**Oat-top Whole Wheat Wild Yeast Bread with 30% Rye**Is this a blog about bread? What does that even mean? I'm a palliative care nurse who bakes bread in his spare time, to have something to eat when at work, and something to do in my off hours -- something that gets my hands immersed in dough, because I feel the need to orient myself back to life, back to earth, and to once again nurture

*growing*things rather than

*dying*people. In my home life, I find I think about bread quite often. The thoughts range widely. I think about how I am feeding myself, and how the entire world feeds humans. I think of these things often enough to write down what I've learned or wondered about, as I try to educate myself about bread. I stumble from idea to idea, and from loaf to loaf. That's what this blog is about, mostly. My stumbles.

*One of my latest stumbles:*

**a walnut loaf**, made with my sandwich bread recipe.*Certainly no bliss-bread, no utopia bread here.*

Today I'm thinking about math. But of course, the chain of thought doesn't end there.

**Math Complacency**

I once read that most bedside nurses can make do with mathematics no greater than what is learned at a grade six level. Nurse

*researchers*should know more, of course - they will have to deal with statistics in a coherent way. And I'm certain that

*some*bedside nurses will have to use more in the context of their jobs, but it wouldn't surprise me that a generalization of this sort is generally true. Grade six sounds about right.

For the most part, then, a nurse such as myself can get away with minimal mathematics. In my everyday work, I mostly deal with ratios of mg to ml. It's pretty easy, and once you have some facility with it, you enter a "math comfort zone." I know that others have stepped into this complacent math place too: sometimes, for example, other nurses will ask me to check their work before they give an unfamiliar IV drug that they've diluted in solution and must give over a certain length of time. That is all to the good, to be cautious and have someone double-check the results, if one is doing something unfamiliar, especially when life and death are on the line. But I speak of all this not to denigrate nurse math skills, but rather to discuss the feeling of math complacency anyone gets when one doesn't encounter any new and challenging mathematics after a while.

**Segue to Bread Math**

Minimal math is also all that is required for most bread recipes. By grade six, you probably already learned that parts of the whole must all add up to 100%, but that is something that must then be

*unlearned*when you take up baker's math. Baker's percentages are a little bit weird, in that the flour is always the ingredient that is 100% by weight, and other values are determined from that. Once you have that strangeness figured out, the math itself is not all that difficult. I still struggle with the interpretations of various ingredients, but that is simply a matter of fine-tuning the method to individual recipes.

**Beyond Baker's Math**

But my interest in bread and dough has taken some queer turns at times, and I often find myself immersed in articles where the math simply baffles me. The study of dough rheology has turned up tons of equations alone, as everyone from Newton to modern mathematicians has been curious about how flowing solids (which is one way to describe dough) can be mathematically modeled. Furthermore, engineers continue to study and experiment on foam and bubbles and chemical structures, all of which have significant application to bread making. Open an article in the Journal of American Association of Cereal Chemistry, for example, or look at a modern book that discusses colloids, or the engineering applications of foam, or have a look at the Ph.D. thesis of some engineer who is studying new methods of how to measure bubbles in dough, and probably you will encounter math that will seem somewhat unfamiliar, if you have become complacent at grade-six math levels.

If you are like me, you will wonder what all this math shows, what it all proves, and how to make sense of it. A lot of the engineering math has industrial bread-making applications, for shaping and extruding dough on a large-scale. What can we little folk take from this new math, and how can we apply it to our home-baked loaves? I am interested in the way the mathematics suggests new ways of dealing with dough and bread-making, I have this

*so-far*insatiable curiosity about the process and the mysteries. But the math continues to baffle me, and therefore understanding eludes me.

**Mathematical Modelling**

The other day while reading some of these articles I found another reference to

**Baker and Mize**, who back in the late 30's and throughout the 40's did what is considered the seminal scientific research in bread crumb. I have yet to read their original articles (

*if I had to pay for every article I want to read, I would quickly go broke*), but their work has been cited often since. They apparently proved, by mixing dough in a vacuum, and in the environment of other gases, that

**.**

*no new bubbles are formed in bread during the stages of fermentation or proofing*From this research, I am given to understand that the bubbles that you've achieved during mixing are what you get. During mixing of water and a tiny bit of salt with flour, gluten structures form a web of interconnections, and within this moist net gas molecules (Oxygen and Carbon dioxide) are captured. The number of bubbles is determined by chemical bonds, which can be affected by (1) the elements that make up the mixture (thus the importance of hydration -- Hydrogen and Oxygen -- and other ingredients like salt that may act as cations to reinforce bonds, or other ingredients that may act as surfactants or stabilizers etc.), as well as (2) other things important to the chemical reaction (like mechanical manipulation, temperature, pH, and perhaps even other things like electrical stimulation).

