Biggest science or math pet peeve

[JaredJames]

(which for some inexplicable reason Americans & Brits seem to be so attached to).

To be fair for the UK, imperial isn't taught in schools, metric is. It's uncommon to come across imperial units used without a metric equivalent stated with it in everyday life (driving excluded). I'd say there's a definite effort to do away with imperial.

Generally, it's only the (heavy industry?) products which haven't changed much over time that seem to maintain the imperial sizes, such as beam sections, pipe fittings etc. Even in those cases, there are a lot of far cheaper metric equivalents available.

In my job, it's usually only because we need a very specific product that's only been made in imperial for many years, or because some old boy in charge of a project has always done it that way and breaks out in a sweat anytime progress approaches.

 

[Student100]

Three dimensional diffusion does require NO energy when modeled in two dimensions.

Then I stand corrected.

 

[Bystander]

Then I stand corrected.

... but, there are no two-dimensional biological systems.

 

[jtbell]

My pet peeve is teaching the Bohr model of the atom too seriously, that is, going through the full math of deriving the hydrogen energy levels, speed of the electron in a circular orbit, etc. Students just have to unlearn it all a few lectures later when they start real quantum mechanics.

I discuss Bohr's model mostly only as part of a brief qualitative history of atomic theory. The only quantitative thing I take from the Bohr model is the discrete energy levels, which I present as being strongly suggested by the empirical Rydberg formula for the wavelengths of the hydrogen spectrum, and the Planck formula E = hf. The actual derivation of the energy levels from first principles has to come from solving Schrödinger's equation, of course.

 

[StatGuy2000]

To be fair for the UK, imperial isn't taught in schools, metric is. It's uncommon to come across imperial units used without a metric equivalent stated with it in everyday life (driving excluded). I'd say there's a definite effort to do away with imperial.

Generally, it's only the (heavy industry?) products which haven't changed much over time that seem to maintain the imperial sizes, such as beam sections, pipe fittings etc. Even in those cases, there are a lot of far cheaper metric equivalents available.

In my job, it's usually only because we need a very specific product that's only been made in imperial for many years, or because some old boy in charge of a project has always done it that way and breaks out in a sweat anytime progress approaches.

So you Brits are on the right side of history and embracing progress after all! (well, apart from the whole Brexit issue, that is, but that's a whole different debate in another thread)

So all of you Americans, get with the program! Go metric!

 

[Student100]

So all of you Americans, get with the program! Go metric!

We wanted to rename French fries freedom fries. We aren't adopting the meteric system anytime soon. :)

Maybe we'll define our own base ten system!

 

[epenguin]

I don't peeve at the way notation and what's around it is often pedantically precise and teachers fuss about it, which I don't think students mind all that much because 'if there are rules you know where you are' - it can be actually reassuring, helpful, necessary.

Rather I peeve at the combination of this with a slangy inconsistency. A pet peeve is expressions like sin²x . It makes no sense – sin² is not an operator. We have to think of the weaker students and I have come across some who couldn't get their heads round this.

But after nearly a lifetime of subliminal peeve I suddenly realized a reason for it whilst writing this post! Agreed that it should be (sin x)² which is unambiguous, that's alright in writing. But when talking e.g. in lessons 'sine of x squared' or 'sin x squared' would be easily confused with sin x². And I expect more errors would creep in when writing (sin x)² through omission of the brackets for carelessness, distraction or other reason, which we often see here. So a price is paid but maybe we gain overall from this illogicality.

So I'll change my peeve - I'm peeved that nobody ever gave me this justification.

Is it only me?

 

[f95toli]

So all of you Americans, get with the program! Go metric!

To be fair, USA was one of the first countries to adopt the metric system (late 19th century?); it has just taken them a while to get used to it...

All primary and secondary standards etc. ARE metric in the USA and if you deal with people at NIST they only use the metric system. If you want something calibrated in imperial units you have to start use a metric standard and then multiply by a defined constant (which is why the 1 inch=25.4 mm is exact by definition)

 

[epenguin]

And then there's the AM and PM business. If you grew up with it, it's very natural. But take it from me, somebody who has never grown up with this finds this very confusing. Something like 16:00 is a lot easier for me than 4pm.

And then there is no year 0. They just skip from 1 BC to 1 AD. Why not calling it 1 BC and 1 AC anyway...

And then for math. The notation $A\subset B$ should be outlawed. It makes no sense. Use $A\subseteq B$ instead.

I think the notation $f^{-1}(x)$ and $f^{-1}(B)$ is also very confusing. I would have preferred very much if they would have used another notation there such as $f^{\leftarrow}(B)$ or $f^*(B)$. I think it's a missed opportunity. Of course I know it's not going to change now. But come on, $\sin^{-1}(x)$ and $\sin^2(x)$ following very different conventions, that's messed up.

