omenti

probing ignorance a bit more deeply...

I'm not happy with the way science is usually taught in secondary school.  It is rendered boring - memorize a number of "facts" and either replay them on a test or use some recalled formulae to plug in a few numbers to find an answer.  It completely misses the fun of science and also something rather fundamental about how new knowledge is found and why, at least to a scientist, answers and fact aren't the real product - even though they may be useful and advance knowledge.  It also creates a view of science that has opened a divide between scientists and non-scientists - something that in a society that depends so much on science and technology is a serious disconnect and perhaps a danger.

 

As it happens a beautifully cultivated ignorance and questions is more fundamental to the forward motion of science. I suspect applying some of the techniques may be very important to other fields where "out of the box" creative thinking is required and I sometimes rely on it in my consulting practice. The recent post on ignorance brought some email reaction, so it makes sense to wade in a bit deeper..

 

The general notion of what a scientist does is to collect data (information is a better term) by observing and manipulating bits of the natural world by doing something called experiment.  There is a methodology - the scientific method - which is based on observation, hypothesis, manipulation, further observation , a new hypothesis and so on...  There is a sense of order, but that turns out to be far from the truth.  You experiment to learn something - ideally to discover something.

 

Discover, dis - cover, is the act of revealing.  What is revealed can be very beautiful and it often becomes a "fact" in text books and teaching, but what many consider the end product of science are known to be unreliable to the scientist.  Nothing is safe - nothing is above question.  Not even something like the absolute speed limit of the speed of light.¹  Scientists don't know things absolutely, but rather report how well it is known.  Newtonian mechanics turn out to be incorrect - but at the scale where humans live and observe everyday things it is more than accurate enough that we still routinely use it as a "good enough" descriptive model.  We know where it begins to fall apart and have made other discoveries to more accurately describe those areas - special and general relativity for example.  

 

In the 19th century it was believed the universe was permeated with with a luminiferous ether to allow a substance through which light could propagate.  It was the wrong path and, in 1907, Albert Michelson became the first American physicist to be splashed with the Swedish holy water for failing to observe the ether in his extremely clever measurements of the speed of light. 

 

Think about it for awhile - Michelson got the Nobel Prize for an experiment that didn't work.

 

Some would later describe the ether as the black cat physicists had been theorizing about, experimenting and trying to measure in a pitch black room for decade.  Literally hundreds of approaches and many many scientist years of effort.  Michelson somehow found the light switch and it became clear the ether didn't exist to a rather high degree of accuracy.  The confusion that resulted led to an entirely new line of questioning - several doors to new rooms, all pitch black with their own black cats, appeared with the light provided by Michelson.  A patent clerk who went by the name of Albert was pushed to a line of novel questions that gave us a fundamentally new understanding of the universe.  And even better he opened the way for many rich new questions - questions that were beyond our imagination until we saw a bit of the nature of his black cat.  

 

Sure we had learned something, but  it gave us a new appreciation for how much more ignorant of the universe we really were.  

 

We keep discovering and adding to this area we call knowledge and people often make practical use of these discoveries, but the meaningful product of science is not facts or knowledge, but rather the expansion of an informed and cultivated ignorance.²  

 

One of my mathematical heroes is Kurt Gödel.  Mathematicians had a sense that everything - at least everything in mathematics - was comprehensible and could be explained with math itself.  Gottfried Leibniz, one of the inventors of the calculus, tried to construct an alphabet of human thoughts that would allow you to take combinations of thoughts and form any idea just as letters can make words and words can make sentences.  A few hundred years later David Hilbert made an attempt to similarly code knowledge. 

 

The impressive achievement of Gödel was to show that all of this was impossible.  Gödel was a shy and quirky person - hardly anyone's candidate for a revolutionary - but he is incompleteness theorems rocked mathematics and physics.  I can't give a rich general level discussion of what he did, but at its core he showed an consistent system in math (like the whole numbers and the operations - like addition, multiplication and so on) can't be complete and consistent.³ This may seem to be a depressing notion - finding a fundamental limit in mathematics, but rather it opened an incredibly rich source of new questions to Gödel and others.  It is fair to say that unknowability and incompleteness led to questions, reasoning and discoveries that have impressively benefited computer science - and to think that computer science is fundamentally based on absolute and complete logic:-)

 

This ignorance - the recognition that we really don't know something as deeply as we thought we did - is a fundamental driver of science.    The problem of the unknoweable isn't a real obstacle, but is really just a serious of paths to deeper understanding.  Also, to a scientist, the explosion of information isn't terribly important either - at least not at a fundamental level.  The rich sources of discovery are more dependent on new questions that arise from cultivated ignorance.  Questions are the goal of science - it just happens to generate results (with attached confidence levels!) that have historically advanced civilization and cultivated ignorance is a necessary component of making the process move.  

