which means that when it’s going fast, the arrow would
experience a lot of drag.
After ten seconds of flight, the arrow would have traveled 400 meters,
and its speed would have dropped from 85 m/s to 25 m/s; 25 m/s is about
how fast a normal person could throw an arrow.
At that speed, the arrow would be a lot less dangerous.
We know from hunters that small differences in arrow speed make big
differences in the size of the animal it can kill. A 25-gram arrow
moving at 100 m/s could be used to hunt elk and black bears. At 70 m/s,
it might be too slow to kill a deer. Or, in our case, a space deer.
Once the arrow leaves that range, it’s no longer particularly
dangerous . . . but it’s not even close to stopping.
After five minutes, the arrow would have flown about a mile, and it
would have slowed to roughly walking speed. At that speed, it would
experience very little drag; it would just cruise along, slowing down
very gradually.
At this point, it would have gone much farther than any Earth arrow can
go. High-end bows can shoot an arrow a distance of a couple hundred
meters over flat ground, but the world record for a hand bow-and-arrow
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know one antiderivative of a function, we know them all: An antiderivative of cos 𝑥 is sin 𝑥; our
lemma then guarantees that every antiderivative of cosine has the form sin 𝑥 + 𝐶 for some constant 𝐶.
Exercises.
12. An important rule you should immediately memorize: To find an antiderivative of 𝑐𝑥 𝑟 , where 𝑐 is a constant,
we increase its exponent by 1 and divide by the new exponent.
a) Verify that an antiderivative of 𝑐𝑥 𝑟 is 𝑐𝑥 𝑟+1 ⁄(𝑟 + 1), as claimed.
b) Write down antiderivatives for the following functions:
1
3
𝑥 3 , 2𝑥 9 , 𝑥, −5√𝑥, √𝑥 2 ,
𝑥2
,
−8
𝑥 3/7
, 𝑥 −𝜋 .
c) State the one value of 𝑟 for which this rule does not apply. Why doesn’t the rule apply in this case?
13. Think of an antiderivative of each of the following functions:
a) cos 𝑥
b) −sin 𝑥
c) sin 𝑥
d) sec 2 𝑥
e) 𝑒 𝑥
f) sec 𝑥 tan 𝑥
g)
1
1 + 𝑥2
h) − csc 2 𝑥
i) 1⁄𝑥
14. You can sometimes find an antiderivative by guessing something close, then adjusting your guess to make its
derivative come out right. For example, to find an antiderivative of sin(3𝑥), we’d guess, “It will be something
like cos(3𝑥). But this function’s derivative is −𝟑 sin(3𝑥), which is off by a constant factor of 3. To compensate,
let’s try multiplying our prospective antiderivative by −1/3. Will that work? Yes! A quick check shows that the
derivative of −(1⁄3) cos(3𝑥) is indeed sin(3𝑥), so we’ve found our antiderivative.”
Use this guess-and-adjust method to find antiderivatives of the following functions.
a) cos(5𝑥)
b) sin(𝜋𝑥)
c) 𝑒 −𝑥
d) 𝑒 3𝑥
e) sec 2 (𝑥 ⁄2)
f) 10𝑥
g) 5−𝑥
h)
1
1 + 4𝑥2
15. Verify that ln(𝑥) and ln(−𝑥) are both antiderivatives of 1/𝑥, and yet they do not differ by a constant!
a) Why does this not violate
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Random
Sneeze Call
Q. If you call a random phone number and say “God bless you,” what are
the chances that the person who answers just sneezed? —Mimi
A. It’s hard to find good numbers on this, but it’s probably about 1 in
40,000.
Before you pick up the phone, you should also keep in mind that there’s
roughly a 1 in 1000,000,000 chance that the person you’re calling just
murdered someone.1 You may want to be more careful with your blessings.
However, given that sneezes are far more common than murders,2 you’re
still much more likely to get someone who sneezed than to catch a
killer, so this strategy is not recommended.
Mental note: I’m going to start saying this when people sneeze.
Compared with the murder rate, the sneezing rate doesn’t get much
scholarly research. The most widely cited figure for average sneeze
frequency comes from a doctor interviewed by ABC News, who pegged it at
200 sneezes per person per year.
One of the few scholarly sources of data on sneezing is a study that
monitored the sneezing of people undergoing an induced allergic
reaction. To estimate the average sneezing rate, we can ignore all the
real medical data they were trying to gather and just look at their
control group. This group was given no allergens at all; they just sat
alone in a room for a total of 176 20-minute sessions.3
The subjects in the control group sneezed four times during those 58 or
so hours,4 which—assuming they sneeze only while awake—translates to
about 400 sneezes per person per year.
Google Scholar turns up 5980 articles from 2012 that mention “sneezing.”
If half of these articles are from the US, and each one has an average
of four authors, then if you dial the number, there’s about a 1 in
10,000,000 chance that you’ll get someone who—just that day—published an
article on sneezing.
On the other hand, about 60 people are killed by lightning in the US
every year. That means there’s only a 1 in 10,000,000,000,000 chance
that you’ll call someone in the 30 seconds after they’ve been struck and
killed.
Lastly, let’s suppose that on the day this book was published, five
people who read it decide to actually try
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zero in the denominator usually means that the integral is undefined. However, the only value of
α for which cos α sin θ could possibly be as small as −1 (for 0 ⩽ θ ⩽ π/2) is π (and of course 3π,
etc). From the point of view of the integral, the only restriction should be α 6= π (etc). There is a
slight awkwardness in the answer when α = 0 but this can be overcome by taking limits:
α
lim
=1
α→0 sin α
which you can easily verify is the correct answer in this case.
You may by now have noticed a curious thing: increasing α by 2π does not change I but does change
the answer. If you work through the solution with this in mind you see that the only step where
it can make a difference is in the line where you work out tan−1 u , which by definition lies in the
range −π/2 to π/2 . It is this that determines the given restriction. (Note that negative values of α
are not required because setting α → −α changes neither the integral nor the given solution.)
