Thursday, February 15, 2018

Monthly Finance Post

I think I said last time that if I made it through running out of oil then the major problem would be that needing to get the stopgap oil and then normal oil would make it so I wasn't prepared when the non-monthly expenses next rolled around and thus would act as a bridge that past crisis could use to move into the future or . . . something like that.

Anyway, it's happened.  Taxes and insurance.  I've lost track of how much the insurance is (I'm not at home right now, which is good because I can turn down the heat, within reason, and make the oil last longer) but it and the taxes together add up to $910 +/- $12

And I really wish I were paying down debt instead.  I'm $392.48 away from eliminating my highest interest debt, which seems reasonable to hope for (though not to expect) and $1,467.84 away from paying off the next highest interest debt, which is clearly beyond my means.

And I need stuff, too

My threadbare shirts are beginning to sprout holes in scandalous places.  I could really use some kind of shorts/leggings/yoga pants/whatever that could be worn beneath a skirt to prevent my legs from rubbing each other raw.  My only belt broke on the 4th day of Christmas which has seriously fucked with my ability to wear any of the pants I own.

I could use shelving to help in house cleaning efforts.

Things.  Stuff.  Things and stuff.

That's my finance post.

Woo.

Friday, February 9, 2018

Early exposition for a fantasy game with rideable animals

[Originally posted at Ana Mardoll's Ramblings.]

This came from thinking about the idea of a game where you ride non-traditional stuff.  Main character has just woken up from prolonged medically induced sleep and not-actually-a-doctor is delivering exposition by way of seeing what the character knows and filling in any gaps.

Main character has most emphatically not received retrograde amnesia rendering them a blank slate.  Name, rank, serial number, home address, and person in power at the time of going under are all recalled quite well (except rank and serial number as the character has neither), the procedure can, however, leave fuzzy spots and, importantly, things have changed, which is part of why the character is being helped by not-actually-a-doctor instead of a doctor as would have been expected..

-

Not-actually-a-doctor: Ok, that's all good, next question is what you know about humans.

Main character: I've never actually met one, so just the basics: short ears, short lives, short tempers.

Not-actually-a-doctor: That covers most of it.  Many of their strengths are likely coping mechanisms which allow them to survive when they'll never have more than a century of experience to help them out.  They're adaptable almost beyond comprehension.  I once saw one seamlessly change strategy twelve times in the space of two minutes because of changing conditions.

Not-actually-a-doctor: That's not important though, more of a curiosity.  While you were sleeping the human nation to the west was destroyed with nearly unimaginable speed.  The time that passed from the start of the attack to when the humans were forced to give up all hope of victory and instead concentrate on evacuating as many as possible was less than a week.

Not-actually-a-doctor: Anyway, this area is filled with refugees and you most definitely will be meeting humans now.  So, with that in mind, the most important thing for you to understand is that humans are heavy.

Main character: Heavy?

Not-actually-a-doctor: Yeah, really heavy.  They look a lot like us but the weight difference is absurd.  Snow or mud that you'd walk over the top of with ease they'll sink into and struggle through.  They can also use it to their advantage, if one runs right into you or jumps on you from above you will go down.  Hard.

Not-actually-a-doctor: But I'm mostly telling you this because of riding.  Never assume that because you can ride something a human can too. You'll break backs or cause lifelong injury if you do.  Donkeys, camels, horses, moose*, elephants, and dragons.  Don't put a human on anything else because the simple fact is that you don't know.  Something that can carry multiple elves no problem might not be able to take the strain of a human.

Main character: Rhinoceros?

Not-actually-a-doctor: I don't know, but my guess would be that the deciding factor in attempting that is how badly you wanted to be rid of the human.

-

* Can anyone confirm or deny moose?  They can and have been ridden (the plan for a moose cavalry in relatively modern times was only nixed when it turned out the moose could not be trained to be ok with sound of gunfire) but I can't find anything saying whether that hurts the moose's spine.  I wouldn't expect it to given how . . . moosey moose are, but as noted by the fictional elf above, you don't actually know how it's going to work out.

Also, interesting fact discovered when I was trying to find out about the resilience or lack thereof of moose spines:

Some reindeer have been bred to be ridden which makes them have the reindeer equivalent of super spines.  This is not, in itself, enough.  Special saddles must be used to reduce the load on the the spine so that the effects of the breeding actually allow them to be safely ridden.s

The saddle is designed to put weight (I'm not sure how large a portion we're talking about) onto the withers (shoulder blades) thus having the legs (which are durable enough for the job) bear a portion of the weight meaning that less needs to be supported by the animal's spine.

Sunday, February 4, 2018

Infinity and Gaps, well . . . mostly the gap at infinity (Mathematics)

[This is basically mathematical brain dump, and the only real editing was to remove sections that got duplicated in the dumping process.  Read at your peril.]

In high school I came up with my own definition of infinity:
Infinity is the point at which things stop making sense.
Throughout university I stuck to this definition.

I've come to realize that many (though by no means all) of the oddities I have long associated with infinity are actually properties of gaps.  This is because the infinity that we almost always talked about in the branches of math I partake in was sideways eight infinity (∞) which is in fact the gap at infinity.

We occasionally touched on things like the alephs (the ℵ numbers) which are cardinals, but my chosen path through math seldom dealt with cardinal numbers (and basically never touched ordinals) and instead "infinity" almost always was ∞ in our discussions.

