1184: "Circumference Formula"

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Dr. Diaphanous
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Re: 1184: "Circumference Formula"

Postby Dr. Diaphanous » Mon Mar 11, 2013 5:20 pm UTC

orthogon wrote:Grr. My favourite newspaper insists on using Coulombs as a unit of temperature, e.g. "Temperatures in parts of the UK dropped to -5C last night".


In a swimming pool near me the deep end is labelled 1.8 MTRS, and the shallow end was 0.9 MTRS. I don't know what kind of bizarre device they had hidden in the wall that could be measured in Mega-Tesla-Roentgen-Siemens. I suspect it is part of some mad scientist supervillain's origin story.

Also, the Food and Agriculture Organization lists crop yields in MT, leaving me off by a factor of a million when I assumed it meant Megatonnes (Mt) and not metric tonnes (t). Those guys also use hectograms. Who the hell uses hectograms?
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Re: 1184: "Circumference Formula"

Postby ctdonath » Mon Mar 11, 2013 5:23 pm UTC

Bellomy wrote:I honestly don't get it. :oops:

Area of circle = πr2
Circumference of circle = 2πr

Marking something with a footnote involves appending a superscripted number1.
Footnoting an equation can confuse the superscripted exponential notation with the superscripted footnote indicator notation, driving people (like xkcd readers) nuts.
Circumference of circle = 2πr2
Especially when the footnote indication provokes the reader with a "no wait, that's wrong, you've mixed up the circumference of the circle with the area of the circle!" reaction.

1 - like this
2 - like this

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Re: 1184: "Circumference Formula"

Postby jgh » Mon Mar 11, 2013 5:42 pm UTC

Dr. Diaphanous wrote:In a swimming pool near me the deep end is labelled 1.8 MTRS, and the shallow end was 0.9 MTRS. I don't know what kind of bizarre device they had hidden in the wall that could be measured in Mega-Tesla-Roentgen-Siemens. I suspect it is part of some mad scientist supervillain's origin story.
I had to fight and fight and fight to stop some software I was writing being specified to label quantities in megamoles and megalitres - and this was a medicine prescription database!!!!

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Re: 1184: "Circumference Formula"

Postby orthogon » Mon Mar 11, 2013 6:46 pm UTC

... and times measured in millisiemens. Again by people who should know better...
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 1184: "Circumference Formula"

Postby MotorToad » Mon Mar 11, 2013 7:14 pm UTC

Dr. Diaphanous wrote:In a swimming pool near me the deep end is labelled 1.8 MTRS, and the shallow end was 0.9 MTRS. I don't know what kind of bizarre device they had hidden in the wall that could be measured in Mega-Tesla-Roentgen-Siemens. I suspect it is part of some mad scientist supervillain's origin story.

I want to swim in that pool, even if it'll be a brief dip. I think I'd interpret the "RS" eventually as "R/R," but I'm not sure if that makes more or less sense. :)
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Re: 1184: "Circumference Formula"

Postby Coyne » Mon Mar 11, 2013 7:41 pm UTC

alvinhochun wrote:
Coyne wrote:My second thought lead me to check the Wikipedia Circle article, to see if someone was actually lame enough to footnote the formula.

Wait I still don't see any xkcd vandalism. Perhaps it is a bit difficult to add footnote to an equation?

The thought didn't have anything to do with, "Is it possible?" (And if you think it isn't...prove it. Remember that software often has bugs that permit unintended things to happen.) It had more to do with, "Surely he didn't get this idea from [real life example]..."
In all fairness...

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Re: 1184: "Circumference Formula"

Postby jonbly » Mon Mar 11, 2013 8:00 pm UTC

What if the circle doesn't have any arms?

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Re: 1184: "Circumference Formula"

Postby brenok » Mon Mar 11, 2013 8:14 pm UTC

jonbly wrote:What if the circle doesn't have any arms?


Who are you asking this to?

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Re: 1184: "Circumference Formula"

Postby Coyne » Mon Mar 11, 2013 8:15 pm UTC

Bellomy wrote:I'm sorry, I know I'm an idiot, but...I honestly don't get it. :oops:


The comic is making fun of "overloaded" symbols: Those that serve more than one purpose...and the people that misuse them without paying attention to what their misuse might imply.

