Biggest science or math pet peeve

[fresh_42]

So, $\log_2 32 = 5 \text{ trees ?}$

Well almost. But at least in terms of quality.
I found $\ln V_t = 1.34 + 0.394 \ln G_0 + 0.346 \ln t +0.00275 \, S_h t^{-1}$

"Such equations have not been used much in mixed forests, but Mendoza and Gumpal (1987) predicted yield of dipterocarps in the Philippines with an empirical function of initial basal area, site quality and time since logging, where $V_t$ is timber yield ($m^3 ha^{-1} , 15+ cm \; dbh$), $t$ years after logging ($t>0$), $G_0$ is residual basal area ($m^2 ha^{-1}$) of dipterocarps ($15+ cm \; dbh$) after logging, and $S_h$ is site quality ($m$) estimated as the average total height of residual dipterocarp trees ($50–80 cm$ diameter)."

[Modelling forest growth and yield : applications to mixed tropical forests; Jerome K. Vanclay; Southern Cross University; 1994]

 

[PeroK]

3p+2q makes sense to you, dunnit?

Not really. Yes, I know what you mean, but it's not the way I or any maths text would write it. It would be:

$3p + 2q$

The spaces are important and indicate that I have two terms added together. I wouldn't go so far as to say that 3p+2q is wrong, but it's not something I would ever write.

In general, I would tend to agree with the ISO standard on mathematical symbols:

http://www.ise.ncsu.edu/jwilson/files/mathsigns.pdf

This, I believe, is closer to what most professional mathematicians naurally would adhere to. There is no mention of PEMDAS or order of operations there.

 

[PeroK]

Let's write $3x^2 + 5x + 7 = 0$ without PEDMAS:

(((3\cdot x)\cdot x) + (5\cdot x)) + 7 = 9

Don't know about you, but I prefer to have this whole PEDMA convention...

I refer you also to the ISO standard, which makes the quadratic expression quite clear without the need for PEMDAS.

There is no more need to ignore spaces in a line of mathematics than a line of text.

 

[micromass]

Not really. Yes, I know what you mean, but it's not the way I or any maths text would write it. It would be:

$3p + 2q$

The spaces are important and indicate that I have two terms added together. I wouldn't go so far as to say that 3p+2q is wrong, but it's not something I would ever write.

In general, I would tend to agree with the ISO standard on mathematical symbols:

http://www.ise.ncsu.edu/jwilson/files/mathsigns.pdf

This, I believe, is closer to what most professional mathematicians naurally would adhere to. There is no mention of PEMDAS or order of operations there.

?? You're proposing to replace PEMDA's by "spaces"?? Come on...

 

[micromass]

I refer you also to the ISO standard, which makes the quadratic expression quite clear without the need for PEMDAS.

There is no more need to ignore spaces in a line of mathematics than a line of text.

I personally don't know any professional mathematician who has even heard of this particular ISO standard, sorry. All of them has heard of PEMDA's though...

 

[micromass]

Seriously, I have read many books on sound mathematical writing. None of them says to use "spaces" instead of PEMDA's. That most professional mathematicians prefer "spaces" is just wrong.

 

[PeroK]

I personally don't know any professional mathematician who has even heard of the ISO standard, sorry.

I never said they had. I said that if you look at maths publications they naturally follow the standard. A case of the standard describing how things are done, rather than the standard coming first.

 

[PeroK]

Seriously, I have read many books on sound mathematical writing. None of them says to use "spaces" instead of PEMDA's. That most professional mathematicians prefer "spaces" is just wrong.

Then why did you put spaces in your quadratic expression?

 

[micromass]

I never said they had. I said that if you look at maths publications they naturally follow the standard. A case of the standard describing how things are done, rather than the standard coming first.

I have read hundreds of math publications and I have never seen what you describe.

 

[micromass]

Then why did you put spaces in your quadratic expression?

I didn't. LaTeX did it.

 

[PeroK]

I didn't. LaTeX did it.

I wonder why?

 

[micromass]

I wonder why?

Name me one professional mathematician or article that thinks 2p+3q is invalid.

 

[PeroK]

I wonder why?

Or, should I say "Iwonderwhy?"

 

[PeroK]

Name me one professional mathematician or article that thinks 2p+3q is invalid.