Now, some of the tyrosine side-branches of the 3D structure of gluten may stretch and break down during mixing, leading to some of those bubbles breaking apart and joining with other bubbles; and the yeast may continue to feed and add their CO

_{2}to the spaces between the network's cells, increasing the

*size*of the bubbles, but no

*new*bubbles are going to form. The old traditional method of knocking down the dough after the first rise is designed to even out the gas within the bubbles so the final crumb will not have so many large, irregular holes. This knocking down remains a part of many of the industrial mechanical methods in this country, methods which have been modeled on older traditional hand-baker methods. It is curious that these days, you often find artisan bakers foregoing an official knock-down process in order to achieve a more varied and irregular holey crumb. I think that because industrial methods have achieved a uniform crumb size and shape, independent bakers have gone to an irregular crumb to show that they are baking an artisan-style bread.

**Oat-top Whole Wheat Wild Yeast Bread with 30% Rye***I no longer have to think about this bread*.*

**Bubbles in Bread**

While looking for Baker and Mize's research, I found an article online that references their work, and yet remains quite accessible to mathematically-challenged readers such as myself.

**Dr. Peter Martin**is an engineer who studied at Oxford and Cambridge, and continues to work on the rheology of "cereal-based food foams." His article, Martin, P. "Controlling the Breadmaking Process: The Role of Bubbles in Bread" (2004). Cereal Foods World: American Association of Cereal Chemists, vol 49, no. 2. pp. 72-75 discusses three different bread-making processes (Straight Dough Process, Chorleywood Bread Process, and Sponge and Dough Process), examining bubble manipulation during each phase of each process. There are three schematic diagrams in his essay that portray at a glance each of these different bread-making methods, and the diagrams divide the whole process of dough-to-bread into different process-parts.

As I read this article, it occurred to me that these different process-parts represent the

*physical-world*manifestation of

*ideas*that were first conceived and understood mathematically. What do I mean by that? Well, we have a process that mixes flour and water and salt and perhaps other ingredients; this mixture is manipulated in certain ways, and we end up with bread. Stated

*that*simply, this represents

*all*bread. But precisely

*how*we mix,

*what*we mix, how we

*manipulate*the mixture, and what we do with it are all processes which have been examined by scientists, who have described the methods more or less accurately by

*mathematical modelling*of what is taking place. Once mathematics has defined these newly-defined parts of the process, machines can be designed to meet the mathematical projections. And so the parts of the process become enshrined in not only understanding, but in metal too: but the point is, they were first conceived of mathematically. Where before we had a nebulous understanding of dough becoming bread, now we have more clearly defined parts to the method. In reality, the dough still becomes bread, and it is

*one process*. The mathematical breakdown of each part of that process that we have described

*tells*us something, but the whole process occurs whether or not we have described it as an aggregate of partial processes or not. And the three methods described in Martin's article show that the breakdown of the sub-processes and their description are somewhat arbitrary. They are inventions by us, mere models by which we have described the overall process.

**Martin's Mystery**

Martin's article is unique because he examines all those models using the point-of-view of the bubbles, and he reinterprets the parts using bubbles as touchstone. The bread-making process from the POV of bubbles is described in the literature, he says, through the steps of

**Mixing**(Bubble creation, coalescence, and breakup),

**Bulk Fermentation**(Bubble growth and rupturing),

**Makeup**(Bubble manipulation)

**Proofing**(Bubble growth),

**Baking**(Bubble growth and setting), and

**Final Crumb**(Bubble stability). And Martin says that there have been studies within all these areas, but that

*Makeup*requires much more research.

*Bubble manipulation*is Martin's Black Box, that has to be better described, better understood. In Martin's opinion, we don't yet know enough about what happens to bubbles when we form our loaves. Makeup is his mystery.

How important is the forming of our home-made loaves? Very important. I believe it was Daniel Wing, writing of the late Alan Scott (both co-authors of "The Bread Builders: hearth loaves and masonry ovens") who said that in the oven, Alan's loaves could rise to double the size of his student's loaves, from the same dough, even though Alan was telling them and showing them how to form their loaves. All because he knew how to handle the dough when forming the bread. That is the artisan's touch.

If you bake 70-300 loaves a day by hand you are going to get pretty good at handling dough. If you only bake every week a couple of loaves,

*as I do*, it will take a lot longer, and in fact, you may

*never*learn how to properly handle the dough. Especially if you are never told or shown, and have to get your info from books. William Alexander, the author of "52 loaves" really only became expert at breadmaking after undergoing rigorous breadmaking training while in France, which enabled him, a short time later, to teach the monks of the Abbey of St. Wandrille. Real artisan bread bakers toil daily in unenviable circumstances, their work grueling, demanding, time-consuming, rigorous, repetitive yet precise. I believe they deserve our admiration and respect. So far no machine has been able to duplicate their efforts. Their hands know more than we can yet describe mathematically.

**What you don't know, you don't know**

As I write this, I'm wearing a t-shirt that I picked up in Disneyland. It has a picture of Goofy on it, shrugging. "

*World's Best Kept Secret*", it says. "

*The Blissful State of Simplicity. Your Own Personal Utopia Awaits. Thinking causes thoughts. Goofy is what Goofy does. The Goofy Mind is a Happy Mind. What you don't know, you don't know. Trust your heart for answers*".

