Biggest science or math pet peeve

[fresh_42]

What's wrong with simply writing:

$a \times a \times a$

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

... well, it depends ...

 

[micromass]

... well, it depends ...

Well, you just need power-associativity.

 

[PeroK]

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

For the reason that the rules cause ambiguity. This is evidenced by the fact that the two Microsoft calculators gave different answers for the same expression. And that 76% of the population gave the "wrong" answer.

If 76% of the population can't do basic arithmetic - and unfortunately that includes me - then maybe the rules are a bit obscure?

I also question whether these rules help or hinder maths education - a question apparently I'm not at liberty to ask.

I did Dr Peter Price a disservice in a previous post. He was responsible for the 76% survey and, although he is a supporter of PEMDAS, this caused him at least to question the status of these rules, if so few people know them.

Are you really denying my inalienable human right to have a pet peeve? Must I kowtow to the sacred cow that is PEMDAS?

 

[micromass]

For the reason that the rules cause ambiguity. This is evidenced by the fact that the two Microsoft calculators gave different answers for the same expression.

And how exactly would calculators be programmed without PEMDAS? How would the removal of PEMDAS over some other convention like white spaces by beneficial here?

And that 76% of the population gave the "wrong" answer.

Also 60% of the US population says the evolution is false or is not sure about it.
Also, this http://blog.sciencegeekgirl.com/2009/11/09/myth-because-the-astronauts-had-heavy-boots/
Referring to the ignorance of the total population isn't really helpful.

 

[S.G. Janssens]

Referring to the ignorance of the total population isn't really helpful.

I thought this is the principle behind national elections?

 

[micromass]

I thought this is the principle behind national elections?

Sadly...

 

[PeroK]

And how exactly would calculators be programmed without PEMDAS? How would the removal of PEMDAS over some other convention like white spaces by beneficial here?
Also 60% of the US population says the evolution is false or is not sure about it.
Also, this http://blog.sciencegeekgirl.com/2009/11/09/myth-because-the-astronauts-had-heavy-boots/
Referring to the ignorance of the total population isn't really helpful.

I'm not the only one:

http://www.math.harvard.edu/~knill/pedagogy/ambiguity/

This issue is not as clear cut as many of you would like to pretend.

 

[PeroK]

There may be more on this forum but the brow beating I've taken would deter most from uttering a word in my defence!

 

[micromass]

I'm not the only one:

http://www.math.harvard.edu/~knill/pedagogy/ambiguity/

This issue is not as clear cut as many of you would like to pretend.

Again, how would the removal of this rule be beneficial in programming?

 

[S.G. Janssens]

There may be more on this forum but the brow beating I've taken would deter most from uttering a word in my defence!

No, I agree with you on this, but I have other peeves to pet

 

[PeroK]

Again, how would the removal of this rule be beneficial in programming?

Programmers would have to tighten their syntax rules. That may be no bad thing. An over reliance on obscure and complicated rules of precedence might be deemed poor programming practice.

I wonder how uniformly implemented the current rules are, in any case.

 

[micromass]

I also question whether these rules help or hinder maths education - a question apparently I'm not at liberty to ask.

No, please do address this. I'm interested how you would teach this to children. How would you teach children to evaluate $2p+3q$?

 

[ShayanJ]

There may be more on this forum but the brow beating I've taken would deter most from uttering a word in my defence!

Its not "the brow beating" that you've taken, but that this doesn't seem to me as black and white as its being implied by this discussion. It seems to me that those rules are like Bohr's model for arithmetic. They seem important for educating children but you should get rid of them as soon as possible, i.e. when you're sure the children have the intuition about algebra(cases mentioned by micromass that imply we seem to use some rules there) that we grown ups have now.

 

[micromass]

Its not "the brow beating" that you've taken, but that this doesn't seem to me as black and white as its being implied by this discussion. It seems to me that those rules are like Bohr's model for arithmetic. They seem important for educating children but you should get rid of them as soon as possible, i.e. when you're sure the children have the intuition about algebra(cases mentioned by micromass that imply we seem to use some rules there) that we grown ups have now.

I would most definitely agree with this assessment.