Also sad is the discrepancy between exponentiation $x^y$, function spaces $A^B$ and logical implication $p\Rightarrow q$. They should have invented a uniform notation for these since they're special cases of the same thing, really...

I don't like the $\text{ln}(x)$ notation either. No professional mathematician uses this anymore. I don't get why they still teach this in high school.

The notation $\mathbb{Z}_p$ for integers modulo $p$ is very unfortunate too.

And why are there authors mixing up $f\circ g$ and $g\circ f$? Sure, it might have been a historical mistake to let $(f\circ g)(x) = f(g(x))$, but please do use it in your books.

I just commented on one thing you mention. But I don't agree with you on the convention for f^-1.

This convention of indices to functions to indicate the repeated application is very convenient and, because with caveats you can validly add the indices just as you can when multiplying something raised to a power. That is f(f(f(x))) can validly be written f³(x) and this is the same as , f(f(f(x))) and as f(f²) and f²(f(x)). You can just do an algebra with the operators themselves, and fⁿf^m = f^n+m. This algebra is validly extended to negative indices representing the inverse operation, and it is generally true that f^-1f(x) = ff^-1(x) = x. The caveat would be that x is not necessarily the only value of f^-1f(x).

 

[ShayanJ]

The most tragic thing in science education, is the way some teachers/university professors think about education. My pet peeve is teachers/professors that don't seem to understand the golden rule of education:

 

[StatGuy2000]

We wanted to rename French fries freedom fries. We aren't adopting the meteric system anytime soon. :)

Maybe we'll define our own base ten system!

The whole "freedom fries" farce was based on a knee-jerk response to France (and other European countries, plus Canada) being opposed to the second Bush Administration's war in Iraq. I don't believe most Americans really wanted to rename French fries "freedom fries". Btw, French fries may not even be French, but may actually be of Belgian or even Spanish origin! Consider the Wikipedia article below.

https://en.wikipedia.org/wiki/French_fries#Culinary_origin

And Americans not adopting the metric system (at least in common usage) only shows their stubbornness.

As a totally unrelated aside, there is a history in the US of renaming foods due to political events at the time. For example, during World War I, there were attempts to rename various foods of German origin (e.g. sauerkraut to "liberty cabbage", hamburger to "Salisbury steak"). These never really stuck except for hot dog (which had been referred to as "wiener" or "frankfurter" in the past), although in this case, the term predates WWI.

 

[gmax137]

One of my pet peeves involves temperatures: when people say things like, "it's 40 degrees outside now, that's twice as hot as last night when it was 20..." Unless we are using an absolute temperature scale that is complete nonsense. I've even seen percentages used in comparisons (100 degrees is 80% of 125). Arrgh...

 

[PeroK]

If a good mathematician wants to write $a + b \times c \div d$ in a clearer fashion, then there is no other way than:

$a+\frac{b\times c}{d}$

That is the only way it can be read. Maybe novice mathematicians prefer the second way, but it doesn't make the first one more ambiguous.

It's like saying everybody should write or say "do not" instead of "don't" while using the english language because it is clearer to people only having a basic knowledge of the language. I don't know why these contraction rules exist (and they make no sense grammatically, at least to me), but they do and once you know them, it is all perfectly clear. Although, when speaking the language with a bad accent (or not having a good hear when you listen), "can" and "can't" can be confusing and if the negation is really important, one would prefer saying "cannot".
Isn't the answer -53.3333 ? It all seems clear to me. Not even a single doubt ... because I follow the rules.

I can even see how adding brackets would make it clearer? I think it would look worst:

(((((6 + 3) - (1 / 3)) + (1 * 0)) - (4^3)) + (1 x 2))

And I was kind enough to use spaces. Imagine the nightmare of debugging when coding something like that in computer programs. When I do something like that in coding - to make sure I don't mismatch brackets - I do the following:

(
    (
        (
            (
                (6 + 3)
                - (1 / 3)
            )
           + (1 * 0)
        )
        - (4^3)
    )
   + (1 x 2)
)

Just awful! Thank God, no computer programs require brackets and don't understand PEMDAS. But I agree that space make it much better and clearer to use:

6 + 3 - 1 / 3 + 1 * 0 - 4^3 + 1 x 2

Or even better:

6 + 3 - 1/3 + 1*0 - 4^3 + 1x2

But if we decide to imply that spaces replace brackets as a rule instead of PEMDAS, it would be way more confusing. Imagine those two equations:

6 + 3-1 / 3 + 1 * 0-4^3+1 x 2
6+3 - 1/ 3+1 * 0 - 4^3 + 1 x 2

What the heck would that mean?

What's wrong with simply?

