What a Waste

When life gives you lemons, sometimes they are awful and you have to throw them away.

This is a story about one of those "craft fails."  It was way more involved than making cupcakes that don't look like Martha Stewart's, and therefore, way more heartbreaking.  Once upon a time, about 4 years ago, George thought it would be a wonderful idea to collect beer caps.  After all, beer is great, the logos are cool, and there are thousands of craft projects you can do with caps.  Right?  Well - no.  There's the classic bottle cap tabletop.  There are bottle cap magnets and jewelry pendants.  Coasters and trays.  Picture and mirror frame decorations.  Wind chimes that don't chime.  There's really not that much stuff, actually.  But as the "creative" half of team L&G, it was sort of my job to make it happen.  It was a job I should have had the foresight to quit before I started.

We took great pride in protecting each cap from dents or scratches, and allowed only one of each kind into the collection.  Caps like "Bud Light Lime" didn't make the cut simply because they weren't honorable.  Naturally with such a nice assortment, I wanted to encase the caps in resin to protect them.  I didn't want something as big and cumbersome as another table, and there were too many caps for a set of coasters.  That only left trays.  Trays are nice because they come with a built in rim to hold the resin, and you can put them away when you're tired of looking at bottle caps.  It was a reasonable decision, despite the lack of creativity.  The next step was to make the project a little more personal.  As we've been called "L&G" ever since the day my mom threw us an "L&G party" and pronounced us man and wife (that really happened), I decided to make an "L" tray and a "G" tray, and purchase a little ampersand bottle opener to tie the two together ($7).

Meanwhile, I bought 2 black rectangular trays ($7 + $15 + $15) and 32 ounces of Castin' Craft Polyester Resin ($7 + $15 + $15 +$30).  How exciting - our first resin project.  When the trays came, I noticed that the handles were less than a quarter inch from the bottom of the tray.  Since the height of a bottle cap is about a quarter inch, these trays wouldn't hold enough resin to encase the caps, so I returned them ($7 + $30).  I also started making posts in a resin forum to get more advice on the whole project.  It's not like I wanted this to become some sort of failure or something.

For the second round of trays, I ordered 2 16-inch circular fiberglass trays ($7 + $30 + $15 + $15), this time in brown.  Meanwhile, I heard back from the resin forum and realized it was necessary to order 2 16-ounce packages of of Envirotex Lite High Gloss Resin ($7 + $30 + $15 + $15 + $25 + $25).  This kind of resin didn't need to be sanded or buffed, unlike Castin' Craft Polyester Resin.  But Castin' Craft Polyester Resin couldn't be returned because it was "too flammable to be put in the mail."  I bought 144 black bottle caps for the letters ($7 + $30 + $15 + $15 + $25 + $25 + $8).  This was our first draft.

The trays came, and our collection wasn't big enough.  We bought 45 new beers ($7 + $30 + $15 + $15 + $25 + $25 + $8 + $80).  The design looked a lot cleaner with a solid border, so we delved into our personal stash of caps from Austin Homebrew.  At this point, I realized that circular caps fit together into hexagons, and circular trays are anything but hexagons.  Rectangles are a little bit like hexagons, but not circles.  I agonized over how to deal with the circles-minus-hexagons space.  Then there was the issue that the black lettering blended into the brown background.  We switched to white letters.  The white logo caps blended into the white letters.  We threw out 20 white bottle caps and I changed the color of the L to orange.  But the letters still didn't look right.

An "L" is built with lines, whereas a "G" is built with arcs.  It eventually dawned on me that we could not treat both letters in the same way.  The solution was to build the "L" into a hexagon inscribed in a nearly circular border, but build the "G" with concentric circles, evenly distributing the circles-minus-hexagons space.  Duh.

At last, we were ready to go.  We sorted and traded caps for a while, mixed the Castin' Craft Polyester Resin, and used syringes to fill the back of each cap.  This was necessary to avoid air bubbles during the final curing process.  The house was full of fumes for 4 days, but other than that, this part went pretty well.

