Basic, soft, chewy chocolate chip cookies

17 May

I haven’t been feeling very inspired baking-wise lately, so I was happy that a friend brought over some frozen chocolate chip cookie dough balls before we left Chicago.  They were so tasty that she emailed me the recipe.  She then emailed me a few more times about said cookies vs. another recipe, and sent me the delightful line: “And now I’ve sent you too many emails but cookies: serious business”

What if the general of the Confederate States of America actually transmogrified and moved to Scotland?  So everyone's been saying the Loch Ness monster, or Nessy, but really she's a he and is Ness Lee?

What if the general of the Confederate States of America actually transmogrified and moved to Scotland? So everyone’s been saying the Loch Ness monster, or Nessy, but really she’s a he and is a Ness Lee monster?

I baked a half batch of these a few weeks ago and dutifully melted the butter, which really does turn the cookies from a normal soft cookie to a delightful chewy cookie.  But I was lazy this time and wanted to finish off my Earth Balance (from when I had a potentially vegan person over and made some awesome vegan mac and cheese) so that’s what I did, and ended up with a basic, solid chocolate chip cookie.  This blog is usually pretty adventurous, but everyone needs a basic chocolate chip cookie recipe!

First, cream the butter with the sugar.  I love how much brown sugar is in this recipe.

I've worked out a code to transmit messages via rolls and dairy products.  But you can trust me with your secrets; I won't butter a word.

I’ve worked out a code to transmit messages via rolls and dairy products. But you can trust me with your secrets; I won’t butter a word.

Then add eggs and vanilla.

Make no mixtakes- I'll make puns no matter who reads this

Make no mixtake- I’ll make puns no matter who reads this

Finally you add the dry ingredients.  Since I use salted butter I rarely add salt to cookies, but I am incorrect and you should add salt.  It really brings out flavor!  I’m just lazy (also note that I didn’t use one egg + one egg yolk, because why would I separate out one egg?)

Mix that up, and stir in the chocolate chips.

How bad are my puns?  Bad, batter, or baddest?

How bad are my puns? Bad, batter, or baddest?

I also bought parchment paper the other day because I am not good with silpats despite my professed love for them.  I made cookies on them about a year ago that tasted like dishwashing liquid because I was putting the silpats in the dishwasher.  Parchment paper is so easy! (But so wasteful.  But so easy!  Dang it I feel bad enough for switching from cloth to disposable diapers when we moved.  Now I feel guilty about parchment paper.)

To freeze cookies, just scoop them out into balls on a baking sheet and shove the whole thing in the freezer til they’re hard.  Then dole them out into freezer bags, and label them.  Bake for about 2 minutes longer than normal.

If Tom Petty was a ball of chocolate chip cookie dough: "Cause I'm freeeeeeeze, freeze fallin"

If Tom Petty was a ball of chocolate chip cookie dough: “Cause I’m freeeeeeeze, freeze fallin”

Puns were worse than usual this time around.  But the cookies were still good!

20150517_135752

Chocolate chip cookies, adapted from Smitten Kitchen which adapted from allrecipes

2 c flour

1/2 tsp baking soda

1/2 c + 2 TB butter (1 stick + 2 TB)

1 c brown sugar

1/2 c white sugar

1 TB vanilla

2 eggs

2 c chocolate chips

Cream together the butter and sugars.  Preheat oven to 325.  Prepare a baking sheet (parchment paper or silpat or nothing).

Add in the vanilla and eggs and cream.  Add the flour, and sprinkle with baking soda (this is because you are lazy like me and didn’t sift them together earlier).  Mix.  Add the chocolate chips and stir.

Drop by tablespoons onto your cookie sheet (I fit a dozen per sheet).  Bake for ten minutes, or until the edges just start to look toasty.

Prees, prees, pretty prees

13 May At least one diagonal of the rectangle and at least one chord of the pentagon exist.  Colors don't mean anything

Last weekend I had a wonderful time at the Cornell Topology Festival- I went because my internet and now real life friend tweeted about it!  Good things can come out of the internet!

Another very talented friend made an icosohedron out of balloons (following a template by Vi Hart, so you can do it too!) and now I have a picture of me holding it:

icosohedronye

Anyways, apologies for delay in posting.  I’ll try to double up this week to make up for it.  There were a bunch of great talks at the conference, and here’s a post about one of them that really intrigued me, “Universal Groups of Prees” by Bob Gilman.  I thought “prees” was a typo and meant to say “trees”, but nope, the word is “pree.”