As I said, I wouldn't say it's actually wrong, but I've never seen a textbook that doesn't have spaces between terms. Perhaps there are some, but it's always the way LATEX renders it on here. All the books I have would have:

$ax^2 + bx + c$

I've never seen ax^2+bx+c.

 

[micromass]

As I said, I wouldn't say it's actually wrong, but I've never seen a textbook that doesn't have spaces between terms. Perhaps there are some, but it's always the way LATEX renders it on here. All the books I have would have:

$ax^2 + bx + c$

I've never seen ax^2+bx+c.

You clearly never read older textbooks that didn't use LaTeX then.

Sure, nowadays LaTeX using spacing accurately because it increases readability. There is no actual formal rule that acknowledges spacing though...

 

[micromass]

Well, in my newest math paper, I'm going to write something like

2~\cdot ~x\! + \! y

to mean $2(x+y)$. I'm pretty sure the reviewer will look at it and say "hey, he used spaces, so of course it's correct".

 

[PeroK]

You clearly never read older textbooks that didn't use LaTeX then.

Sure, nowadays LaTeX using spacing accurately because it increases readability. There is no actual formal rule that acknowledges spacing though...

I never said there was. I said that some of us naturally use spacing the way we use it when writing - to separate terms.

If what I would like to be rules was the rules it wouldn't be my pet peeve would it? It's only my pet peeve because I know there's PEMDAS out there and I know we're all supposed to have memorised the whole damn thing and we're all supposed to think that:

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

Makes perfect sense. And the question of whether this mess equals 951 or 67 is of some mathematical consequence. And that there is no rule (which I think there should be) that says that (a) is a mess and not maths at all. I know that some people think that evaluating (a) is the pinnacle of arithmetic achievement. And, if I made the rules, then yes I would declare (a) to be mathematical nonsense. The fact that it is not deemed nonsense is my peeve.

 

[PeroK]

Well, in my newest math paper, I'm going to write something like

2~\cdot ~x\! + \! y

to mean $2(x+y)$. I'm pretty sure the reviewer will look at it and say "hey, he used spaces, so of course it's correct".

Sorry, micromass, that's deliberately misunderstanding!

 

[micromass]

I never said there was. I said that some of us naturally use spacing the way we use it when writing - to separate terms.

If what I would like to be rules was the rules it wouldn't be my pet peeve would it? It's only my pet peeve because I know there's PEMDAS out there and I know we're all supposed to have memorised the whole damn thing and we're all supposed to think that:

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

Makes perfect sense. And the question of whether this mess equals 951 or 67 is of some mathematical consequence. And that there is no rule (which I think there should be) that says that (a) is a mess and not maths at all. I know that some people think that evaluating (a) is the pinnacle of arithmetic achievement. And, if I made the rules, then yes I would declare (a) to be mathematical nonsense. The fact that it is not deemed nonsense is my peeve.

So you would build math software that declares (a) to be an erroneous expression?

 

[Mark44]

Let's write $3x^2 + 5x + 7 = 0$ without PEDMAS:

(((3\cdot x)\cdot x) + (5\cdot x)) + 7 = 9

Don't know about you, but I prefer to have this whole PEDMA convention...

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 ...

 

[micromass]

Sorry, micromass, that's deliberately misunderstanding!

No, it isn't. You said you used spaces to declare the order of operations. I took you at face value. If I misunderstood you at all, it's not deliberate.

 

[JaredJames]

Can you pair not just agree that the "rule" is there to give guidance on approaching any potential ambiguity, whilst in any reputable use it would have ambiguity explicitly prevented by appropriate means (brackets, parenthesis etc.)?

I remember when threads were killed for less sidetrack than this...

 

[micromass]

Can you pair not just agree that the "rule" is there to give guidance on approaching any potential ambiguity, whilst in any reputable use it would have ambiguity explicitly prevented by appropriate means (brackets, parenthesis etc.)?

I remember when threads were killed for less sidetrack than this...

No, I can't agree on that. PEDMA's are a completely valid mathematical tool. If you claim otherwise, you should provide evidence.

 

[JaredJames]

I'm not saying it's invalid. I use it all the time, fully support it. But I also agree with perok in that anywhere there could be ambiguity (let's not pretend we mean quadratics and such, it's clear the type of equation being referred to) must be made explicit. This has become some attempt at black and white debate, when in fact, both sides make valid points. Maybe it's because I'm now so used to laying out for various programming languages that makes me think that way.