We flipped them over and glued them down.  After 4 years, there was a light at the end of the tunnel.

Then came Wednesday, the 16th of April.  It was time to pour the Envirotex Lite.  We had set up a dust free zone in the gym and borrowed a hot air crafting gun to zap bubbles during the cure.  One coat of Envirotex Lite "equals 50 coats of varnish," but you're supposed to pour only 1/8 of an inch at a time.  This meant we needed two coats to cover the caps.  We had done the calculations.  We had the right amount of resin.  What could go wrong?

Well, a lot.  For one, the container we had saved to mix the resin was a little small, so we probably didn't mix the catalyst thoroughly enough.  Also, we should have done something magical and tedious, like syringing resin into each and every crack between the bottle caps with no spills.  But we didn't do that; we poured the resin from a container, much like the way a human being would typically pour resin.  Then, to our utmost horror, the resin didn't flow into the crevices at all.  This left us no option but to pour an additional layer to flood the caps.  "Maybe it would work."

A few air bubbles came up.  We zapped them with the hot air gun, and things still looked pretty good.  After 25 minutes of zapping bubbles that appeared from nowhere, we were still hopeful.  But then bubbles didn't stop.  The hours came and went.  Every time we checked on the trays, more bubbles needed zapping.  We cancelled grocery shopping.  We cancelled going to the gym.  We cancelled our plans to see the Mozart Requiem Undead that evening.  We zapped bubbles all day, for we had worked too hard to let one day ruin our entire project.

Suddenly, one spot on the "G" tray cured hard, trapping several unsightly bubbles and blemishing an otherwise smooth and glossy surface.  The "G" tray was officially ruined, and we didn't want to take too many chances with the "L."  We were helpless.  In desperation, we ordered another 16 ounces of Envirotex Lite, since another layer could at least smooth out the top surface ($7 + $30 + $15 + $15 + $25 + $25 + $8 + $80 + $25).

By the next day, the "L" tray had acquired several large bubbles and the "G" tray remained sticky.  As the days passed, the "G" tray proved incapable of a complete curing.  Both trays almost looked good.  But sometimes, "almost good" is still "very bad," and this was one of those times.  The last container of Envirotex Lite came in the mail yesterday, but we have since grown so loathsome of the very bad trays that we'd rather save the resin for another future craft fail.  We'll throw these trays away tomorrow.  And so the nightmare continues.

And just so you know, $7 + $30 + $15 + $15 + $25 + $25 + $8 + $80 + $25 = $230, including the price of 45 beers of which 40 were just okay.

And before you question my judgement, these really do look a lot worse in real life than in the photos.

And who wants trays anyway?  Trays, especially heavy trays filled with resin, are totally impractical and useless.  This being a failure has saved us from having to own trays.  We now have one new bottle cap (it was pretty?) and 16 ounces of resin.  And a stupid ampersand bottle opener.

Logic

George is terrible at arguing, and this morning, he said he wished he were "better at logic."  Being the very loving wife I am, I decided to type up a summary of the 2 logic pages in wikibooks.  Isn't that cool?

  Section 1  
Proposition - statement.  Propositions can be true or false, and represented by lower case letters: p, q.
Propositional function - a function where a proposition is an input, and True or False is the output.
Compound propositions - propositions combined with any of the 3 logical operators.
Operator - and, or, not.
Conjunction - ∧ and.  In order for a ∧ b to be true, a must be true and b must be true.
Disjunction - ∨ or (inclusive).  a ∨ b means a is true, b is true, or both are true.
Negation - ¬ not.
Order of Precedence - brackets, ¬, ∧, ∨.