In the main comic, the superscript (2), in common usage, could be either an exponentiation or a footnote reference number. In this case, it is a reference number, but even a relatively cautious reader could conclude it means the radius of the circle should be squared.

In the tooltip, the joke is over the apostrophe (') and quote (") symbols. In common usage, apostrophe can indicate "prime" (primary), foot (length), minute (angle or time interval), contraction (as in "don't") or glottal stop; and quote can indicate "secondary", inch, second (angle or time interval), or quoted text. That's right: Six different common meanings for apostrophe; five for quote.

In all of these cases, the actual meaning depends upon context. So, if any of these symbols or formats is misused, the overloading can cause the result to be very confusing and misleading.
In all fairness...

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Re: 1184: "Circumference Formula"

Postby waidh » Mon Mar 11, 2013 8:17 pm UTC

alvinhochun wrote:
Coyne wrote:My second thought lead me to check the Wikipedia Circle article, to see if someone was actually lame enough to footnote the formula.

Wait I still don't see any xkcd vandalism. Perhaps it is a bit difficult to add footnote to an equation?

It may have something to do with the article being already protected since 8 March because of other vandalism.

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Re: 1184: "Circumference Formula"

Postby Bellomy » Mon Mar 11, 2013 8:38 pm UTC

ctdonath wrote:
Bellomy wrote:I honestly don't get it. :oops:

Area of circle = πr2
Circumference of circle = 2πr

Marking something with a footnote involves appending a superscripted number1.
Footnoting an equation can confuse the superscripted exponential notation with the superscripted footnote indicator notation, driving people (like xkcd readers) nuts.
Circumference of circle = 2πr2
Especially when the footnote indication provokes the reader with a "no wait, that's wrong, you've mixed up the circumference of the circle with the area of the circle!" reaction.

1 - like this
2 - like this


Ahhhhh, got it. Thanks. :)

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Re: 1184: "Circumference Formula"

Postby Jinxed » Mon Mar 11, 2013 8:48 pm UTC

Alright, I'm sure a few people have already said this, but I have become smitten with this comic. It's simple, it's funny, and it's iconic, in an xkcd kind of way.

And it makes quite a few people of a certain profession mad :lol:

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Re: 1184: "Circumference Formula"

Postby IainIsm » Mon Mar 11, 2013 8:54 pm UTC

In all of these cases, the actual meaning depends upon context. So, if any of these symbols or formats is misused, the overloading can cause the result to be very confusing and misleading.


"Introduction To Mathematical Analysis" (Hutchinson 1994) does exactly this on p21 (amongst other places)... and I'm not even joking.

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Re: 1184: "Circumference Formula"

Postby Diadem » Mon Mar 11, 2013 9:10 pm UTC

Coyne wrote:In the tooltip, the joke is over the apostrophe (') and quote (") symbols. In common usage, apostrophe can indicate "prime" (primary), foot (length), minute (angle or time interval), contraction (as in "don't") or glottal stop;

Within science the most common meaning is probably derivation though. Also "prime" generally means secondary, since the unprimed variables will be the primary ones.

Overloading is an often necessary evil though. There's only so many clearly distinguishable ways you can put a small number of lines on a paper.

(I was going to give an example here, but for some reason latex notation is not working anymore??)
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Re: 1184: "Circumference Formula"

Postby dudiobugtron » Mon Mar 11, 2013 9:35 pm UTC

brenok wrote:
jonbly wrote:What if the circle doesn't have any arms?


Who are you asking this to?

I guess it was aimed at someone who knows about human (or circle) anatomy; specifically the names of the bones in the arm. :P
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Re: 1184: "Circumference Formula"

Postby bmonk » Mon Mar 11, 2013 10:33 pm UTC

RAGBRAIvet wrote:You know, the same formula can be expressed as πD (where "D" is diameter of the circle).  No footnote needed.
For that matter, since when did common formulae require footnotes to explain the accepted standard symbols for constants and variables?

Also, τr, where τ = 2π
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Re: 1184: "Circumference Formula"

Postby brenok » Mon Mar 11, 2013 11:04 pm UTC

dudiobugtron wrote:
brenok wrote:
jonbly wrote:What if the circle doesn't have any arms?


Who are you asking this to?

