How many calories do we burn when we try to understand mathematical proofs?

How many calories do we burn when we try to understand mathematical proofs?

While thinking we burn calories. For comparison: "And if it's the right wood and the right chess grand masters in the middle of a tournament, they are going through 6,000 to 7,000 calories a day thinking" from here…

How many calories do we burn when we try to understand mathematical proofs? How does it depend on the representation of the proof? For example, there are plenty of proofs for the Pythagorean theorem, even some without words…

Not many.

Although firing neurons summon extra blood, oxygen and glucose, any local increases in energy consumption are tiny compared with the brain's gluttonous baseline intake. So, in most cases, short periods of additional mental effort require a little more brainpower than usual, but not much more. Most laboratory experiments, however, have not subjected volunteers to several hours' worth of challenging mental acrobatics.

-Scientific America Does Thinking Really Hard Burn More Calories?

Our results conclude that the measured Ff,ATPase reflects the oxidative phosphorylation rate in resting rat brains, that this flux is tightly correlated to the change of energy demand under varied brain activity levels, and that a significant amount of ATP energy is required for “housekeeping” under the isoelectric state. These findings reveal distinguishable characteristics of ATP metabolism between the brain and heart, and they highlight the importance of in vivo 31P MT approach to potentially provide a unique and powerful neuroimaging modality for noninvasively studying the cerebral ATP metabolic network and its central role in bioenergetics associated with brain function, activation, and diseases.

-PNAS Tightly coupled brain activity and cerebral ATP metabolic rate

The Calorie Theory – prove it or lose it

During June and July of 2009 I approached the British Dietetic Association (BDA), Dietitians in Obesity Management (DOM), the National Health Service (NHS), the National Institute for Clinical Excellence (NICE), the Department of Health (DoH), the National Obesity Forum (NOF) and the Association for the Study of Obesity (ASO) to ask all of these expert organisations for proof of the 3,500 formula (also known as the calorie theory).

British Dietetic Association (BDA)

On 10 June, I sent the following query to the BDA: “I am doing some research on obesity and I would be most grateful if you could help me. Please can you explain where the ‘One pound of fat contains 3,500 calories…’ comes from?”

I received a prompt and pleasant reply, “Unfortunately we do not hold information on the topic that you have requested.” It was suggested that I contact a dietitian. I happened to be with several dietitians at an obesity conference later that month, so I asked fellow delegates and no one knew where the 3,500 formula came from. No one knew where the ‘eatwell’ plate proportions came from. One dietitian said to me “You’ve made us think how much we were just ‘told’ during our training, with no explanation. A group of us over there don’t even know where the five-a-day comes from.” (This may help)

So, after the conference, on 29 June, I sent the following email to the NHS: “I am an obesity researcher and I am trying to find out the rationale behind the statement: “One pound of fat contains 3,500 calories, so to lose 1lb a week you need a deficit of 500 calories a day”. This specific reference is a verbatim quotation from the British Dietetic Association’s Weight Loss Leaflet Want to Lose Weight and keep it off? The BDA reply was ‘we do not hold information on the topic.’ As this formula is the foundation of all current weight loss advice, it is critical to be able to prove it. Please can you let me know where this formula comes from and the evidence for it?”

On 30 June I received another prompt reply: “Unfortunately our Lifestyles team do not hold this information and are unable to assist you with your enquiry. I would suggest you contact the Department of Health to see if they can help.”

On 1 July I forwarded the email exchange with the NHS to the Department of Health. I had to chase on 6 July and then got a response saying they would get back to me within 20 working days. Meanwhile, I had also written to NICE (1 July) and they responded on 2 July saying they would get back to me within a maximum of 20 working days.

National Obesity Forum (NOF)

On 2 July I sent the same email to the NOF and the ASO and received a very prompt email back from the NOF (two hours later) suggesting that I contact the ASO. I thanked the NOF for this, but pointed out that their own web site quoted the 3,500 formula verbatim and also had the following classic example: “one less (sic) 50 calorie plain biscuit per day could help you lose 5lbs (2.3kg) in a year – and one extra biscuit means you could gain that in a year!” I have heard nothing back from the NOF since. I sent Dr. David Haslam, NOF chair, an email on 6 July attaching An Essay on Obesity, which I had written, for his interest and comment. On 10 July I also sent Dr. Haslam the exchange I had had with the ASO, so that information could be shared.

Association for the Study of Obesity (ASO)

The ASO response was the most helpful by far, but it still completely failed to prove the 3,500 formula. My query was circulated to board members and two kindly replied:

One reply was: ”Basic biology tells us that 1kg pure fat, converted to energy = 9000 kcal, 1lb pure fat = 0.453 kg = 4077 kcal. The approximation to 3500 kcal is made on the basis that ‘adipose tissue’ is not 100% fat (some water and some lean tissue). Hence to lose 1lb pure fat = 4077 kcal deficit, or 1lb fat tissue in the body = approx 3500kcal deficit. This equates to 500kcal per day to lose 1lb in a week. This has been supported by numerous studies using whole body calorimetry.” There were no sources put forward, for these “numerous studies”. I asked on 21 July and again on 11 August for “even one obesity study that proves this formula” and have received nothing back.

You can make 1lb = 2,843 calories or 3,752 calories without much effort. (This error could have a weight impact of a two stone loss or a six stone gain each year if any of this nonsense were true.) (Please see footnote for calculation).