So, here's the thing, ∞ is not a number (which we always acknowledged by saying: "infinity is not a number") it's a gap.  A lot of the weirdness of ∞ (for example the fact that ∞ + 1 = ∞, the fact that ∞ + ∞ = ∞, and the fact that ∞ * ∞ = ∞) has nothing to do with the fact that ∞ is infinite, and everything to do with the fact that ∞ is a gap.

As one can probably guess from the name, gaps are generally between things.  ∞ itself is the gap between positive finite and positive infinite numbers.  More generally, anything with an absolute value smaller than it is positive, anything with a larger absolute value is infinite.  The only things equal absolute values are ∞ and −∞, which are gaps rather than numbers.

It's kind of obvious, once you have that understanding, how gaps work.  The thing is, I didn't.  I thought that how gaps worked was how infinity worked.

Things would have been clearer if I'd spent more time thinking about 1/∞

But 1/∞ is zero.

Well . . . ish.

That's what I was taught and that's what I thought, but it's only true under certain circumstances.  The key point is that zero is undirected.

What?

+0 = −0

So?

So if 1/∞ = 0 then:

1/∞ = 0 = −0 = −1/∞

which would mean that ∞ = −∞.

That's not a bad result.  It actually works for various theories of stuff and it'll remove all those pesky discontinuities from things like the graph of the tangent function or y = 1/x (but not y = 1/x2), but usually we do not intend for ∞ to be equal to −∞, and so, in those cases, we have to accept that 1/∞ does not equal zero.

Then the question becomes what it does equal.

What we know about reciprocals helps here.

We're dealing with positive infinity, so we'll think in terms of positive numbers.  We know that for x > y > 0 it is true that 1/y > 1/x > 0.

Since ∞ is greater than all positive numbers, 1/∞ must be less than them while still being greater than zero.

I've seen people call this result η (eta.)

The reason that thinking about this would have helped me is that η has many of the same properties as ∞ (η + η = η and η * η = η, for example) but it is most definitely not infinite.  It's actually really, really small.

It is, in fact, the gap between the positive infinitesimals (numbers so small that you need infinite quantities of them just to add up to the smallest positive real numbers) and the rest of the positive numbers.

So very much not infinite, but the same as ∞ in many ways.  Why?  Because they're both gaps.  So let's talk about properties of gaps.

The first thing about gaps is that they don't play well with others.  When it comes to addition, they devour anything smaller (in absolute value) than them.  That's why ∞ plus or minus any real number is still ∞.

This result is not true of infinite things in general.

If we take the "simplest" infinite number, ω, and add one to it we get a new number which is larger than it is.  How much larger?  One larger.  Just like we'd expect when adding one to any number.

It is true of all gaps though.  If we adjust for scale we see that the same rule that makes ∞ eat any finite number added to or subtracted from it makes η eat any infinitesimal added to or subtracted from it.

The second thing for gaps is that they play strangely with themselves.

If you add gaps of different scales the larger one eats the smaller one and you're left with just the larger one, but interesting things happen when you add gaps of the same scale.

A gap minus itself is zero, just like you'd expect.  A gap plus itself is . . . the same gap.  From that we can extend to the fact that a gap times any finite number is the same gap.

Going back to the same reasoning we use to prove that a gap plus itself is the same gap, we can also show that a gap times itself is the same gap.

Note that I'm not proving (or even demonstrating) any of this now.  Just telling you about is.  Regardless, so far we've got some decent properties.

For a gap "g" and any non-zero real number "x":

g − g = 0
g + g = g
g * x = g
g * g = g

This leads to some of the more extreme wonkyness you'll meet in ∞.  In fact, you just need the first two to get things to a really weird place.

For example, I give you the infinite sheep theft and con:

Someone has done great evil to you and therefore, by way of revenge, you decide to steal all of their infinite (as in {1, 2, 3, . . .}) sheep and get away with it.

Here's how you do it.

When they're not looking you steal some of their sheep.  You line them up and take every second one.  You leave sheep number one, take sheep number two, leave sheep number three, and so forth.

How many sheep do you have?

Well your sheep were {2, 4, 6, ...} but that's not how one counts.  Sheep 2 is clearly your first sheep, sheep four is clearly your second sheep, and it doesn't take too much thought to realize that sheep 2n is your nth sheep.  So even though they are sheep {2, 4, 6, ...} you count them as sheep {1, 2, 3, ...} which happens to be infinity.  The exact same infinity as the total number of sheep in their flock before you stole any.

You just took infinite sheep from an infinite flock, and both those infinities were the same infinity.  Surely someone will notice!

Actually, no.

When your enemy counts up their sheep they're going to find that they have the same amount as before.  We don't really care what order they count them in, it only matters that when one is counted it's taken out of the equation and not counted again, so we can put the sheep your enemy counts into the same order as when you put the sheep in a line.

Or we can just assume that the sheep always line up in the same order, moving forward to fill in any empty spaces resulting from removed sheep.  Thus sheep one is right in front again, while sheep three has moved forward to stand behind, and so on.

Either way.

Your enemy has sheep {1, 3, 5, ...} but they don't know you took the even ones so when they count sheep three they'll be counting it as though it were sheep two, when they count sheep five they'll count it as though it is sheep three, and so forth.  Sheep 2n-1 is counted as though it is sheep n.

At the end of the count they find they have {1, 2, 3, . . .} sheep, which is exactly how many they had before.  (This in spite of the fact that their remaining sheep are really only the sheep that had odd numbers when you divided them.)  They conclude none have been stolen.

You're in the clear.

But you wanted to take all their sheep as your revenge.

