The Twelve Days of Christmas (or, what am I going to do with all these birds?)

A fun question was put to me yesterday that’s sure to put the math-minded in the holiday spirit:

“How many of each gift is given in the song The Twelve Days of Christmas?”

Beginning at the beginning, the Partridge in a Pear Tree is on the first day and so is given twelve times. The Turtle Doves are given the second day and so are given eleven times. Continuing on to the end, the Drummers Drumming are only given once, on the twelfth day.

So I thought, “Total days – day… 12 – 1 = 11. Nope. Total days + 1 – day? 13 – 1 = 12 (partridges); 13 – 2 = 11 (Turtle Doves). Ok, so far so good. But then I remembered that the number of each also depends on the day given (TWO Turtle Doves, THREE French Hens, etc.)

The total number is simply the number given multiplied by the number of times given, and since I had already figured out how to find out how many times each item is given according to the day the solution was straightforward:

Total items given = day * (13 – day)

This led, naturally, to a couple of follow up questions:

“So what do you get the most of? And how many gifts is that total?”

The questioner set to work calculating the value for each day, which is fine but boring. If you have a basic calculus course under your belt (or are teaching one and would like a softball example question), you would see that we’re looking for a maximum of an inverse parabola. The solution is then found where

d/d(day) [day * (13 – day)] = 0

ie, where 13 – (2 * day) = 0

The maximum lies at day 6.5, but remembering that there is no such day, days 6 and 7 should be equal and at the maximum and indeed my true love gives to me 42 Geese-a-Laying and 42 Swans-a-Swimming.

As for the total number, a discrete problem calls for a discrete sum, ie the sum from day 1 to day 12 of day * (13 – day). The solution turns out to be 364. If my true love also gives me a birthday present, that’s one gift for every day of the year!

I would love to have finished off the story by saying that what we’re really looking for is the area under the curve of  day * (13 – day) between 1 and 13 (again, nudge nudge calculus 101 teachers). So instead of tallying up the sum, we could have taken the definite integral of the function from 0 to 12 as

(13 * 13^2)/2 – (13^3)/3 – (1 * 12^2)/2 – (1^3)/3 = 360

which, unfortunately, is false, for a reason similar to why the most gifts didn’t come on day 6.5. However, I think it stands as a useful exercise, possibly to highlight the difference between discrete and continuous problems.

Not to mention the problem of what to do with all those birds.

Alfred Hitchcock's "The Birds"

Seriously, just send cash.

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Incidentally, an exact summation function can also be constructed from something like (1+2+3 …+n) * mean(n + 1 – {1,2,3, …n}) that simplifies to:

n(n+1)(n+2)/6

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Tell Someone “No”, Get Called a “Whore” – #StandingwithDNLee #batsignal

quicktothelab:

Everyone needs to speak out against this kind of thing and stop ignoring it. Shaking our heads and sighing is not a good enough solution. Thank-you for sharing your story and for standing up!

Originally posted on :

If you’ve come here looking for DNLee’s original post, it has been restored to her blog at Scientific American. You should go read it there.

Thank you for all the love and support.

XOXOXO,

Isis the Scientist

View original

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Education is a right. Right?

All over my campus there are posters and flyers informing me that post-secondary education is a right, not a privilege, and that I should joint the fight against rising tuition fees. Many places in Canada, where a majority of the universities are public, have recently been protesting against similar hikes in tuition or just to drop current fees.

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IMG_00000069

I think they need more posters. I might be missing the point.

I live and attend school in Ontario where tuition rates (undergrad and graduate) are the highest in the country. Here are some facts (fun!):

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  • We have the worst per-student funding in the country
  • We have the largest class sizes
  • Collective student federal debt in Canada is about $15 000 000 000 (ON student share is about $9 billion)
  • Average student debt after graduation = $37 000
  • 95% of grad students cannot access an ON graduate scholarship
  • More than 25 other countries have some form of free post-secondary education

The situation for my friends south of the border is even worse:

  • A collective $1 trillion in student debt
  • Average tuition for a 4-year university is about $18 000/year
  • Grad school tuition can run from approximately $10 000 (public) to $30 000/year (private)
  • More than half of the students in the US have to take out student loans (about 12 million students)

Most of us will still be struggling to repay this debt well into our 30’s (when many are still in school) and 40’s. Coupled with the current economy and poor job market, and the idea of free education becomes very attractive.