Hopefully you remember or know what a group is.  A pree is something on the way to being a group, but not quite: it’s a set with partial multiplication, identity, inverses, and the associative law when defined.  So in a group, whenever you have two elements and b, closure ensures that the product ab exists and is an element of the group.  In a pree, it’s not necessarily the case that ab exists.  But if it does, and bc exists and a(bc) exists, then (ab)c must also exist, and equal a(bc).  [If it’s hard to think of something non-associative, check out this wikipedia article on the cross product and use your right hand and a friend’s right hand].  We can show this visually:

This shows that a*b=ab

Start from the top vertex.  If you follow the arrow right and the arrow up, you’ll end up at the bottom left vertex.  This tells us that we should label the edge from the bottom left vertex to the top by ab.

This part of the triangle just shows that a*b=ab, that is, the product of and are defined in our pree.  Next we’ll add a triangle for b*c:

Notice that the arrow for b is the same direction as the previous picture; I just took the arrows out of the big triangle for cleanness

Notice that the arrow for b is the same direction as the previous picture; I just took the arrows out of the big triangle for cleanness

Now we add the blue triangle in to the big triangle.  There are two different ways to read the last face, and that fact means that those two expressions better be equal.  This is associativity.

Using the big triangle labels, we get a(bc).  Using the small triangle, we have (ab)c.  These are the same edge, so they must be equal

Using the big triangle labels, we get a(bc). Using the small triangle, we have (ab)c. These are the same edge, so they must be equal

If you’ve done any group theory you might have the same reaction I did: “THIS IS SO WEIRD TELL ME MORE I WANT TO KNOW!”  This combinatorial pictorial thing is reminiscent of vector multiplication, but with group elements and it intrigues me no end.  For short, they say this is an axiom of associativity:

The official axiom lacks smiley eyes, but smiley eyes make everything better

The official axiom probably lacks smiley eyes, but that’s clearly an oversight

So you can think of prees as partial multiplication tables, and they determine a graph.

But I tagged this post “group theory”, and prees do relate to groups.  In fact, it’s a theorem that any finitely presented group (see here for reminder of definition) is a universal group of a finite pree.  This group is defined as having generators equal to the elements of the pree, and relators are the products of the pree.

Here’s the first example.  If your pree (which is a set with partial multiplication) consists of two groups K and L which share a subgroup A, then the universal group of that pree is K \ast_A L, the free product of K and L amalgamated over A.  If you don’t know what that means, don’t worry about it.  We’ll do amalgamated products some other time and I’ll add a link here for that.

You can also do this with letting your pree be a graph of groups, and get the correct corresponding group.

Something whacky! This isn’t an open problem, but an undecidable problem: whether a finite pree embeds in its universal group (this means that there’s a function sending the elements of the pree into the group which respects the pree multiplication and doesn’t send two different pree elements to the same group element).  So even if you might be able to tell, given a specific pree, whether it embeds in its universal group, there’s no algorithm that works for all finite prees.

Here’s one of the main theorems of the talk: if, every time you have a collection of elements that can be put together to form a triangulated rectangle or pentagon, as in the picture below, one of the orange lines exists, then the resulting universal group is biautomatic.

At least one diagonal of the rectangle and at least one chord of the pentagon exist.  Colors don't mean anything

At least one diagonal of the rectangle and at least one chord of the pentagon exist. Colors don’t mean anything

Remember, prees only have partial multiplication.  So in the rectangle case, if we have ab and bc along the diagonal, the orange line means that ac also exists.

Like you, dear reader, I also don’t know what biautomatic means, and Gilman didn’t explain it during his talk.  But he did draw lots of pictures of this sort-of group-like thing.

More information: here’s slides from a talk he gave somewhere else

Here is a survey article on prees.

On deck if I get around to it: more blog posts from this conference- talks by Denis Osin and Mladen Bestvina.  Also, I really need to bake something new.  I’ve made that super easy lime pie a bunch by now; I even made it at this conference with ingredients from a mini-mart.  The limes had no juice so this was mostly a sweetened condensed milk pie, which was still delicious but too sweet.

IMG_20150509_080410290

Introduction to random groups

26 Apr Beware the infinite group presentation

Last summer, I participated in an awesome research program which ended up with a good handful of original research projects all having to do with random groups.  Random group theory is rather modern- the first definition of a random group came about in the 1980s (just like me!)  It’s a very rich field with lots and lots of open problems, since you can dive into most properties of groups and ask if they apply to random groups. [Here’s the post defining groups if you forgot.]

Some brief motivation: sometimes you want to say things about a “typical” group.  Like, if you picked a group at random out of all possible groups, it very likely has property A.  Example: if you pick an alumna from Mount Holyoke at random, she very likely is/was a woman.  If you ask me to name a random private college in the United States, I will very likely say “Mount Holyoke”.  Instead of having to say “very likely” all the time, we say “random groups have property P” if the probability that they have property P approaches 1 (this will be more precise below).