 

[PeroK]

No, please do address this. I'm interested how you would teach this to children. How would you teach children to evaluate $2p+3q$?

You don't have to hit that with a sledgehammer like PEMDAS.

I've already answered that above: the precedence of multiplication is a universal rule.

What I wouldn't do is insist on PEMDAS and then have to explain:

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

And why you do the additions before the division. That's what I as a 15 year old would have taken exception to! I fail to see it ad a logical consequence of PEMDAS.

I think I would just treat fractions on their own merit. This is how we evaluation a fraction. There are all sorts of other things to deal with. Common factors, addition of fractions, partial fractions. Order of operations is the least of it.

 

[micromass]

I wonder how uniformly implemented the current rules are, in any case.

They're not, and that's a big problem. I would much prefer there to be one standard that everybody follows, no matter what that standard is. Note however that most professional scientific software does seem to follow the standard convention.

 

[ShayanJ]

But I should say that I have no memory of learning the order of operations in my elementary school years. But I don't have a good memory so I can't remember how I did it!

 

[S.G. Janssens]

I am tempted to say one thing specifically about programming.

In the programming languages that I know, there are many more unary and binary (and ternary) operators than in basic school arithmetic. (Probably C++ tops it all in this regard.) Textbooks and references usually come with a table of precedence. I found that in practice it did not at all contribute to the clarity of code when these rules of precedence were fully exploited by the programmer. Usually I found it much, much clearer when parentheses were used to remove ambiguity from complicated expressions, such as those involving both ordinary and pointer arithmetic.

Ok, now I go back to my own peeves, although I do enjoy reading along with this discussion.

 

[ShayanJ]

I am tempted to say one thing specifically about programming.

In the programming languages that I know, there are many more unary and binary operators that in basic school arithmetic. (Probably C++ tops it all in this regard.) Textbooks and references usually come with a table of precedence. I found that in practice it did not at all contribute to the clarity of code when these rules of precedence were fully exploited by the programmer. Usually I found it much, much clearer when parentheses were used to remove ambiguity from complicated expressions, such as those involving both ordinary and pointer arithmetic.

Ok, now I go back to my own peeves, although I do enjoy reading along with this discussion.

I think even programmers forget most of that and just use intuition and parentheses. At least that's the case about me!

 

[gmax137]

I have no recollection of learning "order of operations" until I was doing programming in Basic on a PDP something. I thought it was just a convention to save space (no need for the parentheses). As far as the equations on the blackboard, I never had any question that when teacher wrote "3 X-squared" she meant the 2 goes with the X alone, not with the 3. I certainly never saw the word PEMDAS before this morning. I have no basis for this notion, but I bet some kids get turned off by these memory devices, and the associated testing ("oh look, here's a pathological example, can you evaluate it correctly?"). If that's how they teach math in fourth grade now, I'd hate it too.

Spelling bees aren't literature.

 

[Mark44]

For the reason that the rules cause ambiguity. This is evidenced by the fact that the two Microsoft calculators gave different answers for the same expression.

I used to work in the Windows team at Microsoft, but not with the bunch that does the calculator. If I had to guess, the intent of the designers of the "four-banger" calculator, was to do simple (i.e., with two operands) add/subtract/multiply/divide calculations. I would further guess that it's stack-based, meaning that it takes the two operands and an operator (+, - *, /) and carries out the operation.

And that 76% of the population gave the "wrong" answer.

It wouldn't be the first time in history that 76% of the population gave the wrong answer, so I'm not impressed by that statistic.

I'm not the only one:

http://www.math.harvard.edu/~knill/pedagogy/ambiguity/

This issue is not as clear cut as many of you would like to pretend.

The expression in this article of the link seems clear-cut to me.
As written in the post, it is
$2x/3y - 1$, which we're supposed to evaluate for x = 9 and y = 2.
If it had been written like this:
$$\frac{2x} {3y} - 1$$
it would have been clear that 2x is to be divided by 3y, as the fraction bar serves to separate the numerator as a group from the denominator as a group.

As it was written, the expression on the left should be interpreted to mean 2 * x / 3 * y. The M and D operations of PEMDAS are at the same level in the hierarchy of operations (as are the A and S). If a multiplication appears before a division (going left to right), you do the multiplication first. If a division occurs first, you do the divison and then the multiplication.