 

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What my current student loan could look like as a down payment.

What my current student loan could look like as a down payment.

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Yet as I take a (terrifying) leave from school due mainly to financial difficulties and Matt faces possible exclusion from a master’s program because of a lack of funding, I can’t help but question the idea of higher education as a right and not a privilege.

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Sound a little backwards?

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Free post-secondary education at the level of a bachelors degree makes complete sense. It has the chance of being economically viable and ensures that everyone receives the opportunity to attend college or university. And at this level education should be a right. Whether it’s trade, business or science, getting a job in today’s market is virtually impossible without some type of degree.

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But what about higher degrees at the graduate and professional level? Should these also be fully funded? My personal education is funded through a combination of research grants and assistantships – so I work for the majority of it. Amazingly (to me) this will amount to just under $100 000 in the 5 years I’m here.

Whoa whoa whoa. I feel the need to insert some perspective at this point. $100 000 over 5 years is $20 000/year. Minimum wage in Ontario is $10.25/hour, so a full-time Starbucks barista or Wal-mart cashier will make $21,320/year – in other words her highly specialized, high value research position is costing her $1320 a year. Not only that, but  over that same time she’ll give $40 000 to the school for tuition, and a significant portion of the rest back to the government repaying some of that undergrad debt mentioned above. Add to that the college’s restrictions on TA hours and off-campus employment and she might actually be making less than nothing to expand the sphere of human knowledge.  /perspective

Wait – what?

Carleton_600

My current ball and chain. Which I am very happy to be dragging along.

So I’m still unable to manage without working off campus and maintaining a very restrictive diet (Kraft dinner anyone?). But seeing as I chose this educational path, does that automatically qualify me for support? Do I have a right to this degree? Unfortunately, the current view of higher education seems to say no. Graduate students are expected to supplement their research income mainly by applying for external grants and scholarships. And while this is not an unreasonable expectation, what happens to those of us who are unsuccessful or don’t qualify? The many who are denied government loans because they are being ‘paid by the school’ and yet also don’t have access to private loans? How does the system work for us?  What is scientific research and higher education really worth to us as a society and how can we ensure it’s future 

http://www.cfs-fcee.ca/html/english/home/index.php
http://www.usstudents.org/
http://nces.ed.gov/fastfacts/display.asp?id=76
http://www.asa.org/policy/resources/stats/
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Whoot!!

I just want to take a minute and say congratulations to Matt who is GRADUATING TODAY!!

He’s successfully finished his 4-year undergrad with many distinctions. His family, friends, and I’m sure our 5 blog readers, are all extremely proud of him.

We can only hope that he will continue to struggle endeavour to scientific mastery! After the ball of course…

Classing it up at RMC!

Classing it up at RMC!

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What Do You Mean I’m Eating Duck Feathers?!

But I suppose it’s better than eating human hair. Confused? Let me back track.

Sometimes being a vegetarian is difficult. And I’m not just talking about the temptation of eating meat. At times, I don’t even know I’m consuming animal products. Chances are you don’t either. I recently came across this claim that I (as a consumer) may be eating a large, albeit unknown, quantity of duck feathers – in the form of L-cysteine hydrochloride (also known as additive number E920).

Cysteine is an amino acid used in foods mainly as a processing aid in baking, it stabilizes the structure of leavened bread. It is also used in the production of artificial flavours – specifically meat flavour (yes, I realize the irony). The majority of commercially used L-cysteine is derived via the hydrolysis of duck feathers, mostly from suppliers in China. The other major sources of cysteine for use in commercial food products are human hair and hog bristles.

Fun fact: The European Union allows the addition of E920 to baked breads only from synthetic sources.

Quesadilla foie gras anyone?

An Oklahoma duck. Probably not in your tortilla.

Actually, some sources* still claim that human hair is the main source for L-cysteine used in baked goods because it’s very rich in protein and very cheap to get. Most cysteine ends up in breaded foods such as bagels and tortillas. As taking pictures of product ingredients is frowned upon in grocery stores (apparently) I was forced to turn to internet research. Luckily, most brand names now provide their ingredient list online.