I guess it was aimed at someone who knows about human (or circle) anatomy; specifically the names of the bones in the arm. :P


Oh, right. In portuguese, we call that bone "radio", as in, the electronic device. I didn't get it at first,

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Re: 1184: "Circumference Formula"

Postby PolakoVoador » Mon Mar 11, 2013 11:34 pm UTC

brenok wrote:
dudiobugtron wrote:
brenok wrote:
jonbly wrote:What if the circle doesn't have any arms?


Who are you asking this to?

I guess it was aimed at someone who knows about human (or circle) anatomy; specifically the names of the bones in the arm. :P


Oh, right. In portuguese, we call that bone "radio", as in, the electronic device. I didn't get it at first,


Ahh! Now I get it!

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Re: 1184: "Circumference Formula"

Postby drummerpatch » Tue Mar 12, 2013 1:13 am UTC

orangustang wrote:Of course, r''' is the second derivative of the radius of Earth Prime.


Given that the radius is likely constant, wouldn't that just be 0?

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Re: 1184: "Circumference Formula"

Postby penguinoid » Tue Mar 12, 2013 3:01 am UTC

orthogon wrote:Grr. My favourite newspaper insists on using Coulombs as a unit of temperature, e.g. "Temperatures in parts of the UK dropped to -5C last night".


I'm guilty of doing this, sometimes. Only because I can't find the key for the 'degrees' symbol on my phone keyboard. On my laptop keyboard I think it's ... here ° Right-Alt+:

Unless they're editing the newspaper on their mobile phones, they don't really have much of an excuse, though...

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Re: 1184: "Circumference Formula"

Postby CinIN » Tue Mar 12, 2013 3:41 am UTC

It reminded me of this one,

√3 → 2

for sufficiently large values of 3

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Re: 1184: "Circumference Formula"

Postby Coyne » Tue Mar 12, 2013 4:05 am UTC

Diadem wrote:
Coyne wrote:In the tooltip, the joke is over the apostrophe (') and quote (") symbols. In common usage, apostrophe can indicate "prime" (primary), foot (length), minute (angle or time interval), contraction (as in "don't") or glottal stop;

Within science the most common meaning is probably derivation though. Also "prime" generally means secondary, since the unprimed variables will be the primary ones.

Overloading is an often necessary evil though. There's only so many clearly distinguishable ways you can put a small number of lines on a paper.

(I was going to give an example here, but for some reason latex notation is not working anymore??)


I was thinking in terms of common usage, as the average person might see it in books or daily use. I would argue, though, that strict "derivation" is the same meaning as "prime" (secondary). Or did you mean mathematical deriviative, which I would regard as being distinct?

R' = F(R) → "prime", meaning secondary, and marking a derivation of the original R
vs
F'(x) = F(x) dx → indicating mathematical derviative


There's also another use of exponents I overlooked, indicating inverse, such as "sin-1(x)". And since I'm thinking about it, superscript is also used in atomic notation for mass (left position) and ionization state (right position), as 24Mg2+.

Maybe these things are way too overloaded?
Last edited by Coyne on Tue Mar 12, 2013 4:10 am UTC, edited 1 time in total.
In all fairness...

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Re: 1184: "Circumference Formula"

Postby Elmach » Tue Mar 12, 2013 4:42 am UTC

Coyne wrote:24Mg2+.

Reparsing as if written on paper...
Coyne wrote:24 Mg2.

24 Megagrams squared? What?

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Re: 1184: "Circumference Formula"

Postby Eternal Density » Tue Mar 12, 2013 5:05 am UTC

rpresser wrote:Ryan's a few dozen years late with this. See "Mathmanship" by Nicholas Vanserg (1958):

The other side of the asterisk gambit is to use a superscript as a key to a real footnote. The knowledge‐seeker
reads that S is –36.714 calories and thinks "Gee what a whale of a lot of calories" until he reads to the bottom of
the page, finds footnote 14 and says "oh."


(Vanserg was actually a psuedonym.)

Is Ryan a pseudonym for Randall?
Diadem wrote:
Coyne wrote:In the tooltip, the joke is over the apostrophe (') and quote (") symbols. In common usage, apostrophe can indicate "prime" (primary), foot (length), minute (angle or time interval), contraction (as in "don't") or glottal stop;

Within science the most common meaning is probably derivation though. Also "prime" generally means secondary, since the unprimed variables will be the primary ones.