So, to build our intuition in the example above: if I pick one person who’s graduated from Mt. Holyoke, maybe he’s transgender and is not a woman.  But if I pick, say, 1000 alums, chances are that fewer than 10 identify as men (I do not know any research on incidence of trans but I think 10 is a safe bet here).  And if I pick 10000, probably there’s very very few [also maybe there aren’t this many alums in all time?].  So I’ll say a random alum is a woman, even if there are a few edge cases.

Probability of being a man in first 5: 20% in first 25: 8% in first 100: 3% in first 1000: 0.3%

Probability of being a man in first 5: 20%
in first 25: 8%
in first 100: 3%
in first 1000: 0.3%

Of course, the massive issue with this example is that the number of Mt. Holyoke alums is finite, and the probability of being a woman is a fixed number between 0 and 100%.  Hopefully this example illustrated the idea though- we want to look at the probability of having property A as the number of cases goes to infinity.

Let’s add some more precision to this idea.  First, we need a good way to describe groups- I (secretly) claimed that there are infinitely many, but how do we know that?  Well, we’ve already seen the group of integers, $latex \mathbb{Z}$.  And you can also have ordered pairs or triples of integers, \mathbb{Z}^2, \mathbb{Z}^3.  So there’s already infinitely many groups:n-tuples of integers, a.k.a. \mathbb{Z}^n.  But not all groups are copies of the integers (and I didn’t prove that these all aren’t the same group, but I’ll let you convince yourself of that)- for instance, we’ve thought about homeomorphisms of the torus.  We’re going to use group presentations to describe our groups- every element will be written as a word in the alphabet of generators.  So we’ll use letters like a,b,c… to represent generators, and we’ll put them together like aba, aa, babb as words to represent group elements.  Let’s do an example that we’ve seen before.

Symmetries of a square.

Symmetries of a square.

In the group of symmetries of a square, we have two generators, which we named (for the clockwise rotation by 90 degrees) and (for flipping over the horizontal axis).  And we wrote all of our group elements as words in the letters and s, above.  One presentation for this group is \langle r, s | \ r^4=s^2=1, sr^2=r^2s \rangle.

So for a group presentation we have < letters of the generating alphabet | relations >.  A relation is an equation in the letters which is true in the group.  And if you list enough relations, you’ll be able to characterize a finitely presented group.  There are some groups which can’t ever be finitely presented: no matter how many relations you write down, there’ll still be more relations which aren’t derived from the ones you wrote down.  Wikipedia has a good list of examples of group presentations.  Also, there are groups which aren’t even finitely generated: that means the generating alphabet is infinite.  If you aren’t finitely generated, you’re definitely not finitely presented.

So when we talk about random groups, we’re *only* going to talk about finitely presented groups.  This is just something that happens when you try to make things precise: you might cut out other cases that you wanted to talk about.  Anyways.

In the few-relators model of random groups, we fix a number K ahead of time, like K=4.  And we fix the size of our alphabet ahead of time too, like m=2.  So we’re looking at two-generator groups with four relations.  Our relations will be in the form word=1.  Pick a length for the words, so the word abbab has length 5, and so does the word $latex b^{-1}a^{-1}b^2a$.  Out of all possible words of length l, choose four at random: in our example, we have 324 possible words of length 5 in the letters a,b and their inverses.  [Note that the word aa^{-1}b = b, so it has length 1, not 3.]  We say a random group has property P in the few-relators model if the probability that a group with m generators and relators has property P goes to 1 as approaches infinity- so as the length of the relators goes to infinity.

How’d I get 324 in the previous paragraph?  Well, we have four choices for the first letter: a, b, a^{-1},b^{-1}.  The second letter only has three options: it can’t be the inverse of the first letter.  And the third letter can’t be the inverse of the second, so it also has three options.  Same deal for the fourth and fifth letters.  So I have 4*3*3*3*3 options, which is 324.  Instead of picking exactly five of those as relations, I could pick some proportion of them.  This is called the density model of random groups: instead of fixing K as the number of relations ahead of time, we fix d, a number between 0 and 1.  Then we say a random group has property P in the density model if the probability that a group with generators and $latex 2m(2m-1)^{dl}$ relators has property P goes to 1 as approaches infinity.

The density model is pretty common, and when people talk about random groups they often mean the density model.

Here’s a cartoon I drew because there aren’t enough pictures in this post:

Beware the infinite group presentation

Beware the infinite group presentation

Moosewood ricotta cake- so easy! Also we have internet!