The ASO member uses the word “approximation”, as do many references to the calorie formula, so there may be some acknowledgement of the number of variables. However, the diet advice that follows takes no account of this word “approximation”. If we take just one variation – the difference between 3,555 and 3,500 equates to five to six pounds a year (footnote). The NOF cautions that eating, or not eating, one biscuit a day could cause a person to gain, or lose, five pounds in a year. Well, the formula being inaccurate can also do this without any biscuit involvement at all. In fact, if 3,555 is correct and not 3,500 (notwithstanding the fact that there is no proof for either formula), this would have made a difference of 172 pounds over the past 30 years (the obesity epidemic period). Fortunately the error would be ‘in our favour’ so we should have all been able to eat nearly 11,000 biscuits and get away with it, or be over 12 stone lighter.

The second reply from the ASO was ‘evidence’ from NICE and a web link to the full NICE document Management of obesity: Full Guidance, December 2006. The specific proof offered was one study (Table 15.14) of 12 subjects, given a deficit of 600 calories a day, where the outcome was “a change of approximately -5 kg (95% CI -5.86kg to -4.75kg, range -0.40 kg to -7.80 kg) compared with usual care at 12 months. Median weight change across all studies was approximately -4.6 kg (range -0.60 kg to -7.20 kg) for a 600 kcal deficit diet or low-fat diet and +0.60 kg (range +2.40 kg to -1.30kg) for usual care”.

So, let me understand this, the people on the 600 calorie-a-day deficit (the NICE recommendation) were 5 kilograms (11 pounds) lighter than those not doing this “at 12 months.” Applying the basic maths formula, these 12 people should each have lost 600*365/3,500 = 62.57 pounds of fat. Not an ounce (of fat) more or less. AND, there should have been no range of results – everyone should have lost exactly the same (that’s what happens with a mathematical formula). The least anyone lost (let’s put it all into pounds) was 0.8 pounds and the most anyone lost was 17.2 pounds. Even the highest weight loss was 45 pounds lower than it should have been. This is also all about fat – we haven’t even started looking at muscle or water loss. This is also a study of 12 people. There are 1.1 billion overweight people in the world and we can’t prove a formula using 12 of them.

There were 15 other studies in Table 15.14, 10 of which had data for where a calorie deficit had been created over a specified period of time. This enabled me to analyse what the weight loss should have been (using the 3,500 formula) and what the average weight loss actually was (from the study data). Again, in every single study, there was a wide range of results (which means that the formula failed per se). In all of the other ten studies, the actual weight loss was multiples away from what the weight loss should have been. The smallest gap between actual weight loss and ‘should have happened’ weight loss (according to the formula) was 28.7 pounds (we continue to ignore water to try to give the formula a chance). At the other extreme, the biggest difference between the fat that should have been lost and the fat that was lost was 143.9 pounds.

Department of Health (DoH)

I was still digesting the immense implications of all this when the DoH reply arrived, on the 21 July, saying “The Department is unaware of the rationale behind the weight formula you refer to.” Pause for a second – the UK government Department of Health, has no idea where their founding piece of diet advice comes from. They kindly suggested another lead, (Dietitians in Obesity Management UK (DOM UK) – a specialist group of the British Dietetic Association), which I followed up on 24 July.

National Institute of Clinical Excellence (NICE)

I chased NICE on 27 July, as the 20 working days were ‘up’ in my calendar. I appeared to have been passed between NHS and NICE during July and a helpful woman called me back to say she had found the right department to deal with the query. A couple of days later, the reply came “Whilst our guidance does contain reference to studies involving 500 calorie deficit diets we do not hold any information about the rationale behind the statement ‘one pound of fat contains 3,500 calories, so to lose 1lb a week you need a deficit of 500 calories a day’.” That is to say – although we are an evidence based organisation, we have no evidence.

Dieticians in Obesity Management (DOM)

On 10 August I received a response from DOM UK: “I have asked our members and this answer was returned. It’s a mathematical equation, 1gram of fat is 9kcal, therefore 1kg fat equals 9000kcal. There are some losses but 1 lb of fat is approximately 4500kcal divide that by 7 days and its (sic) approximately 643kcal hence the deficit.” I went back to DOM UK, on the 10 August, to request an answer to the second part of the calorie theory – if that is how 600 calories is derived (and I have never before seen the 3,500 become 4,500), how can we then say with such confidence that each and every time this deficit is created one pound will be lost.

On the 18 August, I received a reply from one of the DOM UK Committee members: “My understanding is that it comes from the thermodynamics of nutrition, whereby one lb of fat is equivalent to 7000kcals, so to lose 1 lb of fat weight per week you would need an energy deficit of 7000kcals per week, or 500kcals a day. In or around that, depending on whether or not you use metric system and your clinical judgement, some people use a deficit of 600kcals a day and others 500kcals a day. There is good evidence that this level of deficit produces weight differences of approx 5kg at 1 year.”

This time the 3,500 deficit ‘needed’ has doubled to ‘7,000’ calories. Or, to put it another way, one pound of fat has become 7,000 calories. You can start to see what I have experienced as a researcher – how widely this formula is used as fact and yet how little it is understood and how few people know how to use their own ‘fact’.

So, in the example from Dietitians in Obesity Management, key proponents of the calorie formula, one year of a 600 calorie a day deficit will produce a weight loss of approximately 11 pounds – not the 62.5 pounds of fat alone that should be yielded.

When I pointed this out and suggested “I really think we need to fundamentally review the basis of current diet advice and stop saying ‘to lose 1lb of fat you need to create a deficit of 3500 calories’”, the final reply I got was “I guess a key to all of this is that weight loss doesn’t appear to be linear, any more than weight gain is.”

At last, an admission that the formula has no basis of fact.

The organisations approached have been helpful and accessible, but none is able to explain where the 3,500 comes from, let alone to provide evidence of its validity.

I have a simple and reasonable request. I would like proof of this formula – that it holds exactly every single time – or I would like it to be banished from all dietary advice worldwide.