Still drifting... I suppose if you can't beat em...

 

[Mark44]

I remember when threads were killed for less sidetrack than this...

I don't see the dialog as being a sidetrack. PeroK's peeve is with the (in his opinion) over-reliance on PEDMAS/BODMAS.

A very wellknown formula in the context of science is $E = mc^2$. Should we interpret the right side as $(mc)^2$ or as $m(c)^2$? Having a convention allows us to rule out the first choice.

 

[JaredJames]

I don't see the dialog as being a sidetrack. PeroK's peeve is with the (in his opinion) over-reliance on PEDMAS/BODMAS.

A very wellknown formula in the context of science is $E = mc^2$. Should we interpret the right side as $(mc)^2$ or as $m(c)^2$? Having a convention allows us to rule out the first choice.

To be fair, the thread is "what is your peeve" - he's given it. Didn't say everyone had to agree / debate it as that wasn't the question. I'd have thought it would make an interesting thread of its own.

 

[micromass]

I'm not saying it's invalid. I use it all the time, fully support it. But I also agree with perok in that anywhere there could be ambiguity (let's not pretend we mean quadratics and such, it's clear the type of equation being referred to) must be made explicit. This has become some attempt at black and white debate, when in fact, both sides make valid points. Maybe it's because I'm now so used to laying out for various programming languages that makes me think that way.

Still drifting... I suppose if you can't beat em...

I absolutely agree that something like $a/b/c$ or $1+3/2+5$ should never be written in formal writing. It's just too hard to decypher.

 

[JaredJames]

More of an Engineering one, but it's the American refusal to use the metric system (backs onto the unit one above). Aside from cost of converting, there's no valid reason to do so (consider Britain as an example of living with both systems to avoid cost).

Arguments of good or bad aside, the rest of the world use it (well, minus 3 or so small countries) so just get on board.

 

[micromass]

More of an Engineering one, but it's the American refusal to use the metric system. Aside from cost of converting, there's no valid reason to do so (consider Britain as an example of living with both systems to avoid cost).

Arguments of good or bad aside, the rest of the world use it (well, minus 3 or so small countries) so just get on board.

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

 

[JaredJames]

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

I add the ISO 8601 link to my email signature at work (http://www.cl.cam.ac.uk/~mgk25/iso-time.html). There's no other way!

 

[micromass]

I add the ISO 8601 link to my email signature at work (http://www.cl.cam.ac.uk/~mgk25/iso-time.html). There's no other way!

Yes, I think that makes the most sense of all. The European way 1/3/2015 is logical, but 2015/3/1 would be the best system. It even would agree with alphabetical sorting.

 

[Mark44]

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

It makes sense to me, because we (in US) write the day of the month with the month first; e.g., March 1, rather than 1 March.

 

[micromass]

It makes sense to me, because we (in US) write the day of the month with the month first; e.g., March 1, rather than 1 March.

I know. You're used to it. But it makes no logical sense to do it that way...

 

[Mark44]

I know. You're used to it. But it makes no logical sense to do it that way...

It's a convention. However, I do see some logic in having the month first, which is how calendars are arranged. I've never seen a calendar with 31 pages, where each page lists the various months that have that particular date.

 

[micromass]

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.

 

[micromass]

It's a convention. However, I do see some logic in having the month first, which is how calendars are arranged. I've never seen a calendar with 31 pages, where each page lists the various months that have that particular date.

Sure, but then you need to put the year first and not last.

 

[Charles Link]

One of the more difficult things I have found in doing science has been when you get a textbook that is only mediocre or of some value, but contains a lot of mistakes and/or poor or slightly inaccurate explanations. It can save a lot of trouble for the student when the author puts some extra time into making sure his calculations and derivations are correct and that the explanations are precise. Most of the time, after a week or so with a mediocre text, it is determined to be just that and I would find a better one. On occasion, even a very good textbook will be found to contain an error. One example of this is the Quantum Mechanics book by Gordon Baym. (I think it is currently out of print.) In his chapter on Second Quantization, he missed a factorial (!) symbol in one formula. When I was trying to prove another result using that equation, I was on it for a couple weeks before I figured out the error and got the equation to work. Much extra effort just because of a missing exclamation mark !