Advanced Problems in Core Mathematics: edition September 2010
96
Question 40(∗∗)
The line ` has vector equation r = λs , where
s = (cos θ +
√
√
√
3 ) i + ( 2 sin θ) j + (cos θ − 3 ) k
and λ is a scalar parameter. Find an expression for the angle between ` and the line
r = µ(a i + b j + c k) . Show that there is a line m through the origin such that, whatever the
value of θ , the acute angle between ` and m is π/6 .
√
A plane has equation x − z = 4 3 . The line ` meets this plane at P . Show that, as θ varies, P
describes a circle, with its centre on m. Find the radius of this circle.
Comments
It is not easy to set vector questions at this level: they tend to become merely complicated (rather
than difficult in an interesting way). Usually, there is some underlying geometry and it pays to try
to understand what this is. Here, the question is about the geometrical object traced out by ` as θ
varies.
You will need to know about scalar products of vectors for this question, but otherwise it is really
just coordinate geometry.
Vectors form an extremely important part of almost every branch of mathematics (maybe every
branch of mathematics) and will
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SAT
Guessing
Q. What if everyone who took the SAT guessed on every multiple-choice
question? How many perfect scores would there be?—Rob Balder
A. None.
The SAT is a standardized test given to American high school students.
The scoring is such that under certain circumstances, guessing an answer
can be a good strategy. But what if you guessed on everything?
Not all of the SAT is multiple-choice, so let’s focus on the
multiple-choice questions to keep things simple. We’ll assume everyone
gets the essay questions and fill-in-the-number sections correct.
In the 2014 version of the SAT, there were 44 multiple-choice questions
in the math (quantitative) section, 67 in the critical reading
(qualitative) section, and 47 in the newfangled1 writing section. Each
question has five options, so a random guess has a 20 percent chance of
being right.
The probability of getting all 158 questions right is:
That’s one in 27 quinquatrigintillion.
If all four million 17-year-olds took the SAT, and they all guessed
randomly, it’s a virtually certain that there would be no perfect scores
on any of the three sections.
How certain is it? Well, if they each used a computer to take the test a
million times each day, and continued this every day for five billion
years—until the Sun expanded to a red giant and the Earth was charred to
a cinder—the chance of any of them ever getting a perfect score on just
the math section would be about 0.0001 percent.
How unlikely is that? Each year something like 500 Americans are struck
by lightning (based on an average of 45 lightning deaths and a 9–10
percent fatality rate). This suggests that the odds of any one American
being hit in a given year are about 1 in 700,000.2
This means that the odds of acing the SAT by guessing are worse than the
odds of every living ex-President and every member of the main cast of
Firefly all being independently struck by
lightning . . . on the same day.
To everyone taking the SAT this year, good luck—but it won’t be enough.
1 I took the SAT a long time ago, okay?
2 See: xkcd, “Conditional Risk,” http://xkcd.com/795/.
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Definition 1.12: Angle between vectors
Let x, y ∈ Rn with x ̸= 0 and y ̸= 0. Then the angle θ between the two vectors is
defined by
x·y
cos θ =
.
∥x∥∥y∥
Notice that this definition makes sense because the Cauchy–Schwarz inequality holds, namely
Cauchy–Schwarz gives us
x·y
−1 ≤
≤1
∥x∥∥y∥
12
CHAPTER 1. VECTORS IN EUCLIDEAN SPACE
and therefore there exist an θ ∈ [0, π) such that
cos θ =
x·y
.
∥x∥∥y∥
Notice that if our vectors are orthogonal as defined in Definition 1.8 this corresponds to
cos θ = π2 as expected.
We can now use this definition to compute the angles between vectors.
Example 1.13
If v = (−1,
√7) and w√= (2, 1), then we find v · w = 5, ∥v∥ =
cos θ = 5/ 250 = 1/ 10.
√
50 and ∥w∥ =
√
5, hence
If we are working in R2 we can prove that this definition of the angle using the dot product
does indeed coincide with the geometric method of finding the angle. The proof of this is left
as an exercise.
1.3
Polar form in the Euclidean plane
As well as defining a vector in R2 based on its components in the x and y directions, we could
also define it based on its length and its angle from the x-axis. This is known as polar form,
and is illustrated in Figure 1.3.
y
v
λ
θ
x
Figure 1.3: A vector v in R2 represented by Cartesian
p coordinates (x, y) or by polar coordinates λ, θ. We have x = λ cos θ, y = λ sin θ and λ = x2 + y 2 and tan θ = y/x.
In particular, a unit vector has length one, hence all unit vectors lie on the circle of radius one
in R2 , and a unit vector is determined solely by its angle θ with the x-axis. By elementary
geometry we find that the unit vector with angle θ to the x-axis is given by
cos θ
.
(1.1)
u(θ) :=
sin θ
1.3. POLAR FORM IN THE EUCLIDEAN PLANE
13
We can then multiply by a scalar order to obtain any vector in R2 , and this gives us a unique
vector. In particular, the scalar that we multiply our unit vector by is the norm of the vector.
Theorem 1.
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of the
continuity of the sine and cosine functions.
(a) The inequality \sinx( < (xl, valid for 0 < 1x1 < BT, was
proved in Exercise 34 of Section
2.8. Use this inequality to prove that the sine function is continuous
at 0.
(b) Use part (a) and the identity COS 2x = 1 - 2 sin2 x to prove that
the cosine is continuous
at 0.
(c) Use the addition formulas for sin (x + h) and COS (x + h) to prove
that the sine and cosine
are continuous at any real x.
27. Figure 3.5 shows a portion of the graph of the functionfdefined as
follows:
f(x) = sin k
i f x#O.
For x = l/(nn), where n is an integer, we have sin (1/x) = sin (na) = 0.
Between two such
points, the function values rise to + 1 and drop back to 0 or else drop
to - 1 and rise back to 0.