Any proof needs to source the origin of the formula. Then the proof needs to hold in all cases. There needs to be overwhelming, irrefutable and consistent evidence that each and every time a deficit of 3,500 calories is created, one pound of fat is lost.

Since, we already have overwhelming evidence that such proof cannot be provided, it is not enough that we quietly stop using this formula – it is too widely assumed to be true for us to just sweep it under the carpet. We need to issue a public statement saying that it does not hold and should not be used again. We need to tell people that they will not lose one pound of fat for every deficit of 3,500 calories that they create. We need to tell people that there is no formula when it comes to weight loss and we have been wrong in giving people the hope that starvation will lead to the loss of 104 pounds each and every year, in fat alone.

This calculation is done as follows: It assumes that a person can maintain weight at a daily intake of the calories assumed to equal one pound of fat. If we think one pound equals 3,500 calories and in fact one pound equals 2,843 calories, over a year, 657 ‘extra’ calories a day, simply from the formula ‘being wrong’, would add up to 239,805 extra calories and this, divided by 2,843 gives 84 pounds, or six stone. Adjust the calculations for women more typically maintaining at 2,000 calories a day and men more typically at 2,600 calories a day and the inaccuracy of the formula still creates wide disparity.


The popularity of natural bodybuilding is increasing rapidly. In the United States, over 200 amateur natural (drug tested) bodybuilding contests occurred during 2013 and the number of contests is expected to increase in 2014 [1]. Preparation for bodybuilding competition involves drastic reductions in body fat while maintaining muscle mass. This is typically achieved through a decreased caloric intake, intense strength training, and increased cardiovascular exercise. Competitors partake in numerous dietary and supplementation strategies to prepare for a contest. Some have a strong scientific basis however, many do not. Therefore, the purpose of this article is to review the scientific literature on topics relevant to nutrition and supplementation for bodybuilding competition preparation. Dietary modifications during the last week to enhance muscle definition and fullness (peaking) and psychosocial issues will also be covered. Ultimately, evidence-based recommendations will be made for nutrition, supplementation, and “peak week” strategies for natural bodybuilders. As a final note, this paper does not cover training recommendations for natural bodybuilding and the training methodology used will interact with and modify the effects of any nutritional approach.

The Development of Mathematics - The Egyptians and the Babylonians

Of course, this division into two broad fields is a little crude and arbitrary, with statistics and probability, topography, geometry, and calculus all standalone subjects in their own right. They use their own language and methods, as different from each other as biology is from physics, or psychology from engineering. However, this division into two disciplines hails back to the formation of the subject thousands of years ago.

Babylonian Numerals (Public Domain)

Applied math developed because of necessity, as a tool to watch the stars and develop calendars, or build architectural marvels. The Egyptians devised a mathematical system designed to meet their needs, based around the need for accurate surveying. Their methods were functional and approximate, using brute force and trial and error to find solutions. As their great monuments attest, this worked for them and, for example, they did not need to know the value of Pi down to 40 decimal places, only an approximation that did the job.

Babylon Clay Tablets (Creative Commons)

By contrast, the Babylonians, with their skill in astronomy and the need to devise ever more accurate calendars, began to look at the theoretical side of mathematics, studying relationships between numbers and patterns. Like the Egyptians, they passed much of their knowledge on to the Greeks, with great mathematicians such as Thales and Pythagoras learning from these great cultures.

Why tracking your macros gives you an advantage

Just in case you’re not sure, let’s start by defining what macros, or macronutrients, actually are.

There are three major macronutrients: Protein, carbohydrates, and fat. (The fourth macronutrient is alcohol.)

Your body breaks down the macronutrients you eat into compounds used to help create energy, build body structures, create chemical reactions, and stimulate the release of hormones. Which means they can impact how you feel, perform, and even behave.

When you track macros, you don’t need to count calories directly. Instead, you log how many grams of each macronutrient you eat every day.

That’s because each macronutrient provides a certain number of calories:

  • 1 gram of protein = 4 calories
  • 1 gram of carbohydrate = 4 calories
  • 1 gram of fat = 9 calories
  • (1 gram of alcohol = 7 calories)

As a result, tracking macros means you’re automatically tracking calories. It’s just that you’re ensuring a certain number of those calories come from protein, carbohydrates, and fat, respectively. This is known as your macronutrient ratio.

For example, let’s say you eat:

  • 30% of your calories from protein
  • 40% of your calories from carbohydrate
  • 30% of your calories from fat

Your macronutrient ratio would then be: 30:40:30.

By adjusting your macronutrient ratio based on your age, sex, activity levels, goals, and preferences, you can optimize your eating plan.

If you’re trying to lose weight, you might eat a higher proportion of protein, since it can help you feel satisfied longer after meals. Or if you’re a very active athlete, you might want a higher ratio of carbohydrates to meet your greater energy demands.

The good news: Our calorie, portion, and macro calculator will figure all of this out for you.

Just enter your information and, within milliseconds, you’ll get a macro ratio that’s customized exactly for your body, goals, and preferences. (Plus, the Precision Nutrition Calculator gives you the option to further adjust these numbers, in case you want to try a different macronutrient ratio.)

Like calorie counting, though, conventional macro tracking has its downsides. Perhaps the biggest challenge: Because it requires careful food measuring and weighing, most people won’t stick to it for long.

Many say it feels cumbersome and even takes the joy out of eating. Which can limit its effectiveness to very short periods of time. That’s where the Precision Nutrition hand portion tracking system comes in.

If you feel like you’re doing everything right and still can’t lose weight, this could be why

Calories consumed minus calories burned: it’s the simple formula for weight loss or gain. But dieters often find that it doesn’t work.