Thus begins the con.

You contrive a situation where your flock and their flock have to be combined for a time.  Maybe they're put in quarantine in case they have the much feared sheep blight, maybe . . . anything really.

Whatever the case, your enemy and you don't exactly get along so to make sure you both get back the same number of sheep as you put in, you make a tally.  You do it in public and above board and squeaky clean.

First they put in one of their sheep and make a tally mark (perhaps in their family crest or some such) then you put in one of your sheep and make a tally mark (perhaps in your initials or some such.)  You repeat this until all the sheep are put in.

Some interesting things have happened here.  One is that they have all the odd tally marks and you have all the even.  The other is that sheep {1, 2, 3, 4, 5, 6, . . .} are the correct numbers again.  The odds are the ones you didn't steal, the evens are the ones you did.

You make sure that you take your sheep first, perhaps complaining about how long the alternating thing took.  (It took infinite time, by the way.)

Every second tally corresponds to one of your sheep.  The deal was that you get the same number of sheep back, not the same sheep, so to simplify things you just grab the sheep from the front of the line.

At tally mark two, which is marked in such a way to let everyone know it really is yours, you take sheep 1, at tally mark 4 you take sheep 2, and so on with taking sheep n for mark 2n until you run out of tally marks.

You then go back home with your infinite sheep and have them graze at the infinite pasture.

When it comes time for your enemy to take their half of the sheep, they find there are none left.  What the fuck?

Everyone knows that you didn't take extra sheep, you did the whole thing in public and you only took one sheep for each of your tally marks.

You're unimpeachable.  They're out of sheep.

What happened?  Well for mark two you took one of their sheep, for mark four you took on of yours, and you alternated until you ran out of marks.  We've already shown that there are as many even numbers (the marks you used) as there are odd numbers (their sheep) and even numbers (your sheep) combined (the sheep you took) so you took all the sheep.

All the sheep?

ALL THE SHEEP!

In more formal language, you abused the fact that addition of gaps is non-associative to unbalance the equation at every stage of the game.

Recall that for any gap "g"
  1. g − g =0
  2. g + g = g
Short version:

For the theft you did (1), for the con you did (2):
(1) ∞ + (∞ − ∞) = ∞ + 0 = ∞
(2) (∞ + ∞) − ∞ = ∞ − ∞ = 0

(Short version is over.)

You were only able to reach those points (which are themselves perfectly sound mathematical statements) by ignoring the fact that, when discussing gaps the rules for addition are different than they are for numbers.

The associative property is the one that states:
a + (b + c) = (a + b) + c

That clearly doesn't work for gaps.  (1) above is the same as the left side and it evaluated to ∞, (2) above is the same as the right side and it evaluated to 0.  Since 0 ≠ ∞, we know that the associative property doesn't hold for addition of gaps.

(Long version of the explanation)

Again, for any gap "g"
  1. g − g =0
  2. g + g = g
In the beginning there were ∞ sheep.

Using property two
∞ = ∞ + ∞
which you achieved by separating the sheep into even and odd numbered sheep.

Then you took only the even numbered sheep
∞ + (∞ − ∞) = ∞ + 0 = ∞
which left them with ∞ sheep, the same amount they started with.

That was how you stole infinite sheep without anyone noticing.

Then you each created tally marks equivalent to your each of your sheep
∞ + ∞ = ∞ + ∞

Then when it came time to take the sheep back out, you combined the sheep (by taking them from the front rather than every other) and removed an amount equivalent to your tally marks from that.
(∞ + ∞) − ∞ = ∞ − ∞ = 0

Thus leaving zero sheep.



Presumably everyone has stopped reading by now, so lets take things even more into the weeds.  Not formal proofs, per se, but let's demonstrate things.

I've said that gaps eat everything smaller then themselves (under addition.)  How do we know this?

Well, this is really easy to see with ∞.

Everything (positive) on one side is finite, everything on the other side is infinite, and we know certain things about such numbers.

For example: any finite number, any finite number, is a finite number.

For any finite numbers x and y,
if x + y = z
then z is a finite number.

This is where I ask you to imagine ∞ − y.  Why minus instead of plus?  Why "y" instead of "x"?  Because I wrote a lot of this before thinking through simple ways to do things.

Now then, if ∞ − y is less than ∞, then it must be finite.  (I should probably be using absolute values, but we aren't seriously expecting subtracting a finite number from will bring it to negative ∞ or beyond, are we?)

So take the finite number "∞ − y" and call it "x".  Take the finite number "y" and call it "y".  Plug it into the above note on finite numbers and we get x + y = z where z is a finite number.

Now solve for z.

Well that becomes (∞ − y) + y = z.

The associtive property might not work for gaps, but it's still as stellar as ever on numbers like y, so we can swap that to ∞ + (− y + y) = z, which is ∞ + 0 = z, and thus ∞ = z.

But z is finite and ∞ is infinite.  Thus there's a contradiction.  Thus ∞ - y can't be less than ∞ for any finite number y.

In symbols:


If ∞ − y < ∞,
then ∞ − y is finite.

We know that for x, y finite, and x + y = z
z is finite.

We set x = (∞ − y), y = y, and solve for z:
∞ − y + y = ∞ + (y − y) = ∞ + 0 = ∞
z = ∞
But z is finite and ∞ is infinite.
Contradiction
🡒🡐
Thus: ∞ − y is not less than ∞
(Or: thus ∞ − y ≥ ∞)

And, for the record, I'm somewhat pissed off that I can find this symbol "🡘" but not the inverse where the two arrow heads are colliding in the middle.

