Beer Space

Lately, I’ve been writing a number of posts about quantum mechanics, a field where coordinate spaces play a big role. One of my earliest posts on this blog was about applying coordinate space concepts to real life, a thread I picked again up last year.

Long ago I introduced my buddy (I call him “Scott” here), who is also an aficionado of good beer, to the concept of beer space. I’ve mentioned it here once or twice in passing, and I have notes about it that date back to 2011 when I started this blog.

So it seems high time I actually wrote a post about beer space.

Informally, beer space is the (parameter) space of all possible beers. Not just beers that exist or have existed, but all possible beers that could ever exist.

More formally, beer space is a conceptual abstract parameter space with axes for all possible ingredients and techniques of beer brewing. I say conceptual for two reasons: Firstly, as with many complex human notions, it’s hard to define exactly what a beer is — the boundaries are quite fuzzy. Secondly, in part because of the fuzzy boundaries, it’s very hard to define the required axes.

The latter issue is quite a challenge. To start, there must be an axis for every possible ingredient. For any given beer, the ingredient list is small, in some cases consisting only of malted barley, hops, and yeast (and, of course, water, but that is more of a background than an ingredient).

Yet there is a vast variety of different kinds of hops and malted barley, and many beers combine multiple types. For instance, as a first cut, there is two-row barley and six-row barley (the former has less protein content and more fermentable sugar).

There are even more (way more) varieties of hops (see this Wikipedia page). In fact, the varieties of hops, and how it they are used, contribute hugely to the nature of beer. The primary contribution of the malt is to provide sugar for the yeast to ferment into alcohol.

As you might imagine, there are also different varieties of yeast critters. The first cut is between lager yeast and ale yeast. The former use cooler conditions (and, to my palette, create less complex beers), whereas the latter require warmer conditions (and make, I think, more complex and interesting beers; I’m not a huge fan of most lagers, especially pilsners, which I generally find insipid).

Yeast and hops are often closely guarded secrets of master brewers, especially the yeasts. Their contributions are crucial to the final product.

Each of these ingredients needs an axis in the parameter space even though, for any given beer, the coordinate on nearly all of them will be zero.


We also need axes describing how these ingredients are prepared and used.

Barley, for example is malted, which includes roasting, and the degree of roasting is part of what defines it. Lightly roasted malt makes pale beers while darker roasting makes darker beers. Black patent malt is roasted to the point of being carbonized, which tends to destroy the fermentable sugars, but adds a smoky flavor and blackness to porters and other dark beers.

Any given variety of hops can be used fresh or dried, and can be added early during the boil (to add bittering) or late (to add fragrance and flavor). These techniques also contribute to a beer’s character.

Other brewing techniques are significant and need their own axis, too.


What’s more, barley, hops, and yeast, are merely the canonical beer ingredients. (In fact, even hops came along a bit later. In 15th century Britain, an ale was a fermented barley beverage. Adding hops made it a beer.)

Beers made with the canonical three (four counting water) are called Reinheitsgebot beers after the German beer purity law from 1516. (It’s not that Germans didn’t make other kinds of beers, it’s that they couldn’t call their product “bier” unless it adhered to the Reinheitsgebot.)

Brewers use many kinds of grains (wheat, rice, and rye, are very common) to provide sugar for the yeast, but fermentable sugars can include actual sugar (white, brown, or raw), maple syrup, honey, and even fruit. Each requires an axis.

There are also adjuncts added for flavor or character (or just for kicks). Common ones include chocolate and coffee, but creative brewers toss in almost everything except the proverbial kitchen sink. One beer I knew better than to even try had lavender flowers (and sunflower seeds and dates). Scott did buy it and reported it to be wretched.

As you might imagine, this expands the number of required axes considerably and is part of what makes beer space so conceptual. How can one list all possible ingredients a brewer might try? They could be almost anything edible.


That’s hardly the end of the difficulties in defining beer space. Some things are hard to quantify as a coordinate on an axis.

Brewing techniques are especially challenging. They tend to be binary properties, either used or not used. That means the axis only has two possible coordinates, zero (not used) and one (used).

There are also qualities that are outcomes of brewing rather than inputs to the process. While the inputs should account for all outcomes, these properties tend to be how beer drinkers perceive beer.

Very common formal ones include ABV (amount of alcohol), IBU (how bitter a beer is), and specific gravity (how heavy a beer is). Making that a bit more complicated are competing standards as well as poorly followed testing methods to derive these supposedly formal parameters.

