# Why Biology Students Have to Learn Calculus

Have you ever found yourself sitting through required college courses, thinking, “I’m a [major] Major, dangit, so why am I sitting through this [seemingly unrelated] class! I’ll never use this [actually valuable] information later!”

As a major in a biological science, I heard a lot of fellow bio majors gripe about the calculus requirement. (I happen to love math, so taking math classes didn’t bother me.) There are a lot of reasons why you’re required to take those “useless, required” courses in college: you should be a well-rounded student; you might find that you enjoy a different field than what you’re majoring in; learning new subjects helps your brain to grow and mature; etc.

But apparently there is a new reason: so you don’t waste your time reinventing basic calculus. Case in point, this paper:

A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves

(If you are not laughing your ass off right now, you may have slept through math class too many times.) Published in 1993 (yes, in the 20th-fucking-century) in a biology journal. Do you think if this person took a basic calculus class in college, they would’ve written a paper on how to figure out one of the fundamental concepts of calculus?

According to the abstract:

In Tai’s Model, the total area under a curve is computed by dividing the area under the curve between two designated values on the X-axis (abscissas) into small segments (rectangles and triangles) whose areas can be accurately calculated from their respective geometrical formulas. The total sum of these individual areas thus represents the total area under the curve. Validity of the model is established by comparing total areas obtained from this model to these same areas obtained from graphic method Gess than ±0.4%).

(Emphasis mine.) What a concept–you calculate the area under the curve by using shapes, and calculating the area of the shapes. (Of course, that assumes that you know basic algebra and trigonometry–I’m not sure we can make that assumption.) Genius! If we would’ve had this method around in the 17th century, just think of how advanced our society could be right now! (Before the “Tai Model,” the way that people calculated the area under a curve was physically cutting out the graph and dropping it into a tub of water, then running out naked screaming, “Eureka!” Right?)

It gets better.

Other formulas widely applied by researchers under- or overestimated total area under a metabolic curve by a great margin.

Seriously? Other researchers have no clue what an integral is? (Take a look at the number of times this paper has been cited for another laugh–even up through 2013.)

Fellow life science majors, this is why you need to take math classes, so that you don’t “invent” a centuries-old formula and then name it after yourself. On that note, is there some sort of formula to calculate the number of rotations that Newton and Leibniz (and every high school math teacher) have taken in their graves? (Note: there is likely no such formula, and thus I will invent one and call it “Mary’s Postulate.” Muhaha.)

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### Mary

Mary Brock works as an Immunology scientist by day and takes care of a pink-loving princess child by night. She likes cloudy days, crafting, cooking, and Fall weather in New England.

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1. Actually, this scares the living befuckingjesus out of me. Next thing will be, each lab has to prove with 100 patient samples that the method works, and keep the results on file for the auditors. I fucking shit you not.

1. Sorry, the befuckingjesus hasn’t been scared out of me, though it wasn’t in me to begin with… How many patient samples do you think you would need to prove a method to work? How much variability could there really be where you couldn’t prove a method to work with 100 intelligently selected samples that had the best variability (especially with everything we know and could monitor before prescribing a particular method)? I mean, if your “medicine” could be audited, that must mean you would also get to call on the “full spectrum of treatment options” instead of just developing some miracle pill that works without any prior knowledge of a particular individuals category. It seems by this point there would be sufficient knowledge to do that sort of thing.

1. Also, why would keeping all of your results be a bad thing? Why would you ever get rid of scientific data? Even if your method was corrupted by human errors or you started with incorrect testing procedures, why would you ever get rid of it, especially now that a terabyte of storage is about \$100 and labeling what was flawed or what didn’t contribute and what did contribute to your conclusions would be extremely easy?

2. Also, why would keeping all of your results be a bad thing? Why would you ever get rid of scientific data? Even if your method was corrupted by human errors or you started with incorrect testing procedures, why would you ever get rid of it, especially now that a terabyte of storage is about \$100 and labeling what was flawed or what didn’t contribute and what did contribute to your conclusions would be extremely easy?

3. Also, why would keeping all of your results be a bad thing? Why would you ever get rid of scientific data? Even if your method was corrupted by human errors or you started with incorrect testing procedures, why would you ever get rid of it, especially now that a terabyte of storage is about \$100 and labeling what was flawed or what didn’t contribute and what did contribute to your conclusions would be extremely easy?