  Review 1  
Two plus five equals eleven.  Proposition.
Drakeson Miner is adorable.  Proposition.
Will it rain tomorrow?  Nothing.
3x + 6y = 9.  Propositional function.
It will rain tomorrow and Drakeson Miner is not adorable.  Compound proposition.  (F)
Two plus five equals eleven or two plus five equals seven.  Compound proposition.  (T)
¬(p ∨ q) ∧ p.  According to the Order of Precedence, evaluate p ∨ q first, then ¬, then ∧ p.

  Section 2  
Truth tables - tables that chart every possibility and every outcome of T's and F's.  This is blogger, so I can't really insert tables without too much trouble, and besides.  That would be really boring to type.  If you're so inclined, click on the original wikibook to see some examples.
Each cell contains a T or a F.
If there are n propositions, there will be 2ⁿ rows in a truth table.
Also, the first 2ⁿ rows and n columns will display every possibility of T's and F's for the n propositions.
In a truth table for an expression that involves a p and a q, the first two columns (8 cells) would display the four possible combinations of T's and F's for p and q (TT, TF, FT, FF).
The number of columns that are necessary depend on the possible changes in outcome, due to operators.
For example, ¬, ¬p, ∧, p ∧, ∨, p ∨, p ∧ q are all examples of column headings.
Columns (not rows) are worked through to determine all final outcomes of each truth table.
Equivalence - ≡.  Equivalence between two expressions occurs when the outcomes of both truth tables are the same.
Tautology - an expression that is always true.

  Review 2  
In constructing a truth table for p and q, how many rows are necessary?  4.
Construct a truth table for p ∧ q.  4 rows (not including column headings p, q, p ∧ q), 3 columns.
Construct a truth table for p ∨ q.  4 rows, 3 columns.
Construct a truth table for ¬p.  2 rows, 2 columns.
Construct a truth table for q ∧ (p ∨ r).  8 rows, 5 columns.
If p is "Mommy is in a good mood" and q is "Mommy loves Drakeson," what is p ∨ q?  A tautology.

  Section 3  

This part is even more fun.

Commutative Laws

p ∧ q ≡ q ∧ p

q ∧ p ≡ p ∧ q

Associative Laws

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)

(p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

Distributive Laws

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

Idempotent Laws

p ∧ p ≡ p

p ∨ p ≡ p

Identity Laws

p ∧ F ≡ F

p ∨ F ≡ p

p ∧ T ≡ p

p ∨ T ≡ T

Involution Law

¬(¬p) ≡ p

De Morgan's Laws.  My dad says these are "pretty cool."

¬(p ∨ q) ≡ ¬p ∧ ¬q

¬(p ∧ q) ≡ ¬p ∨ ¬q

Complement Laws

p ∧ ¬p ≡ F

p ∨ ¬p ≡ T

¬T ≡ F

¬F ≡ T

  Review 3  
Pick one of each and prove it with truth tables or laws.

  Section 4  

Implication - p ⇒ q means "if p, then q."  In this case, p is a sufficient condition rather than a necessary condition.  In other words, it is still possible for q to be true without p.

Biconditional propositions - p ⇔ q means "p if and only if q."  This also means that p ⇒ q and q ⇒ p.  In this case, p is a sufficient and a necessary condition for q, and q is a sufficient and a necessary condition for p.

Predicate - a series of words used to modify an object.  Predicates are notated with uppercase letters, and their objects are notated with lowercase letters.
P(x) is called a propositional function where P is the predicate.  Depending on how P and x are defined, P(x) is either true or false.
For example, if the predicate "tooTall" means "is too tall" and the object is "George," then P(x), or tooTall(George), would mean "George is too tall."  In this case, the propositional function is true.
Also, for P(x), the universe of discourse is the set that x belongs to.
For tooTall(George), because George is a person, the universe of discourse could be "people."

  Review 4  
Assume "badCommunicating" is a predicate meaning "bad at communicating."
badCommunicating(Lan) ∨ badCommunicating(George) ⇒ working on logic will be frustrating.
The universe of discourse in this case is "people."
Also, George makes sushi ⇒ Lan loves George.
Also, George lifts weights at least once a week ⇔ George is alive.

