The Peanut Butter and Jelly World

        It's here, the first article in Volume $1$ of the Journal of Peanut Butter and Jelly Sandwich Studies! Finally, the time to talk about peanut butter and jelly (or jam for the subjects of the Queen) sandwiches has come. I actually spent some time researching the topic in order to write this post, but there's a surprisingly limited amount of academic sources documenting the PB&J! I was hoping for some old looking tome like the infamous "The History and Social Influence of the Potato" that you see online from time to time.

One day... look forward to it.

        Instead of just copying the history of the PB&J sandwich which can be easily found anywhere online; I'll talk about its relationship and history with yours truly. (Or as some circles like to call it, an autoethnography!)

~~~~~~~~~~~~~~~~

        PB&J sandwiches are, as far as my investigation showed, truly as American as baseball. Or at the very least, they're something you would almost never see in Mexico. When I was young I had seen peanut butter on supermarket aisles, and American media had already invaded TV; so the concept was not really "alien" to me. However, they were nothing more than a curiosity, something that kids in a stereotypical sitcom/cartoon ate as a snack or took to school as part of their lunch in America. Me, I ate gansitos or chocoroles as snacks; while peanuts (salty and/or spicy) were reserved to be eaten as botana before lunch. Even now every time I go back home I eat them pretty often.

It doesn't matter when you read this: I would kill for a bag of Mafer enchilados.

        I lived the first 18 year of my life in Mexico City, not knowing what I had been missing out on. Knowing this you may be wondering: how did a Mexican kid ended up becoming a PB&J connoisseur? Well, perhaps it was fate, since I decided to go to America for university and it would be there where I would finally taste one of those mythical sandwiches for the first time.

~~~~~~~~~~~~~~~~

        I still remember the first time I tried a PB&J. It was a snowy February night during my freshman year at Cornell, on the way back to my dorm after a study session where Lebesgue measure finally clicked for me. I was feeling pretty tired after that and fighting with the infamous blizzards that hit the Slope from time to time, but I wanted to reward myself so I went to the convenience store at Noyes. I was certainly in the mood for something, but I was not quite sure of what... then my gaze fell upon it, the little make-a-sandwich station on the side. It was (is?) a counter with various typed of sliced breads, spreads, toppings, etc... for making your own sweet sandwiches. I had seen it since the first time I went in, but never really considered getting something from there. 

Where it all began. It was much darker and snowier though.

        That time was different. I went to take a look and saw all the offerings: from chocolate chips to marshmallow fluff, from blueberry jelly to rye bread, and anything in between. Having had eaten among Americans for some months already, I had been witness to the legendary PB&J in person; so when I saw the peanut butter I decided to make one myself. Nothing weird, I went for a fairly standard one for my first time: white bread, smooth peanut butter, and Concord grape jelly; made more or less with random proportions. I bought it and went to my room to enjoy it with a glass of cold milk (my drink of choice for dough-based treats, and one of the few things I actually have in my refrigerator even to this day). I then took a bite.

        The soft and fluffy, yet perfectly firm outer structure created by the traditional classic white bread slices; containing but letting the ingredients inside it shine. The smooth, creamy and thick peanut butter texture that is so familiar; together with that unmistakable and very slightly salty peanut flavor. The relative sweetness and light tartness of the Concord grape jelly, bringing with it some chunks of grape that added vital fruitiness to the bite. And finally the cold, refreshing wave of a sip of whole milk that managed to tie it all at the end, just when you feel you might be needing a bit of liquid... it was heaven! It goes without saying that the sandwich didn't last too long. 

~~~~~~~~~~~~~~~~

        The PB&J sandwich instantly managed to become one of my go-to sweet snacks/desserts; together with other staples like ice cream, choco-chip cookies, and bubble tea. A feat by no means small! Luckily for me, good quality PB&J ingredients were (are??) available readily on most Cornell dining halls during breakfasts; so I had no trouble making one when I felt like it. Incidentally, Cornell has the best food of any university, don't @ me.  (Actually, do @ me if you feel like it.)

PB&J's should never be cut imo, but sometimes I get an odd number of bread slices.

        At more or less the same time, I had started experimenting with mixology, trying to create the perfect cocktail. Or so I like to put it, in reality I just liked to mix soft drinks available in dining halls, and kept track of what worked and in which proportions. Story for another day, but Dr.Pepper + Milk (aka Dr.Milk) is awesome! Regardless, it was these experiments with drinks that led me to start thinking about doing something similar for PB&J sandwiches, and so my research began!

        During the rest of my undergrad and (aborted) grad school years, I investigated several different angles: What type of bread is the best? Smooth or crunchy peanut butter? Toasted? Add normal butter to the mix? Fruit? Is milk the best drink to pair it with? Bacon? What proportions? Does the forgetful functor  忘 $: \text{PbJ} \rightarrow \text{Top}$  preserve limits jelly flavors? (The category of PB&J sandwiches in case you were wondering.) The answers to some of these and more will be included in follow up posts in case you're curious.

Just defining homotopy fibers (pun intended) between $\text{Pbj}$ and $\text{Top}$.
And yes, it's an image since blogspot doesn't support tikz-cd :(

        Unfortunately, it was around the time I was due to start exploring the jelly side of  the equation that I took the decision to abandon it all and travel to Japan. Not only was my life in a rather complicated situation; I was also going into a completely different culture thousands of kilometres away from all the places I had lived in before. As such, I had no choice but to leave a lot of stuff back in America. Excuses, I know, but there were so many new dishes to try and adjustments to makes so I let both my math and PB&J research lay down for a while.

        Eventually, I decided to actually settle down here for the time being and my life became much more stable with a job and a regular schedule. With it, several old interests began to revive like finally reading about group cohomologies (I may write some stuff about eventually, but I suggest you take a seat if you're going to wait) and PB&J sandwiches. Picking up from where I had left, I decided to focus my research into finding the best jelly flavors for a sandwich. 

The jelly section on an average Japanese supermarket.

        You may be thinking that it would be difficult to get the ingredients for a PB&J in Japan; you would be kind of wrong. There's sliced bread, but not that much variety and the quality is a bit average (bar some exceptions); same story for the peanut butter. I had already drawn conclusions regarding those two factors though, so I quickly found the best available options. As for the jelly, standard flavors are not uncommon on Japanese supermarkets as seen in the picture above: strawberry, blueberry, orange, apple... so I started with some of those. However, once I was done with that limited (but still delicious) selection, I could not just stop. After all, we can't draw a conclusion from such a sample. It would not be much of an investigation if $n$ was that small! 

        Luckily we live in the 21st century and even in Japan there are several specialty stores that carry some unexpected products from all over the world, among them quite a good selection of jellies. Bilberry, passion fruit, lingonberry, lemon & vanilla, kiwi & chardonnay (?!), etc... And so I've dedicated quite a few months to tasting and cataloging an ever increasing list of jellies. Each one compared to each other and ranked according to different criteria; but overall focusing on how they fit in $\text{PbJ}$ (spoiler: they're the morphisms!).

Almost all jellies in this shelf are on my "to try" list.
Don't ask me what Strawberry&Strawberry is though.

        I've been sharing some of my experiments on Twitter once in a while, but it was only recently that I decided to expand my thoughts on a series of blog posts rather than in 280 characters. As with other chains of posts in here, how often I update this depends a lot on my free time (summer break right now!) and how addictive the videogames I'm playing are (I get the feeling Iron Harvest will put a stop to any writing for a while once it's out). Regardless, rest assure that the research continues and you'll get to see the findings here or on the book I'll publish about the topic once I become a bitter old man.

また！