Cannibalism is NOT COOL people. Don't try it at home.

Human additives….nom nom nom nom……

A few brands that don’t use L-cysteine-a include Dempster’s, Country Harvest, and Old Mill (bagels and flat breads). Where you might find duck related ingredients: President’s Choice brand, Einstein Bros. and Dunkin Donuts. Weather or not there’s human hair involved is (APPARENTLY) an open question.

Animal ingredients might be included foods and products where you don’t expect them and they’re hard to spot because they don’t use common names like “crushed fly wings” or “sheep stomach enzyme.” They may also be plant based or synthetic – manufacturers usually don’t have to label ingredient sources. Here is a short list of some commonly animal derived ingredients that you may be using or eating:

  • Adrenaline-  hormone extracted from pigs, cows and sheep
  • Allantoin-  uric acid from cows, found in cosmetics
  • Amino acids –  proteins may be animal or plant derived
  • Ambergris (AKA porpoise hork)-  from whale intestine, can be found in perfumes
  • Anchovy-  small fish, used on pizza’s
  • Arachidonic Acid-  found in the livers and brains of animals
  • Aspic-  a jelly made from gelatin(e)
  • Bone, Bone charcoal, Bonemeal-  derived from boiled animal bone
  • Bristles-  derived from animal hair normally pigs, sometimes used in toothbrushes
  • Caviar(e)-  fish eggs, may also come from belluga’s and other marine mammals
  • Cochineal/carmine/carminic acid-  made from the red pigmentation of the cochineal insect  (approximately 70,000 insects used to produce one pound of red pigment)
  • Cetyl Alcohol-  derived from spermacetti in whales
  • Chitin-  found in outer shells of insects and crustaceans
  • Collagen-  derived from animal tissue
  • Elastin-  found in the muscle fibres of animal.
  • Fatty acid derivatives-  used in cosmetics
  • Gelatin(e)-  derived from boiled animal bones and cow/sheep collagen
  • Glycerol-  normally animal derived found in soaps and cosmetics
  • Isinglass-  a type of gelatin(e) derived from fish
  • Keratin-  formed from ground animal hooves and hair, found in shampoo and conditioner
  • Lactic Acid-  found in animal tissue, used as a preservative (can also be produced by bacteria)
  • Lecithin-  fatty acid found in blood and animal tissue.
  • Lipoids-  found in animals as well as plants.
  • L-cysteine hydrochloride-  made from animal hair and chicken feathers
  • Marine Oil-  derives from seals, whales, porpoises and fish
  • Mono and Di-glycerides of fatty acids-  can be derived from animals
  • Musk-  derived from deer
  • Oleic acid/oleoic oil-  obtained from animal fats, may be obtained from vegetable fat
  • Oleostearin-  made from beef fat
  • Pepsin-  found in pigs stomachs, Pepsi’s eponymous enzyme
  • Proteins (e.g. elastin, keratin, reticulin)-  from animal proteins
  • Progesterone-  used in anti-ageing creams
  • Rennet (animal rennet)-  enzymes found in calve stomachs
  • Sable-  fur or hair from a weasel found in paint brushes and cosmetic brushes
  • Squalene/squalane-  found in shark liver
  • Suet-  fat from the kidneys of sheep and cattle
  • Stearates, Stearic acid-  found typically in cows and sheep and used in cosmetics
  • Tallow/ tallow acid-  made from beef fat and found in cosmetics, crayons and wax
  • Urea-  from animal excretion (urine)
  • Roe-  ovaries and eggs from fish
  • Seal Oil-  derived from seals generally from Canada and Namibia.
  • Spermaceti-  a wax found in the head cavities of sperm whales.
  • Vitamin A/ Vitamin B-12/ Vitamin H-  can be animal derived
  • Volaise-  ostrich meat

I realize that in today’s market world it’s practically impossible to avoid all products that have somehow harmed animals. Commercial milk and egg farming practices are sometimes ethically questionable; vaccines are made using chick embryos; some dyes have beetle parts in them; my ground coffee probably contains a cockroach or two. But I try. Don’t get me wrong, if animals are going to be used I completely support the use of the entire animal, I’d just prefer it if where the animal bits end up was a little clearer.