We're actually already done, we just have to say it.

Specifically:
Take the resulting expression
∞ − y ≥ ∞
and add y to both sides
∞ ≥ ∞ + y


For every finite number "y" there is a finite number "z" such that y = −z.
Substitute "−z" for "y"
∞ ≥ ∞ − z

We have already proven
∞ > ∞ − z is false
for all finite numbers z.

Therefore:
∞ = ∞ − z

Putting y back in to make things all neat and additive again:
∞ = ∞ + y, for all finite numbers y

Woo!  Headache.

I could not find damn "not >" and "not <" signs.  This is also the point where I realized I'd already used "z". Whatever. The above shows what happens when we add things smaller than ∞ to ∞.  We can, however, add things larger.  ω + ∞ is a thing.  It's the gap that separates ω + x from ω + y for all positive finite x and positive infinite y.

When not using infinite numbers or larger gaps, though, ∞ devours everything we might meaningfully throw at it.  With two exceptions.  Those exceptions are ∞ itself and -∞.



We made use of how ∞ + ∞ is equal to ∞ above.  We can work it out here using the properties of gaps.

Say that ∞ + ∞ = [?].  Now pick any number between ∞ and [?].  Call that "x" (because we pretty much always call it "x" unless we have a good reason not to.)

x is larger than ∞ and so infinite.  x is lower than [?].  So half of x must be smaller than ∞.  Anything smaller than ∞ is finite.  With x infinite and half of x finite, the question becomes, "What's the finite fucking number that becomes infinite when you double it?"  Or we could say, "Solve for x/2."

Either way, it doesn't work.  There can't be anything between ∞ + ∞ and ∞, which means they're the same thing.  (Informal proof by contradiction for the win.)

We can do more or less the same thing for η, except upside down and backwards.

And we can do the same thing for multiplication.  You can't have an infinite number with a finite square root.



Or, we could finally talk about eta a bit

Let η * η = [?].  We're dealing with positive things less than one, so if [?] doesn't equal η then it must be smaller.  (0 ≤ |x*x| ≤ |x| for all x such that |x| ≤ 1)  With that in mind, choose a y such that [?] ≤ y ≤ η.

Consider √y.  Since [?] ≤ y, η ≤ √y.

As I noted, this turns out to be the same thing we did with addition.  Everything larger than η is not infinitesimal, everything smaller (or equal) is.  You can't have a non-infinitesimal whose square is infinitesimal.  Thus √y = η = y = [?]

The key point is that since [?] = η * η we've just shown η * η = η.

Not that that really matters to us.

Addition is where it's at.

Or at least it was back when the sheep theft came right after this.



Beyond stealing sheep it's worth noting that since g + g = g we can collapse any finite length of g-only addition.

So g + g + g + g + . . . + g = g.  Thus g*n = g, for a any natural number n.  We can actually expand that to g*x = g provided that x is comparable to 1.  Comparable, here, means that if the absolute value of x is less than one there's some natural number (we use those a lot) for which |n*x| > 1, and if the absolute value of x is greater than one there's a natural number n such that n*1 > x.  If I'd used "y" instead of "1" then I'd have to stipulate that the inequalities used "|y|" instead of "y".

The infinitesimals are not comparable to the reals which are not comparable the infinites.





Anyway, back on point, most of the weird properties I associated with infinity came from attributes of gaps, such as that.  Not all, though.  The thing about parallel lines converging, for example, is totally unrelated to gaps.

Why does any of this matter?

It turns out that there's a wonderful and rich number system that allows you to go beyond infinity (way beyond), as well as dive into the infinitesimals.  There's just one problem with it: it's riddled with gaps.

To start off, consider η and ∞ once again.  η*x is the gap below everything comparable to x, ∞*x is the gap above everything comparable to x.  Since η and ∞ are themselves times one, they're the gaps below and above (respectively) everything comparable to the positive reals.  You can also multiply them by any power of ω.  That'll get you uncountably infinite gaps right there.

There is a question of "Where does this end?" as the η*ωxs get smaller and smaller and the ∞*ωys get larger and larger.  (We could ask for the reverse, but it makes intuitive sense to ask as the lower bounds get to be of progressively smaller sets and the upper bounds become of progressively larger ones.)  Well the η*ωxs approach the gap between zero and all of the positive numbers.  The ∞*ωys approach a thing called "On".  It is the gap above all numbers (no matter how infinitely infinite their infinitude) and the reciprocal of the little gap.

The little gap is more meaningful to us when talking about how many gaps there are.  Since the gap between zero and the positives is less than the absolute value of x for all non-zero x, it can be added to or subtracted from every single number other than zero to create a new gap, with itself and negative itself basically standing in for adding it to zero, the only thing it can eat.  In other words, for every surreal number there are two of these gaps.

Those are in addition to the already infinite ones we were discussing by multiplying η or ∞ by powers of ω.  And, about those, every one of them, indeed every pure gap other than On and -On, is smaller in absolute value than infinitely many numbers.  The infinite η / ∞ times powers of ω gaps plus or minus any legal number (of which there will be infinite for whichever η or ∞ gap you're talking about) will produce brand new gaps.  At this point I shouldn't have to point out there will be infinite of them.
It turns out that we don't have a word for a collection so damn large it can contain all of the gaps.  This even though we do have words for infinite sets and proper classes, which are larger than infinite sets.

This seems to be where my rambling ran out.


