It should come as no surprise that food, chemistry and mathematics meet in baking. For once I will leave the chemistry aside for a while and turn to the mathematical aspects of baking. More precisely I will delve into geometrical problems encountered in baking. When cutting cookies from a rolled out dough or placing cookies on a sheet for baking you actually attempt to solve a mathematical problem known as a packing problem. The purpose is to maximize the distance between the cookies and maximize the size of the cookies, paying attention that the cookies should not touch. Many will perhaps start with a square packing (see below), but soon figure out that a hexagonal packing will fit even more cookies onto the rolled out dough or onto the baking sheet (especially when the dough/sheet is large compared to the cookies). The optimum way of placing 2-17 circles in a square are shown below (and the solution for up to 10.000 circles is also available).

My challenge for you however is a different one as I’m interested in eliminating the leftover dough when cutting cookies. To achieve this the cookies cannot be circular. Using a square cookie cutter (or simply a knife) would be the easiest way to leave no gaps, but how cool are square cookies? What I’m really looking for are cookie tessallations which are aesthetically pleasing, and at the same time transferable to a baking sheet. Oh yeah: a tessallation “is the process of creating a two-dimensional plane using the repetition of a geometric shape with no overlaps and no gap” according to Wikipedia. So – no gaps – no leftover cookie dough!

Should you ever want to place circular cookies on a square baking sheet, this is how to maximize the size of the cookies! (Illustrations CC-BY-SA by Toby Hudson)

This is one way of solving the problem with leftover dough shown in the top picture. A tree can quite easily be transformed into a shape that fills the plane without any gaps. This image was made using the Tess software mentioned below.

Tessellations are frequently encountered in the art of M. C. Escher, and his Regular Division of the Plane Drawings are all based on tessellations. Most of Escher’s drawings however are not useful for making cookies because they are too interlocking – it would be impossible to take the cookies apart and transfer them to the baking sheet (and baking them “interlocked” would not be an option as cookie dough inevitably will raise/expand a little, making everything stick together). But I did find one example of an Escher inspired cookie cutter as well as some other nice examples of cookie cutters especially designed to make tessellations:

Over at Thingiverse the design file for this Escher inspired cookie cutter can be downloaded (Photo by Bas Pijls via Thingiverse). And should you want to transfer your own designs into a 3D printable format, check out this cookie-cutter-generator.

From Cox & Cox you can buy this Jigsaw cookie cutter (Photo from Cox & Cox product page). If you have access to a 3D printer you can also print your own jigsaw cookie cutter.

These elaborate cookie cutters are designed by Keith Kritselis. Over at Kickstarter you can find more information about his special cookie cutters for Halloween and Christmas. What makes them special is that each tessellation is made up of three or four different shapes.

If you rather want to make your own tessellations there are a couple of different software and online apps available, but I’ve found Tess to be one of the best. An evaluation copy of Tess (no save function) can be downloaded for free. Below are a couple of designs I’ve made. The patterns are nice, but would I want to each cookies with these shapes?

And finally the challenge for you all: Make your own cookie tessallations and share it! It’s not a competition, but rather an invitation to contribute. If the design is great I might have it 3D printed on a friends MakerBot or order it in metal from Shapeways and blog about it here If you send me a picture (preferably at least 620 pixels wide/high, email to webmaster/a/khymos.org) I’ll put up a gallery to display the submitted designs.

Update: I’ve written up a short post about no-knead bread in Norwegian – Brød uten å kna – to accompany my appearance in the popular science program Schrödingers katt.

I know – since the NY Times article about Jim Lahey in 2006 the no-knead breads have been all over the internet, newspapers and now even appear in numerous books – this is really old news. But the no-knead breads are really tasty as well, so I hope you’ll forgive me! When I give popular science talks about chemistry in the kitchen the one thing I’m always asked about is the no-knead recipe I show, so I thought it was about time to publish a recipe. Surely, everyone can google it – but regrettably many (if not most?) recipes are given in non-metric, volume based units – even Jim Lahey’s original recipe. And for baking this is really a drawback because the density of flour depends so much on how tight you pack it. Oh yeah, and I will also try to explain why and how the no-knead bread works.