*Most of the sources I could find that discussed the use of L-cysteine in foods either did not provide references or just kept citing each other. While there is a fair amount of peer-reviewed work concerning cysteine, little of it discusses commercial sources of the amino acid. Therefore, this entire post might need to be taken with a grain (perhaps a lick?) of salt due to the difficulty in substantiating these claims with trusted sources. It also makes me question why finding out where food additives come from is so damn difficult.
http://en.wikipedia.org/wiki/Cysteine
http://www.vrg.org/blog/2011/03/09/l-cysteine-in-bread-products-still-mostly-sourced-from-human-hair-duck-feathers-hog-hair/
http://blogs.discovery.com/dfh-sara-novak/2012/01/common-bread-ingredient-l-cysteine-derived-from-human-hair.html
http://www.motherjones.com/blue-marble/2010/03/human-hair-additive-your-food
http://www.naturalnews.com/032718_L-cysteine_commercial_bread.html
http://www.yourethecure.com/cart.php?target=product&product_id=215
http://www.veganpeace.com/ingredients/company_product_information.htm
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Water Woes

Like many people, I tend to carry a water bottle around with me most of the time. Unlike a lot of those other people, however, I actually enjoy drinking the contents. I love water, and drinking it continually throughout the day is not a chore for me.  Even more than tea and coffee (and occasionally wine and beer – I am a grad student), water is my main go-to liquid.  If you’re a guest in my home (and weren’t able to think of an excuse to get out of it) there’s a very good chance that the only beverage I’ll have to offer you is cold water (filtered or tap).  You will also not be able to locate any water “enhancements” such as Crystal Light or Kool-Aid to appease your palate. If you’re lucky I may have ice cubes.

If you’re really super lucky they won’t have bugs in them….

I know that many people do not share my love of plain, ordinary water. And yet they continue to dutifully chug back bottle after seemingly awful (judging on facial expressions) bottle. Why? Well, it probably has something to do with the idea that as humans we are supposed to consume at least 8-8oz glasses of H2O per day to maintain a healthy lifestyle. This adage has been around for a while and chances are you’ve heard it from popular media sources, parents, dietitians, and possibly even a doctor or two. It’s one of those things – you just know you’re supposed to do it. So people are regularly trying to consume 1 893ml (2qt, ½ gal(US), 4 pints, 1.9leters or 1892cm3) of water each and every day.

4 days worth of water.

And it has to be water. Caffeinated beverages don’t count because they act as diuretics. Same goes for alcohol. Water used and found in food doesn’t really count either. In addition to keeping you hydrated, drinking 8 glasses of water is purported to aid in all kinds of ailments. Adequate water intake has been indicated in the prevention of kidney stones, headaches, coronary diseases, urogenital cancers (bladder, ureter, kidney, renal pelvis, prostate, testicular), colon and breast cancer. It will help you lose weight, improve your skin tone, and boost your cognitive performance. In short, water is a wonder drug!

The best part of all this? It’s a myth. An untruth. Medical propaganda, or whatever. There is no actual tested scientific proof that you need to consume at least 2L of water a day to be healthy. So where exactly did it come from?

Valtin (2002) conducted an extensive review of the available literature and found a 1974 passage that might be the origin (or one of them). The quote states that the average adult should consume 6 to 8 glasses of liquid per 24 hours. It also states, however, that this can be from coffee, tea, milk, soft drinks, etc., and points out that fruit and vegetables are also good sources of water. There is also the possibility that the “8×8” rule originated much earlier in a 1945 report from the Food and Nutrition Board of the National Research Council.  They suggested that most adults require about 2.5L of water daily, but that the majority of this will be contained in food. Apparently the latter part of this recommendation got lost…

Peer reviewed studies have indeed shown that caffeinated drinks, and to a lesser extent mild alcoholic ones, can and should count towards a daily fluid intake amount. Given the amount of these beverages consumed by the “average” healthy adult, plus the amount of water contained in solid foods, it is unlikely that most people need to observe the 8×8 rule. It seems more probable that if you consume 2-4 glasses of water a day, in addition to other liquids, you are probably adequately hydrated.