20 Apr IMG_20150228_093918346

We are moved into our house and have internet!  The movers came several days late (they said Thursday-Saturday; they came Tuesday) and everything in our house needed fixing (water heater, AC, plumbing) but we live here now with internet.  Quick post because I want to find my math and start doing it again (amazing how much I can miss math).

For Christmas my in-laws gave me a copy of the Moosewood Cookbook (note: that’s an amazon affiliate link, which means if you buy from that link I get money hopefully maybe).  IT’S AMAZING.  I never follow recipes nor use cookbooks, but that statement is no longer true because I loooooove this cookbook.  No fancy pictures, and ingredients like “2 or 3 large eggs.”  I’m not into measuring precisely (yes this is a baking blog) so I like the give-and-take.  Also every single thing I’ve made so far from this cookbook is incredible.  You should go buy it.  Or give it to someone you love.

Anyways, this cake.  You beat things in a bowl, then pour into a pan and bake.  EASIEST RECIPE.

I know a guy named Ric, but he's vegan.  If he weren't vegan, I'd say Ric otta make this cake

I know a guy named Ric, but he’s vegan. If he weren’t vegan, I’d say Ric otta make this cake

First, butter and flour a pan.  I used to use a little square of paper towel and put butter on it to wipe across a pan, but then I baked with a friend who just used his (clean) fingers to spread a pat of butter around.  It’s actually much easier.  Or you can leave the butter in stick form, unwrap the top like a popsicle, and just spread that around- also easy.

I made this in winter, but I think it'd still be great in Spring.  Form your own opinion, though.

I made this in winter, but I think it’d still be great in Spring. Form your own opinion, though.

Then you throw all your ingredients into a bowl.  I didn’t have almond extract so skipped it.  Do not skip salt!

This cake is grate!  And making it is no (g)rind!

This cake is grate! And making it is no (g)rind!

Use a mixer, food processor, or lots of arm strength and beat til smooth (I used my KitchenAid, also a gift from in-laws).

It's surprisingly cool here in Texas right now.  Beat ya didn't see that coming!

It’s surprisingly cool here in Texas right now. Beat ya didn’t see that coming!

Pour the batter into your pan, and bake it for just under an hour.

Once baked, this cake is quite pourtable-it's not too crumbly.  Of course, before it's baked it's also pour-able

Once baked, this cake is quite pourtable-it’s not too crumbly. Of course, before it’s baked it’s also pour-able

I don't know Nathan Dunfield at all (he's a mathematician in 3-manifolds), but I hope whenever he finishes something he yells DONE-field!  I would if that were my last name.

I don’t know Nathan Dunfield at all (he’s a mathematician in 3-manifolds), but I hope whenever he finishes something he yells DONE-field! I would if that were my last name.

IMG_20150228_093918346

Moosewood Ricotta Cake (adapted lazily from the Moosewood cookbook which you should buy) [I’ll post this recipe because it’s amazing and a good introduction to how great the recipes are, but I’ll likely refrain from posting any more from the cookbook]

2 15-oz containers of ricotta

2 eggs

2/3 c sugar

1/3 c flour

1 TB vanilla extract

1/2 tsp salt

1 lemon

Preheat oven to 350, and butter and flour a spingform pan (or a regular cake pan would be fine too, just not as pretty)

Grate the rind from the lemon, and then juice the lemon.  Put all ingredients into a bowl and mix them until smooth.

Bake in the pan for 50 minutes.  Serve cold (so chill it in the fridge).  It just gets tastier the more you let it sit.

Kissing numbers, current research in hyperbolic surfaces

30 Mar

I just got back from the fantastic Graduate Student Topology & Geometry Conference, where I gave a talk and also brought my baby.  I tried to google “bringing baby to academic conference” as I’ve seen one baby at a conference before (with his dad), and I knew this kid would be the only baby at ours.  But it was cold enough/uncomfortable enough that I just had him stay in the hotel with my mom, and I ran back during breaks to feed him.  Also, it was my first time being “heckled” by both of these two brother professors famous for “attacking” speakers- they happen to know just about everything and are also suckers for precision, which I am not (and should be).  But I got a lot of good feedback on my talk, and I’m generally a very capable speaker (though I was not as prepared as I would’ve liked, thanks to somebody who likes to interrupt me every five minutes…)  IMG_20150328_104129098Anyways, this is not about me, this is about my friend who gave one of the best talks of the conference and more importantly, her research.  This post is based on notes I took during her talk + skimming her paper (joint with her advisor) on which it is based.