More informal ones include sourness, effervescence, transparency, mouth feel, finish, after taste, head formation, and so forth. Some of these are especially hard to quantify and often a matter of perception.


It seems impossible to pull off practically (how does one quantify mouth feel?), but conceptually there is a beer space. Obviously it’s very complex, but it’s still true that any given beer has a set of properties that place it uniquely somewhere in that space.

What the idea does is provide a way to think and talk about beer. One can speak of general areas that especially appeal (or don’t). Given beer styles form fuzzy neighborhoods within the space.

For one example, I’ve explored, slowly at first, and then with commitment, the IPA (India Pale Ale) part of that space. And over time I’ve left behind other parts of it (I don’t drink brown ales or porters much anymore).

The first time I had a Surly Furious, the hop load made me think I was drinking a pine tree. It was hard to choke down. Now I see it as a mildly hopped beer I enjoy if a place doesn’t have something more interesting.

There is also how, long ago, Newcastle Brown Ale was my default beer in places that didn’t have anything better, but I haven’t touched it in many years (in part thanks to greater availability of craft beer).

Later I was a fan of Fat Tire, made by New Belgium, but it, too, has gone the way of Newcastle. I’d enjoy either in a pinch (say if the only other choices were (regular) Coors and Budweiser or — much worse — “lite” beers of some kind), but I don’t drink them anymore if something better is available.


If one drinks a specific beer most of the time, one live in a very small part of beer space. If one drinks only one beer, one lives at a single point in the space.

Others like to actively explore the space, finding joy in the variety (which is considerable — the almost infinite variations provide a rich tapestry to experience).

What’s in my fridge right now. The two on the left are local brews.

I like my little neighborhoods. There are enough beers in them for considerable variety. There are neighborhoods I’ve learned aren’t really for me. The Belgian sours for one and most pilsners for another. I’m not typically a fan of “big” (high alcohol content) beers — what I classify as barley wines — but I’ve had some that were smooth and tasty.

I used to explore more often, but I don’t have a refined enough palette to care that much. I think it was author Robert B. Parker who said, “The best beer I’ve ever had? The last one.”

Still, it’s fun trying a beer I’ve never had before. I recommend it; variety, after all, is a life spice.

§ §

Human experience has many such parameter spaces. For any given area of interest, there is a parameter space. Generally, the more interesting a thing is, the more complex its parameter space. (Kind of obvious, really.)

Wine, for instance, has a parameter space (“wine space”) that easily rivals beer space. Other examples might include cigars, cars, boats, candy, gardening, painted art, books, movies, music, and much much more.

What makes these things interesting and enduring is, to a great degree, that their parameter spaces are so vast and interesting. There is much to explore and often a neighborhood for almost any taste.


As a closing note, for years I used the name phase space but that was a misnomer. A phase space encodes the dynamic behavior of a system. It’s not a way to represent lots of different systems.

Parameter space is more correct, but I thought phase space sounded cooler. They’re both multi-dimensional coordinate spaces which was the main point. There is also that a parameter space isn’t really a vector space, and I liked vectors. (But what would it mean to take the inner product of two different beers? Other than making the product inner to you, I mean.)

So beer (parameter) space it is.

Stay hoppy, my friends! Go forth and spread beauty and light.

About Wyrd Smythe

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

10 responses to “Beer Space

  • Wyrd Smythe

    “What’s in my fridge right now,” is a good example of me sticking to the IPA neighborhood of beer space. Even so, the five shown involve considerable variation within that neighborhood.

    From left to right:

    Indeed Flavorwave IPA, a new beer I’m trying for the first time. It’s well named; it’s delicious, and I’ll be buying that one again. Indeed is a local Minnesota brewery.

    Furious IPA, which I mentioned in the post. I don’t usually buy it, but only because I usually buy other IPAs. I bought some this time because some of the beers I usually buy were out of stock last time I shopped. Surly is also a local company.

    Deschutes Fresh Squeezed IPA, one of my favorites. It uses fresh hops! Deschutes is an Oregon brewery.

    Dogfish Head 60 Minute IPA is also a regular in my fridge these days. As the name suggests, it’s hopped for 60 minutes. They also have 90 Minute IPA and 120 Minute IPA, although I don’t see those in the store as often. Dogfish Head is a brewery in Rehoboth Beach, Delaware.

    Stone IPA is another favorite, a not-juicy very bitter “west coast” IPA. (I drank a lot of these on the train trip to and from Seattle.) Stone is based in Escondido, California. (You might notice something about the label. I’ll tell you about that another time.)