The stretchy gluten which gives a dough its elasticity is formed when the two proteins glutenin and gliadin bind together. Kneading can speed up this process, but in a wetter dough the mobility of glutenin and gliadin increases, and given enough time they can actually manage it all by themselves. That’s why a wet dough needs time to develop the gluten network, but no kneading.

This is to show what 3 g fresh yeast looks like, in case you don’t have a balance that can accurately weigh such a small mass.

I’ve often seen it mentioned that a longer fermentation and/or less yeast gives a richer aroma. I think it’s true, but I’m not quite sure why this is the case. If the flavor compounds are produced proportionally to the carbon dioxide, the easiest way to increase flavor would be to up the amount of yeast. A lower temperature and/or less yeast would only mean that it takes longer to produce the same amount of carbon dioxid and flavor compounds. However, most of the advice I’ve seen about baking suggests that there is a flavor improvement by extending the fermentation time. So to rephrase the question: Why is the desirable bread flavor not proportional to the amount of yeast added? Some claim that the bitter flavor of pure yeast can dominate the flavor of the resulting bread if used at to high levels – but I have never been bothered by yeast flavor, even when using 50 g of fresh yeast for 1-2 kg of flour. But maybe I’m just insensitive to this bitterness? It could also be that the flavor profile produced by the yeast benefits from the lower temperature, but I doubt that one would actually be able to tell the difference in bread (you can easily tell the difference in beer, but here the fermentation may take from days to weeks – see also my post on Baking with hefeweizen yeast). Another possible explanation could be that enzymes, which are present in the flour or slowly produced by the yeast, contribute significantly to the flavor if given enough time. Amylase is one such enzyme which converts starch to sugar. It’s naturally produced by yeast, but it’s often added in pure form to “industrial doughs” to speed things up. Yet another explanation is that a long proofing time will allow a certain production of organic acids by the bacteria which are always present (this of course is what gives sour doughs their characteristic flavor).

The most unusual step in making no-knead bread is that it’s baked in a preheated heavy cooking pan, also known as a Dutch oven, usually made from cast iron. But this is indeed very clever! Professional bakers are lucky to have steam inlets in their ovens, because steam has a heat capacity which is much higher than that of dry air. Because of this the loaf will heat up quicker, giving a better oven spring. But the moist air inside the covered pan does more: as long as the loaf is colder than the pan the moisture will actually condense on the surface of the bread, thereby keeping it moist. This ensures that the oven spring is not hindered by a dry crust. Secondly, this moisture is important for a proper gelatinization of the starch: we are setting the stage for the Maillard reaction.

After about 30 min the lid is removed. At this point one will see the nice oven spring, but also notice that no browning has occured sine the temperature in the crust has been kept below the boiling point due the condensation of moisture on the surface. Once the lid is removed moisture can escape and the temperature in the crust rapidly rises above 110 °C where the Maillard reaction proceeds more rapidly. This is what gives the crust it’s nice brown color and also gives rise to the beautiful smell of fresh baked bread. At this point, the total baking time should be determined by the color of the loaf. When the surface is sufficiently browned your no-knead bread is finished.

Salt is very important, so don’t omit it from the bread. If you try to reduce the amount of salt in your diet – do so by eating less fast food and industrially prepared food. Don’t mess with the salt levels of home baked bread. It’s there for the taste, but it also improves the strength of the gluten network.

No-knead bread (based on Jim Lahey’s recipe)

390 g all purpose white flour
300 g water (77%)
7 g salt (1.8%)
~1-3 g fresh yeast

Mix everything until the flour is completely moistened. Cover and leave for 15-25 hours. Pour onto a floured surface, fold 3-4 times, shape rapidly into a boule, place it on a generously floured cloth/towel seamside down and proof until doubled in size (~2 hours). Dump seam side up into a cast iron pan preheated to 230 °C and bake with the lid on for 30 min. Take the lid of and bake until the crust has a dark golden color – approximately 15 min.