“For me, a calorie is a unit of measurement that’s a real pain in the rear.”

Bo Nash is 38. He lives in Arlington, Texas, where he’s a technology director for a textbook publisher. And he’s 5’10” and 245 lbs–which means he is classed as obese.

In an effort to lose weight, Nash uses an app to record the calories he consumes and a Fitbit band to track the energy he expends. These tools bring an apparent precision: Nash can quantify the calories in each cracker crunched and stair climbed. But when it comes to weight gain, he finds that not all calories are equal. How much weight he gains or loses seems to depend less on the total number of calories, and more on where the calories come from and how he consumes them. The unit, he says, has a “nebulous quality to it.”

Tara Haelle is also obese. She had her second son on St Patrick’s Day in 2014, and hasn’t been able to lose the 70 lbs she gained during pregnancy. Haelle is a freelance science journalist, based in Illinois. She understands the science of weight loss, but, like Nash, doesn’t see it translate into practice. “It makes sense from a mathematical and scientific and even visceral level that what you put in and what you take out, measured in the discrete unit of the calorie, should balance,” says Haelle. “But it doesn’t seem to work that way.”

Nash and Haelle are in good company: more than two-thirds of American adults are overweight or obese. For many of them, the cure is diet: one in three are attempting to lose weight in this way at any given moment. Yet there is ample evidence that diets rarely lead to sustained weight loss. These are expensive failures. This inability to curb the extraordinary prevalence of obesity costs the United States more than $147 billion in healthcare, as well as $4.3 billion in job absenteeism and yet more in lost productivity.

At the heart of this issue is a single unit of measurement–the calorie–and some seemingly straightforward arithmetic. “To lose weight, you must use up more calories than you take in,” according to the Centers for Disease Control and Prevention. Dieters like Nash and Haelle could eat all their meals at McDonald’s and still lose weight, provided they burn enough calories, says Marion Nestle, professor of nutrition, food studies and public health at New York University. “Really, that’s all it takes.”

But Nash and Haelle do not find weight control so simple. And part of the problem goes way beyond individual self-control. The numbers logged in Nash’s Fitbit, or printed on the food labels that Haelle reads religiously, are at best good guesses. Worse yet, as scientists are increasingly finding, some of those calorie counts are flat-out wrong–off by more than enough, for instance, to wipe out the calories Haelle burns by running an extra mile on a treadmill. A calorie isn’t just a calorie. And our mistaken faith in the power of this seemingly simple measurement may be hindering the fight against obesity.

The process of counting calories begins in an anonymous office block in Maryland. The building is home to the Beltsville Human Nutrition Research Center, a facility run by the US Department of Agriculture. When we visit, the kitchen staff are preparing dinner for people enrolled in a study. Plastic dinner trays are laid out with meatloaf, mashed potatoes, corn, brown bread, a chocolate-chip scone, vanilla yogurt and a can of tomato juice. The staff weigh and bag each item, sometimes adding an extra two-centimeter sliver of bread to ensure a tray’s contents add up to the exact calorie requirements of each participant. “We actually get compliments about the food,” says David Baer, a supervisory research physiologist with the Department.

The work that Baer and colleagues do draws on centuries-old techniques. Nestle traces modern attempts to understand food and energy back to a French aristocrat and chemist named Antoine Lavoisier. In the early 1780s, Lavoisier developed a triple-walled metal canister large enough to house a guinea pig. Inside the walls was a layer of ice. Lavoisier knew how much energy was required to melt ice, so he could estimate the heat the animal emitted by measuring the amount of water that dripped from the canister. What Lavoisier didn’t realise–and never had time to find out he was put to the guillotine during the Revolution–was that measuring the heat emitted by his guinea pigs was a way to estimate the amount of energy they had extracted from the food they were digesting.

Until recently, the scientists at Beltsville used what was essentially a scaled-up version of Lavoisier’s canister to estimate the energy used by humans: a small room in which a person could sleep, eat, excrete, and walk on a treadmill, while temperature sensors embedded in the walls measured the heat given off and thus the calories burned. (We now measure this energy in calories. Roughly speaking, one calorie is the heat required to raise the temperature of one kilogram of water by one degree Celsius.) Today, those ‘direct-heat’ calorimeters have largely been replaced by ‘indirect-heat’ systems, in which sensors measure oxygen intake and carbon dioxide exhalations. Scientists know how much energy is used during the metabolic processes that create the carbon dioxide we breathe out, so they can work backwards to deduce that, for example, a human who has exhaled 15 liters of carbon dioxide must have used 94 calories of energy.

The facility’s three indirect calorimeters are down the halls from the research kitchen. “They’re basically nothing more than walk-in coolers, modified to allow people to live in here,” physiologist William Rumpler explains as he shows us around. Inside each white room, a single bed is folded up against the wall, alongside a toilet, sink, a small desk and chair, and a short treadmill. A couple of airlocks allow food, urine, faeces and blood samples to be passed back and forth. Apart from these reminders of the room’s purpose, the vinyl-floored, fluorescent-lit units resemble a 1970s dorm room. Rumpler explains that subjects typically spend 24 to 48 hours inside the calorimeter, following a highly structured schedule. A notice pinned to the door outlines the protocol for the latest study:

6:00 to 6:45pm – Dinner,
11:00pm – Latest bedtime, mandatory lights out,
11:00pm to 6:30am – Sleep, remain in bed even if not sleeping.

In between meals, blood tests and bowel movements, calorimeter residents are asked to walk on the treadmill at 3 miles per hour for 30 minutes. They fill the rest of the day with what Rumpler calls “low activity.” “We encourage people to bring knitting or books to read,” he says. “If you give people free hand, you’ll be surprised by what they’ll do inside the chamber.” He tells us that one of his less cooperative subjects smuggled in a bag of M&Ms, and then gave himself away by dropping them on the floor.