FIGURE 3.5 f(x) = sin (1/x) if x # 0. This function is discontinuous at 0
no matter
how f(0) is defined.
Therefore, between any such point and the origin, the curve has an
infinite number of oscillations. This suggests that the function values
do not approach any fixed value as x + 0. Prove
that there is no real number A such thatf(x) -+ A as x + 0. This shows
that it is not possible
to define f(0) in such a way that f becomes continuous at 0.
[Hint:
Assume such
an A exists and obtain a contradiction.]
28. For x # 0, let f(x) = [l/x 1, w here [t] denotes the greatest
integer 2 t. Sketch the graph of
f over the intervals [ -2, -51 and [i, 21. What happens to f (x) as x + 0
through positive
values? through negative values ? Can you define f (0) SO that f becomes
continuous at O?
29. Same as Exercise 28, when f(x) = ( -1)t1/21 for x # 0.
30. Same as Exercise 28, whenf(x) = x( -l)tl’al for x # 0.
31. Give an example
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Hockey
Puck
Q. How hard would a puck have to be shot to be able to knock the goalie
himself backward into the net?—Tom
A. This can’t really happen.
It’s not just a problem of hitting the puck hard enough. This book isn’t
concerned with that kind of limitation. Humans with sticks can’t make a
puck go much faster than about 50 meters per second, but we can assume
this puck is launched by a hockey robot or an electric sled or a
hypersonic light gas gun.
The problem, in a nutshell, is that hockey players are heavy and pucks
are not. A goalie in full gear outweighs a puck by a factor of about
600. Even the fastest slap shot has less momentum than a ten-year-old
skating along at a mile per hour.
Hockey players can also brace pretty hard against the ice. A player
skating at full speed can stop in the space of a few meters, which means
the force they’re exerting on the ice is pretty substantial. (It also
suggests that if you started to slowly rotate a hockey rink, it could
tilt up to 50 degrees before the players would all slide to one end.
Clearly, experiments are needed to confirm this.)
From estimates of collision speeds in hockey videos, and some guidance
from a hockey player, I estimated that the 165-gram puck would have to
be moving somewhere between Mach 2 and Mach 8 to knock the goalie
backward into the goal—faster if the goalie is bracing against the hit,
and slower if the puck hits at an upward angle.
Firing an object at Mach 8 is not, in itself, very hard. One of the best
methods for doing so is the aforementioned hypersonic gas gun, which
is—at its core—the same mechanism a BB gun uses to fire BBs.1
But a hockey puck moving at Mach 8 would have a lot of problems,
starting with the fact that the air ahead of the puck would be
compressed and heated very rapidly. It wouldn’t be going fast enough to
ionize the air and leave a glowing trail like a meteor, but the surface
of the puck would (given a long enough flight) start to melt or char.
The air resistance, however, would slow the puck down very quickly, so a
puck going at Mach 8 when it leaves the launcher might be going a
fraction of that when it arrives at the goal. And even at Mach 8, the
puck probably wouldn’t pass through the goalie’s body.
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are equal. Also, recall exercise 5a.]
13. Just as there are various criteria for congruence, so there are various criteria for parallelism. Here’s one you
probably know: If the two angles in a Z-shape are equal, then the Z’s “top” and “bottom” are parallel. Use this
parallelism criterion to prove that every rhombus is a parallelogram. [Hint: How will you show those angles are
equal? Remember the hint from exercise 11.]
14. Is every parallelogram a rhombus? Is every square a rhombus? Is every rhombus a square? Is every square a
parallelogram? How do you know?
* For example, two triangles that each have a 20° angle surrounded by sides of length 4 and 6 must be congruent, since they
share the same SAS data.
136
Precalculus Made Difficult
Chapter 8: Triangle Basics
Similar Triangles
Triangles with the same shape (i.e. same proportions) are said to be similar. For example, if you enlarge
a triangle on a computer screen, the enlarged triangle will be similar (but not congruent) to the original.
There are various similarity criteria for triangles, but we’ll need only one in this course: AAA.
AAA Similarity. If two triangles have the same angles, they are similar.
Proof. In the figure at right, if the dotted lines are parallel, then the two
triangles (one inside the other) must be similar. Most people find this obvious
after a little thought, and I’m going to assume that you will too.*
Now suppose ∆𝐴𝐵𝐶 and ∆𝐴′ 𝐵′ 𝐶 ′ are two triangles with the same angles.
Superimposing them so that angles 𝐴 and 𝐴′ coincide leads to a figure like the
one above. Thus, to establish our triangles’ similarity, it suffices to show that
𝐵𝐶 and 𝐵′𝐶′ are parallel. But these lines must be parallel since they meet the
same line (𝐵𝐵′) at equal angles. Hence, the triangles are similar, as claimed. ■
The AAA similarity criterion could be called the AA similarity criterion, since if triangles have two angles
(𝛼 and 𝛽) in common, then they automatically have all three angles in common; in both triangles, the
third angle must be 180° − (𝛼 + 𝛽). We shall use the symbol ~ to mean “is similar to”.
The proportionality of similar figures is precisely what allows us to extract information
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+ 5 is continuous at c.
2.5 EXAMPLE
Let f (x) = x sin (1/x) for x ≠ 0 and f (0) = 0. From the graph in Figure 2 it
appears that f may be continuous at 0. Let us prove that it actually is. Since
1
f ( x) − f (0) = x sin
for all x,
≤ x ,
x
given ε > 0 we may let δ = ε. Then when | x – 0 | < δ we have | f (x) – f (0) | ≤
| x | < δ = ε . Hence f is continuous at 0. We shall return to this example
later to see that f is continuous on R.
Figure 2
218
f (x) = x sin (1/x) for x ≠ 0 and f (0) = 0
Limits and Continuity
By taking the negation of (a) and (b) in Theorem 2.2, we obtain the
following useful characterization of discontinuity.