Here's a simple example that should elucidate my reasoning. It uses addition and subtraction instead of multiplication and division, but it should throw some light on the expression of the blog by Knill.
a) 3 + 2 - 1
b) 3 - 1 + 2
Both BEDMAS and PEMDAS have A before S. If you interpret this to mean that additions should be done before subtractions, then the value of expression a) is 4, while the value of expression b) is 0.
OTOH, if you treat addition and subtraction as having the same precedence, then in any expression involving only these operators, you do whichever one comes first (i.e., in left to right order). With this in mind, expression a) yields 5 - 1 = 4, and expression b) yields 2 + 2 = 4, as well.

For Knill's expression, I maintain that the same idea holds with multiplication and division, as well.

 

[Mark44]

In the programming languages that I know, there are many more unary and binary (and ternary) operators than in basic school arithmetic. (Probably C++ tops it all in this regard.) Textbooks and references usually come with a table of precedence. I found that in practice it did not at all contribute to the clarity of code when these rules of precedence were fully exploited by the programmer. Usually I found it much, much clearer when parentheses were used to remove ambiguity from complicated expressions, such as those involving both ordinary and pointer arithmetic.

I agree, but then it wasn't a problem of ambiguity, but rather, a problem of comprehension by humans.

 

[Mark44]

You don't have to hit that with a sledgehammer like PEMDAS.

I've already answered that above: the precedence of multiplication is a universal rule.

What I wouldn't do is insist on PEMDAS and then have to explain:

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

And why you do the additions before the division.

As I have already explained, the above means exactly the same as (a + b)/(c + d). That is the purpose of the bar between the top and the bottom and the bar above the radicand in a radical. Why is this so hard?

That's what I as a 15 year old would have taken exception to! I fail to see it ad a logical consequence of PEMDAS.

I think I would just treat fractions on their own merit. This is how we evaluation a fraction. There are all sorts of other things to deal with. Common factors, addition of fractions, partial fractions. Order of operations is the least of it.

 

[jack action]

What I wouldn't do is insist on PEMDAS and then have to explain:

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

And why you do the additions before the division. That's what I as a 15 year old would have taken exception to! I fail to see it ad a logical consequence of PEMDAS.

But that is a fraction, not a division. The horizontal bar adds meaning to the division implied (i.e. the parenthesis, as told by @Mark44 earlier). See this example in Latex:
\frac{\frac{a}{b}}{\frac{c}{d}}
Latex (not me) makes one of the 3 horizontal bars longer than the other two. It adds meaning to how this equation must be evaluated. And you can't assume that it means $a \div b \div c \div d$. Of course, there are other ways that would make this particular equation a lot more clearer, no doubt, such as:
\frac{^a/_b}{^c/_d}
\frac{\left(\frac{a}{b}\right)}{\left(\frac{c}{d}\right)}
\frac{a \div b}{c \div d}
\left(a \div b\right) \div \left(c \div d\right)
Of course, you are allowed to your opinions and your pet peeves, but I'm not ready to say that those rules are useless and complicate everything.

 

[PeroK]

As I have already explained, the above means exactly the same as (a + b)/(c + d). That is the purpose of the bar between the top and the bottom and the bar above the radicand in a radical. Why is this so hard?

That's because you're determined to stick with PEMDAS, so you need your implied parenthesis. Whereas, I never learned PEMDAS so I'm free to say in this case we do the division last. As I have no a priori rule that operations must be done in a set order it doesn't upset my mathematic apple cart

 

[micromass]

That's because you're determined to stick with PEMDAS, so you need your implied parenthesis. Whereas, I never learned PEMDAS so I'm free to say in this case we do the division last. As I have no a priori rule that operations must be done in a set order it doesn't upset my mathematic apple cart

Every notation you use and introduce has their own precendence rules. And those precedence rules need to be introduced whenever the notation is introduced. Just because schools introduce PEMDAS before they introduce the notation $\frac{a}{b}$ or $e^{2\pi i x}$ doesn't mean that PEMDAS are in any way invalid, or that you can't just make a consistent set of rules easily that takes into account this notation.