Using a bank of screens just outside the rooms, Rumpler can monitor exactly how many calories each subject is burning at any moment. Over the years, he and his colleagues have aggregated these individual results to arrive at numbers for general use: how many calories a 120-lb woman burns while running at 4.0 miles an hour, say, or the calories a sedentary man in his 60s needs to consume every day. It’s the averages derived from thousands of extremely precise measurements that provide the numbers in Bo Nash’s movement tracker and help Tara Haelle set a daily calorie intake target that is based on her height and weight.

Measuring the calories in food itself relies on another modification of Lavoisier’s device. In 1848, an Irish chemist called Thomas Andrews realised that he could estimate calorie content by setting food on fire in a chamber and measuring the temperature change in the surrounding water. (Burning food is chemically similar to the ways in which our bodies break food down, despite being much faster and less controlled.) Versions of Andrews’s ‘bomb calorimeter’ are used to measure the calories in food today. At the Beltsville center, samples of the meatloaf, mashed potatoes and tomato juice have been incinerated in the lab’s bomb calorimeter. “We freeze-dry it, crush into a powder, and fire it,” says Baer.

Humans are not bomb calorimeters, of course, and we don’t extract every calorie from the food we eat. This problem was addressed at the end of the 19th century, in one of the more epic experiments in the history of nutrition science. Wilbur Atwater, a Department of Agriculture scientist, began by measuring the calories contained in more than 4,000 foods. Then he fed those foods to volunteers and collected their feces, which he incinerated in a bomb calorimeter. After subtracting the energy measured in the feces from that in the food, he arrived at the Atwater values, numbers that represent the available energy in each gram of protein, carbohydrate and fat. These century-old figures remain the basis for today’s standards. When Baer wants to know the calories per gram figure for that night’s meatloaf, he corrects the bomb calorimeter results using Atwater values.

This entire enterprise, from the Beltsville facility to the numbers on the packets of the food we buy, creates an aura of scientific precision around the business of counting calories. That precision is illusory.

The trouble begins at source, with the lists compiled by Atwater and others. Companies are allowed to incinerate freeze-dried pellets of product in a bomb calorimeter to arrive at calorie counts, though most avoid that hassle, says Marion Nestle. Some use the data developed by Atwater in the late 1800s. But the FDA also allows companies to use a modified set of values, published by the Department of Agriculture in 1955, that take into account our ability to digest different foods in different ways.

Atwater’s numbers say that Tara Haelle can extract 8.9 calories per gram of fat in a plate of her favourite Tex-Mex refried beans the modified table shows that, thanks to the indigestibility of some of the plant fibres in legumes, she only gets 8.3 calories per gram. Depending on the calorie-measuring method that a company chooses–the FDA allows two more variations on the theme, for a total of five–a given serving of spaghetti can contain from 200 to 210 calories. These uncertainties can add up. Haelle and Bo Nash might deny themselves a snack or sweat out another few floors on the StairMaster to make sure they don’t go 100 calories over their daily limit. If the data in their calorie counts is wrong, they can go over regardless.

There’s also the issue of serving size. After visiting over 40 US chain restaurants, including Olive Garden, Outback Steak House and PF Chang’s China Bistro, Susan Roberts of Tufts University’s nutrition research center and colleagues discovered that a dish listed as having, say, 500 calories could contain 800 instead. The difference could easily have been caused, says Roberts, by local chefs heaping on extra french fries or pouring a dollop more sauce. It would be almost impossible for a calorie-counting dieter to accurately estimate their intake given this kind of variation.

Even if the calorie counts themselves were accurate, dieters like Haelle and Nash would have to contend with the significant variations between the total calories in the food and the amount our bodies extract. These variations, which scientists have only recently started to understand, go beyond the inaccuracies in the numbers on the back of food packaging. In fact, the new research calls into question the validity of nutrition science’s core belief that a calorie is a calorie.

Using the Beltsville facilities, for instance, Baer and his colleagues found that our bodies sometimes extract fewer calories than the number listed on the label. Participants in their studies absorbed around a third fewer calories from almonds than the modified Atwater values suggest. For walnuts, the difference was 21 per cent. This is good news for someone who is counting calories and likes to snack on almonds or walnuts: he or she is absorbing far fewer calories than expected. The difference, Baer suspects, is due to the nuts’ particular structure: “All the nutrients–the fat and the protein and things like that–they’re inside this plant cell wall.” Unless those walls are broken down–by processing, chewing or cooking–some of the calories remain off-limits to the body, and thus are excreted rather than absorbed.

Another striking insight came from an attempt to eat like a chimp. In the early 1970s, Richard Wrangham, an anthropologist at Harvard University and author of the book Catching Fire: How cooking made us human, observed wild chimps in Africa. Wrangham attempted to follow the entirely raw diet he saw the animals eating, snacking only on fruit, seeds, leaves, and insects such as termites and army ants. “I discovered that it left me incredibly hungry,” he says. “And then I realised that every human eats their food cooked.”

Wrangham and his colleagues have since shown that cooking unlaces microscopic structures that bind energy in foods, reducing the work our gut would otherwise have to do. It effectively outsources digestion to ovens and frying pans. Wrangham found that mice fed raw peanuts, for instance, lost significantly more weight than mice fed the equivalent amount of roasted peanut butter. The same effect holds true for meat: there are many more usable calories in a burger than in steak tartare. Different cooking methods matter, too. In 2015, Sri Lankan scientists discovered that they could more than halve the available calories in rice by adding coconut oil during cooking and then cooling the rice in the refrigerator.