2.6 THEOREM
Let f : D → R and let c ∈ D. Then f is discontinuous at c iff there exists a
sequence (xn) in D such that (xn) converges to c but the sequence ( f (xn)) does
not converge to f (c).
2.7 EXAMPLE
Let D = (– ∞, 0) ∪ (0, ∞) and let f (x) = 1/x for x ∈ D. Since limx → c 1/x =
1/c for all c ∈ D by Theorem 1.13, f is continuous on D. But f is not
continuous on R for two reasons. In the first place, f is not defined at 0 so it
cannot possibly be continuous there. In the second place, even if we were to
define f (0) = k for some k ∈ R (as we did in Example 2.5), then f would still
not be continuous at 0. Indeed, since 1/n → 0 and lim f (1/n) = + ∞, the
sequence ( f (1/n)) is not convergent. Thus there is no way to define f at 0 to
make it continuous there.
2.8 EXAMPLE
To obtain a function that is discontinuous at every real number, we let
f : R → R be the Dirichlet function defined by
⎧1,
f ( x) = ⎨
⎩0,
if x is rational,
if x is
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rims and the
ground).3 This means that if a car hits a small speed bump, the rim
won’t actually touch the bump; the tire will just be compressed.
The typical sedan has a top speed of around 120 miles per hour. Hitting a
speed bump at that speed would, in one way or another, probably result
in losing control of the car and crashing.4 However, the jolt itself
probably wouldn’t be fatal.
If you hit a larger speed bump—like a speed hump or speed table—your car
might not fare so well.
How fast would you have to go to definitely die?
Let’s consider what would happen if a car were going faster than its top
speed. The average modern car is limited to a top speed of around 120
mph, and the fastest can go about 200.
While most passenger cars have some kind of artificial speed limits
imposed by the engine computer, the ultimate physical limit to a car’s
top speed comes from air resistance. This type of drag increases with
the square of speed; at some point, a car doesn’t have enough engine
power to push through the air any faster.
If you did force a sedan to go faster than its top speed—perhaps by
reusing the magical accelerator from the relativistic baseball—the speed
bump would be the least of your problems.
Cars generate lift. The air flowing around a car exerts all kinds of
forces on it.
Where did all these arrows come from?
The lift forces are relatively minor at normal highway speeds, but at
higher speeds they become substantial.
In a Formula One car equipped with airfoils, this force pushes downward,
holding the car against the track. In a sedan, they lift it up.
Among NASCAR fans, there’s frequently talk of a 200-mph “liftoff speed”
if the car starts to spin. Other branches of auto racing have seen
spectacular backflip crashes when the aerodynamics don’t work out as
planned.
The bottom line is that in the range of 150–300 mph, a typical sedan
would lift off the ground, tumble, and
crash . . . before you even hit the bump.
BREAKING: Child, Unidentified Creature in Bicycle Basket Hit and Killed
by Car
If you kept the car from taking off, the force of the wind at those
speeds would strip away the hood, side panels, and windows. At higher
speeds, the car itself would be disassembled, and might even burn up
like a spacecraft reentering the atmosphere.
What’s
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The Republic by
Plato
Introduction
Plato’s The Republic is a book about Socrates (Plato’s
teacher) and several interlocutors attempting to find the nature of
justice, and to prove that justice is superior to injustice. While Plato
is the author, Socrates is the main character who presents Plato’s
arguments. It seems likely that Socrates usually speaks with Plato’s
voice throughout the text. To prove this point about justice, Socrates
proposes to first examine justice in the state, since it will be larger
and more readily apparent in a larger community, and then use this as a
metaphor for the individual. As a result, The Republic
is a work that combines both political and moral philosophy. I
would call it mostly a political philosophy text. Of its eleven
chapters, seven of them are devoted purely to the details of Plato’s
ideal state. Of the remaining four, two of those chapters contain
significant political elements, as they discuss morality explicitly
through the metaphor of the state. Thus, we can call The Republic
a political philosophy book with an undertone of moral
philosophy included.
Thus, in order to examine the book and it’s conclusions, we have to ask
the following:
- What is the nature of justice, according to Plato?
- What was Plato’s ideal political state like?
- What was Plato’s ideal morality, and how did it relate to the state?
After this, I’ll give my own thoughts on the matter.
It is worth noting that in this review, I’ll often be using gendered
terms such as “craftsman” when looking at Plato’s arguments. This is
because these are the words he generally uses, and thus using these
terms stays closer to his own statements. When making my own thoughts or
refutations, I’ll aim to switch back to gender-neutral terms.
The Nature of Justice
At the start of the book, Socrates enters a dialogue about the nature of
justice, and demonstrates what justice is not. First to step up is
Polemarchus, who claims justice is a techn ē that
enables us to help our friends and hurt our enemies. Techn
ē is a Greek word that can mean various types of
professional and creative skills. One could think of it as a skill, art,
or craft. Socrates argues against this with several arguments. But the
most important argument, the one we will come back to, is this.
Justice is what lets us help our friends, but harm our enemies. However,
if we harm someone, we make them worse, by the standards of
chapters 0.04190484806895256
top
five names among high-end and low-end families, in order of their
relative disparity with the other category:
Most Common High-End White Girl Names
1. Alexandra
2. Lauren
3. Katherine
4. Madison
5. Rachel
Most Common Low-End White Girl Names
1. Amber
2. Heather
3. Kayla
4. Stephanie
5. Alyssa
And for the boys:
Most Common High-End White Boy Names
1. Benjamin
2. Samuel
3. Jonathan
4. Alexander
5. Andrew
Most Common Low-End White Boy Names
1. Cody
2. Brandon
3. Anthony
4. Justin
5. Robert
Considering the relationship between income and names, and given the
fact that income and education are strongly correlated, it is not
surprising to find a similarly strong link between the parents’ level of
education and the name they give their baby. Once again drawing from
the pool of most common names among white children, here are the top
picks of highly educated parents versus those with the least education:
Most Common White Girl Names Among High-Education Parents
1. Katherine
2. Emma
3. Alexandra
4. Julia
5. Rachel
Most Common White Girl Names Among Low-Education Parents
1. Kayla
2. Amber
3. Heather
4. Brittany
5. Brianna
Most Common White Boy Names Among High-Education Parents
1. Benjamin
2. Samuel
3. Alexander
4. John
5. William
Most Common White Boy Names Among Low-Education Parents
1. Cody
2. Travis
3. Brandon
4. Justin
5. Tyler
The effect is even more pronounced when the sample is widened beyond the
most common names. Drawing from the entire California database, here
are the names that signify the most poorly educated white parents.