1. Unless you were trying to cover up something that was illegal…

2. Boy, that escalated quickly.

1. What was the point I missed? Maybe he was being sarcastic and I didn’t pick up on it? I had a genuine question, I wasn’t trying to be hostile…

2. We (or at least, I) were making light of the fact that something as fundamental to math as “integrations” could be unknown to other biotech scientists (for example, the ones who cited this paper as recently as 2013), and thus they would need a sample size to “prove” the theory.

4. Jakob, in the event you aren’t a POE or trollish idiot, but are genuinely confused, I’m going back to your first real comment (the earlier one being a throw-away snipe or a joke itself), and will try to explain it to you. The data (patient samples) you refer to are confirmation of a mathematical method (integral calculus) independently derived by Newton and Leibniz over 300 years ago. That the area under a curve can be computed as the limit of successive finer scale approximations based on the sums of the areas of rectangles (or triangles or any other geometric shape) is based on the methods first discovered by Eudoxus and Archimedes (hence the bathtub reference) in the 4th and 3rd centuries BCE. There is no need to confirm this with experimental data any more than there is need to confirm that if you take two beans and add two more beans, you have four beans* before you can use arithmetic in a scientific paper.

If you are a student who has not yet studied Calculus, you might not know that, but for any scientist or journal editor to be unfamiliar with it is unforgivable. Hence the mockery.

* Baldrick’s Theorem

1. You are far kinder than me ;)

2. Buzz, I thought Baldrick’s Theorem was that “2 beans plus 2 beans equals some beans”? Works for me…

2. Mary – “Boy that escalated quickly”.

Well, not really, if you read what he said and then read what I said, its kind of a smooth flow… Perhaps your taking it as if I was being hostile? I wasn’t trying to attack, just trying to clarify something I didn’t understand. When he said, “each lab has to prove with 100 patient samples that the method works, and keep the results on file for the auditors.” that kinda sounds reasonable if you account for intelligently selecting the 100 samples to test (as in these aren’t random samples, but samples that are deliberately spread out along the spectrum of variation that your hypothesis is testing) and the basic idea that you never ever delete your data since its so easy to store and would be vital to building up the knowledge base of science and so specifying that keeping results (under any circumstances) would be a pain, doesn’t make sense unless you look for other explanations and the only one I was able to come up with is if you’re trying to hide from the legal punishment.

1. But it was just based on a joke. This is really the wrong thread to discuss the ins-and-outs of pharma regulations and procedures.

1. That’s a good point, I just randomly stumbled on this post and saw something that didn’t look right, so I commented. There’s probably a much better forum out there with a lot better information on pharma regulations, though you do have a public blog and you are in a highly technical field and so kinda voluntarily signed up to be a public intellectual (especially when you post things that bash other intellectuals) and so would hopefully not be posting incorrect information for laymen to read and get the wrong impression. I’m not an expert on pharma, but I do have ‘some’ idea of the basics of how science works, so I wanted to ask.

1. I’m not exactly bashing “intellectuals” here. But OK if you say so.

1. Well, your article was all about how other biotech experts were stupid for not knowing something in Mathematics.

2. Anyone who is a scientist and doesn’t know basic high school math isn’t much of an “expert” in my book.

3. Mary – “We (or at least, I) were making light of the fact that something as fundamental to math as “integrations” could be unknown to other biotech scientists (for example, the ones who cited this paper as recently as 2013), and thus they would need a sample size to “prove” the theory.”

I guess I can understand what your saying about having to “prove” a mathematical theory with sample sizes since math isn’t a physical phenomenon, I’m actually very interested in learning about proofs in Mathematics, have you ever studied them?

I suppose the part that really threw me was when you said you completely knew what he was talking about because you work in pharma, which is definitely not pure mathematics, and so would hopefully have its theories verified through the testing of samples (which gets back to my point about having the full spectrum available, instead of developing a miracle pill that works without any prior knowledge of a particular individuals category) and so not verified through mathematics alone, I’m assuming.

1. BUT MARY! I must explain why you’re wrong. Just listen to me explain to you in length why you’re wrong!

1. Calling it a semantic stop sign doesn’t meant that you aren’t missing the point.

1. Using a semantic stop sign to dodge the point about being a public intellectual means you are avoiding my point.

1. “I’m not exactly bashing “intellectuals” here. But OK if you say so.”

Also, heh, I don’t think she’s the one avoiding the point here, buddy: You missed the point AND the joke and you just. won’t. drop. it.

2. And what is up with throwing out a not often used logical fallacy as a way to prove a point that doesn’t even exist?! How is that going to help get your point across? TALK ABOUT A SEMANTIC STOP SIGN, man.