 

It is ignorance rather than data that moves science along.

 

A very import and somewhat subtle point of doing science is that scientists use ignorance to work and the management of this ignorance is incredibly important.  Sometimes it is called the taste in picking and progressing with problems.  It is often chaotic with communication and collaboration often being extremely important.  At the leading edge it is often cross disciplinary.  I have a tendency to not be able to describe exactly what I do.  This is really common among scientists and the area they are currently working in is often shifting dynamically.  It is messy and may even seem inefficient, but it is a proven path to real discovery.

_____

¹ Which is why the recent neutrino experiment got so much attention.  People have been testing the limit for over a century and so far all of the results that suggest it can be violated, including the most recent, have turned out to be so flawed as to be invalid.  A good deal of pseudo-science is based on experimental "results" that are incorrect - they are often trivial, but sold to non-scientists as something absolute.

² The time gap between discovery and practical use can be very long.  Faraday thought his early work with electricity and magnetism would have no practical use. A practical use for general relativity seemed a crazy notion for fifty years, but it turns out to be a critical component of making the global positioning system work as accurately as it does.

³ Consistency is the characteristic that a system's rules will not  result in self contradictory statements.  Think of science fiction as a rich source of counter examples - when Captain Kirk defeats machine logic with simple logic puzzles.  Take a card and write "the other side of this card is true" on one side and "the statement on the other side of this card is false" and think about it for awhile:-)

At least two readers of this blog are mathematicians and my appologizes for the very rough high-level treatment of something that is very rich and deep.  If you are a student just study the work!  If you aren't technical I strongly recommend Rebecca Goldstein's book on the subject.

 

_____

Maple pecan pie - really good with vanilla ice cream or gelato!

 

Ingredients

° 1 unbaked pie shell

° 215 grams/2 cups pecans (coarsely chopped)

° 55 grams/¼ cup dark brown sugar

° 25 grams/¼ cup tapioca starch

° 4.5 grams/ ¾ teaspoon kosher salt

° 240 grams/1 cup grade B maple syrup. Grade A or "fancy" may not be strong enough

° 60 grams/¼ cup heavy cream

° 4 grams/1 teaspoon vanilla

° 2 large eggs

 

Technique

° Preheat the oven to 425°F

° Place the chopped pecans in the unbaked pie shell. Whisk together the sugar, tapioca starch and salt in a medium sized bowl. Whisk in the maple syrup, cream and vanilla. Whisk in the eggs. Pour over the pecans.

°  Bake for 20 minutes and then turn the heat down to 350°F without opening the oven. Bake for an additional 30 minutes. Let pie cool at room temperature for at least 30 minutes before serving.

 

 

a pre-review

Jon Gertner's new book on Bell Labs has just been published and a few people have written to ask what I think about it.  I haven't read it yet, but am very curious as I was part of that organization from the end of its golden years through its demise.  It was a unique and amazing place - a fundamentally different approach to "innovation" than what is common today.  It isn't clear to me which approaches are better or worse - the old Bell Labs approach doesn't square with how companies work these days.

 

The old AT&T was a regulated monopoly divestiture in 1984.  A few percent of its income was channeled into running the labs - known as the Bell Telephone Laboratories and, through a series of regulatory consent decrees - funding was incredibly stable and sufficient to insure very long term research and development projects.  After a decree in 1956, inventions were licensed under very liberal terms to the rest of the nation and the Labs had become something of a national laboratory.  

 

I won't go into the history of the place and will be interested to see how it is charted in Gertner's book, but the core DNA of the place needs to be explained.

 

Innovation had a very specific meaning.  It didn't mean invention or discovery, but rather was discovery taken through stages of development and finally implemented at a scale that would change society.  

