Tag Archives: mathematics

The Surgeon General of Bacotania

I find that news releases on health research often do a lousy job of communicating what the findings actually are, and how they might inform people’s decisions. Often, in order to make sense of them at all, you have to know some statistics, read between the lines, and cut through the hype. The problem seems to be especially severe in the case of a study on the scale of something impacting populations, but hyped for the public because the authors don’t trust the reader to care unless they’re scared. There’s a difference between public health and personal health, and although the two are connected, statistically, the conclusions can be wildly different depending on your point of view – managing populations, or managing your own choices. Also, when people make decisions about their own health and safety, they fall prey to some particularly nasty logical fallacies (all natural means harmless, or it’s not cancer, so it’s fine – or, “not likely to be me” means that “it won’t happen to me”). Even nastier, research on sensational subjects – like all scientific research – often turns up complicated or ambiguous results that get distilled into inaccurate clickbait. Never fear, though, let’s play pretend, and sort through, now and forever, how to think about statistics and clickbait-y health headlines. (I sourced the images in this article from Wikimedia Commons, as usual, and the attributions are at the bottom of this page, to help maintain the suspension of disbelief.)

About Bacotania

Vintage photo of a woman wearing bacon slabs on her feet, standing in a giant skillet.

1. Skillet Skating is a Bacotanian folk dance, recently nominated for inclusion in the UNESCO Intangible Cultural Heritage Lists in which the dancer wears slabs of bacon on their feet and skates around a giant skillet with a giant spatula. A good performance is said to prevent the sticking of eggs in the coming year.

Bacotania is an imaginary country with a rich cultural history deeply intertwined with the consumption of cured pork. The total population is about 12 million, and national holidays include February 4th, Remembrance Sausage Day, and October 16th, Bacotanian Liberation Day. The festivities of Liberation Day culminate in a Liberation Day Bonfire Feast in which chunks of pork belly are roasted on sticks over Liberation Day Bonfires in honor of the heroic air drop of canned bacon into the besieged capital city of Schlachteplatte.

A giant can of bacon, 70 years old, WWII rations from the UK.

2. One of the historic bacon cans in the National Museum of Bacotania.

A fire pit with two long forks full of fresh raw bacon held over the flames.

3. Bacontanian Liberation Day Bonfire with skewers of bacon sizzling over the open flames.

Needless to say, bacon is very important to the people of Bacotania, and the loss of cured pork products would cause immense damage to the economy and culture of the country. The 2015 decision by the World Health Organization’s International Agency for Research on Cancer to classify processed meat consumption as a Group 1 Carcinogen was met with increasing public unrest, including mass demonstrations outside the Surgeon General’s office in Schlachteplatte, which led to the Surgeon General stepping down from their post.

Congratulations! YOU have just been appointed Surgeon General of Bacotania.

What is your advice, concerning the consumption of cured pork products?

You’ll need some further information:

What is a Class 1 Carcinogen? In a masterpiece of shoddy journalism, a lot of press outlets didn’t discuss what the classes even meant. The IARC classifies substances based on how conclusive the evidence is that they cause cancer at all, NOT even remotely based on how dangerous they are. There’s only one item in Group 4, the Probably Does NOT Cause Cancer group, and that’s Caprolactam. I’d never heard of caprolactam before doing the research for this post. It’s used in nylon manufacture, and it’s definitely not harmless, but we’re pretty sure it doesn’t cause cancer. Nobody seems to have studied whether, say, pure water causes cancer.

What is an individual’s chances of getting cancer from bacon? The average lifetime chance of getting colon cancer is about 4%. According to the World Health Organization, the chance of getting colon cancer rises by 18% for every 50 grams of processed meat consumed per day. Now, we need one more bit of information, and that is the average consumption of processed meats. According to this study, average daily consumption of meat (all types) was 128 grams per day, and 22% of that was processed meat. So (22% of 128 grams gives you how many grams are processed meat) that means that the average person eats 28.16 grams of processed meat per day. So, if you start at 4% with 28.16 grams, and add 18% of 4% for every 50 grams eaten over the 28.16 gram starting point, you end up with an average Bacotanian’s cancer risk.

How much bacon does the average Bacotanian citizen eat? Bacotanians are very fond of processed meat, and a traditional Bacotanian Breakfast involves lots of sausage, so they eat twice the processed meat that Americans do, at 56.32 grams per day.

What is the average Bacotanian’s cancer risk then? Well, we need to figure out how much more processed meat than the American average an average Bacotanian eats, and then figure out what proportion of 50 grams it is, and then add that proportion of the 18% of 4% to the average 4%. Got it? Let’s go!

56.32 – 28.16 = 28.16, because it’s twice, remember? Easy!

28.16 extra grams eaten divided by 50 (grams to raise risk by 18% of 4%) = 0.5632 (amount of the 18% excess risk we should add)

0.5632 of 18% = 10.1376% Cool. Now we’re getting somewhere.

10.1376% of 4% = about 0.004, which is 0.4%

So, the average Bacotanian faces an elevated lifetime colorectal cancer risk of 4.4% on account of their huge processed meat habit. This means that for the average bacotanian, their MORTALITY ROULETTE WHEEL lands on DEATH BY BACON not much more often at all compared to the American population. (Bacotanian healthcare and mortality from colorectal cancer are comparable to ours.)