So sangria totally counts towards my liquid intake right?

But what about all those alleged benefits of drinking copious amounts of water?  Some research has shown that individuals who drink larger quantities of water may reduce their risk of certain types of urogential cancers and heart disease. These results, however, display clear gender biases and could only represent correlations and not true causal relationships between the disease and water intake alone. The fact that increased water intake is often associated with changes towards a healthier lifestyle in general should be taken into account.

So how much water should you be drinking? Well it really depends on your lifestyle. If you aren’t out running marathons every day and you eat a well balanced diet that includes fruits and vegetables, you should probably aim to drink 2-4 glasses of water a day, in addition to other beverages. The more active you are, the more you should drink. If you’re thirsty, also drink. If you hate water, try low sugar fruit drinks or increase solid fruit and veg in your diet. But don’t feel like you have to balance all that Coke-zero with equal amounts of H2O.

Kleiner SM. 1999. Water: An Essential but Overlooked Nutrient. Journal of the American Dietetic Association. 99:200-205.
Negoianu D. And Goldfarb B. 2008. Just Add Water. Journal of the American Society of Nephrology. 19:1041-1048.
Valtin H. 2002. “Drink at Least 8 Glasses of Water a Day.” Really? Is There Scientific Evidence for “8 x 8”? American Journal of Physiology-Regulatory, Integrative, and Comparative Physiology. 283:R993-R1004.
http://www.scientificamerican.com/article.cfm?id=eight-glasses-water-per-day
http://well.blogs.nytimes.com/2011/11/07/really-the-claim-drink-eight-glasses-of-water-a-day-to-protect-the-kidneys/
http://www.mayoclinic.com/health/water/NU00283
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Scientific Journal Retractions are Definitely Not on the Rise

A disturbing trend is developing: the number of retractions in scientific journals is increasing at an exponential rate. This article found in the April 16th New York Times  gives a good description of the problem and a couple of its causes. In essence, the pressure to churn out paper after attention-grabbing paper is so high that researchers are more  willing than ever to submit bad or even false work.

Source: Journal of Medical Ethics via New York Times

The number of publications is now one of the major determinants of a researcher’s “worth” at a university. The paucity of tenure-track positions, along with the dwindling number and value of scientific grants and increasing dependence on grants to subsidize salaries, make a well-padded publication list necessary for young and ambitious scientists.

The “publish or perish” mentality isn’t just a reality for new and established professors, as any of my fellow grad students (trying desperately to gain funding) can attest.

The problem with expecting a researcher to produce a steady stream of ground-breaking innovations is that science doesn’t work that way! In fact, most of the time scientific research feels more akin to this:

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The other problem is monitoring and verification. Even though reproducibility is practically the definition of scientific knowledge, re-doing someone else’s experiment doesn’t build your standing in the scientific community or savings account. A surprising number of published results can’t be reproduced, creating a corollary problem to the number of retractions: negative results are rarely published. Undetected false positive results inject falsehoods and confusion into our collective knowledge and damage science’s deserved perception of legitimacy.

So what can be done? University of Virginia Psychologist Brian Nosek‘s answer is the Reproducibility Project, an open collaboration to audit all of 2008’s original research published in Psychological Science, Journal of Personality and Social Psychology, and Journal of Experimental Psychology: Learning, Memory and Cognition.

Are the authors of those studies worried (insulted)? Maybe. Should that dissuade Nosek from trying to improve the scientific reliability and accuracy of his field? Definitely not! Nosek is careful, and correct, to note that failure to reproduce does not necessarily mean the original study is faulty nor that the results are not true, but the overall project results will improve psychology’s accumulation of knowledge.

The continuation of a publication-based reward system that values quantity over quality is eroding the quality of the literature and public faith in science. It’s time for all scientific fields to embrace the honesty and necessity of this type of self-audit. After all the first step of healing is admitting you have a problem.

Also Shown: Published Science vs. Actual Science. Source: xkcd.com/683

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Evolution in Canadian Currency*

Today the world is a little awsomer than it was yesterday. Why? Because the Royal Canadian Mint has been taken over by twelve year olds.

On April 16th (just 4 days!), the mint will release a new quarter design:

Canadians love to put theropods on coins. Pachyrhinosaurus lakustai http://www.mint.ca

But wait. It gets better.