 

The Labs was primarily advanced and applied development with a core basic research arm (area 10 - later renamed area 11 about the time I joined it).  Fundamental researchers were presented with an amazing array from curious problems.  The notion was not the standard approach of engineering where you attack a problem by tallying your resources and try to build an optimal result, but rather something a bit more zen.

 

In the research unit you defined and attacked problems by looking for the unknown and then trying to understand as much as your could about it.  You had to go deeply into uncharted territory not knowing if your efforts would pay off or if you had the right intellectual tools for the job.

 

This approach - solving a jigsaw puzzle not by identifying your pieces and putting them together, but rather looking for the missing pieces and trying to solve a puzzle by understanding what was missing - required a multidisciplinary approach.  It is close to the approach of physics and basic research had a high percentage of Ph.D. physicists.  Really good ones.  Their specialties were not as important a their taste in problem solving.  I was an experimental particle physicist.  Bell Labs never dabbled in particle physics, but that was "the right stuff" and they saw an immediate match.

 

We worked with computer scientists, mathematicians, statisticians, mechanical engineers, electrical engineers, opticians, chemists, acoustics experts, material scientists, psychologists, neurologists, biologists, musicians and artists to name a few backgrounds.  The central laboratory at Murray Hill, New Jersey was built around a five story corridor a quarter mile long with a sometimes maze-like structure of smaller buildings.  Going to lunch or visiting someone else's lab would force interaction with others. It was said a researcher going to lunch was like a magnet rolling by iron filings.  It was a brilliant architecture and aspects of it have been duplicated elsewhere.¹

 

Some of the projects had very long horizons - digital communications took about four decades and thousands of researchers years of effort.  This type of time frame is only seen universities and national laboratories these days and is rarely directly coupled efficiently with commercial development.

 

But the next step in innovation - and one where the majority of Bell Labs people worked - was development research and engineering.  This is enormously difficult to get right. Most of the projects were defined by either Bell Labs management based on needs of the Bell System or by the government for national defense.  Many were difficult projects that advanced the state of the art by an order of magnitude and this was something of a model for DARPA, which came about in the 1950s with a clearer focus on military needs.

 

As the applied research and development proceeded it was productized and turned over to Western Electric - the manufacturing arm.  People in the various units spent time with each other.  Small branch development labs were built into Western Electric factories and the development folks often worked directly on the lines to understand the problems.  

 

The approach wasn't as clean as I describe it and there were tensions that had to be dealt with, but it was an innovation engine that changed the world.  It even paid a lot of attention to education creating everything from science and engineering ciricula to identifying promising students - mentoring them and getting them through their Ph.D.s in the best universities at no expense.

 

A very different approach than what is used, and perhaps needed, today.  The model today has universities and national labs doing the basic work with companies mostly engaged in short term development - real corporate research is not common.  Even long term development is rare^.2  True corporate research is mostly dead as is an integrated multi-disciplinary approach.  

 

Companies identify the pieces of the puzzle they have and try to build something optimal rather than trying to understand the missing pieces deeply.

 

As the Labs started to crumble in the late 80s I switched my focus from physics to something more applied - broadband to the home.  The problems were how do you do it and why do you do it.  The later lead to work in digital music and both led me to the notion that I *really* needed to understand social research.  I immersed myself in a human computer interaction department and hopefully helped out a bit with a bit of experimental rigor, very different thinking and a lot of naïve questions that turned out not to be so naïve.  I learned a lot in the process, but the efforts of the group were never coupled to the company at that point.  We did a lot of neat stuff that is finally beginning to be realized now.

 

I still try to search for projects that are looking for a bit of deeper understanding when I consult.  There are a lot of diamonds on the beach these days - as there probably always are.  The approach is rare and I find it odd that I'm sometimes seen as much broader than I see myself.  It is really just a bit of curiosity and the luck of having an amazingly rich chance to work in an environment that makes places like Apple and Pixar look lame when it comes to "multi-disciplinary".  I think there is great value to bits and pieces of the approach as suspect we'll see more of it as the tech world matures and energy becomes a more pressing issue.

 

I don't know what picture the book will paint.  I was witness to an amazing dinosaur and hope some of the better features of the place can be replicated.