Wrangham’s findings have significant consequences for dieters. If Nash likes his porterhouse steak bloody, for example, he will likely be consuming several hundred calories less than if he has it well-done. Yet the FDA’s methods for creating a nutrition label do not for the most part account for the differences between raw and cooked food, or pureed versus whole, let alone the structure of plant versus animal cells. A steak is a steak, as far as the FDA is concerned.

Industrial food processing, which subjects foods to extremely high temperatures and pressures, might be freeing up even more calories. The food industry, says Wrangham, has been “increasingly turning our food to mush, to the maximum calories you can get out of it. Which, of course, is all very ironic, because in the West there’s tremendous pressure to reduce the number of calories you’re getting out of your food.” He expects to find examples of structural differences that affect caloric availability in many more foods. “I think there is work here for hundreds and probably thousands of nutritionists for years,” he says.

There’s also the problem that no two people are identical. Differences in height, body fat, liver size, levels of the stress hormone cortisol, and other factors influence the energy required to maintain the body’s basic functions. Between two people of the same sex, weight and age, this number may differ by up to 600 calories a day–more than a quarter of the recommended intake for a moderately active woman. Even something as seemingly insignificant as the time at which we eat may affect how we process energy. In one recent study, researchers found that mice fed a high-fat diet between 9am and 5pm gained 28 per cent less weight than mice fed the exact same food across a 24-hour period. The researchers suggested that irregular feedings affect the circadian cycle of the liver and the way it metabolizes food, thus influencing overall energy balance. Such differences would not emerge under the feeding schedules in the Beltsville experiments.

Until recently, the idea that genetics plays a significant role in obesity had some traction: researchers hypothesized that evolutionary pressures may have favored genes that predisposed some people to hold on to more calories in the form of added fat. Today, however, most scientists believe we can’t blame DNA for making us overweight. “The prevalence of obesity started to rise quite sharply in the 1980s,” says Nestle. “Genetics did not change in that ten- or twenty-year period. So genetics can only account for part of it.”

Instead, researchers are beginning to attribute much of the variation to the trillions of tiny creatures that line the coiled tubes inside our midriffs. The microbes in our intestines digest some of the tough or fibrous matter that our stomachs cannot break down, releasing a flow of additional calories in the process. But different species and strains of microbes vary in how effective they are at releasing those extra calories, as well as how generously they share them with their host human.

In 2013, researchers in Jeffrey Gordon’s lab at Washington University tracked down pairs of twins of whom one was obese and one lean. He took gut microbes from each, and inserted them into the intestines of microbe-free mice. Mice that got microbes from an obese twin gained weight the others remained lean, despite eating the exact same diet. “That was really striking,” said Peter Turnbaugh, who used to work with Gordon and now heads his own lab at the University of California, San Francisco. “It suggested for the first time that these microbes might actually be contributing to the energy that we gain from our diet.”

The diversity of microbes that each of us hosts is as individual as a fingerprint and yet easily transformed by diet and our environment. And though it is poorly understood, new findings about how our gut microbes affect our overall energy balance are emerging almost daily. For example, it seems that medications that are known to cause weight gain might be doing so by modifying the populations of microbes in our gut. In November 2015, researchers showed that risperidone, an antipsychotic drug, altered the gut microbes of mice who received it. The microbial changes slowed the animals’ resting metabolisms, causing them to increase their body mass by 10 percent in two months. The authors liken the effects to a 30-lb weight gain over one year for an average human, which they say would be the equivalent of an extra cheeseburger every day.

Other evidence suggests that gut microbes might affect weight gain in humans as they do in lab animals. Take the case of the woman who gained more than 40 lbs after receiving a transplant of gut microbes from her overweight teenage daughter. The transplant successfully treated the mother’s intestinal infection of Clostridium difficile, which had resisted antibiotics. But, as of the study’s publication last year, she hadn’t been able to shed the excess weight through diet or exercise. The only aspect of her physiology that had changed was her gut microbes.

All of these factors introduce a disturbingly large margin of error for an individual who is trying, like Nash, Haelle and millions of others, to count calories. The discrepancies between the number on the label and the calories that are actually available in our food, combined with individual variations in how we metabolize that food, can add up to much more than the 200 calories a day that nutritionists often advise cutting in order to lose weight. Nash and Haelle can do everything right and still not lose weight.

None of this means that the calorie is a useless concept. Inaccurate as they are, calorie counts remain a helpful guide to relative energy values: standing burns more calories than sitting cookies contain more calories than spinach. But the calorie is broken in many ways, and there’s a strong case to be made for moving our food accounting system away from that one particular number. It’s time to take a more holistic look at what we eat.

Wilbur Atwater worked in a world with different problems. At the beginning of the 20th century, nutritionists wanted to ensure people were well fed. The calorie was a useful way to quantify a person’s needs. Today, excess weight affects more people than hunger 1.9 billion adults around the world are considered overweight, 600 million of them obese. Obesity brings with it a higher risk of diabetes, heart disease and cancer. This is a new challenge, and it is likely to require a new metric.

One option is to focus on something other than energy intake. Like satiety, for instance. Picture a 300-calorie slice of cheesecake: it is going to be small. “So you’re going to feel very dissatisfied with that meal,” says Susan Roberts. If you eat 300 calories of a chicken salad instead, with nuts, olive oil and roasted vegetables, “you’ve got a lot of different nutrients that are hitting all the signals quite nicely,” she says. “So you’re going to feel full after you’ve eaten it. That fullness is going to last for several hours.”