How is that even possible?!?!?

Because:

The skeleton of Pachyrhinosaurus lakustai http://www.mint.ca

It’s a (insert choice of expletive exclamation here) glow-in-the-dark dinosaur skeleton coin!!! That’s right all you other countries, Canada now has photo-luminescent currency.

The only way it could be more like the margins of my grade six math notebook is if it were fighting a series of jet-pack robot pirate dimes.

The design is the first of 4 in a new Prehistoric Creatures collection and only 25000 will be minted. You can purchase them (at a super inflation rate) for $30 from Canada Post outlets or the mint website

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*Seriously, you can track evolution through Canadian coins. The penny is going extinct, we have dinosaurs on our quarters, followed by birds on our $1, mammals on the $2, humans on the $5, and microchips in the future.  Maybe some protozoa on our nickles to even things out?
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Too Hot For Nuts? Warm Winter Hurts Acorn Crop

So? So what. Who cares about acorns.

Um…squirrels…obviously. And the people at this website.

No really, who cares about acorns? I mean, let’s talk about the poor maple syrup harvest, early strawberries, or low water tables – these things are important, not acorns!

As it turns out, ecology doesn’t work that way. This acorn shortage might make you very sick, in maybe the least predictable way imaginable.

20120411-183447.jpg

Our hero possibly?

Have a look at this story from South Coast Today:

Open Season: Expect rise in Lyme disease this year
By MARC FOLCO
Open Season
April 08, 2012 – 12:00 AM
Experts say that this year will be an extremely bad year for Lyme disease in the Northeast but not because of an extreme jump in tick populations (which carry the disease) or the warm winter, but because of a low acorn crop this past fall and the resulting decrease in mouse populations, which feed on acorns. Warm winters can affect tick behavior as they become active a few degrees above freezing, but mild winters themselves don’t typically affect populations, unless it’s due to other circumstances associated with warmer temperatures.

Boom and bust years are typical for acorn production with boom years resulting in the forest floor being covered with them, and bust years with oak trees producing few acorns. This past fall was a bust year, and white-footed mice, which feed on the acorns, had an extremely low winter survival. Without their staple food source, many mice died off through the winter, causing a crash in their population.

The white-footed mouse is also the favorite and most common host of the black-legged tick, which transmits Lyme disease. The ticks need a meal of blood at three different stages — larvae, nymph and adult. So without their favorite restaurant (white footed mice), the ticks will be looking to dine elsewhere.

“This spring, there will be a lot of Borrelia burgdorferi-infected black-legged ticks in our forests looking for a blood meal. And instead of finding a white-footed mouse, they are going to find other mammals — like us,” Richard Ostfeld, a disease ecologist at the Cary Institute of Ecosystem Studies in Millbrook, N.Y., told HealthDay News. Borrelia burgdorferi is the bacterium that causes Lyme disease. It doesn’t affect mice, but can cause Lyme disease in humans, which can cause chronic fatigue, joint pain and neurological problems if it goes untreated.

Ostfeld and other experts predict the surge will begin in May and last until July. A similar boom-bust cycle of acorn crops and mouse populations happened in 2006 and 2007 resulting in numbers of nymphal black-legged ticks reaching a 20-year high. Sportsmen and outdoors people are urged to use precautions, such as wearing insect repellent, long pants and long sleeves when venturing into the woods, and to check themselves carefully for ticks when they get home. The larval stage of the black legged tick is tiny and can go unnoticed if you’re not looking for it.

Lyme disease, in case you’re not up on your arthropod transmitted diseases, it is caused by a bacterial infection that can have serious systemic effects, including long term nerve and joint damage, if left untreated.

So make sure you know who your designated “tick-checking-buddy” is! The CDC has a handy instruction guide on how to do this.

Isn’t that amazing! A shortage of acorns is putting humans at risk! Now I’m just as guilty as everyone else for thinking it, but stories like this remind me that the world isn’t actually split into “human” and “nature” – it’s all nature.

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Everything You Ever Wanted to Know About Tooth Staining and More! (way, waaaaaaay more).