 

[jack action]

I never learned PEMDAS so I'm free to say in this case we do the division last.

«La mia macchina è rotta.»

I never learned Italian so I'm free to say in this case that sentence means «I'm the most beautiful man alive.»

Couldn't care less what Google translate says.

 

[Mark44]

What I wouldn't do is insist on PEMDAS and then have to explain:

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

And why you do the additions before the division. That's what I as a 15 year old would have taken exception to! I fail to see it ad a logical consequence of PEMDAS.

But that is a fraction, not a division. The horizontal bar adds meaning to the division implied (i.e. the parenthesis, as told by @Mark44 earlier).

A fraction implies division.

 

[Mark44]

It adds meaning to how this equation must be evaluated.

Nitpicky, I know, but the thing you're talking about is an expression, not an equation.

 

[vela]

Nitpicky, I know, but the thing you're talking about is an expression, not an equation.

Heh, I was about to post that was one of my pet peeves.

 

[russ_watters]

There may be more on this forum but the brow beating I've taken would deter most from uttering a word in my defence!

Since you are soliciting more opinions, I agree......with @micromass and @Mark44!

I guess I have a minor pet Pete about calculators not always being clear about which convention they use, but if we'really going to go there, I have a long list of Excel pet peers too...and also the autocorrect on my phone is trying to drive me insane.

 

[russ_watters]

But I should say that I have no memory of learning the order of operations in my elementary school years. But I don't have a good memory so I can't remember how I did it!

I don't either. I had to Google "PEMDAS" before adding my 2 cents. The rule gets converted to instinct and ultimately forgotten after a while.

 

[TeethWhitener]

The expression in this article of the link seems clear-cut to me.

Wait, so does this mean that we can't write binomial coefficients inline as $n!/k!(n-k)!$ ? Because $n!/(k!(n-k)!)$ looks atrocious to me. Just my two cents.

 

[TeethWhitener]

One small peeve of mine that's starting to come up more and more in chemistry is the insistence on using IUPAC nomenclature. Sometimes it's good, but for reaction following it can be a pain. For instance, an example I ran into recently involved a Heck addition of perfluorobutyl iodide to ethylene. You get an ethylene attached to a perfluorobutyl group. Some older authors call this compound perfluorobutyl ethylene, which is immediately understandable and makes it clear which groups were combined and how. But the IUPAC name for this compound is the hideous 3,3,4,4,5,5,6,6,6-nonafluoro-1-hexene, which gives essentially no information about how it was derived and requires at least several brain cycles (and possibly pencil and paper) to decipher that, yes, it's just a perfluorobutyl chain attached to an ethylene.

 

[sophiecentaur]

Ye Gods. 184 posts. We are a grumpy lot, aren't we!

 

[JaredJames]

Ye Gods. 184 posts. We are a grumpy lot, aren't we!

Well, about 5 peeves and 9 pages of arguing why perok's peeve is wrong.

 

[OmCheeto]

Ye Gods. 184 posts. We are a grumpy lot, aren't we!

Educators OmCheeto should fill this thread!

I have so many...
Though, I recognize that most of mine are my own personal problem.
But still, even the ones that aren't that personal, still peeve me.
I think most are very, very old, from my younger days...

Back in college:

Om; "What is the proper 'chemistryish' name for water"?
Chemistry book; "Water"
Om; "That's stupid. Why does everything else have a logical name?"
Chemistry book; "Wait until you get to hydrocarbons. Ha Ha!"
Om; "Grrrrrr..."
[ehr mehr gerd.... I ain't studyin' any more chemistry until you kids get your, um, stuff together...]
​

More recently:

Om; "Who and when was it decided to change the Latin name of the "Guppy"? I learned that when I was 7, and now I see it's been changed."
Botanists; "We did".
Om; "When"?
Botanists; "Um..."
Om; "And why"?
Botanists; "Well..."
[ehr mehr gerd... see: Synonyms]​

I could go on all day...