Goofy appears to be no less a Zen master than

**Ch'ing yuan Wei-hsin**(Seigen Ishin), who reportedly said, "Before I had studied Zen for thirty years, I saw mountains as mountains, and waters as waters. When I arrived at a more intimate knowledge, I came to the point where I saw that mountains are not mountains, and waters are not waters. But now that I have got its very substance I am at rest. For it's just that I see mountains once again as mountains, and waters once again as waters."

Since before the days of Aristotle, the philosophical underpinnings of observation and science itself would have us take apart everything to get an understanding of its elements, and then combine them again to get an understanding of the whole. There is some question as to whether this approach is even likely to succeed. The whole is so very often greater than its parts, different than a prediction of an aggregate of its elements would expect (

*bread itself is a good example*). But we have taken apart molecules to get an understanding of the atoms that comprise them, and have arranged these atoms in tables which enable us to probe their properties; we have devised mathematical models that describe those atoms, and even the sub-atomic particles that comprise them. And with our particle accelerators we have smashed atoms together to learn what those sub-atomic particles are made from. This is a more "

*intimate knowledge*". But each level of discovery has resulted in a new black box, a new unknown, that we have similarly wanted to open up and examine and describe ("

*thinking causes thoughts"*). And mathematics has been the language of description. But a description of the whole still eludes us. Do we know more about the Whole because we can describe something about its parts?

Or are we better off not thinking about these things? My sidebar profile says that I dream of a bread that leads to Nirvikalpa. After more than three years of study of the various parts of bread, I want bread to be bread again. I want Goofy Bread, Trust-in-you-heart-bread. I want to forget the math. I long to forget what I think I know, and just get to know bread again.

Or is that just the math complacency in me talking? I still really really want to know. Goofy shrugs and guffaws, happy in his ignorance. He is wise, but I still struggle with the math and stumble from loaf to loaf.

I'm wondering this too: will it take daily toil in unenviable circumstance (the baking equivalent of the boredom of daily zazen for thirty years), before I manage to arrive at a familiar facility with real bread?

**Notes to Myself**

**An Example of some Math Beyond Baker's Math**

Here is a recent example of "math beyond me" that I encountered, from Campbell, G. et. al. "Measurement and Interpretation of Dough Densities" (1993) 70(5). Cereal Chemistry. pp 517-521 The pdf can be found online among the back issues of Cereal Chemistry.*This is old math.*

"The void fraction, or volume fraction, of gas in a dough (

*α*) can be calculated format he measured dough density (*ρ*):

*α*= 1 -*ρ*/*ρ*_{gf}

Clearly, to calculate the void fraction using this equation, the gas-free dough density (*ρ*_{gf}) must be known. Baker and Mize (1937) estimated*ρ*_{gf}by mixing dough under a very high vacuum. However, this deprives the dough of oxygen during mixing, altering the dough chemistry and possibly affecting the gas-free dough density…"

This equation looks elegant. It is almost understandable. But although Baker and Mize went on to streamline their techniques for measuring dough density using a series of CaCl_{2}solutions, their math modelling was still a poor estimation and their methods inconvenient, for modern industrial dough engineers. Campbell and his team tweaked the math, and carried out further experiments. Their final equation is terrible to behold, for such a one who is math-challenged as me:

*Wince.*

And this is just about the easiest math one can encounter in the challenging journals.

**Walnut and Raisin Loaf**

This was a high-hydration sandwich loaf, similar to the ones I've been making lately, but with a couple of differences. I added walnuts (200g - that was a lot) and some raisins (~100g, I'd guess) during the second last turn. And instead of using 300g of firm starter, I used 400g.

The sourdough culture was about 3 days old before I used it to build my firm starter. That's pretty old; the yeast in it wasn't very lively any more. I refreshed it and the firm starter was left overnight. And then I added it to 700g of water as usual, and added that to 700g of whole wheat. The turns were made every 30 minutes for about 3 hours, then I added the walnuts and raisins, and then turned them in. Following the next turn, I formed the dough as tightly as I could and then placed it in a buttered tin. The dough was scored lengthwise immediately.

Then it sat under a box for another 3 1/2 hours, at which point I pre-heated the oven, despite the fact that there wasn't much rise visible. The dough was then coated with kefir and baked with steam for 20 minutes. Then I removed the tray from the bottom of the oven, turned the tin 180 degrees, and baked it for another 20 minutes. At this point, I place some tinfoil over the top of the loaf and baked it another 15 minutes.

Results: Far too gooey, and an underbaked interior. Ate it anyway because the walnuts were costly. Mostly ate it toasted.*** Nothing to learn about the**.**Oat-top Whole Wheat Wild Yeast Bread with 30% Rye****It is an everyday bread, just with some oats on top. I wanted to give one away, but didn't see my friend until it was too late, and my wife had sliced into the second loaf. We ate both boules.**

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