About 3 weeks ago, Lisa asked us why adding cream to your coffee (or milk to your tea for those of us with British heritage) would prevent or reduce staining to your teeth.  When I first started looking into this question I thought there would be no problem finding a straight-forward, highly researched answer. After all, we live in a society that’s clearly obsessed with a whiter smile. When visiting a new dentist this past month, half the questions on the intake sheet had to do with my level of concern over how white my teeth were (turns out I was more concerned by the inability to close my jaw – but it’s good to know someone’s looking out for my aesthetics).

No one's smile is perfect. Doesn't mean you shouldn't share it.

Yet despite all of the commercial interest in whiter teeth (most consumer reports site Americans as spending just over $1 billion on whitening products a year), scientists apparently have better things to research as there is very little in the scientific literature on the causes of tooth staining.  What little research there is tends to focus on the staining of tooth composites – things like resins that are used in crowns or false teeth.

Never fear though! After an exhaustive search (more on the physical than amassing side), we have come up with some extensive great background information on exactly what causes tooth staining that is sure to bore wow you!

Stained teeth look like new! (new what exactly?) royalyorkdental.com

Before you go running off to get the newest, fastest “bleaching kit” to ensure your pearly whites* stay their brightest, you should understand that not all teeth are created equal. In colour that is. In fact, tooth colour not only varies between people, but also on individual teeth. For example, the gingival (gum) margin is usually darker than the rest of the tooth; canine’s are typically darker than the central teeth; younger people have lighter teeth;  and due to differences in lighting your teeth can change colour throughout the day!

But tooth discolouration does exist, and it can be classified based on if it’s caused by intrinsic or extrinsic factors.

Intrinsic discolouration results from changes to the actual dental tissue.  While ‘normal’ tooth colour is determined by the pigments of the enamel and dentin, metabolic diseases and systemic factors can affect the developing dental tissue, resulting in changes to tooth colour.

Extrinsic factors are those that cause staining to the tooth after development, from things like food or metals. Many foods contain organic chromogens which impart the natural dark pigment you see in coffee and red wine. Unfortunately, chromogens can be easily incorporated into the outer layer of the tooth (the pellicle) resulting in staining. The more often you drink, the more staining you see.

Tannins are a related group of large polyphenols found in a bunch of plant extracts – including coffee, tea, and red wine – that readily bind to proteins. In fact, binding to proteins is how tannins got their name – tree bark solutions rich in these molecules were used to tan leather back in the days of yore. The teeth in your mouth are covered in a thin layer of protein, the pellicle, which will bond to tannins in coffee and tea and cause tooth staining. Chromogens can also bind to tannins, increasing the chance of staining.

As a grad student who’s diet consists of vast quantities of coffee, tea, and red wine, this is distressing news for my smile.

Munsell colour rating of 10YR 3/6.

So what if you add milk or cream to your coffee?

You might remember from our brief explanation of why old milk curdles in coffee that dairy proteins, such as casein, bond to tannins and other phenolic compounds in tea and coffee. In the same way that the protein-tannin bonds reduce the astringency (the “fullness” of tea, coffee, and red wine, caused by tannins binding proteins on the inside of your mouth), it also limits the number of free tannins available to bond with your tooth pellicle. I couldn’t find a study that compared the binding kinetics, how fast and tightly the binding occurs, of dairy and pellicle proteins, but considering the amount of time the tannins have to interact with the milk versus the pellicle, I’d say it’s a safe bet that few tannins that pass through your mouth release the bonded dairy proteins in favour of your teeth.

In fairness, there are some gaps in the evidence, but the logic train goes like this: tannins in coffee and tea bind to the pellicle and cause tooth staining, dairy proteins found in milk and cream readily bind to tannins, tannins bound to dairy proteins will be unavailable to bind to your teeth, so adding milk or cream to coffee and tea reduces tooth staining.

Unfortunately, because not all tannins will bind with the cream, and because the chromogens will still stain your teeth, the only way to avoid tooth discolouration is to completely forgo that cup of java. But really, who’s gonna go that far?

Thanks for the question Lisa! As always, we love getting your comments. Please take a moment to ask your own question or say what you think about this or any other article!

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*Ever notice how pearls aren’t actually all that white? Also how they’re iridescent? What if you really like black pearls???
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