⁂ ⁂

* We talked about parallel lines converging at infinity (sometimes it was a point, sometimes it was a line).

We noted how there are different sizes of infinity by looking at how there are more irrational numbers than rational ones even though there's a rational number between every two irrationals (and vice versa) so it would seem impossible for there to be more of one than the other.

One professor shared with us the story of the infinite hotel** which, though full, could accommodate (countably) infinite additional guests by shuffling rooms.

We demonstrated that there were the same number of even numbers as there were odd plus even numbers combined.

We showed that there were the same number of rational numbers (q/p for integers q and p) as there were natural numbers (1, 2, 3, . . .) in spite of the fact that natural numbers make up a tiny part of the rational numbers (the bottom of the fraction is always jammed at 1.)

We showed that there were infinitely more irrational numbers than there were rational ones, this even though we also showed that between any two irrational numbers there was a rational one.  (You try making a sequence of things from sets X and Y such that there's an element of Y between every two elements of X and have the number of Y things used be infinitely smaller than the number of X things used.)

We did all kinds of weird shit.

One definition of infinity is that a set has infinite elements when it's possible for a proper subset of it to have a one to one correspondence with the whole set.

Proper subset just means that it's not the whole set itself.  So if we've got the set {cow, cheese} the subsets are {cow}, {cheese}, {cow, cheese} and the empty set {},  The proper subsets are {cow}, {cheese}, and the empty set {}, because we get all of them by removing actual stuff from the original set.

One to one correspondance is why tally marks and counting on your fingers both work.  For every element of one set there's one and only one element of the other.

For each tally mark there is a sheep, for example, and as of the most recent rewrite I already did the sheep thing above.

The sheep thing, as demonstrated above, shows that:
infinity minus infinity is infinity
and
infinity minus infinity is zero

Like I said, the point at which things stop making sense.



** It was not as formal, or German, as Hilbert's original, and went something like this:
The hotel has rooms 1, 2, 3, and so on to infinity.  (We call this "countable infinity, by the way.)  They're all full.  In spite of this, the sign reads, "Vacancy".

A new guest arrives, and one of the people at the counter is all, "I told you we should have lit the 'No' part of the sign,"

The other just says, "No problem.  We told our guests they might be forced to move from one room to the next.  We'll put the new person in room one, have the person in room one move to room two, the person in room two move to room three . . . "

And the new guest is thus added to the roster of guests.  The same can happen if a million, a billion, a googolplex, or whatever show up.  Any finite number is fine, just move all the existing guests to the room [that number]+1.

Then infinite new guests arrive, first person is again negative, second person again says, "No problem."

"We can't move the guest in room one to room infinity plus one.  Infinity plus one is infinity!"

"No, no.  Here's what we do.  We move the guest in room one to room two, then--"

"Where does the guest in room two go?"

"To room four.  And the guest in room three goes to room six."

"We move guest in room N to room 2N."

"Exactly.  Then we put the first guest new guest in room 1, the second in room 3, and--"

"New guest N to room 2N-1."

"You got it."

And so the infinite hotel, which was already full, gives empty rooms to infinite new guests without leaving any of the old guests without a room of their own.

Then there are buses with (countably) infinite guests on them, and how many buses?  1, 2, 3, so on, infinity!

Still not a problem.

Then the irrationals arrive and the people at the desk say, "Fuck it."

Wednesday, January 31, 2018

Invoking Tash after the battle

[Originally posted at Ana Mardoll's Ramblings. Rabadash makes a big deal about being decended from Tash. He's not the only to have such ancestry, though.]
[Underlined text is taken from the original book. I'm trying out a new thing to see how it looks as I've traditionally used bold italic for that.]

"I know you. You are the foul fiend of Narnia. You are the enemy of the gods. Learn who I am, horrible phantasm. I am descended from Tash, the inexorable, the irresistible."

"As am I!" shouted Aravis.

All heads turned to Aravis, Aslan's with an eyebrow raised.

"You have come into a foreign land, made war upon it, and lost," Aravis said, walking toward Rabadash as she did. "You are now counted amongst the battle spoils and can be dealt with as the victors please. The only claim you might have laid is that you are the son of the Tisroc, may he live forever as his son is an unworthy successor, but that claim was eradicated when you set out to abduct, with the intent of raping, the ruler of another country: High Queen Susan of Narnia, ally to Archenland."

Aravis and Rabadash were now scarcely more than an arm's length apart.

"I am still the descendant of Tash, traitor," Rabadash spat, "and if you side with these barbarians then the curse of Tash is upon you. Lightning in the shape of scorpions shall be rained on you."

"No," Aravis said firmly. "No, I call upon our common ancestor --Tash, the inexorable, the irresistible-- to deal with you. If you wish to bring our gods into this land then let them come. If you wish to act as though we are still within Calormen then you will answer to the authority that can lawfully destroy even a Tisroc.

"Tash, inexorable and irresistible, I, Aravis bint Kidrash ibn Rishti ibn Kidrash ibn Ilsombreh ibn Ardeeb al-Tash, call on you to judge Rabadash,"

"Judge me!?" Rabadash shouted.

From the clear blue sky a bolt of lightning in the shape of a scorpion descended, followed almost immediately by a bone rattling crack. It was so brilliant every mortal was dazzled for a moment, and when they blinked the visible world back into existence they beheld a figure floating above where the lightning had struck the earth.