As a result of her research, Roberts has created a weight-loss plan that focuses on satiety rather than a straight calorie count. The idea is that foods that help people feel satisfied and full for longer should prevent them from overeating at lunch or searching for a snack soon after cleaning the table. Whole apples, white fish and Greek yogurt are on her list of the best foods for keeping hunger at bay.

There’s evidence to back up this idea: in one study, Roberts and colleagues found that people lost three times more weight by following her satiety plan compared with a traditional calorie-based one–and kept it off. Harvard nutritionist David Ludwig, who also proposes evaluating food on the basis of satiety instead of calories, has shown that teens given instant oats for breakfast consumed 650 more calories at lunch than their peers who were given the same number of breakfast calories in the form of a more satisfying omelette and fruit. Meanwhile, Adam Drewnowski, an epidemiologist at the University of Washington, has his own calorie upgrade: a nutrient density score. This system ranks food in terms of nutrition per calorie, rather than simply overall caloric value. Dark green vegetables and legumes score highly. Though the details of their approaches differ, all three agree: changing how we measure our food can transform our relationship with it for the better.

Individual consumers could start using these ideas now. But persuading the food industry and its watchdogs, such as the FDA, to adopt an entirely new labeling system based on one of these alternative measures is much more of a challenge. Consumers are unlikely to see the calorie replaced by Roberts’s or Drewnowski’s units on their labels any time soon nonetheless, this work is an important reminder that there are other ways to measure food, ones that might be more useful for both weight loss and overall health.

Down the line, another approach might eventually prove even more useful: personalized nutrition. Since 2005, David Wishart of the University of Alberta has been cataloguing the hundreds of thousands of chemical compounds in our bodies, which make up what’s known as the human metabolome. There are now 42,000 chemicals on his list, and many of them help digest the food we eat. His food metabolome database is a more recent effort: it contains about 30,000 chemicals derived directly from food. Wishart estimates that both databases may end up listing more than a million compounds. “Humans eat an incredible variety of foods,” he says. “Then those are all transformed by our body. And they’re turned into all kinds of other compounds.” We have no idea what they all are, he adds–or what they do.

According to Wishart, these chemicals and their interactions affect energy balance. He points to research demonstrating that high-fructose corn syrup and other forms of added fructose (as opposed to fructose found in fruit) can trigger the creation of compounds that lead us to form an excess of fat cells, unrelated to additional calorie consumption. “If we cut back on some of these things,” he says, “it seems to revert our body back to more appropriate, arguably less efficient metabolism, so that we aren’t accumulating fat cells in our body.”

It increasingly seems that there are significant variations in the way each one of us metabolizes food, based on the tens of thousands–perhaps millions–of chemicals that make up each of our metabolomes. This, in combination with the individuality of each person’s gut microbiome, could lead to the development of personalized dietary recommendations. Wishart imagines a future where you could hold up your smartphone, snap a picture of a dish, and receive a verdict on how that food will affect you as well as how many calories you’ll extract from it. Your partner might receive completely different information from the same dish.

Or maybe the focus will shift to tweaking your microbial community: if you’re trying to lose weight, perhaps you will curate your gut microbiome so as to extract fewer calories without harming your overall health. Peter Turnbaugh cautions that the science is not yet able to recommend a particular set of microbes, let alone how best to get them inside your gut, but he takes comfort from the fact that our microbial populations are “very plastic and very malleable” – we already know that they change when we take antibiotics, when we travel and when we eat different foods. “If we’re able to figure this out,” he says, “there is the chance that someday you might be able to tailor your microbiome” to get the outcomes you want.

None of these alternatives are ready to replace the calorie tomorrow. Yet the need for a new system of food accounting is clear. Just ask Haelle. “I’m kind of pissed at the scientific community for not coming up with something better for us,” she confesses, recalling a recent meltdown at TGI Friday’s as she navigated a confusing datasheet to find a low-calorie dish she could eat. There should be a better metric for people like her and Nash – people who know the health risks that come with being overweight and work hard to counter them. And it’s likely there will be. Science has already shown that the calorie is broken. Now it has to find a replacement.

You can hear more on ‘End of the calorie’, the Gastropod episode accompanying this story, on Soundcloud or through iTunes.

[protected-iframe info=”//” width=”640″ height=”450″ frameborder=”0″ >

Listen to the podcast accompanying this story on SoundCloud and iTunes.
Audio titled The End of the Calorie by mosaicscience

This article first appeared on Mosaic and is republished here under a Creative Commons licence.

It is NOT as simple as Calories In Calories Out (CICO)

In my experience, weight loss trends or "fads" that come and go don't work because they aren't sustainable. Why do these fads keep coming and going? I believe it is because weight loss is not as simple as CICO. People know it and some look to make a buck selling a new approach that may appear somehow easier at first blush.

If you are struggling, and someone is telling you that it is as simple as CICO, they are wrong. The truth is, weight loss and weight management is easier for some than others for a bunch of reasons too long to list. Telling anyone who is struggling that it is as simple as CICO and they just need to eat less is tantamount to calling them a failure and is mean spirited. It is much more complicated than will power.

Change is hard, DAMN HARD, and we humans stumble along the way. All of us do. Those of us who are trying to accomplish something hard and stumble, or don't see the results we hoped for on the scale aren't failures. We are BRAVE. It takes courage to work for positive change and even more courage talk about it.

kEEP AT IT BRAVE WARRIORS! You are strong!

Battling obesity with better mathematical models

Credit: NIH

In the war to lose weight it may be something other than willpower or junk food that's preventing victory: it could be faulty use of mathematics.

Traditionally, nutritionists and researchers have assumed that all you need to do to lose weight is cut calories -- about 500 calories per day to lose a pound per week for most dieters, from the assumption that each pound of weight lost represented 3,500 calories in reduced calorie intake or increased exercise.