Om; "Oh, so I can't say; "Degrees Kelvin", to reduce the confusion of whether or not I'm talking about "the man" or "the weather"?"
Pedants' "No. We have spoken..."
Om; "Grrrrrrrrr..."​

ps. I recently got interested in geology, after trips to Ceres and Crater Lake National Park, and I think geologists may be the worst of all.

Om; "Where did you guys come up with these names"?
Geologists; "We made them up."
Om: "And the numbers?"
Geologists; "Eyeballing".
Om; "I like your honesty. ps. Do you ever get jealous of that "Howard" guy"?
Geologists; "Kind of".​

 

[Mark44]

Wait, so does this mean that we can't write binomial coefficients inline as $n!/k!(n-k)!$ ? Because $n!/(k!(n-k)!)$ looks atrocious to me. Just my two cents.

If it's written like this, no problem: $\frac{n!}{k!(n - k)!}$, but as you wrote it the first time, it's ambiguous.

The main problem with PEMDAS is that, IMO, it's sort of a work in progress, that hasn't been as well thought out as, say, what the computer science folks have done in specifying the precedence of operators in programming languages, and specifically the languages that stem from C. These precedence tables not only specifiy which operations should be performed before which others, they also specify the associativity of each operator, so that a + b + c should be evaluated left to right, the same as if it were written (a + b) + c. Note that on computers, addition is not necessarily associative; due to overflow or underflow, (a + b) + c might give a different result from a + (b + c).

It seems to be fairly well agreed on that for the addition and subtraction operations (the A and S in PEMDAS), the operations are at the same level of precedence and should be performed left to right.
In a footnote on the Wiki page for Order of Operations (https://en.wikipedia.org/wiki/Order_of_operations), emeritus Berkeley math professor George M. Bergman has this to say: (https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html)

For expressions such as a−b+c, or a+b−c, or a−b−c, there is also a fixed convention, but rather than saying that one of addition and subtraction is always done before the other, it says that when one has a sequence of these two operations, one works from left to right: One starts with a, then adds or subtracts b, and finally adds or subtracts c.

IOW, 3 + 4 - 2 should be thought of as meaning (3 + 4) - 2, yielding 5. Similarly, the expression 3 - 2 + 4 should be thought of as meaning (3 - 2) + 4, again yielding 5.

What is not well accepted is that multiplication and division (the M and D of PEMDAS) should be treated as having the same precendence, and be evaluated left to right, making these operations consistent with the treatment of addition and subtraction.
Another quote from the George Bergman footnote (italics added by me):

Presumably, teachers explain that it means "Parentheses — then Exponents — then Multiplication and Division — then Addition and Subtraction", with the proviso that in the "Addition and Subtraction" step, and likewise in the "Multiplication and Division" step, one calculates from left to right. This fits the standard convention for addition and subtraction, and would provide an unambiguous interpretation for a/bc, namely, (a/b)c. But so far as I know, it is a creation of some educator, who has taken conventions in real use, and extended them to cover cases where there is no accepted convention.

With no clear-cut convention regarding expressions with multiplication and division, particularly when written inline, you run into problems with expressions as simple as 1/2x. If we hold that multiplication and division are at the same precedence level, and should be evaluated left to right, the expression 1/2x is the same as (1/2)x. OTOH, a number of prominent textbooks, including "Course of Theoretical Physics" by Landau and Lifshitz, as well as the "Feynman Lectures on Physics" interpret 1/2x the same as $\frac 1 {2x}$.

Another area where PEMDAS is deficient with associativity not clearly spelled out is in stacked exponents. Per this Wiki page

https://en.wikipedia.org/wiki/Order_of_operations]Stacked[/PLAIN] exponents are applied from the top down, i.e., from right to left.[/quote]
However, both Microsoft Office Excel and Matlab R2015B evaluate 2^3^2 (i.e., $2^{3^2}$) as if written (2^3)^2 = 64 rather than 2^(3^2) = 512.

 

[late347]

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

lets imagine that we have expression as follows

$2^{2^{2^{2}}}$

why should it be through pemdas, that one calculates from the top right, towards bottom left?

Are you supposed to initially judge that the leftmost number at the bottom, two = "the base number". Therefore, essentially, all the others two's are some sort of powers as themselves. I suppose it makes sense like that. Is that a real math term anyway "base number"?