Proofing the loaf on well floured towel

The percentages in the recipe are so-called Baker’s percentages, giving the amount of the ingredients in percent of the flour. The amount of water is often referred to as the degree of hydration. I’ve had good results with a hydration of 77%, but you may want to adjust this depending on your preferences. In fact, it’s impossible to know exactly what hydration Jim Lahey used because of his volume measurements! The recipe posted on the Sullivan Street Bakery’s homepage has a hydration of 80%, but I wonder whether the amounts are calculated or measured. My advice is to start at 77% and then adjust up/down in the range 75-80%. By adjusting the hydration you will indirectly also adjust the size of the pores (more water = larger pores) and the moistness of the bread. The higher hydration will of course yield a more sticky dough, but don’t forget that it’s a no-knead bread, so you’re supposed to handle the dough as little as possible.

Regarding the amount of yeast I’d start with 3 g, but if you feel that it rises to quickly you can lower this to 1-2 g. The main reason for this variability is that the activity (= number of living yeast cells) of fresh yeast decreases with time. Homebrewers can calculate exact pitching rates for yeast based on a ~5% loss of viability per week for liquid yeast. My guess is that compressed yeast is more stable, but I haven’t been able to find any data on it’s viability.

My no-knead breads look a bit different every time I bake them, but that’s OK.

The required hydration depends a lot on flour as well of course! No-knead breads can greatly benefit from substituting some of the white flour with whole grain flours, or ancient cereals such as emmer (farro), spelt, einkorn etc. Whole grain flours tend to bind more water though and develop a less strong gluten network. This last point is well illustrated by my failed attempt to bake a no-knead bread with 100% emmer. The resulting flat loaf is shown in the picture below.

No-knead bread with 100% emmer did not have a sufficiently strong gluten network – the bread ended up very flat…

Further reading:
The Secret of Great Bread: Let Time Do the Work (original NY Times article)
No-Knead Bread (original recipe from Jim Lahey)
Soon the bread will be making itself
Simple Crusty Bread (recipe)
No-Knead Bread: Not Making Itself Yet, but a Lot Quicker
Speedy No-Knead Bread (recipe)
Fast No-Knead Whole Wheat Bread (recipe)
eGullet thread on no-knead breads

Wheat beers such as hefeweizen, weissbier and wit are all light beers made from a mix of malted barley and wheat. In southern Germany the typical hefeweizen is fermented with a non-flocculating yeast, and it is not filtered before bottling. This gives the beer a yeasty, bread like flavor accompanied by aromas reminiscent of banan, cloves (we’ve encountered that combo before), coriander and citrus. I’ve just begun to read up on brewing and my first batch of a partial mash hefeweizen is bubling along. As I pitched the liquid hefeweizen yeast into the wort I decided to keep a tiny amount for baking. If hefeweizen beer is reminiscent of bread, why not use the yeast for making bread? In particular I was curious whether some of the aroma top notes characterizing hefeweizen beer would stand out in bread made using the same yeast.

The specific yeast I used was obtained as a liquid suspension from White labs. Their hefeweizen yeast strain (catalogue number WLP300) is identical to Weihenstephan 68. And in case you didn’t know – Weihenstephan is the world’s oldest brewery. Wine yeast is the same as beer yeast (or ale yeast to be more precise) and baker’s yeast – and they are all known under the latin name Saccharomyces cerevisiae (which literally translates to something like a “beer producing sugar munching fungi”). Why bother if they are all the same yeast you may ask. It’s a good question, but despite the common name they are different isolates with very different properties. They certainly have a lot in common: in the presence of air they consume sugars to grow, and in a closed environment without access to air the consumed sugars are instead converted to alcohol and carbon dioxide. But besides this main reaction there are hosts of other enzymes present that produce higher alcohols, aldehyes, acids, esters – all of them volatiles compounds that contribute significantly to flavor. And this is typically where the isolates of S. cerevisia differ. There’s a mind boggling array of beer yeasts available. Take a look at the yeast catalogues of White labs, Wyeast or Fermentis to get an idea of the many yeast strains that are available (note that the lists includes both ale yeasts S. cerevisia which are top fermenting and lager yeasts S. carlsbergensis which are bottom fermenting, meaning that the yeast sinks to the bottom when the job is done). And if this doesn’t impress you – consider the fact that there are thousands of S. cerevisia isolates available from culture collections around the world (ATCC and CBS are among the largest – do a search for S. cerevisiae at ATCC and it tells you to narrow your search because there are more than 5000 hits!).