It seemed to be made of smoke rather than of solid flesh. Its shape evoked, rather than resembled, creatures more familiar. A head that called to mind some bird that rent flesh with its beak, a body not entirely unlike that of Dionysus or his ilk, arms that would not have been out of place on a satyr, though four in number, long slender fingers that brought forth thoughts of the toadstool people, each finger tipped in a wicked claw that called to mind the talons of a hippogriff.

That hippogriff talons would never fit on the fingers of a toadstool person, and the hands of a toadstool person did not belong on the arms of a satyr did not seem to matter. The smoky figure was a model of perfection, looking at it one couldn't imagine it being shaped in any other way. Every aspect of it was clearly exactly as it should be, indeed the only way it could possibly be.

Rabadash was first to speak. "Tash, inexorable / inescapable, show these barbarians the price for acting against your scion!"

Aravis looked on with a satisfied smirk.

Tash and Aslan looked to each other. Some wordless conversation took place between the two gods, then Aslan bowed his head and took a step back.

Many there assembled gasped. Neither Narnian nor Archenlander expected to see Aslan simply back down. While he had surrendered once before, that was after parlay and with clear concessions made to him in exchange.

Tash approached Rabadash, and only then did those watching realize how much larger he was than a man. He was no giant, yet adult humans seemed as children when he stood near them.

"Rabadash," Tash said, his words seeming to echo forth from within the skulls of those looking on, "I have come. Do you, mortal who shares my blood, truly wish for me to act regarding this matter, or were your words empty?"

"I truly wish you act, Tash, the inexorable, the irresistible," Rabadash said.

"And you," Tash said, turning to Aravis, "Aravis, also of my blood and devotee of Zardeenah, who have called me forth into a foreign land, wish me to act regarding this matter."

"I do," Aravis said. "Prince Rabadash has refused local judgement, and far away armies may support his refusal, but judgement must be rendered. He, and his father across the sands, must both accept the judgment of Tash, the inescapable.

"I believe this is fitting, my lord," Aravis said as she knelt down and bowed her head, in a show of submission to the will of Tash.

"Very well," Tash said, "mortals of my blood."

Tash returned his attention to Rabadash.

"You have annoyed me, future Tisroc," Tash said, and a feeling of dread radiated from him until it seeped into everyone's very bones. "I will not bend my will to your command and attack those you were unable to defeat yourself.

"No, I see no reason to make war on strange lands with strange gods," Tash paused for a moment, "but I do see reason to deal with you."

Rabadash seemed to shrink in fear for a moment, then the moment passed and he exploded in outrage. But no sound came from his shouting mouth.

"You have used your voice unwisely, so I have taken it from you," Tash said, almost casually.

The feeling of dread deepened, now accompanied by a growing horror.

"I do not think this is enough," Tash said. Then he looked around as if noticing his surroundings for the first time. His eyes settled on the donkey, which Shasta hugged tightly in sudden fear. "Yes," Tash said, then looked back to Rabadash and added, "that will do nicely.

"Strange, inexplicable, undeniable, arbitrary," Tash continued; "it will do nicely indeed."

Tash touched a talon to Rabadash. Rabadash seemed to turn into smoke, which dispersed into a cloud and then reformed into the shape of a donkey. When he became solid again, Rabadash was indistinguishable from an actual donkey.

Seeing Rabadash as another of its kind and taking no heed of Tash, the donkey gave a bray of greeting and tried to approach Rabadash. Shasta, recovering from the fear that Tash would do something to the donkey, loosened his hold on the donkey but pet it in a way that meant "stay".

Shasta pointed to Rabadash and said, "Bad donkey," to the donkey, then stroked the donkey and said, "Good donkey," to the donkey.

Some of those standing very close to Rabadash, Aravis, and Tash thought that Tash made a slight sound of amusement, though none would ever be able to agree on what that sound had been. Neither Rabadash nor Aravis ever commented on it. Tash has, likewise, maintained silence on the matter.

"You have annoyed me," Tash said again, beginning to move in a casual, random way (which some would call pacing, while others maintain that one's feet must touch the ground for that), "but I am not without my share of mercy. When you stand before my altar in Tashbaan at the Great Autumn Feast this year, I will return to you your form.

"As for your voice, which you used to call Aravis, descendant of mine, a traitor," Tash said, "it shall be returned to you when you pay tribute to her patron, Zardeenah."

Tash looked about, this time his eyes settling on Aslan. The sense of a smile, one at having an idea that pleased oneself, was conveyed to all who could see Tash's face, though Tash obviously did not smile. A beak cannot create a smile. Yet all those who could see his face felt as though Tash had smiled.

"For all the remaining years of your life you will give Zardeenah a tithe, delivered to her temple on the longest night of the year, however on the longest night of this year you will do more. You will give a tenth of all that you own to the temple of Zardeenah. When you have done this, your voice will return to you.

"Do not worry that you will be taken as livestock or slaughtered for food," Tash said. "I have placed a mark upon you that ensures none shall hinder your return to Tashbaan. You will come to no harm, save that which you bring upon yourself.

"As to how you will make the journey," Tash said, "I care not. Perhaps you should throw yourself on the mercy of foreign powers," Tash glanced to the present royalty, "or foreign gods," Tash glanced to Aslan. "It matters not how, but if you wish to regain your former form, get there you shall. My altar in Tashban at the Great Autumn Feast. Remember this. Remember also that you have an appointment with the Tashbaan Temple of Zardeenah on the longest night of the year.

"Oh," Tash stopped moving about, "there is one more thing. Tash locked eyes with Rabadash, "there are limits to my mercy. Once you have regained your form and voice, you will never again venture more than two parasangs from my temple in Tashban. That is the extent of my mercy."