  Section 5  

Universal quantifier - ∀ means "for all" or "for each."
Existential quantifier - ∃ means "for some" or "for at least one."
Two-place predicates - predicates that require 2 objects.  For instance, "givesKisses(Mommy, Drakeson)" has the two-place predicate "givesKisses," and the objects are "Mommy" and "Drakeson."  Mommy gives kisses to Drakeson.
Negation of quantified propositional functions:
¬(∀ x, P(x)) ≡ ∃ x, ¬P(x).
¬(∃ x, P(x)) ≡ ∀ x, ¬P(x).

  Review 5  
∀x, cuterThan(Drakeson, x).  Universe of discourse is anything.
∀x, ∃y, Bigger(x,y).  Universe of discourse is numbers.
In English sentences, choose a universe of discourse and a predicate, and write your own examples for the negation of quantified propositional functions.

  Section 6  
Wait a sec.  Those wiki pages didn't have anything on these:
Assume p ⇒ q.
Converse - q ⇒ p.  (Not necessarily)
Inverse - ¬p ⇒ ¬q.  (Not necessarily)
Contrapositive - ¬q ⇒ ¬p.  (Always)

  Review 6  
Notice the next time somebody uses an inverse or converse when trying to argue.  You can disagree, but don't point out the mistake.  It's important to keep your friends.

  Extra Credit Review  
There are 7 additional logic exercises from the original source.

And that's that.
I should add that most of the time I was doing this post, I was also missing story time.

Spring Cleaning

We moved into Castle Grayskull in May of 2012.  By the time the first spring cleaning rolled around, I have no idea what happened.  Maybe we were too busy with a 3 month old.  Maybe we didn't care.  Maybe the house was clean; after all, it had only been a year.  This time, though, it had been two years, and we cared.  In fact, we cared so much, it became more of a makeover than a cleaning.  We didn't remodel anything, because that would be an "extreme makeover."  And you know what?  It's great to look your best, but ultimately, it's what's on the inside that counts.

So here's the grand list of our home improvements from Spring, 2014.  It's doubtful this is of any interest to anybody, but putting it down makes me feel like we accomplished something.  They say, "If you don't write it down, it never happened."  Actually, I don't really get the meaning of that quote, and I'd even go so far as to say I disagree with it.

Organization:

We made a cleaning schedule and put the chores into our calendar.  That didn't really create less or more housecleaning, but nobody has to keep track of that stuff anymore, and nothing sits around accumulating layers of dirtiness.  Like window shutters.
We also reorganized the closets and pantry, and got new baskets for the keys, wallets, glasses, and mail.

Cleaning:

In addition to normal cleaning, we went after those hard to reach spots, like the outside windows, behind and under the oven, and under the fridge.  Those spots are the worst.

Safety:

We childproofed the cabinets with magnetic locks.  The new bathroom trash cans are covered, and there's a new weight rack in the gym holding up all those dumbbells.  Thanks only to George, we finally tuned up the Ford Focus so that "it's no longer a death trap."

Outside:

The back patio is finally furnished.  There's a picnic table, windchime, soft LEDs lining the upper rim, and our very first grill.  We also installed some solar powered path lighting in the front, put in a new doormat, and we're in the process of removing the many unwanted plants that came with the house.

Decor:

There's a new rug under the Volkert and two new puzzles for our wall collection.  Coming at the end of the month is a quilt we commissioned from a friend, made out of Drakeson's receiving blankets.

Detail:

We replaced all the white plastic outlet covers with satin nickel.  Now they match our door handles, towel racks, tp holders, hinges, and faucets.  There are new pillows for the guest room and new towels for the guest bath.

Furnishing:

We replaced the shoe holder with one that matches the rest of our furniture, bought thicker mattresses for the daybed in the guest room, and got Drakeson his very first bed.  And yes, it totally has a fort and a slide.

Can You Find 7 Dragons?