Remember that we had our introduction to hyperbolic space.  This research is focused on hyperbolic surfaces, which are shapes that locally look like hyperbolic space- this means that if you look at one point on the surface and just a little area around it, you think you’re in hyperbolic space.  A good analogy is our world- we live on a sphere, but locally it looks like flat space.  If you didn’t know better, you’d think the earth is flat, based on your local data.  So how can we build a hyperbolic surface?

While hexagons in flat space always have angles that sum to 720 degrees, that’s not true in hyperbolic space.  In fact, you can make right angled hexagons, which means that every single corner has 90 degrees.  If you pick three lengths a,b,c>0 and assign these lengths to three sides of the hexagon like the picture, you’ll fully determine the hexagon- hyperbolic space is wacky!

happyhex

Now glue two copies of a hexagon together along those matching a,b,c sides.  You’ll have a funny shape with three holes in it, and those holes will have circumference 2a, 2b, 2c.  This is called a pair of pants in topology.

happypants

You can glue together a bunch of pants to form a hyperbolic surface, by gluing them together along holes with the same length.  Any hyperbolic surface, conversely, can be cut up into pairs of pants (this pants decomposition is not unique, as you can see below).

PANTS

You could also set one of those lengths equal to 0, so you’d get a right angled pentagon as one of the hexagon’s sides would collapse.  You can still do the pants thing here by gluing together copies of the pentagon, but instead of having a hole with circumference 2a like we had before, you’ll have a cusp that goes off to infinity- it’s like an infinite cone with finite volume.

winkcusp

Now we’ve built every hyperbolic surface (there are some more details, like how you glue together pants, but let’s just stick with this broad schematic for now). As long as the expression 2-2*(number of holes)-(number of cusps)<0, your surface is hyperbolic.  So, for instance, a sphere isn’t hyperbolic, because it has no holes and no cusps, so you get 2 which is not smaller than 0.  And a torus isn’t hyperbolic, because it only has one hole, so you get 2-1=1.  But all the surfaces in the pictures in this post are hyperbolic- try the formula out yourself!

One thing you can ask about a hyperbolic surface is: how long is its shortest essential curve?  By “essential,” we mean that it isn’t homotopic (this is a link to a previous post defining homotopy) to a cusp or a point.  This shortest curve is called the systole of the surface.  Systolic geometry is a whole area of study, as a side note.  But we’re interested in the question: how many systoles can a surface have?  This is called the kissing number of the surface.

A few notes: a “generic” surface has Kiss(S)=1, that is, there’s only one shortest curve if you happen to pick one “random” surface (scare quotes because no precise definitions).  And it’s relatively “easy” to make a surface with Kiss(S)=3*(number of holes)-3+(number of cusps).  Check for yourself that this number is exactly the number of curves in a pants decomposition of a surface.  Using some hyperbolic geometry you can prove that there won’t be any shorter curves if you make all of the pants curves very “short.”

So what Fanoni and Parlier do in their paper is come up with an upper bound on the kissing number of surfaces with cusps.  I won’t go into that, but I will try to explain part of a lemma they use on the way.

If your surface doesn’t have any cusps, then systoles can pairwise intersect at most once.  But if you do have cusps, then Fanoni & Parlier prove that your systoles can intersect at most twice (and they build examples of surfaces with cusps that have systoles that pairwise intersect twice).

First they show that two systoles which intersect at least twice can only intersect in the way pictured to the left below, and not as in the right:

This picture from the Fanoni-Parlier paper I did not make this!

This picture from the Fanoni-Parlier paper I did not make this!

This matters because it implies that two systoles which intersect at least twice must intersect an even number of times.  In particular, if two systoles intersect more than twice, then they intersect at least four times.

So assume for contradiction that two systoles and intersect more than twice.  So they intersect at least four times.  That means that there’s some intersection point somewhere such that the b-arcs coming out of it make up no more than half of the systole length (see picture below)

If the green arc is more than half the length of the circle, then the blue one is less than half the length of the circle

If the green arc is more than half the length of the circle, then the blue one is less than half the length of the circle.

So if you look at these short b-arcs, plus the path, and wiggle things around, you’ll see a four-holed sphere (two holes above” the curve, and two holes “below,” one of each inside a arc).

Left: a schematic of how a and b intersect.  Black dots represent holes or cusps.   Center: the short b arcs plus the full a path Right: the short b arcs plus the a path, after moving four dots to be holes of a 4-holed sphere

Left: a schematic of how a and b intersect. Black dots represent holes or cusps.
Center: the short b arcs plus the full a path
Right: the short b arcs plus the a path, after moving four dots to be holes of a 4-holed sphere

This four-holed sphere has a curve on it, determined by part of and the arcs, which is shorter than the original systoles.  This contradicts the definition of systole, so our premise must be wrong- two systoles can intersect at most twice.