Apart from the specific strain used the fermentation conditions will also greatly influence the volatile profile: temperature, time, pH, micro and macro nutrients present, and the sugars available all have their say. A general advice for artisan breads is to use only a small amount of yeast (2-3 g) to start with and give the dough plenty of time to develop and rise. This gives a richer flavor compared to using 50 g of fresh yeast to obtain a rapid rise. Since I only started with about a 1/4 teaspoon of yeast slurry I first had to let the yeast grow and multiply. Since S. cerevisiae needs oxygen to grow I added 50 g of water to the yeast slurry and then used a hand mixer to whip in air for a minute or so before adding 50 g of flour. I left the pre-ferment (aka poolish or biga) on the benchtop and the next day there was plenty of bubbling activity. I added more water, whipped in more air with a hand mixer and once again added as much flour as water. This yielded an active starter and all was set for baking.

Hefeweizen bread

Pre-ferment (evening before baking day):
65 g starter (100% hydration)
110 g water
110 g all purpose wheat flour

Baking day:
285 g starter (100%) from day before
466 g water
250 g emmer
485 g all purpose wheat flour
12 g salt

Total dough weight: 1498 g
Hydration: 69%

Add water to starter and incorporate air with a hand mixer to give the yeast a good start. Mix in the flour, cover and leave at room temperature. Next day, mix all ingredients and leave to rise (this may take 1-3 hours). Divide in two, fold over repeatedly and shape into boules. Leave to rise. Preheat oven to 250 °C. Use a baking stone, and generate some steam in the oven during the first 10 min (see picture below). After 10 min, turn down to 220 °C and bake until crust has a nice golden crust.

My current steam setup: I use ice cubes since this prevents a sudden gush of steam towards my hands. The stones serve as a heat reservoir ensuring that the ice cubes melt and evaporate within a couple of minutes. To cope with the heat shock I use a plate of stainless steel to hold the stones. After 10 min I open the oven door to vent out steam and remove the plate with the stones to allow an even heating (no reflection!) of the baking stone from below.

So how did it taste? The bread tasted excellent, but to be honest – I couldn’t detect any aroma that I can’t get using conventional baker’s yeast. The reason for this is probably that other flavors (i.e. from the flour, the baking process etc.) dominate. Another factor is that bread is only fermented for a couple of hours compared to several days for beer. This simply doesn’t give enough time for significant concentrations of the volatile compounds to develop. Lastly, the baking process will drive off the most volatile compounds. Nevertheless, I would still encourage you to try this! I didn’t get the result I hoped for (I was a little optimistic), but it’s a fun experiment to do, especially if you have some yeast left over from beer brewing anyway.

I am by no means the first to try this. But it seems that results are mixed. Some complain about slow rising doughs. But there are also many misconceptions around. One is that some yeasts produce more alcohol whereas other yeasts produce more gas. As long as we’re talking about anaerobic fermentation of sugar to ethanol and carbon dioxide this is plain wrong as ethanol and carbon dioxide are produced in a 1:1 ratio. There is also some confusion with regards to the naming (i.e. beer yeast, ale yeast, brewer’s yeast, baker’s yeast etc. – when all in fact are the same yeast).

Since the bread came out just like bread made with conventional baker’s yeast it’s fair to turn the question around: Do the different beer yeasts really make a difference? I did a quick search in the scientific littereature and found a couple of papers that study the effect of yeast strains on the formation of volatile compounds in beer and wine:

Yeast Influence on Volatile Composition of Wines
Ester Concentration Differences in Wine Fermented by Various Species and Strains of Yeasts
Synthesis of volatile phenols by Saccharomyces cerevisiae in wines
Function of yeast species and strains in wine flavour
Expression Levels of the Yeast Alcohol Acetyltransferase Genes ATF1, Lg-ATF1, and ATF2 Control the Formation of a Broad Range of Volatile Esters

I haven’t had the opportunity to dig really into this, but from the abstracts it definitely seems to be the case that the selection of yeast strains also play a vital role in the resulting aroma profile of the beer.