Usually people simply speak 2 squared (for the case of $2^2$. And not e.g. 2 as the base number, and 2 as the exponent.

 

[Mark44]

lets imagine that we have expression as follows

$2^{2^{2^{2}}}$

why should it be through pemdas, that one calculates from the top right, towards bottom left?

PEMDAS doesn't say anything about this, since there are no other operations other than exponentiation. The convention, not always honored (see my previous post) is that the order of evaluation (the associativity) is from right to left.

Are you supposed to initially judge that the leftmost number at the bottom, two = "the base number". Therefore, essentially, all the others two's are some sort of powers as themselves. I suppose it makes sense like that. Is that a real math term anyway "base number"?

We usually say just "base". In $2^8$, the base is 2 and the exponent is 8.
In the expression you wrote, each 2, except the rightmost one, is the base for some exponential expression.

Usually people simply speak 2 squared (for the case of $2^2$. And not e.g. 2 as the base number, and 2 as the exponent.

 

[Mark44]

More recently:
Om; "Who and when was it decided to change the Latin name of the "Guppy"? I learned that when I was 7, and now I see it's been changed."
Botanists; "We did".
Om; "When"?
Botanists; "Um..."
Om; "And why"?
Botanists; "Well..."

I'm not a botanist, but I took one field botany class many years ago, purely for interest, and have managed to hold onto the scientific names of quite a few plants. I've noticed that the scientific names of several plants have changed, including that or Oregon grape, a shrubby plant that grows in my area. It used to be Berberus aquifolium, but now it's Mahonia aquifolium, so they changed the genus the plant belongs to.

They've even changed the names of at least one family - Compositaceae, the family that sunflowers, daisies, and asters belong to. It seems to now be Asteraceae, although I see from wikipedia that the older name is still valid.

 

[Bystander]

That's the difference between "Linnaean" and "cladistic" taxonomies.

 

[TeethWhitener]

If it's written like this, no problem: n!k!(n−k)!\frac{n!}{k!(n - k)!}, but as you wrote it the first time, it's ambiguous.

Sure, but I imagine that if most mathematicians or scientists saw $n!/k!(n-k)!$ in a paper, they'd probably automatically associate it with a binomial coefficient immediately, rather than thinking it means
$$\frac{n!(n-k)!}{k!}$$

 

[Mark44]

Sure, but I imagine that if most mathematicians or scientists saw $n!/k!(n-k)!$ in a paper, they'd probably automatically associate it with a binomial coefficient immediately, rather than thinking it means
$$\frac{n!(n-k)!}{k!}$$

Probably so, but if this appeared in a paper, it would likely be nicely formatted as $\frac{n!}{(n - k)! k!}$.

 

[DrClaude]

In another thread, I just got reminded of another pet peeve that is science related, videos like this:

Image source: at 02:30

It's an audio-visual medium, use the audio! Talk to me! If I want to read, I'll look up a text. And don't force me to read at a given speed.

 

[Kevin McHugh]

Here is a major pet peeve of mine. I had to take QM in my senior year for my BS in Chemistry. Even though I had two semesters each of calculus and physics, I was totally unprepared to fully appreciate QM. I lacked the background in matrix theory, operators and Hamiltonian/Lagrangian formalism to fully grasp the concepts in the course. Of course we were given a cursory glossing over of these topics, but not enough to fully appreciate the course material. I have since gone back and started reading QM by Shankar. The treatment of this material is very rich. I love this text!

 

[Ben Niehoff]

That and the date convention. How does 3/1/15 for 1 march 2015 make logical sense... at all?

Because we actually say "March 1st, 2015", not "1 March 2015". Although I think the date format 2015/03/01 would make a lot more sense.

 

[micromass]

Because we actually say "March 1st, 2015"

I know you say it. My point is that there is no logical reason to say it like that.

 

[Bystander]

"March 1st, 2015", not "1 March 2015".

no logical reason to say it like that.

When asked for my birth date, I reply, "Six March forty-seven."

 

[Ben Niehoff]

When asked for my birth date, I reply, "Six March forty-seven."

Are you American? I am pointing out a dialectical difference. British people do say the day first.