This was proposition 3.2 in their paper- tomorrow I’m going to share propositions 3.1-3.3 with my advisor’s small seminar.  Hopefully I don’t get heckled too badly this time!

OOPS I ALMOST FORGOT: life update.  We bought a house and are moving to Austin, TX.  I’m still planning on finishing my Ph.D., just virtually.  [Up to a finite-index subgroup, obviously.  Bad math joke].  I’ll probably be flying up to Chicago every so often to meet with my advisor/eventually defend my thesis.  But yes, we’re driving in our minivan to Texas on Thursday.  So… we’ll see when we get the internet set up in the new house.  I’ll try not to make too long a break until my next post.

Fun-stuffed peppers

24 Mar IMG_20150224_110024466

I don’t normally like making hors d’oeuvres, dumplings, or even cookies that require anything besides dropping, because I am lazy in this very specific respect.  But my advisor’s weekly “secret” seminar has treats (the speaker from the previous week brings treats for the following week), and I thought I’d try something crazy and wild.  So I bought a can of crescent roll dough (key to making the amazing easy cinnamon buns) and a bag of sweet mini peppers, and figured I’d figure out the rest the day before seminar.

I was surprised that I couldn’t find exactly what I wanted by googling, so here’s a Yen original recipe.  What actually happened was that I wanted to make pigs in a blanket, but then remembered we had a vegetarian in the seminar, so I bought the peppers instead.  These turned out AWESOME- the sweet peppers popped a bit, the paprika + pepper jack made it a little bit interesting, the cheesy filling was so creamy and offset perfectly the crispy buttery crescent roll dough.  I highly recommend.

I hope one day baby gets a tutor named Jack, so I can tell him to go pepper Jack with questions

I hope one day baby gets a tutor named Jack, so I can tell him to go pepper Jack with questions

There are two annoying things to do: one, seed the peppers.  I was lazy and just chopped off the tops to take out the seeds, but they’d look prettier if you left them on and cut a slit to pull out the seeds.  Two, fill the peppers.

Of course Jack won't be useful for taking tests.  Baby will just have to cr(e)am if he doesn't study ahead of time

Of course Jack won’t be useful for taking tests. Baby will just have to cr(e)am if he doesn’t study ahead of time

We'll just want to fill his head up with knowledge

We’ll just want to fill his head up with knowledge

I used a regular knife to fill the peppers.  The filling was a block of cream cheese + a few slices of pepper jack cheese + paprika for color.  These would also be great with some sliced green onion, any other sliced cheese, and any other savory spice.  Using a mixer to whip the cream cheese was key for making the filling spreadable, and it also spread out the sliced cheese very well.

Third annoying thing that was less annoying because it meant we were close to done: wrapping the peppers in crescent roll dough.

But academics isn't everything.  I don't want him to tear up if he messes up on a test.  Just roll with the punches, baby!

But academics isn’t everything. I don’t want him to tear up if he messes up on a test. Just roll with the punches, baby!

Also I got to use our pizza cutter, which we never use!  I don’t know if we’ve ever used it on pizza.  Or made pizza.  Hmm I should make pizza!

I guess that's what happens with kids: you just have to bundle them up and send them off into the world

I guess that’s what happens with kids: you just have to bundle them up and send them off into the world

These are both adorable and misshapen.  If you’re a fancy Pinterest-er who follows food blogs, I’m flattered you look at this and you should make these and make them more beautiful and tell me about it.  If you’re not a fancy Pinterest-er, you could make these and really impress people with them because they are so delicious and don’t need to be beautiful.  And they come out beautiful anyway!

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Fun-stuffed peppers (Makes about 20 peppers, about 7 appetizer-sized servings.  The “about” is how many peppers come in your bag)

1 package of Pillsbury Crescent Roll Dough (or something similar)

1 bag of mini sweet peppers

4 oz cream cheese (half a block)

2 slices of cheese (I used pepper jack, but cheddar or gouda could also be good) [you could also grate some cheese]

1/2 tsp paprika (ideas for other seasonings: garlic salt, oregano, cilantro…)

Set the oven to 350.  Seed your mini peppers by slicing them the long way and scooping out the seeds w/knife, or just cutting off the tops (the seeds are connected to the tops).  You’ll still want them sliced the long way.

Use a mixer to beat the cream cheese w/cheese and paprika.  Use a knife to scoop a small amount of filling into each mini pepper.

