Nearly-No-Sugar Almond Cookies

Pretty much anyone who has meet me in real life knows that I love to cook, and in particular I love to bake. Growing up it was kind of the household hobby to make cookies or cakes or pies on the weekends or whenever we finished the previous one. Cookies in particular were a near constant. We never had soda (unless we were sick or it was a holiday), or chips or any of the various colorful kid junk food, but there was always homemade cookies. In college, cookies were a kind of stress release. Exams were always accompanied by at least two kinds of cookies, one of which had to have chocolate. When I need to give people a thank you gift, I give them cookies.

So it was rather a blow to my reality when I was told that for health reasons, I shouldn't eat cookies. Not in the generic "don't eat junk food sense" but that I needed to avoid refined flour and sugar or suffer serious consequences in short order. Being determined and prone to culinary experimentation anyway, I tried a whole bunch of disastrous healthy cookies. Note: do not ever try to make cookies with rye flour. No amount of flavoring will help.

Earlier this week however, I was struck with inspiration, and an overwhelming desire for a shortbread cookie. A bag of almond 'flour' was sitting in the back of my pantry. Shortbread cookies are significantly less cakey than other cookies, containing in their simplest incarnation flour, butter, sugar and salt. Surely I could approximate it with almond flour?

Low and behold, it worked. As I was cutting the butter into the almond flour in the food processor, it came to me that I might need a little more binding power. What better than an egg? Add a skimpy 2 tablespoons of honey to 2 cups of almond flour and a handful of slivered almonds, chill in the fridge to firm up, and dole out teaspoons of dough to bake at 375, I had 6 dozen bite sized almond cookies that were halfway between a macaroon and a shortbread cookie. Keeping the dough in ball form let it stay softer in the middle and more macaroon light, flattening the cookie let it be more shortbread like.  I calculated that each cookie has just under a half gram of sugar, which is perfect for my needs, and probably most low-carb people. That half gram is the only carb in the whole cookie. If you can tolerate a little bit more sugar, dipping half the cookie in melted chocolate just makes it better. [If you can't have any carbs  whatsoever, I suspect, though have not tested, adding another egg and using an artificial sweetner would work as well]

I left the flat ones in the oven a little too long, but they still taste good. Just, toasted

Recipe for Nearly-No-Sugar Almond Cookies

2 cups almond flour

1/4 cup butter

2 tbsp honey (the darker the better)

1 large egg

1 tsp vanilla 

Optional: 1/2 cup slivered almonds

In a food processor, combine 1 cup of the almond flour with the butter. Pulse until thoroughly combined. Add egg, honey and vanilla. Pulse until a wet dough forms. Add almond flour a 1/4 cup at a time until the dough is the consistency of  a chocolate chip cookie batter. Stir or gently pulse in the slivered almonds. Wrap dough in plastic and refrigerate at least 30 minutes until dough has firmed up. Dish out 1 tsp  worth of dough onto a parchment lined baking sheet (about the size of a grape). Leave in balls for a soft cookie, flatten for a crunchy cookie. Bake 20 minutes at 375 or until just beginning to brown around the edges. Let cool. 

Unlike grain based cookies which stale in a refrigerator from the crystallization of the starches, these cookies keep very well in a closed container in the chill chest. 

Enjoy!

An Apology to My Math Teachers

At this point in my academic career, I feel I owe an apology to every math (and a few physics teachers) I have ever had. At some point in every math class (any my optics classes in college) that I said, either to myself or to the teacher directly, "I will never need this once I finish this class."

Pride goeth before the fall, right?

To date, this is the list of things that I can remember saying I'll never need, and have subsequently found that yes, you do need these things. In fact, most of them are my bread and butter these days:

1) Algebra: solving systems of equations for multiple variables, factoring, expanding and finding roots.

3) Geometry: Mostly the reasoning skills, and some stuff about angles. Learning to use a compass has come in oddly handy.

2) Trigonometry: pretty much everything I can think of. I yell at my own students to learn the unit circle, "All Seniors Take Calculus" comes in handy all the time, and I can't remember the last thing I did that didn't have a trig function somewhere. Also useful for fitting furniture in a car.

3) Calculus: Um, everything. How to do integrals by hand, partial fractions method, complete the square method and integration by parts, all of which I said "I'll get computer to do this", I now do by hand, because the computers don't do it correctly. Calculus in general I'm using a whole lot more than I ever thought I would.

4) Differential Equations: if I had known I'd be dealing with them so much, I would have paid a lot closer attention. They are everywhere, and I have to relearn a lot of stuff from scratch because I seem to have purposely forgotten it all.