 

We had a crisp definition of innovation. The physics people had a crisp definition of data and information.  I find the physics defnition at odds with common usage and I'll post on that in the near future - I've hinted at it before.  Data isn't basic...

 

Om recently commented on creativity talking about John Maeda of RISD.  This caused me to think of some comments from the professor of a graduate physics course I took as an undergrad.  The professor was famous for his creativity having been sprinkled with Swedish holy water.  Somehow he wanted to get over a few points on being creative - he thought you could inspire it.  

 

from my notebook:

 

° be curious about anything and everything. expose yourself to different people and ideas

° don’t be frightened to try the unknown. Many solve puzzles by figuring out what they can do with the puzzle pieces they have. A better approach is to figure out the missing pieces and solve a puzzle you don’t know anything about by learning about them.

° remember it must be play

° the delight is not in finding the answer, but in coming to it yourself

° be totally honest

° deeply know everything about your problem

° real creativity simplifies – aim for simplicity as it is beautiful

° get into something so deeply you forget everything else. you need large pieces of uninterrupted time

 

much more on these later, but back to the old Bell Telephone Laboratories for a bit. When I first started I was delighted to learn that my first director was something of an aurora expert.  He was invovled in the Telstar communications project and was involved in the beginnings of creating the field of what is now called space weather. He would have loved this time lapse of the aurora taken from the ISS a few days ago...

 

 _______

¹ Pixar uses centrally located washrooms and has a design that reminds me of Murray Hill on a much smaller scale.

² IBM, Intel and Microsoft do longer term work in the tech sector. Apple has a ten year horizon for some projects, but anything longer than three years is very rare in industry. One of the longer term interests was video telephony. Here is something on developments in color video telephony .... in 1930.

dealing with incomplete models - understanding nutritional energy balances

What happens when you are trying to modify your behavior with information that comes from measurements that can be difficult that feed into models that are fundamentally inaccurate even though the you may not suspect the models are flawed?  How do you understand this well enough to get a useful signal in a very noisy environment?

 

For many of us the period between Thanksgiving and the New Year involves way too much food. I’m trying to maintain my weight after a serious ten month diet and this means measuring and tracking what I eat as well as my exercise. 

 

It should be simple - after all, energy is always conserved.  Food is just a way to store energy.  If you eat as much as you require to stay alive, your weight should be stable.  Eat a bit less and/or do a bit more physical work and you should lose weight. Take in more than you need and your body tries to hold onto the extra energy by turning it into a energy stored in you - body fat.

 

But to do this simple calculation requires you have to know how much of the energy in food is accessible to your body, how much energy your body uses to run itself and how much energy it takes for you to do any kind of physical work.  All of these are difficult to know to a good degree of precision.  We have published guidelines, but few of us consider the error bars on the underlying measurements and calculations and some of the pieces are still being discovered by basic research.   

 

We tend to assume food nutrition labels are accurate, but it turns out they are based on a technique that is about one hundred years old.  That system, the Atwater System, has known flaws, but nothing has been found to be easy to use and more accurate.

 

Wilber Olin Atwater was a professor at Wesleyan University and a central figure in understanding modern nutrition.  By the mid 1800s people had worked out that proteins, fats and carbohydrates were major components in human nutrition and estimates were made of how much energy was available from each through metabolism.  

 

Atwater spurred the creation of an American nutrition research enterprise - one of the first examples of government funded big science outside of the military - and calculated how much metabolisable energy was available in proteins, fats and carbohydrates accounting for the efficiencies of digestion.  It became possible to measure the chemical energy in food  components and predict how much we could use.  You could simply measure the amount of protein, fat and carbohydrates in a food and determine how much energy the human body would extract.¹

 

The current standard used in the US and many other countries takes into account a few other nutrition sources and food labels are based on the following conversions:

 

	kJ/g	kcal/g
fats	37	9
proteins	17	4
carbohydrates	17	4
fiber	8	2
ethanol (alcohol)	29	7
organic acids	13	3
polyols	10	2.4

 

It turns out this is only a general approximation and to first order you can get away with just looking at the fats, proteins, carbohydrates and alcohol figures if you are creating your own recipes.