"People have used this rule of thumb for decades, and it turns out to be completely wrong," Kevin Hall, a scientist with the National Institutes of Health, said at the American Association for the Advancement of Science annual meeting in Vancouver.  

Hall said the reality is that losing weight slows a person's metabolism -- and the mathematical model typically used doesn't take this slowing into account. When dieters report a "yo-yo" sequence, of weight loss, reaching a plateau in weight and then slowly regaining previously lost pounds, this is part of the reason.

New models may have some of the answers. The science of weight loss isn't new scientists have been struggling to understand it for almost 40 years, said Carson Chow, a senior investigator at the National Institutes of Health in Bethesda, Md. Chow said that what's different now is that scientists are compiling many data sets into a single model.

Hall and Chow are part of a team that has created a new model, and an online weight simulation tool that shows what happens when people of varying weights, diets and exercise habits try to change their weight. Their model was first published last fall in the journal The Lancet.

"Instead of using that old rule of thumb, people input their goal weight in a certain period, and the model shows them what you have to do in [the] short term to get to goal weight and then what they'd have to do permanently," explained Hall. The model takes into account differences in sex and body-fat content.

At the moment, the online tool is not very user-friendly, say the researchers, so it's primarily intended for physicians and researchers who help guide people toward better health. Obesity is on the rise: two-thirds of the adult U.S. population is classified as overweight or obese, and around the globe, obesity rates have doubled in the past 30 years.

Outdated calculations predicted that people could lose weight forever, if they stuck to the calorie-reduction rules.  The new model predicts slower weight loss.

"If I want to lose 10 pounds of weight eventually, I have to cut 100 calories per day out of my diet," Hall explained. "You'll get halfway there in about a year, and then you will eventually plateau, [reaching the goal] after about three years."

Math can also help to drive policy decisions, said Boyd Swinburn of the World Health Organization Collaborating Centre for Obesity Prevention in Australia. He explained that many of the "best buy" policies that tend to have a real impact, such as restricting marketing to kids, taxing sugary substances, and increasing labeling, also tend to be the policies that governments do not want to undertake.

The less cost-ineffective interventions, like after-school programs, tend to be the ones that governments are more interested in undertaking, said Swinburn.

"You get a huge spread in the relative effectiveness of these programs," said Swinburn, adding that mathematical perspectives that parse out health improvements per dollar help shed light on policy interventions.

Questions remain about the science of weight loss. For example, is a calorie of butter burned the same way in the body as a calorie of fruit? Like many other parts of the equation, said Hall, it may vary from person to person.

The same is true of exercise. "For small changes, exercise is more potent than cutting calories -- it speeds up weight loss," said Hall. But at some point, a person will reach a tipping point, where cutting calories will have a larger impact.

That's because someone who is 200 pounds will lose more calories doing the same exercise than someone who is 150 pounds.

"The heavier you are, unlike the popular notion, the more calories you're burning," said Hall.

So, does dieting damage the metabolism?

Despite what you may have heard:

No, losing weight doesn’t “damage” your metabolism.

But because of the adaptations your body undergoes in response to fat loss (to prevent that fat loss, in fact), ‘energy out’ for those who have lost significant weight will always be lower than for people who were always lean.

Losing weight, and keeping it off, is accompanied by adaptive metabolic, neuroendocrine, autonomic, and other changes.

These changes mean that we expend less energy—around 5-10 percent less (or up to 15 percent less at extreme levels) than what would be predicted based on just weighing less.

Unfortunately, because of this adaptive response, someone who has dieted down will often require 5-15 percent fewer calories per day to maintain the weight and physical activity level than someone who has always been that weight.

(Or even less, potentially, because as we learned in the very beginning, the RMR of people of the exact same age/weight/etc. can still vary by up to another 15 percent.)

This means someone who was never overweight might need 2,500 calories to maintain their weight, while someone who had to diet down to that weight may need only 2,125-2,375 calories to hold steady.

We don’t know how long this lowered energy expenditure lasts. Studies have shown that it can hang around for up to 7 years after weight loss (or more 7 years is as far as it’s been studied). This likely means it’s permanent, or at least persistent.

This is extra relevant for people who have repeatedly dieted, or for fitness competitors who may repeatedly fluctuate between being extremely lean and being overweight in the off-season.

I don’t have data to back this up (to my knowledge no one has studied it), but adaptive thermogenesis seems to react more strongly or more rapidly with each successive yo-yo of extreme body fat fluctuations.

All of this explains why some people can feel like they’ve “damaged” their metabolism through repeated dieting. (And why some experts suggest “metabolic damage” is a real thing.)

But nothing really has been “damaged”.

Instead, their bodies have just become predictably more sensitive to various hormones and neurotransmitters. Their metabolic rates are understandably lower than predicted by various laboratory equations.

So, where does this leave us?

✅ Branches of Mathematics

What exactly is mathematics? First and foremost, it is very old. Ancient Greeks and Persians were already utilizing mathematical tools. Nowadays, we consider it an interdisciplinary language.

Biologists, linguists, and sociologists alike use math in their work. And not only that, we all deal with it in our daily lives. For instance, it manifests in the measurement of time. We often need it to calculate how much our groceries cost and how much paint we need to buy to cover a wall.

Simply put, mathematics is a universal instrument for problem-solving. We can divide pure math into three branches: geometry, arithmetic, and algebra. Let’s take a closer look:

It’s true that most high school students don’t like math. However, that doesn’t mean it can’t be a fun and compelling subject. In the following section, you will find plenty of enthralling mathematical topics for your paper.

We'll deliver
a 100% original paper
this fast