Roll out the crescent roll dough.  Use a pizza cutter to cut each triangle into three slimmer triangles, or be lazy as I was above and just cut strips.

Wrap each pepper with a small triangle or strip of dough.  If there’s leftover dough, just press it onto a larger pepper.

Bake for 15-20 minutes, until dough is golden brown.

LIME PIE IS SO GOOD

14 Mar

Pi day is almost over and I almost didn’t post!  Nothing exciting mathematically for this quick post; just a RIDICULOUSLY DELICIOUS AND EASY LIME PIE.  If you buy a graham cracker crust, it has THREE INGREDIENTS.  If you don’t, it has five!

Fun and cutely embarrassing fact: when I was in high school, my best friend and I would come up with codenames for our crushes- hers were a series of colors, and mine was a series of fruits.  Also, how we became best friends is I “stole” her “boyfriend” (we were 14), whom we later dubbed “orange” because it’s the only color which is also a fruit.  Anyways, I saved lime for a really serious one, because it was at the time my favorite flavor.  In fact I think “lime” never got assigned to anyone.  I wish I could go back to my teenage self and ask her if this guy I married is worthy of the “lime” title (hopefully she’d say yes!  I’d say I think he is, but it’s now unclear to me how good the title is.  In any case I like my husband a lot, but maybe not as much as I loved small green fruits when I was 15).

How pi-tiful would it be if I missed a pi(e) day post?

How pi-tiful would it be if I missed a pi(e) day post?

The not-secret ingredient behind lime pie is a can of sweetened condensed milk- this is also the not-secret ingredient behind Vietnamese iced coffee.  You too can make ca phe sua da or ca phe sua nong at home: pour some sweetened condensed milk in the bottom of a glass, add some espresso/very strong coffee, then add ice cubes or some hot water.  Stir.  I used to squeeze sweetened condensed milk over bread pudding as a sort of creme anglaise substitute.  Also, shaved ice + freshly cut chilled fruit + pour over some sweetened condensed milk = DELICIOUS.  And of course you need sweetened condensed milk for magic bars, which I will make and blog someday.  Just thinking about sweetened condensed milk is making me happy right now.

You may notice that this is not a key lime pie.  Key limes are small.  This pie would require juicing 20 or so key limes.  There are four limes in the picture above.  I am fairly lazy. You do the math.  (This is funny because there’s no math to be done here, besides maybe realizing the inequality 4<20.  However, in my meeting with my advisor a few weeks ago he told me that the key point that I had missed somewhere was the fact that 4/3 of three is less than five.  So there is math!  Or something something about me.)

This was my first graham cracker crust, and my friend actually made it (this may be the second time I’ve made a pie with someone.  First time was also in high school, with a friend who coincidentally shared my last name– we made a beautiful apple pie.  She showed me her secret of leaving the apple slices in a bowl of water to keep them from turning brown.)  We microwaved a stick of butter, crushed a bunch of graham crackers in a plastic bag, and mixed the two with a pinch of salt right in the pan.

I feel like graham crackers look much better than they taste- a fool's gold of cookies.  Just like pie, right?  (according to this slate article: http://www.slate.com/articles/news_and_politics/assessment/2011/06/pie.html)  [This is a pun on pyrite]

I feel like graham crackers look much better than they taste- a fool’s gold of cookies. Just like pie, right? (according to this slate article: http://www.slate.com/articles/news_and_politics/assessment/2011/06/pie.html) [This is a pun on pyrite]

I didn’t realize graham cracker crusts were so easy!  To make it a bit prettier you can tamp it down with a measuring cup or anything flat.  Then bake it while you make the filling.

If you code in Pi-thon instead of Python, what comPiler should you use? (consultant on this pun: husband)

If you code in Pi-thon instead of Python, what comPiler should you use? (consultant on this pun: husband, programmer extraordinaire)

Step one of filling is zesting the lemons.  If you don’t have a microplane grater yet, I highly highly recommend buying one.  This is one of very few kitchen tools I’ve bought (rolling pin?  Why not a wine bottle? Any other gadget?  Why not a knife?).  Also, think about how long this would take if you used 20 key limes instead of four normal limes.

I wonder if anyone has analyzed the horoscope data of people who are really good at memorizing digits of pi.  Are there more Pisces and ScorPios?  Are Capricorns pretty good, but more likely to accidentally throw in some other digit?

I wonder if anyone has analyzed the horoscope data of people who are really good at memorizing digits of pi. Are there more Pisces and ScorPios? Are Capricorns pretty good, but more likely to accidentally throw in some other digit?