 

But your efficiency at absorbing food varies.  New work that looks at how the food was prepared suggests that food that is mechanically made into smaller bits is more efficiency absorbed and food that is cooked is absorbed even more metabolised.²  The largest effect is cooking.  Muscle proteins, sugars in starches and other energy laden molecules are physically opened up allowing digestive enzymes to attack their amino acid chains more effectively.  Food that is cooked gets more of its energy into your system than food that isn’t.  The science is still developing, but some researchers speculate cooked foods provide at least 10% more energy than raw foods and the number may be higher than 25% - I wouldn't be surprised given some of the preliminary results. 

 

The effect of cooking is not accounted for by nutrition labels.  So if you want to lose a bit of weight you might try increasing the raw food component of your diet.

 

The energy balance for your body has four general components: energy intake from eating, energy expended keeping your body running, energy spend doing physical work, and energy spent in thermogenesis (shivering for example).  Physical work comprises about  20% of the average person's energy budget, thermogenesis is usually under 10%.  Most of the energy we use goes into keeping our bodies functioning - our  Basal Metabolic Rate (BMR).³

 

Once you have an idea what your BMR is you can add up all of the physical activity during a day and have a fair idea what your intake should be - assuming you have a good idea of how much energy your body is getting from food.  This gets tough, so most people who worry about this talk in terms of basic activity levels that range from 1.2 for sedentary office workers to around 2.0 for people with physically active lives.⁴

 

My BMR approximation is 1,583 kcal a day by the basic calculation.  Colleen’s is 1,724, but her real figure is higher as she is very athletic.⁵

 

If you exercise regularly you can calculate the energy spent during exercise and add that to your BMR for a rough approximation - a lower limit as you move around doing other things during the day and there is some thermogenesis.  Unfortunately energy spent during exercise is only an approximation as our efficiencies vary person to person for various exercises.  That said you can probably get 80 to 90% accuracy using tools like this one.⁶

 

If you have made it this far the act of journaling your calories and exercise appear to be a futile effort as there is a huge amount of underlying complexity.  But you can get around that.

 

Keep track of your weight too.  If you plot the results you can get an idea of what your measurements for activity and eating mean assuming the types of food you eat and the activities you do don’t vary dramatically.  The numbers may not match what you would measure in a lab, but getting the bottom up numbers to match the top down results is extremely difficult even in that setting.

 

Absolute numbers are very difficult to measure in this case, but it is possible to come by a stable relative measure, and that is all most of us need for this purpose.

 

My goal was to lose about 5 pounds a month while dieting.  Using the rough figure that a pound of fat (what I wanted to lose) is about 3,500 Calories, I aimed at an average daily deficit of about 625 Calories through a combination of exercise and eating less food.  It worked and I was able to maintain a fairly constant rate until near the end when I wanted to gracefully transition to an exercise/eating routine that might be sustainable.⁷

 

Even though we have flawed models for how much energy we absorb from our food and how efficient our bodies are, the models are sufficient - with a bit of analysis - to effectively use as a tool for losing and maintaing weight.  It is easy to imagine local refinements - I’ve created a tool that helped me understand my own information flow and ultimately how that translates into weight - and it is likely that activity monitors like accelerometers can help, but in the end simple willpower rules.  I suspect many monitoring and computational aids will ultimately fail unless they can impact our basic urges.  To control something you need to combine motivation, the ability to make a change and some triggering event.  I’ve worked that out for myself.  Building a general tool seems difficult.

 

Perhaps what we really need to do is find the levels of eating and activity that evolution assumes.  Up until the Industrial Age people appear to have been self regulating in weight.  Now foods tend to be more plentiful, have greater energy densities and perhaps are even more palatable.  At the same time many of us are less active.  The balance is thrown and many of us gain weight easily.  Finding the right balance is tricky as evolution did not design us for a long and healthy life - basically we get to the point where we have been able to reproduce and then things begin to fall apart.  So the full nutrition offered by earlier diets may be very suspect even if the energy balance is good.  There is probably quite a bit to learn here.  Some of us (not me) are fortunate enough to have bodies that are great at self regulation.  Exactly how that happens is a very interesting question.

 

_________________

 

So now we shift gears and present a few deadly recipes:-)

 

No one seems to be complaining about the recipes and three people have asked for more, so here are two rich desserts - a banana cream pie and a lemon tart.  Both use the same shortbread crust.    