1. Wow. My eyes glazed over after your FIRST rant. O_o

IT WAS A JOKE. Why can’t you just admit you missed the joke and got really wrapped up in your idea that someone was saying something wrong on the internet?!

4. Mary, I apologise for taking this matter so lightly. After all, somebody from the FDA may see this thread. Something this important should be tested with at least 100,000 patient samples. Data for each quintile, decile and percentile should be stored in separate cohorts. Perhaps a new ISO is required.

That was easy. Next, mandatory testing of the law of gravity prior to each aircraft flight.

1. Shh, delete ALL THE DATA before the auditors find out!! Muahaha NOBODY WILL EVER KNOW!

1. Well, there’s a lot of bad science that gets done, especially in pharma, and as someone who is learning, I was wanting to know what you were talking about since it didn’t seem correct to me. Also, extending my argument to absurdity doesn’t actually disqualify it in this situation, if you go back and read the whole conversation, you will see what I mean.

1. you’re the one that extended your “argument” to absurdity. I mean seriously, it is getting pretty absurd right now.

I’m pretty sure Mary knows how to read.

2. Data? I have no data. At present I would simply use the Trapezoid rule and cite one of the references in tdsmith’s post below.
Just because the FDA may have its head up its ass does not mean that we have to – yet.
I weep for the future though.
Thanks to Jacob for the astute observation that the only cost involved in repeated obsessive and redundant experimental verification of a well known mathematical formula is a hard drive.
It’s no wonder the cost per head of healthcare in the US is more than twice that in the rest of the OECD and yet we seem to be hell bent on copying the same regulatory framework.

5. The follow-up letters and Tai’s response are also quite amusing: http://www.math.uconn.edu/~kconrad/math1131f13/handouts/taicomments.pdf

Calculus curricula don’t make an awful lot of sense to me. I’m a biomedical engineer. Understanding the principles of derivatives and integrals is important to my work; integrating arcana by hand with demi-magical memorized rituals is not. I think most students would be better off if we taught applications more than antique methods.

1. I was a biomedical engineering major too! But now I work in Immunology.

I agree with you that there should be a course like “Math for Biology Majors.” In the lab, I use mostly statistics, but there have actually been a few times where I have needed to use advanced algebra (extrapolation or solving for x) and trigonometry.

6. Although we knew Calculus, “in the old days” of chart recorders, my group used the “Chemists’ Method of Integration”. Print the plot on graph paper; cut it out and weigh it. Then weigh a known # of squares. Boom! A complex function, integrated in a minute or so.

1. Nothing wrong with that!
A slightly later method used an analog circuit to convert voltage to frequency, so the area under a peak was proportional to the number of cycles on the integration trace.

7. I have a theory: this person does, in fact, understand basic calculus to know when they are reinventing integrals. However, they have noticed that nobody else in the field seems to use, understand, or even have heard of integrals. Seizing an opportunity, they write up a basic description of integral calculus, and bank on the hope that none of the editors or peer-reviewers will have remembered it well enough to see it as the rehash that it is. This turns out to work, and this person gets to go down in history for reinventing the wheel.

I honestly can’t tell if I’m being optimistic or pessimistic here.

1. Whoa, there, buddy! I own the copyright on “reinventing the wheel”. You’ll be hearing from my lawyers.

8. But you’ve got to admit, that was pretty clever of Tai to work that out all on her own, with no help from maths teachers or text books or anything. She could go far.

9. I do get the joke, however I find I have to ask what I feel was an obvious question: what’s the function that you’re suggesting they integrate in lieu of this approximation? Because you can’t actually perform standard first-year college-prerequisite integration on an unknown function.

1. The method she proposed was the same one that was invented in the 17th century. Or do you think people used calculators back then?

2. Matt, the formula is on page 2 of the reference linked by tdsmith above – see the comment by Wolever? Near the end.

Sigma from i=1 to n of ti(xi+xi+1)/2

10. It’s not even really calculus. Wolfram claims (without a citation) that the Ancient Greeks used the trapezoidal rule, and the Babylonians may have. The Greeks certainly did more sophisticated things than this with quadrature.

So Dr. Tai was scooped by 2500 years. On the other hand, that may well be a record.

11. One other comment; Tai’s paper was published in a journal with impact factor of 8.1, and has been cited by many many others. (Those of you who’ve taught pre-meds won’t be surprised that most medical researchers seem to have slept through grad-school math.) By most metrics used to evaluate the scientific quality of published work, this paper is a resounding success. Scary.

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