5) Optics: I swore the day I finished my first optics class that I would never ever ever use this stuff. It was stupid, useless and boring. Yeah, about that...

If anyone in school is reading this, take it from me. You will end up using this stuff. One way or another it will all come back to haunt you, especially if you tell it you'll never need it.

To any teacher who finds this, please accept this, my own personal apology, for not believing that this stuff was important. Doesn't matter if you taught me or not. To the great collective of teachers past, present and future, I was young and stupid and so are the kids you teach. They just figure out you were right too late to tell you so. Thanks for teaching them anyway.

Theoretical Research: Reality vs. Fiction

Subtitle: A novice theoretical researcher's perspective

I swear, I will soon get around to the 'food' portions of physics and food, but rewatching a couple of episodes of "The Big Bang Theory" sparked the idea for this post. I thinking specifically of the few episodes where they show Sheldon working on his research. Having hung around theoretical researchers as an undergrad, I had an idea that they portrayal was a little exaggerated. From doing experimental physics for a few years, I knew the experimental labs they show are far too tidy, with too few boxes of old equipment in the corners and not enough of the apparatus held together with office supplies and duct tape. I knew Sheldon's white boards were too small, and oriented the wrong way to hold the kind of equations that he would be working on, for example. 

Now that I have done theoretical research for about 6 months, and had closer contact with theoretical researchers, watching the episodes made me want to shake the producers or writers or whoever decided that doing theoretical physics research looked like this:

Just standing around, staring at a handful of short equations on a white board for a couple of hours until you have an epiphany and write down the answer.

At least for me, the episode where Sheldon stays up for a couple of days and starts using small round objects to represent carbon atoms comes closer to the state of mind I usually end up in, but still misses the point.

From my (admittedly limited experience), doing theoretical research looks a lot more like a cross between a kid doing his math homework and a college kid writing a paper.

First of all, there is paper involved. Lots of paper. Reams of paper. Some people prefer notebooks that force all the paper to stay in order. Some people prefer loose scrap paper. I knew a guy who liked to use old school printer paper, the kind that was perforated but connected so he could write out really long equations all on one line. I have come to love the yellow legal pad that keeps all my stuff in order while I"m doing it but lets me rip it all out when its wrong to use on my grill or to staple together with other correct calculations  for easier reading. Chalk boards/white boards are great for testing out a direction, but they can easily be erased and lost forever. Anything that you think might be good, you want on paper. Possibly with scanned back up copies. *

There is a lot of referencing other people's work. Precursors to your own work. Finding out how to solve this particular form of equation. How to interpret your results. Huge bookmark folders of references. Binders full of them.

Thirdly, there is a lot of frustration, at least if you aren't one of those mathematical geniuses who can keep track of everything in their head. There is a lot of losing minus signs, plus signs, and constants. There is a lot of doing the same calculation over and over and over because you missed something at the beginning. Just recently I had to redo over 50 pages worth of calculations because I missed copying a plus sign on page 1 and turned an addition into a multiplication (and make the problem hugely longer in the process). I nearly wanted to tear my hair, but having done experimental physics for a while I at least had the consolation that the cost was a couple of weeks and some paper, not a couple of weeks and thousands of dollars worth of supplies.

Maybe there are some researchers out there who can use Richard Feynman's method of "Write down the problem, stare at it, write down the answer". Maybe if you do something like this long enough all the math is internalized. I certainly have gotten a lot faster at Fourier Transforms and integrating gaussians. But I doubt I will ever just look at a problem and know the answer. And I seriously doubt my equations will ever been that short in the middle of the solution.

*All that being said, if I had an entire room full of movable chalkboards like they have in some older schools like Princeton, I would totally being doing my calculations on them. Taking lots of pictures with my phone.

What is/are Singular Optics?

This maybe should have been the first post, but I thought if this were the first post it would set a rather more serious tone than I would like for this blog.

I mentioned in my first post that I'm doing theoretical physics, specifically singular optics, but I didn't really say what that was. Partly because it didn't seem needed, and partially because I don't like trying to explain what I research since I don't fully understand what my field encompasses. Somewhat tautologically, the field of singular optics studies optical fields that display singularities. Since pretty much everytime I say I am studying optics people ask, "So, eyeglasses...?" I think its safe to say each of those terms could use some defining.  