 

I think of baking and cooking as two very different arts and suspect few really outstanding cooks are also outstanding bakers.  Cooking demands knowing the state of the food and how flavors link up - there is a lot of improvisation that occurs as you cook so measurements are just a guide.  Baking, at least for me, demands careful measurements for ingredients and cooking, so I use weights rather than volumes.  I have a great $25 scale that measures accurately to the gram and recommend something like this to anyone who bakes.  I’ll leave the conversions to you if you bake using volumes.  

 

Both of these are very easy, delicious and something you should only eat sparingly.  They were part of Sukie’s birthday present a few days ago.

 

The shortbread pastry crust is really simple and no rolling is required.  Just put a few ingredients into a food processor, pulse a few times, and press into a tart pan.  I do recommend very fresh ingredients for baking.  Sugar or flour that has been opened and sitting around for a month or so pick up a funny taste.

 

Shortbread Pastry Crust

 

130 grams all purpose flour

35 grams powdered sugar

 a pinch of fine sea salt (too small for my scale - I’m guessing about 1/8tsp).  Note that iodized salt picks up a strange flavor when baking, so I use a fine grain un-iodized sea salt

 1 stick of cold unsalted butter - about 115 grams

 

 procedure

 

° heat oven to 425°F with the rack in a center position

° butter or lightly spray with a nonstick neutral vegetable oil cooking spray an 8” tart pan with a removable bottom. 9” would probably work too.

° cut the butter into chunks and put all of the ingredients in a food processor 

° pulse the food processor until the pastry starts to form into pea sized clumps - about 30 seconds for me.  don’t let it grow into larger pieces if you can.

° press the dough into the pan and pat as evenly as you can

° pierce the bottom of the crust with a fork to prevent it from puffing up too much during baking.

° Cover the pastry with plastic wrap and put it in the freezer for 15 minutes - this is a really neat trick that prevents the crust from shrinking when it bakes.

° Bake until the crust is golden brown - about 15 minutes for me.  Cool on a wire rack.  You can cover the crust and store it for a day in the refrigerator f you want. 

 

Lemon Tart

3 large eggs at room temperature

150 grams granulated white sugar

80 grams fresh lemon juice (about 3 lemons)

a half stick of butter - about 56 grams - at room temperature - cut into chunks

4 grams of lemon zest (be careful to only get the yellow part!)  I prefer a microplane for doing this

shortbread pastry

30 grams finely chopped almonds

blueberries and maple syrup - thawed frozen blueberries are fine

 

procedure

° In a double boiler over simmering water whisk the eggs, sugar and lemon juice together

° Cook, whisking or stirring with a spatula, constantly until the mixture becomes pale and thick - about 160°F.  This takes about 10 minutes

° Remove from the heat and strain to remove lumps.  

° Whisk the butter into the mixture until melted and add the lemon zest.

° Cover with a plastic sheet pressed to the surface of the lemon curd to prevent a skin from forming and let it cool to room temperature before filling the crust.

° Assemble covering the inside of the crust with finely chopped almond bits and then pour in the lemon curd.  Even out with the back of a spoon or a pastry knife.

° Separate the pie from the pan - just carefully push from the bottom

° Add maple syrup to the blueberries and spoon on to individual pies of the pie when you serve.  Sweeten as much or as little as you like.  

 

 

Banana Creme Pie

 

300 grams whole milk

half a  vanilla bean (you could use a good vanilla extract - maybe about a half tablespoon)

 3 large egg yolks at room temperature

 50 grams granulated white sugar

 20 grams all purpose flour

 20 grams corn starch

 3 large ripe bananas

 40 grams shredded coconut

 whipped cream (recipe at the bottom)

 

procedure

 

° Score the vanilla bean and add to milk in a saucepan and start heating at a medium heat

 ° While this is cooking mix the sugar and egg yolks together. then sift the cornstarch and flour into the egg/sugar mixture to make a thick paste.  Don’t let this sit around as it gets very lumpy if you do.  

 °Stir the warming milk.  Take it off the heat when it begins to foam and remove the vanilla bean.  Slowly add the hot milk to the paste whisking constantly.  

 ° Scrape out the seeds from the bean and add to the mixture.  If you use vanilla extract instead, now is the time to add it.

 °Pour the mixture back into the saucepan and heat over medium heat until it begins to boil and thicken.  

