Biggest science or math pet peeve

[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.

 

[StatGuy2000]

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

It makes no logical sense to you because you were brought up to follow the convention of Day, Month, Year. In North America, the convention of writing dates is to write Month, Day, Year. The thinking (I presume) is that within a given month in a calendar you select a day out of that month.
So in this sense, I am strongly in favour of the North American convention on dates as opposed to (I presume) is the "European" convention (or is the convention you use strictly a Belgian convention?)

 

[micromass]

The thinking (I presume) is that within a given month in a calendar you select a day out of that month.

That would make sense if you also followed the convention yyyy/mm/dd, since you pick a month for ma year and a day from a month. I'm not arguing against the convention mm/dd, that makes perfect sense. I'm arguing against mm/dd/yyyy

 

[PeroK]

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

I suggest that mathematiciuans and physicists interpret mathematical expressions according to intuitive rules including spacing and size and position of text, that are not covered by PEMDAS. In particular, the PEMDAS rule governing exponents does not readily extend to exponents involving expressions. In this case, the entire exponential expression is evaluated first, contrary to PEMDAS. The convention is to use size of text rather than parenthesis for the exponential expression.

When I typed the LATEX, I had to put the exponential expression in braces, to indicate to the LATEX interpreter what was intended, but LATEX rendered this using size and position of text instead of braces or parenthesis.

 

[StatGuy2000]

On my list of science pet peeves include the American and British fondness for the Imperial measurement system (e.g. inches and feet for height).

I am a strong proponent of the metric system, which to me make logical and scientific sense, and feel that old Imperial measurements should be completely abolished and replaced everywhere in the world.

Down with inches and feet, long live centimeters and meters!

 

[micromass]

I suggest that mathematiciuans and physicists interpret mathematical expressions according to intuitive rules including spacing and size and position of text, that are not covered by PEMDAS. In particular, the PEMDAS rule governing exponents does not readily extend to exponents involving expressions. In this case, the entire exponential expression is evaluated first, contrary to PEMDAS. The convention is to use size of text rather than parenthesis for the exponential expression.

It does readily extend to exponents involving expressions. I don't see what the difficulty is with extending it to exponents involving expressions.

 

[micromass]

It does readily extend to exponents involving expressions. I don't see what the difficulty is with extending it to exponents involving expressions.

Here, just add this rule: everything that is placed higher than something else is evaluated first. There, I extended PEDMAS to exponents.

 

[micromass]

(or is the convention you use strictly a Belgian convention?)

No, the convention is used almost internationally. https://en.wikipedia.org/wiki/Date_format_by_country

 

[jack action]

The convention that you need is "if there is any risk of confusion, then brackets must be used". No mathematician would write:

$a + b \times c \div d$

And expect everyone else to know what they mean. First, $\div$ is not actually recognised as a mathematical symbol in the ISO (International Standard) for Mathematical Symbols.

Any good mathematician would write, for example:

$(a+b)c/d$

or $\frac{(a+b)c}{d}$

There is then no ambiguity.

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".

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.

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?

 

[Student100]

On my list of science pet peeves include the American and British fondness for the Imperial measurement system (e.g. inches and feet for height).

I am a strong proponent of the metric system, which to me make logical and scientific sense, and feel that old Imperial measurements should be completely abolished and replaced everywhere in the world.

Down with inches and feet, long live centimeters and meters!

Down with the minute, up with ? I'm not sure what the French called it when they experimented with metric time.

 

[micromass]

Down with the minute, up with ? I'm not sure what the French called it when they experimented with metric time.

deci-day, centi-day, etc.

 

[Student100]

deci-day, centi-day, etc.

Well that makes perfect sense. 10 hours in a day would be a bit odd though.

 

[Mark44]

On my list of science pet peeves include the American and British fondness for the Imperial measurement system (e.g. inches and feet for height).

Hear, hear!
And let's extend this to dates, as well. The old business of 24 hours in a day, and 28 or 29 or 30 or 31 days in a month, and 12 months in a year are just plain old-fashioned. Let's have 10 hours in a day, and 10 days in a month, and 10 months in a year.

I am a strong proponent of the metric system, which to me make logical and scientific sense, and feel that old Imperial measurements should be completely abolished and replaced everywhere in the world.

Down with inches and feet, long live centimeters and meters!

I'm hoping to get a speedometer on my car calibrated in rods per fortnight...

More seriously, the biggest impediment to changing to the metric system in the US (which has been pushed for with no success since the Carter administration) is that fact that every legal property description is described as some portion of a section (640 acres) and the position of the parcel described using measurements in feet.

 

[StatGuy2000]

Down with the minute, up with ? I'm not sure what the French called it when they experimented with metric time.

I should have stated earlier that measurements of time are exempt from the metric system, as I am a proponent of the UTC Time standard. Primarily because it is an universally accepted standard used throughout the world, unlike the (unintuitive, primitive, backward, IMHO) Imperial measurement system (which for some inexplicable reason Americans & Brits seem to be so attached to).

https://en.wikipedia.org/wiki/Decimal_time

https://en.wikipedia.org/wiki/Coordinated_Universal_Time

 

[StatGuy2000]

Hear, hear!
And let's extend this to dates, as well. The old business of 24 hours in a day, and 28 or 29 or 30 or 31 days in a month, and 12 months in a year are just plain old-fashioned. Let's have 10 hours in a day, and 10 days in a month, and 10 months in a year.

I'm hoping to get a speedometer on my car calibrated in rods per fortnight...[/QUOTE]

LOL to both above!

More seriously, the biggest impediment to changing to the metric system in the US (which has been pushed for with no success since the Carter administration) is that fact that every legal property description is described as some portion of a section (640 acres) and the position of the parcel described using measurements in feet.

Fair points -- from a logistic standpoint a change to the metric system may not be practical, at least in the short term for the reasons you cited above. However, that does not mean that I will not continue to advocate for the metric system.

 

[Student100]

What about biologists teaching students that diffusion requires "no energy", whatever that means.

 

[Bystander]

a change to the metric system may not be practical, at least in the short term for the reasons you cited above. However, that does not mean that I will not continue to advocate for the metric system.

On the other hand, (besides four fingers and a thumb) there is something to be said for the mental agility one develops when doing conversions.

 

[micromass]

On the other hand, (besides four fingers and a thumb) there is something to be said for the mental agility one develops when doing conversions.

And the million dollars damages when a spacecraft crashes because engineers forgot the conversions. https://en.wikipedia.org/wiki/Mars_Climate_Orbiter

 

[OmCheeto]

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.

I've been using the ISO format (YMD) since at least 1985, because, as you mention, it simplified computer sorting.
Though, I never thought I'd live to see the year 2000, and computer memory was a bit more scarce back then, so my format was somewhat truncated:

851120 --> November 20, 1985​

I still use a similar version today:

​

By not using the "-" or "/" delimiters, I'm pretty much guaranteed that no matter where I export the dates to, they won't accidentally be interpreted as equations.

But I'm sure someone will be peeved that I've come up with my own "delimiter" convention.

 

[Bystander]

biologists teaching students that diffusion requires "no energy",

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

 

[Bystander]

And the million dollars damages when a spacecraft crashes because engineers forgot the conversions.

You want egg in you beer?