    Not pictured:

    Fulton 300 IPA is a special favorite, my first experience with the Mosaic hops, which is especially yummy. It’s not pictured because the 16 ounce cans don’t fit, so it’s in another spot in my fridge. Fulton is also a local brewery located in Minneapolis.

    Bad Weather Hopcromancer IPA, another favorite. There was hardly any of the Bad Weather beers when I shopped (which I found worrisome), and no Hopcromancer, which is why I bought the Indeed Flavorwave. Bad Weather is another local brewery, based in St. Paul.

    • Wyrd Smythe

      As an aside, while I do like sugar, I’ve always liked it with some substance and flavor. As long as I can remember, I’ve preferred brown sugar or molasses to plain white sugar, and plain sugar cookies are far down on a list that starts with ginger/molasses, puts oatmeal-raisin in second place, with chocolate-chip coming in third.

      I also love horehound candy, which is made from marrubium vulgare, a member of the mint family, but which is bitter. The candy includes sugar to balance the bitter, but it’s not a candy widely loved.

      Point it, IPA beer styles were kind of a natural for me, and it’s no surprise I gravitated towards them!

  • Wyrd Smythe

    (It’s not that I drink a lot of beer; I don’t. But when I do drink beer, I prefer to drink really good beer. “Good” as in high quality and high delicious flavor.)

  • SelfAwarePatterns

    This raises the question, which I think we might have discussed before, of what are the necessary and sufficient properties to call a drink “beer”? I read somewhere that when an ancient recipe for beer was followed, it produced a sweet tasting product vaguely reminiscent of hard cider rather than the modern varieties of beer.

    • Wyrd Smythe

      It’s a very fuzzy space. The most inclusive definition is probably something along the lines of any naturally fermented (not distilled) beverage that uses mainly some sort of grain as the sugar source is a beer.

      On the other end of the spectrum, Reinheitsgebot, which limits it to barley and hops (and yeast). (When that law was created they didn’t even know about the yeast, so it’s not mentioned. They just knew they needed a bit of a previous batch, even just the unwashed stirring spoon, to make a new batch work.)

      Without a bittering agent, fermented grain does make sweet beverage. The whole point of the bittering is changing that balance. These days the “IPA revolution” has swung that balance away from sweet, although I’ve heard rumblings that the younger crowd is getting tired of all that hops.

      • SelfAwarePatterns

        I’m reminded of something else I once read, a Roman general’s impression of a drink the Gauls (I think) brewed, which seems most likely to have been beer. Relating it to what he knew, he described it as a type of grain wine. Although I find it hard to believe the Romans didn’t know about beer.

        Yeah, the bitter aspect generally doesn’t do anything for me. But then, I rarely drink beer. I’m sure if I did, I’d acquire a taste for it.

      • Wyrd Smythe

        The Romans were way into wine, I know, but I’ve never heard anything about them in connection with beer (not that that means anything; I don’t really do history). I think most cultures that discover fermentation probably do have various forms of it, though.

        Most modern beers are balanced at least a bit on the hop side. The exception tends to be brown ales, porters, stouts, although I’ve had dry versions of those (which I prefer). The thing about IPAs is that they use a lot of malt, which leads to higher alcohol content, and then balance that with a lot of hops. And then some more hops. The (not true) legend is that India Pale Ales had extra hops to help preserve the beer for its long trip to India. But British “bitters” have always been a thing. Most pale ales are on the bitter side.

  • Anonymole

    I read a recent article that stated that beer might be the reason for civilization. Gotta stick around to grow the grain, chase off the antelope n’ deer. The Shaman expects us to brew out twenty skull-fulls when the season’s right. Better settle down and mind the beer.

    • Wyrd Smythe

      I’ve seen the suggestion. I think that might be wishful thinking by beer aficionados. Beer probably was discovered in consequence of grain being stored in barrels that got wet and turned into something that seemed nasty. But hunger led to eating it anyway… with unexpected results! “Hey, this stuff tastes like hell, but it rocks!”

      That would imply farming already existed as a much more reliable way to feed a “large” population than hunting and gathering, which is generally only good for small nomadic groups.

      That said, very early humans may have observed animal behavior after eating fermented fruit, and early humans were a lot cleverer than often thought. So who knows? (Not me, certainly. I never could get that time machine to work.)

      There is a story that the Pilgrims landed at Plymouth Rock because the Mayflower ran out of beer. Apparently the original plan was to sail further south to more hospitable places down the coast. The alcohol content of beer was a good way to deal with the impure water — water that comes with disinfectant built in!

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