Tash turned his back on Rabadash and faced Aravis. Placing the first non-opposable talon on his lower left arm under her chin, he lifted her head so her eyes met his own. Then he addressed her, "You have not annoyed me. You have, however, called on me. A payment must be made. It is simple, and it is small, yet it is as great as any task one can be given.

"You will ensure that any children you may have know the ways and gods of your homeland. Likewise for any children, not your own, that you may raise."

Tash looked to the south, and his smoke-like form dissipated on the winds.

-

Ok, that was way longer than I expected. Original concept was more like:

Rabadash: I'm a descendant of Tash!
Aravis: Well, so am I.
Rabadash: Whatever, you're not awesome like me.
Aravis: Why don't we have Tash decide what to do? Then you can't make such a fuss.
Tash: Hey, I'm here.
Aslan: The jerk's yours, do what you will.
Tash: Rabadash, I'm the creepy god. You could have called on any of the gods of Calormen and you picked me: the creepy god who doles out death and punishment. So, you know what I'm going to do? Creepy punishment.
Rabadash: Woo!
Tash: To you.
Rabadash: What!?
Tash: Be happy it wasn't creepy death.

Friday, January 19, 2018

I have oil, may it last

I said that the oil situation wouldn't be truly resolved until the oil was paid for and delivered on the 18th.  It was and is.  Unfortunately I forgot to take my medicine yesterday and so wasn't really in the right frame of mind for accomplishing anything (like, say, writing a post saying that it was resolved.)

On the one hand, even if the previous oil hadn't burned way faster than it should have because of a critical insulation failure, I'd still need to buy new oil eventually.  So it's not like I would never have had to pay this money.  More that when oil needs to be filled has been eternally moved up.

On the other hand, it's stopped me from paying off the house insurance (I'm not overdue in a late fee kind of a way, more a straining the generosity of the family member who effectively made an interest free loan by paying the bill and then deferring collection in order to help fund heating oil) and the purchases of small amounts of stopgap oil to keep everything from going catastrophic while I waited two fucking weeks to get a respectable amount of oil in the tank cost a metric fuckton.

That means that even with help I'm pretty well tapped out with respect to money right now (I will be able to pay the remaining bills of the month) which shouldn't have been the case and will be a problem when non-monthly bills roll around, I believe, next month.

So, basically, the oil problem may have bridged the gap between the ongoing financial crisis that was the final months of last year with the first crunch time this year, and that would suck.

In the middle of February I broke my foot, that and a couple of unfortunate coincidences led to the distraught slog through looming financial collapse that defined the final months of 2017.  It, however, did more than that.  It put everything on hold.

One of the things that it put on hold was dealing with the insulation problem in two parts of the house.  You know: the very thing that would have stopped this whole oil mess from happening.

The two areas of the house are an addition and the hall under the addition (which had to be added to make it so the basement door still reached the outside.)  Whoever built them didn't insulate them.  As it turns out, sealing them off delivers decent insulation.  (Stagnant air is actually a fair insulator, whereas moving air is the polar opposite of insulation.)  This is a working solution, and for the addition as simple as sealing the door.  (The underhall is more complicated.)  The thing is, the reason that this isn't inconvenient is circular.

It's not a problem having those areas of the house non-insulated and closed off instead of properly insulated and open because neither I nor anyone else ever uses them.  The reason that neither I nor anyone else ever uses them is because they're non-insulated and thus need to be closed off (plus they're cold in the winter and warm in the summer.)

That is utter bullshit, in fact it's the single largest problem with the house itself*, and so when planning out what to do with my year a year ago, fixing that was one of the first things on my list.  While the addition, which is a furnished room, would bring the most utility in terms of using space, the underhall would bring the most savings in terms of oil burned.  It is, unfortunately, beyond mere bad.  The door doesn't fit quite right, I think a minor window might be broken, and as such, when the air is allowed to flow instead of kept in a state of enforced stagnation, it might as well be a hole in side of the house when it comes heating and cooling.

Thus, one of the things at the tippity top of the list of things to fix.

I'm not planning on breaking a foot this year, hopefully this is when I fix these two areas.  If it is, then nothing like this oil crisis of mind will be happening agiain.

-

* The fact that the house is a mess, so much more so since I broke my foot, a big problem too, one that I plan to solve, but it's a problem with the stuff in the house instead of the actual house.

Tuesday, January 9, 2018

Never-mind, nothing is good.

So remember the whole "If the stopgap oil lasts" bit?

It lasted about a quarter as long as it needed to.  Now I'm struggling to get money into the right fucking state because I'm not there right now, but even if I can do that and stop things from rupturing between now and when the actual lasting oil arrives, I'm still completely screwed because the money I'm spending on stopgap oil is coming straight from money that I need for the god damned regular oil order.

Among the myriad reasons why one gets regular oil from people who deliver it in trucks with one giant tank on the back instead of a handful of five gallon containers is this:

The amount of stopgap oil it will take to last the nine fucking days from now until when the regular oil arrives will cost (this is a very rough estimate) about $200.  Now with the price of oil at better than $2 a gallon, I couldn't actually make a $200 order from a regular provider given a minimum order of 100 gallons, but if I could I guarantee you it would last longer than nine god damned days.

Oil from non-traditional sources is expensive.  (Think of it as a bulk discount when buying from actual heating oil companies.)