Overloading is an often necessary evil though. There's only so many clearly distinguishable ways you can put a small number of lines on a paper.
Overloading 'prime'1 to mean both primary and secondary is definitely2 evil.

1Those are single-quotes, not primes :P
2But not necessarily defiantly.
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Re: 1184: "Circumference Formula"

Postby Davidy » Tue Mar 12, 2013 5:10 am UTC

Actually, pie are square
Image
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Last edited by Davidy on Tue Mar 12, 2013 5:52 pm UTC, edited 1 time in total.
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Re: 1184: "Circumference Formula"

Postby rpresser » Tue Mar 12, 2013 5:42 am UTC

Eternal Density wrote:
rpresser wrote:Ryan's a few dozen years late with this. See "Mathmanship" by Nicholas Vanserg (1958):

The other side of the asterisk gambit is to use a superscript as a key to a real footnote. The knowledge‐seeker
reads that S is –36.714 calories and thinks "Gee what a whale of a lot of calories" until he reads to the bottom of
the page, finds footnote 14 and says "oh."


(Vanserg was actually a psuedonym.)

Is Ryan a pseudonym for Randall?


D'oh! I did it again, mixed up Ryan North and Randall Munroe. Mea culpa.

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Re: 1184: "Circumference Formula"

Postby ManaUser » Tue Mar 12, 2013 6:01 am UTC

According to the Wikipedia article on superscript, an exponent should be higher than that (r2), so it's actually not ambiguous. A footnote can be written either way (r2 or r²), but fortunately the latter was used.

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Re: 1184: "Circumference Formula"

Postby Red Hal » Tue Mar 12, 2013 11:08 am UTC

IainIsm wrote:
In all of these cases, the actual meaning depends upon context. So, if any of these symbols or formats is misused, the overloading can cause the result to be very confusing and misleading.


"Introduction To Mathematical Analysis" (Hutchinson 1994) does exactly this on p21 (amongst other places)... and I'm not even joking.


a=b ) b=a3


3 By ) we mean implies.
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Re: 1184: "Circumference Formula"

Postby Diadem » Tue Mar 12, 2013 1:45 pm UTC

Red Hal wrote:
IainIsm wrote:
In all of these cases, the actual meaning depends upon context. So, if any of these symbols or formats is misused, the overloading can cause the result to be very confusing and misleading.


"Introduction To Mathematical Analysis" (Hutchinson 1994) does exactly this on p21 (amongst other places)... and I'm not even joking.


a=b ) b=a3


3 By ) we mean implies.

Who the hell uses ) for 'implies'? That's just evil.

My suggestion would be to take that book and burn it, burn it with fire.



Coyne wrote:
Diadem wrote:
Coyne wrote:In the tooltip, the joke is over the apostrophe (') and quote (") symbols. In common usage, apostrophe can indicate "prime" (primary), foot (length), minute (angle or time interval), contraction (as in "don't") or glottal stop;

Within science the most common meaning is probably derivation though. Also "prime" generally means secondary, since the unprimed variables will be the primary ones.

Overloading is an often necessary evil though. There's only so many clearly distinguishable ways you can put a small number of lines on a paper.

(I was going to give an example here, but for some reason latex notation is not working anymore??)


I was thinking in terms of common usage, as the average person might see it in books or daily use. I would argue, though, that strict "derivation" is the same meaning as "prime" (secondary). Or did you mean mathematical deriviative, which I would regard as being distinct?

Yeah I meant the mathematical derivative.

I always like how within general relative the subscript is overloaded: In an equation like AμAμ the μ is just a dummy variable, and you are allowed to use whatever symbol you like ... as long as you pick a lower-case greek letter. If you pick lower-case latin letter the meaning changes, and if you pick an upper-case letter people will just stare at you in confusion.
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Re: 1184: "Circumference Formula"

Postby PolakoVoador » Tue Mar 12, 2013 4:14 pm UTC

Red Hal wrote:
IainIsm wrote:
In all of these cases, the actual meaning depends upon context. So, if any of these symbols or formats is misused, the overloading can cause the result to be very confusing and misleading.