The Twenty White Girl NamesThat Best Signify Low-Education
Parents*(Average number of years of mother’s education in parentheses)
1. Angel (11.38)
2. Heaven (11.46)
3. Misty (11.61)
4. Destiny (11.66)
5. Brenda (11.71)
6. Tabatha (11.81)
7. Bobbie (11.87)
8. Brandy (11.89)
9. Destinee (11.91)
10. Cindy (11.92)
11. Jazmine (11.94)
12. Shyanne (11.96)
13. Britany (12.05)
14. Mercedes (12.06)
15. Tiffanie (12.08)
16. Ashly (12.11)
17. Tonya (12.13)
chapters 0.03907052055001259
body,
whether intentionally or otherwise. Stopping implies that the ball's
trajectory has been interrupted, and its relative velocity reduced to
something near zero meters-per-second. A player may catch the ball with
their basket, which stops it, but the ball may also be stopped by any
part of a player's body, whether or not the basket is used. Stoppage of
the ball, even if unintentional, always results in control. If a player
is struck by the ball, and the ball is stopped, that player's team then
controls the ball.
Occasionally, players are struck by the ball and injured. Injuries
immediately stop gameplay, and the injured player is attended to. When
gameplay resumes, the injured player's team is considered to be in
control of the ball, and may make the pitch. Understand, though, that
the injury does not award control -- it is the stoppage of the ball that
awards control.
Deflecting The Ball
A player that intentionally deflects the trajectory of a ball already in
motion, either by using the basket (usually the smack, in specific), or
by using any other part of the body, is considered to have imparted
control onto it. Even if the ball doesn't go where the player actually
intended, an attempt to deflect the ball that does, in fact, change its
trajectory in a directed way is considered control. Control is awarded
based upon the apparent intention of the player versus the result. Most
contended referee calls arise from player deflections.
Accelerating The Ball
A variant of deflection, acceleration occurs when a player smacks or
pitches a ball already in motion in such a way that control is neither
gained through stoppage, nor imparted through a significant trajectory
change. By definition, acceleration means the ball is moving faster
after the player smacks or pitches it. A successful acceleration imparts
instant control on the ball for the player. This is generally a
difficult thing to do while also maintaining the ball's original course,
but failure to do so often imparts control anyway, through deflection.
(Accelerations are uncommon outside the professional leagues.)
To Be Continued...
chapters 0.0372268483042717
Irish
Pronunciation Guide
Let it be known from the beginning that readers are free to pronounce
the names in this book however they see fit. It’s supposed to be a good
time, so I do not wish to steal anyone’s marshmallows by telling them
they’re “saying it wrong.” However, for those readers who place a
premium on accuracy, I have provided an informal guide to some names and
words that may be a bit confusing for English readers, since Irish
phonetics aren’t necessarily those of English. One thing to keep in mind
is that diacritical marks above the vowels do not indicate a stressed
syllable but rather a certain vowel sound.
Names
Aenghus Óg = Angus OHG (long o, as in doe, not short o, as in log)
Airmid = AIR mit
Bres = Bress
Brighid = BRI yit (or close to BREE yit) in Old Irish. Modern Irish has
changed this to Bríd (pronounced like Breed), changing the vowel sound
and eliminating the g entirely because English speakers kept pronouncing
the g with a j sound. Names like Bridget are Anglicized versions of the
original Irish name
Cairbre = CAR bre, where you kind of roll the r and the e is pronounced
as in egg
Conaire = KON uh ra
Cúchulainn = Koo HOO lin (the Irish ch is pronounced like an h low in
the throat, like a Spanish j, never with a hard k sound or as in the
English chew)
Dian Cecht = DEE an KAY
Fianna = Fee AH na
Finn Mac Cumhaill = FIN mac COO will
Flidais = FLIH dish
Fragarach = FRAG ah rah
Granuaile = GRAWN ya WALE
Lugh Lámhfhada = Loo LAW wah duh
Manannan Mac Lir = MAH nah NON mac LEER
Miach = ME ah
Mogh Nuadhat = Moh NU ah dah
Moralltach = MOR ul TAH
Ó Suileabháin = Oh SULL uh ven (pronounced like O’Sullivan, it’s just
the Irish spelling)
Siodhachan = SHE ya han (remember the guttural h for the Irish ch; don’t
go near a hard k sound)
Tuatha Dé Danann = Too AH ha day DAN an
Places
Gabhra = GO rah
Mag Mell = Mah MEL
Magh Léna = Moy LAY na
chapters 0.025475597009062767
Twitter
Q. How many unique English tweets are possible? How long would it take
for the population of the world to read them all out loud?—Eric H,
Hopatcong, NJ
High up in the North in the land called Svithjod, there stands a rock.
It is a hundred miles high and a hundred miles wide. Once every thousand
years a little bird comes to this rock to sharpen its beak. When the
rock has thus been worn away, then a single day of eternity will have
gone by.
—Hendrik Willem Van Loon
A. Tweets are 140 characters long. There are 26 letters in English—27 if
you include spaces. Using that alphabet, there are 27140 ≈ 10200
possible strings.
But Twitter doesn’t limit you to those characters. You have all of
Unicode to play with, which has room for over a million different
characters. The way Twitter counts Unicode characters is complicated,
but the number of possible strings could be as high as 10800.