How many excess colorectal cancer cases are likely to occur in Bacotania if people continue to eat processed meat at this pace? Well, 0.4% of the total population are going to lose that roulette round, so…

0.04% of 12 million is… 48,000. YIKES! That means that Forty-eight THOUSAND Bacotanians are going to get cancer from bacon, above and beyond even the background colorectal cancer rates. If you factor that in, it’s a staggering 528,000 cancer cases. The cost to society, and the personal emotional toll on all those families is absolutely astronomical. And, clearly, partially preventable.

So, that’s how the same decision – eat the bacon, tell people not to eat bacon – ends up looking very different from the perspectives of an individual Bacotanian and the Surgeon General of Bacotania. The Bacotanian might well accept the risk, shrug, and tuck into a full Bacotanian breakfast of smoked sausages anyway. Note that although it’s a Class 1 Carcinogen, processed meat has a much smaller chance to cause cancer, compared to other Class 1 Carcinogens, like Asbestos, which (depending on your own exposure) can have lifetime risk rates as high as a 25% if you were a construction carpenter in the United Kingdom for a couple decades before 1980. Also, note that this only concerns cancer risk, not whether the cancer has a high mortality rate, and not concerning other health risks associated with the substance. (Remember that although Caprolactam is the sole occupant of Probably Does Not Cause Cancer Group 4, it’ll still cause your skin to slough off. Nice.)

So, maybe suggest that Bacotanians cut back on processed meats, but that the Bacotanian Liberation Day Bonfires likely won’t do you any harm.

Probably want to suggest the closure of Ye Wooly Salamander Particle Board Mill, though…

Vintage Photo, United States of America. No, I have no idea what’s going on here. By UW Digital Collections [No restrictions], via Wikimedia Commons
British Ration Can of Bacon from WW II. Seriously, my heaviest of two cats weighs 12 lbs. That’s a LOT of 70 year old bacon. By KingaNBM [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], from Wikimedia Commons
Hungarian Szalonnasütés By Christo [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], from Wikimedia Commons

Life Skills: Budget

Jim Hawkins pouring pirate treasure coins into a bag.

This illustration by N. C. Wyeth of the Treasure Island edition of 1911 probably won’t be relevant to your life, but even if it was, Jim Hawkins here should make out a budget for all that sw33t l00t. Plenty of people have made lots of money and then lost it because they weren’t paying attention to spending.

You will probably, at some point, want more money than you have. Barring some miracle, like finding pirate treasure, the best way to make sure you have enough money is to take care of what you do have and keep track of it. The best way to keep track of your money is to make a budget. If you’ve ever wondered where your money goes by the end of the month, never fear, I’m here to walk you through exactly how to make a budget, step by step.

The point of making a budget is to find out what you do know about your money situation, what you need to know, what kind of money you have, your expenses, and – most importantly – to make a plan about how to manage that money in the future.

Here’s what you’ll need:

Scratch paper and pencil

And/or

Calculator app (probably already on your phone) or calculator, abacus, whatever

And/or

Spreadsheet program, like you can find on Open Office, Microsoft Office, Google Docs, etc.

That’s a lot of and/or because all you really need is to be organized and think about your money. The procedure for making a budget is as follows.

In a list with two columns, write how much money you have coming in every month:

Income

$100

Then, list everything you spend money on every month, and how much you really do spend (honestly, no cheating: the most important person never to lie to is yourself). This is where it might help to have some scratch paper, so you can make this list really orderly and clear. Be as specific as you can.

Income

$100

Food With Friends

$50

Game Night

$25

Streaming Service

$10

Transportation

$10

This is just an example, of course. Yours will look different. If you don’t know how much you spend on what, it might really help to keep receipts you get whenever you buy things, and actually sort and tally them up for a month, or (even better) a few months, so you can get a real idea of what you’re actually spending, and what you’re spending it on, and not just what you think you’re spending.

Next, subtract your total expenses from your income. This is how much money you can manage to put away every month.

Income

$100

Food With Friends

$50

Game Night

$25

Streaming Service

$10

Transportation

$10

Total Expenses

$95

Left Over

After you look at your budget, think about what you want money for. Make financial goals. It can be as straightforward as buying a new game system, or saving for pottery classes, or new shoes. As you can see, it will be a long time in this example before I can afford a new game system. (If a new game system is $380, and I save only $5 a month, it will be an excruciating 6 years and four months before I can buy one, and by then, we’ll all be going to virtual reality arcades or something.) Here’s my work:

380 (dollars) / 5 (dollars/month) = (dollars cancel out, leaving months) 76 months.

76 (months) / 12 (months/year) = (months cancel out, leaving years) 6.333333… years, which is six years and a third of a year, which is four months. OUCH!

But, if you want to change that, you will have to pay attention to how you spend your money, and on what. With a budget, you can see how much you have coming in, and what it goes out for, and where you can cut expenses. From here, make a plan.