Next, toss in some egg yolks.  You could of course use the whole eggs, but yolks make things more custardy/rich and they’re what I used.  Then I had egg whites for breakfast (you could also use the opportunity to make pavlova, the best thing I’ve ever made).  I used my stand mixer and mixed that up really well, til pretty light.  You could also just use a fork/whisk and a bowl for this recipe, but I do think that using a beater makes the texture super smooth.

I wonder if I can make it through this whole post only doing Pi jokes.  No reason in pi-ticular.  Just kidding, it's Pi Day!

I wonder if I can make it through this whole post only doing Pi jokes. No reason in pi-ticular. Just kidding, it’s Pi Day!

Now add in your can of sweetened condensed milk and beat that too.

Speaking of memorizing digits of pi, I'm horrible at it.  I was pretty bad at P.E. as a kid, but I'm even worse at Pi E.

Speaking of memorizing digits of pi, I’m horrible at it. I was pretty bad at P.E. as a kid, but I’m even worse at Pi E.

I guess I should add "memorizing digits of pi" to the big Pi-le of things I'm bad at (also, editing out weak puns is in this pi-le)

I guess I should add “memorizing digits of pi” to the big Pi-le of things I’m bad at (also, editing out weak puns is in this pi-le)

Ugh I’m using my husband’s stupid little computer and I accidentally published this post here.  Sorry!  Updating as fast as I can to finish it.

Finally, juice those four limes (or 20 key limes) and toss that in to the filling, and mix.  I have some asides about recipes here: generally, key lime pie recipes I found listed graham crackers and lime juice using cups as units of measure: so 1 1/2 c of crushed graham crackers and 2/3 c of lime juice.  The lime juice I understand, because limes come in different sizes/might be juicier or less juicy, and you want recipes to be repeatable.  But aren’t all graham crackers the same size?  Every time you crush X number of graham crackers, you should get 1.5 c of crumbs.  I’m just saying as an amateur graham cracker crust maker, I did not know how many graham crackers to use.

Pour your filling into your parbaked crust (it’s been in the oven for about ten minutes by the way, unless you’re really slow at juicing limes in which case maybe you took it out after ten minutes), and bake for another ten minutes until it looks not jiggly.

I've gotten myself into quite a mess.  I should've brainstormed pi puns ahead of time, then selectively chosen from the list.  Then I'd be out of this pickle by my pi-culling.

I’ve gotten myself into quite a mess. I should’ve brainstormed pi puns ahead of time, then selectively chosen from the list. Then I’d be out of this pickle by my pi-culling.

I want Weird Al to make a parody of that N Sync song, from the point of view of the White and Nerdy.  ("Yo I know Pi to a thousand places") It'd clearly be called "Pi Pi Pi"

I want Weird Al to make a parody of that N Sync song, from the point of view of the White and Nerdy. (“Yo I know Pi to a thousand places”) It’d clearly be called “Pi Pi Pi”

We let this cool for a little bit, then stuck it in the freezer because we wanted to eat it.  You could also put freshly whipped cream on top if you wanted.  But it’s great on its own, and is SO EASY.  We literally went from “hey, do you want to make a pie?” to eating a pie in one hour, which includes the 15-20 minutes of freezer time.

If the singer of "Party in the USA" had been really into saying digits of the ratio between the circumference and diameter of a circle as a kid, would she be called Piley Cyrus?  (instead of Miley, which is short of Smiley, rather than her given name.  Thank you wikipedia)

If the singer of “Party in the USA” had been really into saying digits of the ratio between the circumference and diameter of a circle as a kid, would she be called Piley Cyrus? (instead of Miley, which is short of Smiley, rather than her given name. Thank you wikipedia)

SO GOOD.  SO EASY.  SO GLAD THIS POST IS DONE SO I DON’T HAVE TO KEEP COMING UP WITH PI PUNS.

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Lime pie (adapted from the ever-amazing smitten kitchen)

1 sleeve of graham crackers

1 stick of butter (1/2 c)

Pinch salt

1 can of sweetened condensed milk (14 oz)

4 limes or 20 key limes

3 egg yolks (or eggs)

Crush the graham crackers (we stuck them in a plastic bag then pulverized with a bottle, but a rolling pin or something would work well too).  Melt the butter.  Mix the graham crackers and salt in a pie pan, then pour over the melted butter and mix.  Tamp down into a crust.  Bake at 350 while you make filling (set timer to ten minutes to be safe).

Beat the egg yolks with the zest of the limes for several (5 per SK) minutes.  Meanwhile, juice the limes.  Then add sweetened condensed milk and beat more (3 minutes per SK).  Stir in lime juice.  Pour into parbaked pie crust.  Bake for another ten minutes.

Let cool completely, then chill.  Then eat.

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