(6+3) + (-1/3) + (1*0) + (-4^3) + (1x2)

All those extra brackets are not needed not because of PEMDAS but because addition is associative. If you give up PEMDAS you do not lose the associativity of addition or muliplication as many of you seem to assume!

Also, teaching students to parse a mathematical expression as though they were a C++ compiler is not a good idea.

What would a C++ compiler make of:

$ax^2 + bx + c$

That has a meaning in mathematics that it does not have in C++.

 

[PeroK]

And if we view the above in the context of programming languages (such as C, C++, C#, Java, etc.), we should do this:
$$((((3\cdot x)\cdot x) + (5\cdot x)) + 7) = 9$$
The assignment operator, =, has a precedence lower than almost all of the other operators. If we ignore the precedence rules, sort of akin to ignoring PEDMAS, we would need to use another pair of parentheses around the entire expression on the left.

I'm being a bit facetious, though, as the above wouldn't qualify as an assignment expression ...

That's writing it where you have lost the associativity of addition and multiplication. Also, PEMDAS does not have a monopoly on a simple rule for subscripts and superscripts, nor on a simple convention for the interpretation of a quadratic expression:

$ax^2 = a(x^2)$ and $ax + b = (ax) + b$ would be basic rules in any convention.

One specific example where PEMDAS appears not to work is:

$\sqrt{x + y}$

PEMDAS says "exponent before addition", but in this case it is not possible. You have to do the addition first, regardless of any convention.

For me, it's the understanding of what is and is not associative, what does and does not distribute that leads to my ability to manipulate algebraic expressions. I certainly never have parsed them like a C++ compiler according to some set typographical rules.

 

[Mark44]

,

And if we view the above in the context of programming languages (such as C, C++, C#, Java, etc.), we should do this:
$$(((3\cdot x)\cdot x) + (5\cdot x) + 7) = 9$$
The assignment operator, =, has a precedence lower than almost all of the other operators. If we ignore the precedence rules, sort of akin to ignoring PEDMAS, we would need to use another pair of parentheses around the entire expression on the left.

That's writing it where you have lost the associativity of addition and multiplication.

What I wrote was the example from micromass. Here's the same example with several pairs of parentheses removed. It should solve the problem of associativity of multiplication and of addition that you mentioned.
$$((3\cdot x \cdot x) + (5\cdot x) + 7) = 9$$

Also, PEMDAS does not have a monopoly on a simple rule for subscripts and superscripts, nor on a simple convention for the interpretation of a quadratic expression:

$ax^2 = a(x^2)$ and $ax + b = (ax) + b$ would be basic rules in any convention.

One specific example where PEMDAS appears not to work is:

$\sqrt{x + y}$

No, it doesn't fail here. The vinculum, the bar over the sum, plays the same role as a pair of parentheses, grouping the x and y terms.
If the above were written as √x + y (i.e., with no vinculum), then it's not a failing of the convention -- it's just poorly written, if the intent was to take the square root of the sum.

In ordinary situations (x and y being real, and x + y being nonnegative, $\sqrt{x + y}$ has the same meaning as $(x + y)^{1/2}$. The parentheses force the lower-precedence addition to be performed before the exponentiation.

PEMDAS says "exponent before addition", but in this case it is not possible. You have to do the addition first, regardless of any convention.

For me, it's the understanding of what is and is not associative, what does and does not distribute that leads to my ability to manipulate algebraic expressions. I certainly never have parsed them like a C++ compiler according to some set typographical rules.

 

[TeethWhitener]

And why are there authors mixing up f∘gf\circ g and g∘fg\circ f? Sure, it might have been a historical mistake to let (f∘g)(x)=f(g(x))(f\circ g)(x) = f(g(x)), but please do use it in your books.

The notation for function composition gives me all sorts of problems. It's just ugly. Given:
$$A \xrightarrow{f} B \xrightarrow{g} C$$
we can compose $f$ and $g$ to get:
$$A \overset{g \circ f}{\longrightarrow} C$$
No bueno.

 

[JaredJames]

One of my pet peeves involves temperatures: when people say things like, "it's 40 degrees outside now, that's twice as hot as last night when it was 20..." Unless we are using an absolute temperature scale that is complete nonsense. I've even seen percentages used in comparisons (100 degrees is 80% of 125). Arrgh...

I didn't know that. Interesting one.

I'd say worse than that is swapping from Celsius for cold and Fahrenheit for hot, sometimes without even using units. Always in the newspapers like that.

 

[late347]

Two elevated to the third power. In which the exponent three itself, is raised to the fourth power. And the exponent four is raised to the power of three.

That was one of our homework problems in college. I was scratching my head about the order of operations with that calculation.

My intuitive guess would have been to start calculating from the innermost(uppermost) exponent and work your way with calculating down and left.