Change your goal. Can you get a game system used, and therefore less expensively? This puts your goal closer to your reach.

Change and eliminate expenses. Fifty bucks a month is pretty steep for food with friends. Go out less, or somewhere cheaper, maybe, to save a bit here.

Change your income. Is there some way you could make more money?

Revise your budget to make room for your goal, and trim down expenses. Now, you have a plan to follow. Monitor your own progress by checking whether you really did spend less where you want to, or earned more. If you do this long enough, and keep your receipts, you may find patterns in your spending. Your income might vary seasonally (Summer jobs, more time), or suppose you tend to spend more money when school is in session, because you can’t resist the vending machines and you have to buy school supplies. Every bit of data like this will help you make and meet financial goals, if you use your budget. Let’s see how it all comes together.

Suppose I do want a game system, on the budget shown above. New, it’s about $380. The exact same system (model, specs and everything) refurbished, however, is about $270. That’s $110 cheaper. If I choose to get a used one, then, I automatically jump $110 closer to my goal. Suppose I also start paying more attention to where and what I eat with friends, maybe going out less often, and more like for frozen yogurt or something once a week, rather than go to a movie, with all the popcorn, etc. or to a restaurant. Suppose I also get a bake-a-pizza instead of ordering out for game night, too. Now, my monthly expenses look like this:

Income

$100

Food With Friends

$25

Game Night

$15

Streaming Service

$10

Transportation

$10

Total Expenses

$60

Left Over

$40

Hey, just making some changes opened up a lot more spare $$$. Now, at $40 per month, assuming I save it all for my new (to me, because it’s used) game system, I can afford it in a little over six months flat. How much more money could you open up per month, if you sat down and made a budget, and a plan like this? I think making a budget is definitely worth the time.

BONUS ROUND! If you want to get even more crazy about saving money, though, let me share another tip: take everything a step further, and ask what you want a purchase for, in the first place. In other words, what is the goal your goal achieves?? I want a new game system, so purchasing a game system is my financial goal, but what do I want a game system for?

Do I want a new game system, because I play games with my friends, and they all have new game systems, and I need to keep up, technologically? Do I need to keep up and get a new game system because playing games is fun? Do I want a new game system because hanging out with my friends is fun? Maybe, the even more cost-effective solution is to get a hand-me-down system, or a free app, or stick with your old system, and get (new to you) used games for it (classic games are classic for a reason, after all). You can always find games to play with your friends. You could go on frozen yogurt and augmented-reality-mon-catching (free app!) parties with your friends, and get Ultra Bash Siblings ($10 used!) for your old game system, for game night. (Besides – to be brutally real here – if your friends ditch you just because you don’t have the newest game system that they all do, you don’t have a game system problem, you have a much bigger shallow-jerks-for-friends problem.)

Always think about what you are setting your goals for, anyway. What purpose do they serve? If you do decide to forgo that game system, that’s $40 richer per month anyway. If, however, you do the emotional calculus, and you find that you really do want a game system, then by all means budget and save for it, just be aware that money stuff is almost always tangled up in weird feelings-stuff too. Being aware of the deeper motives for spending money can also help you get control of your spending choices. Spending is a choice, after all. Stuff doesn’t just leap into your shopping basket on its own. So, take control by thinking consciously about money, and you can start by making a budget.

Mathematical!

Romanesco Broccoli: the mascot of awesome mathematical stuff.

You deserve cool things. Mathematical things, in the Adventure Time sense. All too often math is treated like a chore, but it is, and should be, mind-blowingly awesome. It could be the coolest subject you ever study, but textbooks seem to have the special quality of sucking the joy out of everything.

Let’s start with an episode of Adventure Time as an example, specifically the one where Finn gets glasses that make him super smart, and invents a device for blowing bubbles that have any number of dimensions. It’s possibly the most concise explanation of higher-dimension geometry I’ve ever seen. A shadow falling on a flat surface is a projection of an object in two dimensions. A two dimensional bubble casts a one dimensional shadow. A three dimensional bubble casts a two dimensional shadow. A four dimensional bubble casts a three dimensional shadow into our three dimensional space. Another way to think about it is like this: every object of the next-highest order of dimensions has an object of the previous order as its “face.”

A square has a line for each of its four faces that define it in two dimensional space. A cube has a square for each of its six faces. A tesseract or 4D hypercube – a four dimensional object – has a cube for each of its eight three dimensional faces. Watch this video, which shows a tesseract rotating so you can get a good look at it and understand how it’s put together. It may help to realize that none of the cubes pass through each other during the rotation. When they squash and stretch, it’s not a small cube passing through a bigger one, but rather the bigger faces popping out towards you and the smaller ones passing in the distance behind. The lines are all the same size, and the angles are all 90 degrees. It’s perspective, not changing actual shape. Eventually you’ll get it.

Meditate on the tesseract.

You like what you see? Spend some time on Vi Hart’s youtube channel, or Numberphile.

Or, read a breezily-written book on mathematics. Here’s Looking at Euclid is one of the best introductions to math that I’ve encountered. Also, this won’t be the last about mathematical mathematics on this blog. Here’s a teaser, in case the broccoli wasn’t a tip-off.