The general study of optics covers a section of the electromagnetic spectrum that is centered around the visible range. These days it also covers light a little above and below the visible portion, namely ultraviolet (UV) and infrared (IR) radiation. In a sense, optics is very, very old. There is evidence to suggest that the Ancient Egyptians and Mesopotamians used lenses. The oldest known 'lens'  is the Nimrud lens from ancient Assyria, which may have been used as a magnifying glass or to light fires. The contemporary study of optics in some part can be traced to Newton who did a great deal of work with prisms, but optics really could not take off beyond what is now known as geometrical optics until James Clark Maxwell codified existing theories of electromagnetism into Maxwell's equations. This so called 'classical electromagnetism' describes the behavior of light even into the realm of relativity (it is in fact inherently relativistic), but not on the quantum level (you need quantum optics for that). While Maxwell's equations cover the whole of the electromagnetic spectrum, from gamma rays to x-rays to microwaves to radiowaves, 'optics' is considered to only cover a tiny section of that spectrum--the light we can see and the 'colors' just beyond what we can see.

From xkcd.com

The concept of singularities is essentially mathematical, though it has an obvious physical representation. If something is 'singular', that usually means that it is either a) going to plus/minus infinity b) some part of it has gone to zero, making another part undefined.  From the omniscient Wikipedia, "In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability." Singularity is the point where the mathematical equivalent of "Monty Python's" The Colonel declares that everything is getting too silly and to get on with it. There is always something weird, and to certain deranged minds like mine, cool about ill behaved math/physics. The obvious and most well known example of a singularity is a black hole. Everything breaks down  inside a black hole--no one really knows what goes on inside those things other than seemingly infinite gravity and time dilation. 

Singular optics is not quite as dramatic as a black hole. I doubt anyone will be making computer skins depicting singular optical phenomena who isn't directly involved in it in some way. Dr Skull over at "Skulls in the Stars" explains it far better than I can, with really cool pictures. Basically, it boils down to this. Light is made up of waves (try to forget about photons for a moment). Waves have an amplitude and a phase. Think of an ocean wave. Amplitude would describe how high above the surface the wave gets, while phase would describe a point along the wave. We tend to think of this as nice, well behaved math and physics. Sines and cosines are easy. The weirdness comes in if you have two waves that are interfering with each other. Sometimes they cancel each other out and sometimes they double up. When they double up, they are still well behaved, which is to say that they have a well defined amplitude and phase. When they cancel each other out though, you have no amplitude, and the phase is undefined. This is the singularity with which this branch of optics deals. Where the phase is undefined, it takes on all possible phase values at once. Which seems like utter nonsense, but it turns out to be very, very useful. 

How on earth is this useful? Well, one of the nice things about these singularities is that they create what are known as optical vortices. The light goes around in circles in some sense. Two things are nice about this. One, is that the vortices carry angular momentum, which can be used to rotate things, say microscopic objects held by optical tweezers. Another is that these vortices remain stable under perturbation. They will still go clockwise or counterclockwise, for example, when you send them through a lens or some sort of perturbing medium. In theory, you could use this property to send data optically (i.e., a right-handed vortex = 0, a left handed vortex = 1 for computer bits), perhaps even through free space. There are probably many other applications we just haven't thought of yet because this subfield is only about 40 years old, and lasers are only now becoming relatively cheap. 

I am only just starting my research in this field and really only just starting to understand what it all means. I'm sure in a year I am going to reread this blog post and cringe at my pathetic understanding of my own chosen field, but you have to start somewhere. So here it is, my first baby steps of understanding. 

Cheers!

Hello! (aka, What the heck is this blog?)

Greetings, reader! I'm glad you found this blog, and I hope you find it interesting, helpful, etc.

Historically, I've been really bad about any kind of journal-type righting. I've always been better at writing fictional stories on a regular basis than writing about myself. I'm hoping that this blog will bridge that gap for me.

 I am a graduate student doing theoretical physics, specifically doing research into the area known as singular optics. So a lot of my posts will be about physics, and particularly optics. This will especially be true in the next few months as I study for my qualifying exams and use this blog as a tool to study for that great Rubicon of graduate students.

When I'm not working on physics, I'm thinking about or experimenting with what is probably my most useful hobby--food. For health reasons, I frequently need to modify existing recipes or invent new ones from scratch. So some of my posts are going to be about food--my recipes that turned out pretty well (or failed spectacularly, awesome recipes I found, new (to me) ingredients, etc.

Other than those topics, this is my blog and I'm going to feel free to post on whatever seems interesting to me.

I hope to get a proper blog post written at some point, but for now this will have to do. 'Til next time!