So, I'm utterly screwed.  I'm going to pay to keep the heat going (and thus the system from rupturing) but it means that I've got nothing to pay the actual ordeal-ending order with save faith.

I'm tired.  I'm sad all the time.  I'm low on energy.  I'm out of faith.

To the people who helped me out, thank you so much.  I might have only gotten around to making the update earlier today, but I've actually had hope for days.  It was nice while it lasted.  You did what you could, and at any other time it would have been enough.  I'd have had my tank more than half full days ago.

The fact that the problem wasn't, ultimately, solved doesn't make me appreciate what you did any less.

A generally positive update

If the stopgap oil holds out, which it will need to do until the 18th (the 15th was the most optimistic estimate) then I will be getting a respectable amount of oil and I will have the money to pay for it.

I screwed up something somewhere so I'd be a bit short in spite of definitely having enough, but Christmas was recent and that resulted in some incoming funds.  Not much, but enough.

If the stopgap oil holds out.

I haven't been well.  I've been stressed and tired and low on energy and I still want to curl myself up into a ball and cry until the world leaves me alone, but that doesn't detract from the fact that the previous is a very good thing.  Another disaster (probably) averted.

Arisia starts Friday.  Given that every penny I have needs to be saved to pay for heating oil (in cash, if you were wondering) on the 18th, I'm not exactly going to be able to buy anyone a stuffed squid this time around, nor make children's short sighted dreams come true.

That's fine.  Keeping my house livable (the boiler would burst without heating oil to keep it from freezing over at night) is more than worth not having little things like . . . what did I even pay for?

I've still got the pendant watch I got myself.  It's an owl, which means Athena, which reminds me of a friend from university since she's his patron.  I think I loaned money for the munchkin weasel to get that brass telescope.  Like the pendant it has yet to be lost.  She still uses it.

There were other things.

I . . . feel so fucking useless.  I'm not going to look at how long it's been since I wrote fiction because I think it'd be too depressing.

I'll see what I released first-on-patreon and then never got around to releasing over here.  Then I can get some content to whoever still follows this.  You deserve content, even though I'm not producing anything.

Friday, January 5, 2018

I ran out of heating oil again.

[Note: this was written yesterday. Apparently I forgot to publish it.]

There's a blizzard.  If not for the blizzard I would have left today and not realized I ran out of oil.

If not for an appointment yesterday, I would have moved up my travel plans because of the blizzard and likewise not noticed the problem.

At the same time, I knew full well that something was wrong.  Coldness has had a foothold in this house that it should in no way have.  Given where I sleep this has meant enduring frigid conditions every morning and night.

What I couldn't find was the source.  It's not like a window was open or a door was ajar.  There is not some giant hole in the side of my house letting heat out and cold in.

I think I finally found the source.  After running out of oil.

I didn't see this coming at all.  I never burn through oil nearly this fast, even with the obvious heating difficulties, I didn't expect to be out again so soon.  Not even close.

So, I'm kind of fucked.

Minimum order is $289.90 (if the price remains the same) I have $246.44, and of that $275 is already spoken for.  In other words, I have about negative thirty dollars with which to pay a bill that's about three hundred dollars.

If I can postpone paying a bill that's already a month late, and I cash in some Christmas presents, I think I can make that minimum order work.  Maybe.

Or maybe not.  I'm going to need to get some stopgap oil in the tank right now so the pipes don't freeze between now and when the order (the one that I can't place because I can't afford it) is filled.  That costs money.  Money I don't have.

Fuck.

I think I'm going to cry for a bit.  And sleep upstairs for a change I guess.

SHIT!

There's a fucking blizzard.  How the Hell am I supposed to clear a path to the oil intake between now and when I have to leave tomorrow when the pre-blizzard snow level was nearly enough to bury a car?

Fuck fuck fuck FUCK.

Fuck all this shit.

-

My original plan for today involved writing out all of the bad shit that happened between my last post and today, thus getting it out of my system, putting all of the stress and fuckiness behind me, and hopefully having some kind of light and fluffy post in the next couple days to end the god damned dreariness that's descended on my life in general and Stealing Commas this past year.

Not only did I not do any of that, I ran out of oil and am now facing . . . I lack the profanity to adequately express the current situation.

That gives me an idea.

Here:

In today’s modern Galaxy there is, of course, very little still held to be unspeakable. Many words and expressions which only a matter of decades ago were considered so distastefully explicit that were they merely to be breathed in public, the perpetrator would be shunned, barred from polite society, and, in extreme cases, shot through the lungs, are now thought to be very healthy and proper, and their use in everyday speech is seen as evidence of a well-adjusted, relaxed, and totally unf [bleep!] ked-up personality.

So, for instance, when in a recent national speech, the financial minister of the Royal World Estate of Qualvista actually dared to say that due to one thing and another, and the fact that no one had made any food for awhile and the king seemed to have died, and that most of the population had been on holiday now for over three years, the economy had now arrived at what he called, “One whole juju-flop situation,” everyone was so pleased he felt able to come out and say it, that they quite failed to notice that their five-thousand-year-old civilisation had just collapsed overnight.

But though even words like “juju-flop,” “swut,” and “turlingdrome” are now perfectly acceptable in common usage, there is one word that is still beyond the pale. The concept it embodies is so revolting that the publication or broadcast of the word is utterly forbidden in all parts of the galaxy except one - where they don’t know what it means. That word is “Belgium” and it is only ever used by loose-tongued people like Zaphod Beeblebrox in situations of dire provocation.

Belgium man, Belgium.