 

[sophiecentaur]

The dual systems for date format (month day. day month) produce actually significant risk and must have been the cause for people losing money over the years. The 'American' system is not consistent, regarding significance order. The iso date format beats them both because it can be extended seamlessly to time (hhmmss) and onto decimals of seconds. The mdy format seems pretty ridiculous, when viewed from outside and goes against the normal conventions of Maths. Running dmy in parallel with imd, could be confusing but is not subject to misinterpretation in this century, at least because there are no months where MM=20 and a casual Parser could easily sort out the meaning.

P.S. "A real-live nephew of my Uncle Sam, Born on July the Fourth" would sound wrong so why not go along with the Yankee Doodle Dandy convention?

 

[sophiecentaur]

a textbook that is only mediocre or of some value, but contains a lot of mistakes

ditto for many high level exam papers!

 

[PeroK]

No, I can't agree on that. PEDMA's are a completely valid mathematical tool. If you claim otherwise, you should provide evidence.

I've put a PEMDAS hat on. If I understand correctly, powers get done first? So, in this expression:

$e^{ipx/\hbar}$

That should be $e^i (px/\hbar)$

In other words, it's exactly the same as $e^ipx/\hbar$

My "naive" take on algebraic conventions is that you do the $ipx/\hbar$ first because of the size and position of the text. But, that sounds absurd now.

So, under the PEMDAS convention why is:

$e^{ipx/\hbar} \ne e^ipx/\hbar$

 

[micromass]

I've put a PEMDAS hat on. If I understand correctly, powers get done first? So, in this expression:

$e^{ipx/\hbar}$

That should be $e^i (px/\hbar)$

Why would these two be equal under PEMDAs?

 

[PeroK]

Why would these two be equal under PEMDAs?

They are both equal to:

$e^i \times p \times x \div \hbar$

What am I misunderstanding?

 

[micromass]

They are both equal to:

$e^i \times p \times x \div \hbar$

What am I misunderstanding?

You're misunderstanding that $e^x$ is a shorthand for $\text{exp}(x)$. So the expression is $\text{exp}(ipx/h)$.

 

[PeroK]

You're misunderstanding that $e^x$ is a shorthand for $\text{exp}(x)$. So the expression is $\text{exp}(ipx/h)$.

What about?

$a^{ipx/\hbar}$

 

[micromass]

What about?

$a^{ipx/\hbar}$

That's shorthand for $f(a , ipx/\hbar)$ where $f(x,y)$ is defined as $x^y$. We often write $f(a,\cdot) = \text{exp}_a$.

 

[micromass]

And $f(x,y)$ is shorthand for $f[(x,y)]$ with $f$ a function $f:\mathbb{R}\times \mathbb{R}\rightarrow \mathbb{R}$ (or appropriate domain and codomain).

 

[PeroK]

That's shorthand for $f(a , ipx/\hbar)$ where $f(x,y)$ is defined as $x^y$. We often write $f(a,\cdot) = \text{exp}_a$.

That's not what's written and that's not what PEMDAS says. It says nothing about implied parenthesis. I've never heard of implied parenthesis. It doesn't say: "exponents are a shorthand for ...". It says: "do exponents before multiplicatiions and divisions". And it says nothing about size and position of text. It's perfectly clear on this.

https://www.mathsisfun.com/operation-order-pemdas.html

Where is this all documented about implied parenthesis and interpreting an exponent as a function? Where is the evidence for this?

 

[micromass]

That's not what's written and that's not what PEMDAS says. It says nothing about implied parenthesis. I've never heard of implied parenthesis. It doesn't say: "exponents are a shorthand for ...". It says: "do exponents before multiplicatiions and divisions". And it says nothing about size and position of text. It's perfectly clear on this.

https://www.mathsisfun.com/operation-order-pemdas.html

Where is this all documented about implied parenthesis and interpreting an exponent as a function? Where is the evidence for this?

Where am I using implied parenthesis?

 

[micromass]

And you don't think $e^x$ is a function? How would you compute $e^{x+1}$ in your calculator if not for using a function?

I don't care what version of PEMDA's you're using really. Apparently you're using a really odd one.

 

[micromass]

https://www.mathsisfun.com/operation-order-pemdas.html

Well, that site is wrong. I'm not going to defend a strawman.

Well, not really wrong, it just doesn't mention exponents with more complicated expressions since high school children never need them. And since it's perfectly obvious to (apparently almost) everybody how to use them.