Inbfact it seems so confusing you cannot write that in latex code.
$2^3^4^3$

 

[PeroK]

,

No, it doesn't fail here. The vinculum, the bar over the sum, plays the same role as a pair of parentheses, grouping the x and y terms.

It seems to me that expressions can be grouped together in several ways (in addition to parenthesis) and essentially the simple rule suggested by PEMDAS is not so simple.

 

[Mark44]

Two elevated to the third power. In which the exponent three itself, is raised to the fourth power. And the exponent four is raised to the power of three.

That was one of our homework problems in college. I was scratching my head about the order of operations with that calculation.

My intuitive guess would have been to start calculating from the innermost(uppermost) exponent and work your way with calculating down and left.

Inbfact it seems so confusing you cannot write that in latex code.
$2^3^4^3$

Sure you can - you just have to use braces.
$2^{3^{4^3}}$

Here's the LaTeX I used:
$2^{3^{4^3}}$

 

[late347]

Sure you can - you just have to use braces.
$2^{3^{4^3}}$

Here's the LaTeX I used:
$2^{3^{4^3}}$

Where should you start to calculate according to pemdas rule?

 

[micromass]

Where should you start to calculate according to pemdas rule?

From top to bottom. What's on the top must be computed first.

 

[micromass]

It seems to me that expressions can be grouped together in several ways (in addition to parenthesis) and essentially the simple rule suggested by PEMDAS is not so simple.

Sure, if you're going to misrepresent PEMDAS, then it's very easy to show that it doesn't work.

 

[Mark44]

It seems to me that expressions can be grouped together in several ways (in addition to parenthesis)

Offhand, I can't think of any other grouping mechanism, other than the bar that I mentioned, which is also used in typesetting to separate the numerator from the denominator, as in
$$\frac {3 + 4} {8 + 6}$$
The P in PEMDAS and the B in BODMAS refer to any enclosing symbols, including parentheses, brackets, braces, single or double vertical bars (as in |x + y| and $||\vec{x} + \vec{y}||$).

and essentially the simple rule suggested by PEMDAS is not so simple.

Can you provide an example where it doesn't?

 

[Mark44]

the simple rule suggested by PEMDAS is not so simple.

PEMDAS/BODMAS is a piece of cake in comparison to the precedence rules of programming languages.

In the Microsoft documentation for C++ operator precedence and associativity (https://msdn.microsoft.com/en-us/library/126fe14k.aspx), there are 18 groups, several of which list 10 or more operators.

 

[gmax137]

I thought the original peeve was the way people fixate on this PEMDAS "rule" and spend all their energy on it, rather than learning something about numbers or mathematics. If so, it seems the thread proves the point...

Tying in the associative property is worthwhile, but it seems there would be more direct ways to bring that up in class.

 

[clope023]

Calling Entropy 'disorder'.

That and the religious dislike of rote learning and memorization.

 

[micromass]

I thought the original peeve was the way people fixate on this PEMDAS "rule" and spend all their energy on it, rather than learning something about numbers or mathematics. If so, it seems the thread proves the point...

Tying in the associative property is worthwhile, but it seems there would be more direct ways to bring that up in class.

Order of operations is important to teach in the classroom. The students need to evaluate the expressions in the right way. They need to do $6x^2 +5x + 7$ correctly. This means evaluating the square first, then the multiplications and then the additions. The students need to be given clear rules on how to do this.

Sure you can say that people will need to use their own judgement and that the typesetting dictates how it will be read. But that is for us experienced mathematicians. We have no problem with this. But for novice students, they need to be taught how to evaluate expressions correctly. If you're not spending time on this, then they will end up very confused. Take it from somebody who taught mathematics to young students: this is important.

 

[Mark44]

That and the religious dislike of rote learning and memorization.

+1

 

[jack action]

What's wrong with simply?

(6+3) + (-1/3) + (1*0) + (-4^3) + (1x2)

All those extra brackets are not needed not because of PEMDAS but because addition is associative. If you give up PEMDAS you do not lose the associativity of addition or muliplication as many of you seem to assume!

Absolutely nothing is wrong with that equation. The fact is that somehow, somewhere, somebody created a set of rules to further simplify the parenthesis use. @Mark44 gave you a lot of examples of these rules and in your equation, according to PEMDAS, all your parenthesis can be implied.

For some reason that I don't understand, you seem to refuse recognizing the validity of those rules.

This is like if I was saying $a^3$ can too easily be mixed up with $a3$ which means $a \times 3$, hence, exponents shouldn't be thought in classroom and we should all write $aaa$ to make it clear to everyone.

You know what? $aaa$ is not really clear either. What is the sign implied in between variables? Is it addition, subtraction, multiplication, division or even a mix of any of those? Who knows? How can we know for sure?

What's wrong with simply writing:

$a \times a \times a$

There, now it's clear! No ambiguity, since multiplication is associative!