"Introduction To Mathematical Analysis" (Hutchinson 1994) does exactly this on p21 (amongst other places)... and I'm not even joking.


a=b ) b=a3


3 By ) we mean implies.


That hurts my eyes. :evil: Bad book! Bad!

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Re: 1184: "Circumference Formula"

Postby styrofoam » Tue Mar 12, 2013 5:30 pm UTC

drummerpatch wrote:
orangustang wrote:Of course, r''' is the second derivative of the radius of Earth Prime.


Given that the radius is likely constant, wouldn't that just be 0?


That's why you should always write derivatives either as primed functions [r'(t)] or using fraction notation [dr/dt]. (Assuming r is a function of t).

You could still write r'''(t''') as the second derivative of the radius of Earth Prime as a function of the time there in seconds.
Last edited by styrofoam on Tue Mar 12, 2013 5:46 pm UTC, edited 1 time in total.
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Re: 1184: "Circumference Formula"

Postby RogueCynic » Tue Mar 12, 2013 5:39 pm UTC

Everyone knows pi is exactly 3. When you place an object on a curved surface, it stretches to retain the same length. The earth's surface is curved, so all tables, etc are stretched to conform. All devices used to calculate pi therefore have that stretch, throwing off the measurement.
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Re: 1184: "Circumference Formula"

Postby Carteeg_Struve » Tue Mar 12, 2013 6:47 pm UTC

What? No E=mc12 jokes to really throw the numbers off? 8-)

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Re: 1184: "Circumference Formula"

Postby bunch » Tue Mar 12, 2013 7:21 pm UTC

The joke about the radius bone was humerus!!!

(Sorry for that, I'm French, and this is my first english play on words ever)

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Re: 1184: "Circumference Formula"

Postby Pfhorrest » Tue Mar 12, 2013 9:50 pm UTC

bunch wrote:The joke about the radius bone was humerus!!!

(Sorry for that, I'm French, and this is my first english play on words ever)


Anyone who doesn't appreciate that one doesn't have a funny bone in their body.
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Re: 1184: "Circumference Formula"

Postby bmonk » Wed Mar 13, 2013 12:58 am UTC

Davidy wrote:Actually, pie are square
Image
Q.E.D.

If you had two such square pies, that would be "2 pie are square," as indicated.
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Re: 1184: "Circumference Formula"

Postby Steve the Pocket » Wed Mar 13, 2013 6:43 am UTC

Coyne wrote:In common usage, apostrophe can indicate "prime" (primary), foot (length), minute (angle or time interval), contraction (as in "don't") or glottal stop; and quote can indicate "secondary", inch, second (angle or time interval), or quoted text. That's right: Six different common meanings for apostrophe; five for quote.

Although some of that confusion could have been avoided were it not for early typewriter designers deciding to reduce six symbols into two to save on space. In fact, Unicode takes it even further by making the ASCII ' and " distinct from the prime symbols as well as the proper quotation marks, for a total of eight characters in all. As if to say "These two bastardizations of punctuation are not the correct thing to use in any situation."

I still can't be assed to type the correct characters, mind you. When someone invents a keyboard that has them right there on the key caps, then we'll talk. But I do make a point of fixing errant victims of autocorrect like "Summer of ‘42", because there's lazy and then there's just plain wrong.
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Re: 1184: "Circumference Formula"

Postby tech42er » Wed Mar 13, 2013 8:21 am UTC

I agree with others. This is a quintessential xkcd comic. Randall, if you can hear us, we'd like it on a T-shirt. :D

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Re: 1184: "Circumference Formula"

Postby queueingtheory » Wed Mar 13, 2013 12:19 pm UTC

ejrb wrote:2 OED: a plane figure bounded by a single curved line which is everywhere equally distant from a point within7
3 A number; one more than one.
4 A number slightly more than one more than one6 more than one. Appears as the ratio of different aspects of circles: See Circumference of a circle
5 The distance from the centre of a circle to the edge of the circle
6 See 3

7 Surely that's a disk? A circle is the boundary, being the locus8 of points in a plane equidistant from a single point
8 a locus is just a set of points satisfying a set of rules

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Re: 1184: "Circumference Formula"

Postby orthogon » Wed Mar 13, 2013 1:44 pm UTC

The radius of Earth (prime) is 6373km.
xtifr wrote:... and orthogon merely sounds undecided.


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