Of course, almost all of them would be meaningless jumbles of characters
from a dozen different languages. Even if you’re limited to the 26
English letters, the strings would be full of meaningless jumbles like
“ptikobj.” Eric’s question was about tweets that actually say something
in English. How many of those are possible?
This is a tough question. Your first impulse might be to allow only
English words. Then you could further restrict it to grammatically valid
sentences.
But it gets tricky. For example, “Hi, I’m Mxyztplk” is a grammatically
valid sentence if your name happens to be Mxyztplk. (Come to think of
it, it’s just as grammatically valid if you’re lying.) Clearly, it
doesn’t make sense to count every string that starts with “Hi,
I’m . . . ” as a separate sentence. To a normal
English speaker, “Hi, I’m Mxyztplk” is basically indistinguishable from
“Hi, I’m Mxzkqklt,” and shouldn’t both count. But “Hi, I’m xPoKeFaNx” is
definitely recognizably different from the first two, even though
“xPoKeFaNx” isn’t an English word by any stretch of the imagination.
Our way of measuring distinctiveness seems to be falling apart.
Fortunately, there’s a better
chapters 0.024236716330051422
Informational
- How Does a Sky Ship Fly
How Does a Sky Ship Fly The great sky ships of the Third Age are
considered by many to represent the pinnacle of dwarf magical
technology.But how exactly did they fly?Powered flight involves
generating sufficient lift and thrust to first get an object off the
ground and then move it around. Although this can theoretically be
achieved through purely mundane means, extended flight that doesn't end
in the object involved either crashing or exploding at the end proved
elusive. It turns out that the various mundane explosives and
propellants that the dwarves had developed over the Ages were quite
reasonable for projectiles… but less reasonable for transport.The answer
was to use magic. Runes and spells for flight, weight reduction, and
gravity manipulation have existed since the First Age. Indeed, many of
them were known to the dwarves of the Third Age who used them for
scouting, mining, and transport. However, these runes and spells all
shared the same weakness – they had to be cast by skilled
individuals.There simply weren't enough dwarves who could use proper
flight runes or spells to make flying a viable option on a large scale.
Even worse, none of the dwarves was capable of transporting the sorts of
heavy loads that terrestrial transport could handle with ease. It was a
question of both numbers and raw power.To address these issues, the
dwarves developed two methods for 'capturing' a spell for later use:
dwarven script and spell-stones.Dwarven script can be thought of as an
attempt to mimic runes. Rather than manipulating the story of the world
as runes do, dwarven script is a way of expressing certain ordered
spells in a long-lasting format. That way, rather than relying on
someone continuously casting a particular spell, dwarves runes can be
inscribed onto an object. When sufficient magic is run through the
dwarven scrip, it will cast the required spell.There are several issues
with dwarven script. First and foremost, it is not very flexible. What
you write is what you get. The only variation you can do is to either
give the script more or less power. This makes it well suited for
applications where varying the intensity of the spell is all that is
required and poorly suited for applications where greater flexibility is
necessary.Dwarven script is also much better for certain kinds of spell
than others for reasons that even the dwarves do not understand. In
particular, it is best for spells that modify the status of objects. For
instance, using dwarven script to make an object lighter is generally
easier
chapters 0.023731037974357605
Good Morning
Brother
Chapter 001
Good Morning Brother
Zorian's eyes abruptly shot open as a sharp pain erupted from his
stomach. His whole body convulsed, buckling against the object that fell
on him, and suddenly he was wide awake, not a trace of drowsiness in
his mind.
"Good morning, brother!" an annoyingly cheerful voice sounded right on
top of him. "Morning, morning, MORNING!"
Zorian glared at his little sister, but she just smiled back at him
cheekily, still sprawled across his stomach. She was humming to herself
in obvious satisfaction, kicking her feet playfully in the air as she
studied the giant world map Zorian had tacked to the wall next to his
bed. Or rather, pretended to study – Zorian could see her watching him
intently out of the corner of her eyes for a reaction.
This was what he got for not arcane locking the door and setting up a
basic alarm perimeter around his bed.
"Get off," he told her in the calmest voice he could muster.
"Mom said to wake you up," she said matter-of-factly, not budging from
her spot.
"Not like this, she didn't," Zorian grumbled, swallowing his irritation
and patiently waiting till she dropped her guard. Predictably, Kirielle
grew visibly agitated after only a few moments of this pretend
disinterest. Just before she could blow up, Zorian quickly grasped her
legs and chest and flipped her over the edge of the bed. She fell to the
floor with a thud and an indignant yelp, and Zorian quickly jumped to
his feet to better respond to any violence she might decide to retaliate
with. He glanced down on her and sniffed disdainfully. "I'll be sure to
remember this the next time I'm asked to wake you up."
"Fat chance of that," she retorted defiantly. "You always sleep longer
than I do."
Zorian simply sighed in defeat. The little imp was right about that.
"So…" she began excitedly, jumping to her feet, "are you excited?"
Zorian watched her for a moment as she bounced around his room like a
monkey on caffeine. Sometimes he wished he had some of that boundless
energy of hers. But only some.
"About what?" Zorian asked innocently, feigning ignorance. He knew what
she meant, of course
chapters 0.022305751219391823
High
Throw
Q. How high can a human throw something?—Irish Dave on the Isle of Man
A. Humans are good at throwing things. In fact, we’re great at it; no
other animal can throw stuff like we can.
It’s true that chimpanzees hurl feces (and, on rare occasions, stones),
but they’re not nearly as accurate or precise as humans. Antlions throw
sand, but they don’t aim it. Archerfish hunt insects by throwing water
droplets, but they use specialized mouths instead of arms. Horned
lizards shoot jets of blood from their eyes for distances of up to 5
feet. I don’t know why they do this because whenever I reach the phrase
“shoot jets of blood from their eyes” in an article I just stop there
and stare at it until I need to lie down.
So while there are other animals that use projectiles, we’re just about
the only animal that can grab a random object and reliably nail a
target. In fact, we’re so good at it that some researchers have
suggested that rock-throwing played a central role in the evolution of
the modern human brain.