Oh yeah, one more thing: For this particular bread I used emmer from a local mill, Holli Mølle, specializing in ancient cereals. Emmer (aka farro) doesn’t form as much gluten as conventional wheat (I tried making a 100% emmer no-knead bread which tasted nice but was a fiasco shape wise…), but it does lend a light greyish/brown color to the crumb and also gives the bread a richer flavor. But the use of emmer is of course not a pre-requisite if you want to bake with beer yeast

Looks good and tastes good!

One of the more curious cookbooks I own is a German one entitled “Kochen und Backen nach Grundrezepten” (Cooking and Baking with Base recipes). It was first written in 1932 and has been updated regularily ever since. Each section typically has a standard recipe which indicates the ratios to use followed by suggested variations (just like The improvisational cook). It also has nice summaries of dos and don’ts (just like BakeWise and CookWise), and what really makes the book stand out is that is so compact yet still comprehensive. It’s one of those books I actually use when cooking. Many other books have a little too much text – you have to read a lot to pick up the key points. Anyway – the reason I mention this is that as I read about the new “Ratio” book by Michael Ruhlman (MR books, MR blog), the German cookbook was the first book that came to my mind.

“Ratio: The Simple Codes Behind the Craft of Everyday Cooking” just appeared this month and promises that it “will unchain you from recipes”. That’s a good thing, because by knowing a couple of basic ratios you can cook anywhere without bringing your recipes. I’m quite fond of books like that and look forward to leaf through it once I get my hands on a copy. Bakers have been using ratios for ages, better known as Baker’s percentages, so the concept is not new. When baking bread, knowing that you need 6 dL for each kg flour will make a decent bread (but not necessarily an exceptional one!). Ruhlman extends the concept and describes 33 useful ratios for the kitchen. One examples is cookies, and it’s as simple as 1-2-3: 1 part sugar, 2 parts fat and 3 parts flour. Add flavor according to taste and baking powder and/or eggs for a lighter texture. Now that’s what I call a short recipe! The only thing that puzzles me is why the book has 272 pages… That’s a good 8 pages to explain each ratio But for an experienced cook the only thing you actually need is the ratio. And if you take a close look at the cover it actually displays several of the ratios. I’ve copied them into the table below so they are easier to read. You can find the remaining ratios (covering Stocks & Sauces, Farçir, Fat-based sauces, Custards) in the Barnes & Noble preview of the book. And if you combine these ratios with some of the flavor pairings from “The flavor bible” you should be ready for a lot of fun in the kitchen!

Now this is yet another book I’m looking forward to this fall – I’ve got quite a list now!. Shirley O’Corriher, best known for her book CookWise (not to mention her video “Shirley O. Corriher’s Kitchen Secrets Revealed” and TV appearance in case you live in the US), has been working on this book for a while (NYT article from 2004, free registration requried). Finally it is due to appear in October! The title BakeWise suggests it has the same structure as CookWise. The good thing about CookWise is that the food science theory is applied directly to recipes. In addition it has nice tables on what-went-wrong and what-to-do-about-it. In fact it’s a problem solving manual for the kitchen.

According to the publisher BakeWise “reads like a mystery novel as we follow sleuth Shirley while she solves everything from why cakes and muffins can be dry to génoise deflation and why the cookie crumbles”. And they continue:

Restaurant chefs and culinary students know her from their grease-splattered copies of CookWise, an encyclopedic work that has saved them from many a cooking disaster. With numerous “At-a-Glance” charts, BakeWise gives busy people information for quick problem solving. BakeWise also includes Shirley’s “What This Recipe Shows” in every recipe. This section is science and culinary information that can apply to hundreds of recipes, not just the one in which it appears.