 ° Pour the mixture into a clean bowl and press plastic wrap to the top surface to prevent a skin from forming.  Let it cool to room temperature.

 ° Slice the bananas and fold two in with the cooked mixture along with the shredded coconut.  Pour into the pasty.

 ° Top with whipped cream and carefully release the pie from the pan side ring

 

 

Whipped Cream

 

120 grams heavy cream chilled

 15 grams powdered sugar

 1/2 tsp almond extract

 

procedure

 

° Chill a mixing bowl and beater from an electric mixer in the freezer for about 5 minutes.  You can also get good results with a whisk and copper mixing bowl, but that takes some elbow grease.

 ° Pour the cream, sugar and almond extract into the bowl and beat until peaks form.  

 

 

____________

¹ Atwater showed about 4 nutritional Calories (kcal) were available from carbohydrates, 4 from proteins and 9 from fat. 

² There has been a lot of speculation here, but now serious science is being done that supports the notion that cooking makes more energy available.  A paper by Rachel Carmody and Richard Wrangham in the Journal of Human Evolution is a good example.  Another study found that cooking gelatinizes starch meaning amylopectin and amylose are released and exposed to enzymes making more energy available.  Cooked starches have more available Calories than those that are raw.

 People have known for a long time that people who eat mostly raw food tend to be very thin compared with the general population, but serious studies on those populations are recent and the results spurred a deeper look into the more general question of food processing and available energy.  Women on a purely raw food diet regularly lack the energy to have a functioning menstrual cycle even though they are eating what should be a high quality diet.  The available Calories just aren’t there - we have based our food recommendations on cooked food and our bodies seem to have a body regulation mechanism that is based on cooked food - this may even be a short term evolutionary response, but that is currently speculation waiting on the verdict of science.

³ BMR is difficult to measure directly as it requires the measurement be made while the person is at rest for a long period.  A more common technique is to measure a person’s resting metabolic rate (RMR).  They turn out to be closely related and similar under most conditions.

A frequently used approximation is from Mifflin et. al. (1990):

BMR = 10*weight + 6.25*height -5*age +s  

where weight is in kilograms, height is in centimeters, age is in years and s is +5 for males and -161 for females.  

If you know your lean body mass in kilograms the Katch-McArdle approximation is probably more accurate.

BMR= 370 + (21.6 * lean body mass)

BMR in both of these approximations is in kcal (nutritional Calories)

⁴ One approximation is the Harris Benedict formula:  

sedentary office workers use BMR *1.2 Calories

light exercise 1-3 days a week use BMR * 1.375 Calories

moderate exercise 3-5 days a week use BMR * 1.55 Calories

hard exercise 6-7 days a week use BMR * 1.725 Calories

very hard physical labor use BMR * 2.0 Calories

This is very approximate.  Athletes in training can use incredible amounts.  Colleen was in the 5,000 to 6,000 Calorie a day range when training - easily blowing through the approximation for very hard physical labor.

⁵ Normally men have higher BMRs than women even when they are the same height and weight. Men, on average, tend to have a higher percentage of lean muscle.  Colleen is a bit heavier than me and, at 200 cm, quite a bit taller. She is also younger - all of this is enough to give her a higher BMR.  Since she is thin and athletic you really need to use a different approximation as her body fat is low at around 10%.  The Katch-McArdle formula gives a better BMR estimate of 1,925 kcal

Some unit notes:  Energy is just energy.  kilocalories (kcal) are the same as nutritional calories (Calories).  Converting 1,925 Calories to watt-hours we see Colleen’s BMR is about 2,239 watt-hours a day.  You can divide this by time to get her average power expenditure from BMR -- a bit over 93 watts.

In an inactive office worker mode she would need about 1.2 * BMR or 2,310 Calories a day - a figure that would cause a smaller person, even someone who is fairly active, to gain weight.  Of course a very heavy person would have a very high BMR and their weight loss in pounds per month can be very high.

⁶ Note that this is energy used above and beyond your BMR.  Often people assume the exercise figures are a person's total requirements during the exercise period.

⁷ I strongly recommend a good piece of software for logging exercise and meals.

Now I can deduce my daily requirements to be about 2,190 Calories per day.  This is consistent with my calculated BMR times a factor of about 1.4 for my normal daily activity.  It sort of makes sense.