Throwing is hard.1 In order to deliver a baseball to a batter, a pitcher
has to release the ball at exactly the right point in the throw. A
timing error of half a millisecond in either direction is enough to
cause the ball to miss the strike zone.
To put that in perspective, it takes about five milliseconds for the
fastest nerve impulse to travel the length of the arm. That means that
when your arm is still rotating toward the correct position, the signal
to release the ball is already at your wrist. In terms of timing, this
is like a drummer dropping a drumstick from the tenth story and hitting a
drum on the ground on the correct beat.
We seem to be much better at throwing things forward than throwing them
upward.2 Since we’re going for maximum height, we could use projectiles
that curve upward when you throw them forward; the Aerobie Orbiters I
had when I was a kid often got stuck in the highest treetops.3 But we
could also sidestep the whole problem by using a device like this one:
A mechanism for hitting yourself in the head with a baseball after a
four-second delay
We could use a springboard, a greased chute, or even a dangling
sling—anything that redirects the object upward without adding to or
subtracting from
chapters 0.02204873412847519
A
Hero's War by jseah
Category: FantasyGenre: Adventure, FantasyLanguage: EnglishStatus:
In-ProgressPublished: 2015-02-27 14:00:23Updated: 2019-12-26
07:46:29Packaged: 2020-05-16 12:36:08Rating: TChapters: 126Words:
522,390Publisher: www.fictionpress.comSummary: Morey is summoned to a
fantasy world under siege by the forces of darkness, called a Hero by
the natives. Unknown to them, they got two 'Heroes' for the price of
one. Dumped into a strange and dangerous fantasy world, Cato struggles
to find out what happened to him and where he is. And perhaps there are
advantages to not being a Hero. And perhaps not all the legends are
true...
chapters 0.021386846899986267
more
specialized. And tricky.
HOW TIER 2 JOBS WORK
To get a Tier Two job, you have to combine one or more Tier One jobs.
Sometimes you have to mix in a crafting job, too. When you do that, you
get a specialized job that pulls from the basic themes of its Tier One
Jobs.
Golemists, for example, are a Tier 2 job that mixes Animators and
Enchanters. They craft specialized magical dolls and statues out of
various materials, then bring them to life permanently.
Lycanthropes are Tier Two jobs that draw on the best parts of Shamans
and Tamers. They shapechange into their favored beast, and run with
packs of those beasts.
Gunslingers are a simple mix of Archer and Duelist, with Tinker on the
side so that they can actually make guns.
And so on, and so forth, with so many possible combinations that
nobody's sure that there's a fixed amount. In any case, merely having
the two classes isn't enough, it also takes either a teacher with the
Tier Two class explaining what to do, or some research and
experimentation to find the required unlock.
With this system, it's possible to make just about any class out there,
from combinations of the base 28 and maybe a craft skill. And even
combinations of the same Tier One jobs will unlock different Tier 2 job,
depending on the unlock and the intent. Slap a Cultist with an Oracle
and go live in the woods and cook children, and you can unlock a witch.
Mix Cultist and Oracle another way and go rave on street corners, and
you end up with a Doomsayer, who rouses mobs to madness and murder...
It's worth noting that the Tier 2 jobs aren't necessarily more powerful
than the Tier 1 jobs, but they are more complex, generally, and more
specialized.
Also note that learning a Tier 2 job doesn't negate or replace a Tier 1
job. If you become a Golemist, your Animator skills are still there,
still useful for things the Golemist skills don't cover.
This also means that most adventurers don't have a lot of Tier Two jobs.
And that the ones who do plan very, very carefully for it. Which is
generally a good idea, otherwise you live your life foolishly, wandering
around, grabbing random careers from the unlocks you stumble upon
naturally.
I mean, who the hell DOES that? The sages all agree, that is
chapters 0.021122194826602936
Harry
Is A Dragon, And That's Okay by Saphroneth
Category: Harry PotterGenre: Adventure, HumorLanguage:
EnglishCharacters: Harry P.Status: In-ProgressPublished: 2019-03-10
19:37:40Updated: 2020-06-14 11:39:13Packaged: 2020-06-14 15:42:01Rating:
TChapters: 74Words: 477,850Publisher: www.fanfiction.netSummary: Harry
Potter is a dragon. He's been a dragon for several years, and frankly
he's quite used to the idea - after all, in his experience nobody ever
comments about it, so presumably it's just what happens sometimes.
Magic, though, THAT is something entirely new. Comedy fic, leading on
from the consequences of one... admittedly quite large... change. Cover
art by amalgamzaku.
books -0.009707336314022541
A.
K. Larkwood's The Unspoken Name is a stunning debut fantasy about an orc
priestess turned wizard's assassin.
What if you knew how and when you will die?
Csorwe does—she will climb the mountain, enter the Shrine of the
Unspoken, and gain the most honored title: sacrifice.
But on the day of her foretold death, a powerful mage offers her a new
fate. Leave with him, and live. Turn away from her destiny and her god
to become a thief, a spy, an assassin—the wizard's loyal sword. Topple
an empire, and help him reclaim his seat of power.
But Csorwe will soon learn—gods remember, and if you live long enough,
all debts come due.
books -0.012023785151541233
Fairy
godmothers develop a very deep understanding about human nature, which
makes the good ones kind and the bad ones powerful.
Inheriting a fairy godmother role seemed an easy job . . . After all,
how difficult could it be to make sure that a servant girl doesn't marry
a prince?
Quite hard, actually, even for the witches Granny Weatherwax, Nanny Ogg
and Magrat Garlick. That's the problem with real life – it tends to get
in the way of a good story, and a good story is hard to resist.
Servant girls have to marry the prince, whether they want to or not. You
can't fight a Happy Ending, especially when it comes with glass
slippers and a rival Fairy Godmother who has made Destiny an offer it
can't refuse.
books -0.01761065423488617
Quint
Trilogy I
'Oh, Sky above!' Linius wailed.'If I had known then what I know
now...'Quint, son of a sky pirate captain, and new apprentice to Linius
Pallitax, the Most High Academe, has been given some highly important
tasks. Just how important, Quint is about to find out as he and Linius's
only daughter, Maris, are plunged into a terrifying adventure that
takes them deep within the rock upon which Sanctaphrax is built. Here,
they unwittingly invoke an ancient curse--the curse of the gloamglozer
.. .
books -0.022309398278594017
Mistborn: Secret
History is a companion story to the original Mistborn trilogy.
As such, it contains HUGE SPOILERS for the books Mistborn (The Final
Empire), The Well of Ascension, and The Hero of Ages. It also contains
very minor spoilers for the book The Bands of Mourning.
Mistborn: Secret History builds upon the characterization, events, and
worldbuilding of the original trilogy. Reading it without that
background will be a confusing process at best.
In short, this isn't the place to start your journey into Mistborn
(though if you have read the trilogy - but it has been a while - you
should be just fine, so long as you remember the characters and the
general plot of the books).
Saying anything more here risks revealing too much. Even knowledge of
this story's existence is, in a way, a spoiler.
There's always another secret.
books -0.023662999272346497
The
Wheel of Time is a series of high fantasy novels written by American
author James Oliver Rigney Jr., under his pen name of Robert Jordan.
Originally planned as a six-book series, The Wheel of Time spanned
fourteen volumes, in addition to a prequel novel and two companion
books. Jordan began writing the first volume, The Eye of the World, in
1984, and it was published in January 1990.
[TODO: add actual description of plot/setting or something]
books -0.025743817910552025
Terry Pratchett/The Colour of Magic (320)/The Colour of Magic - Terry Pratchett.epub
books -0.027468577027320862
The
stunning Hunger Games trilogy is complete!The extraordinary, ground
breaking New York Times bestsellers The Hunger Games and Catching Fire,
along with the third book in The Hunger Games trilogy by Suzanne
Collins, Mockingjay, are available for the first time ever in e-book.
Stunning, gripping, and powerful. The trilogy is now complete!
books -0.028571251779794693
Something
is coming after Tiffany...
Tiffany Aching is ready to begin her apprenticeship in magic. She
expects spells and magic — not chores and ill-tempered nanny goats!
Surely there must be more to witchcraft than this!
What Tiffany doesn't know is that an insidious, disembodied creature is
pursuing her. This time, neither Mistress Weatherwax (the greatest witch
in the world) nor the fierce, six-inch-high Wee Free Men can protect
her. In the end, it will take all of Tiffany's inner strength to save
herself ... if it can be done at all.
A Story of Discworld
books -0.030815355479717255
K. J. Parker/How to Rule an Empire and Get Away with It (1040)/How to Rule an Empire and Get Away with It - K. J. Parker.epub
books -0.031961534172296524
By
the age of fifteen, Lasgol has endured a hard childhood and lives,
cornered and hated, in a small village in the North. He is the son of
the traitor, the man who betrayed the kingdom and tried to kill the
King. His only companions are the mountains and the snow, ever-present
in the region. Yet he refuses to believe that his father is guilty, in
spite of all the evidence that points to the fact, even though the King
himself was a witness to the betrayal.Lasgol is determined to clear his
father's name, and to do this he has only a single option: the School of
Rangers, a secret place where the respected and feared defenders of the
lands of the kingdom are trained for four years. Going there is insane,
hate and death await him there. But as the son of a Ranger, he is
entitled to attend.At the Camp he will find himself involved in
political intrigues, disloyalties and murder. He will encounter hatred
and fearsome enemies, but also a handful of friends, novices as much out
of place as he is himself, determined to do whatever is necessary to
pass the first year ... without dying in the attempt.Will Lasgol survive
the first year of instruction at the Rangers' Camp? Will he find out
what happened to his father? Will he be able to clear his name?Find out
while you follow fascinating adventures with a group of characters you
will fall in love with.The Traitor's Son is the first book in the Path
of the Ranger coming of age epic fantasy series. If you like sword and
sorcery, treachery and intrigue, powerful magic and mystery, action and
romance, then you'll love Pedro Urvi's kingdom-spanning tale.
books -0.03355095535516739
The
apprentice Skeeve is just getting used to his duties as Court Magician
of Possiltum. Then King Roderick decides to take a powder, leaving
Skeeve in his place to marry his homicidal fiancee and face the Mob's
fairy godfather--who makes him an offer he can't refuse.
books -0.03417089208960533
Unknown/Beowulf_ An Anglo-Saxon Epic Poem (302)/Beowulf_ An Anglo-Saxon Epic Poem - Unknown.epub
books -0.036206163465976715
Terry
Pratchett/The Amazing Maurice and His Educated Rodents (382)/The
Amazing Maurice and His Educated Roden - Terry Pratchett.epub
books -0.036343831568956375
Terry Pratchett/Making Money (390)/Making Money - Terry Pratchett.epub
books -0.03648901358246803
Terry Pratchett/The Fifth Elephant (378)/The Fifth Elephant - Terry Pratchett.epub
books -0.03824931010603905
AzaleaEllis/A Practical Guide to Sorcery (1392)/A Practical Guide to Sorcery - AzaleaEllis.epub
books -0.03912026062607765
Terry Pratchett/Thief of Time (380)/Thief of Time - Terry Pratchett.epub
books -0.0392368920147419
Terry Pratchett/The Shepherd's Crown (395)/The Shepherd's Crown - Terry Pratchett.epub
books -0.03943955898284912
Terry Pratchett/A Hat Full of Sky (386)/A Hat Full of Sky - Terry Pratchett.epub
books -0.039448902010917664
Peter J Lee/Dear Spellbook, Volume 1_ Sorcerer (1365)/Dear Spellbook, Volume 1_ Sorcerer - Peter J Lee.epub