1047: "Approximations"

This forum is for the individual discussion thread that goes with each new comic.

Moderators: Moderators General, Prelates, Magistrates

User avatar
Eshru
Posts: 146
Joined: Thu Jun 10, 2010 3:51 am UTC

Re: 1047: "Approximations"

Postby Eshru » Wed Apr 25, 2012 11:03 am UTC

RyanfaeScotland wrote:I notice Randall uses billions for the world population but millions for the US population. Why is he being dishonest?

Wait, what?

I was expecting one of the pi approximations but there were none. :(

User avatar
RyanfaeScotland
Posts: 29
Joined: Mon Oct 17, 2011 3:13 pm UTC

Re: 1047: "Approximations"

Postby RyanfaeScotland » Wed Apr 25, 2012 11:26 am UTC

Eshru wrote:
RyanfaeScotland wrote:I notice Randall uses billions for the world population but millions for the US population. Why is he being dishonest?

Wait, what?

I was expecting one of the pi approximations but there were none. :(


http://www.xkcd.com/558/ :)

obarey
Posts: 19
Joined: Wed Mar 31, 2010 9:26 am UTC

Re: 1047: "Approximations"

Postby obarey » Wed Apr 25, 2012 11:34 am UTC

[imath]\pi = \sqrt[3]{31}[/imath], true within 1 in 5000

E'Bahn
Posts: 5
Joined: Mon May 31, 2010 12:22 pm UTC

Re: 1047: "Approximations"

Postby E'Bahn » Wed Apr 25, 2012 12:08 pm UTC

My dad always taught me it as: 10[imath]\pi[/imath] Ms in a year. Yes, you could just say [imath]\pi \times 10^7[/imath], but the more straight-faced you say 'megaseconds', particularly while teaching, the more entertaining it becomes for you.

Noir_Desir
Posts: 5
Joined: Mon Apr 11, 2011 10:05 am UTC

Re: 1047: "Approximations"

Postby Noir_Desir » Wed Apr 25, 2012 12:11 pm UTC

reminds me of my dad's easy way to do simple multiplications:

7*7? Just take 5*10 and subtract 1.

User avatar
shashwat986
Posts: 60
Joined: Wed Mar 24, 2010 10:15 am UTC

Re: 1047: "Approximations"

Postby shashwat986 » Wed Apr 25, 2012 12:12 pm UTC

http://mrob.com/

Awesome page for people interested in RIES
Apparently, 1 in 5 people in the world are Chinese. And there are 5 people in my family, so it must be one of them. It's either my mum or my dad. Or my older brother Colin. Or my younger brother Ho-Chan-Chu. But I think it's Colin -- Tim Vine

User avatar
Klear
Posts: 1965
Joined: Sun Jun 13, 2010 8:43 am UTC
Location: Prague

Re: 1047: "Approximations"

Postby Klear » Wed Apr 25, 2012 12:35 pm UTC

Noir_Desir wrote:reminds me of my dad's easy way to do simple multiplications:

7*7? Just take 5*10 and subtract 1.


How is that better than "Just take 50 and substract 1", or even: "7*7? Just take 49 and you're done"?

Edit: Also 7*7 is trivial since everybody knows 6*7=42.

User avatar
kirkjerk
Posts: 54
Joined: Wed Sep 06, 2006 3:37 pm UTC
Contact:

Re: 1047: "Approximations"

Postby kirkjerk » Wed Apr 25, 2012 1:00 pm UTC

Tuinkabouter wrote:Even now you're too much of a mathematician to dare to say [imath]\pi \approx \sqrt{10}[/imath]. kudos.

Oh, man, that was one of my favorite bits from high school physics, when the teacher (walking us through a new type of problem on the board) rhetorically asked as permission to treat pi^2 as 10, for ease of calculation... we were of course aghast (esp. since in practical terms we generally learned to leave pi in there, it usually comes out in the wash) but then we went to show it's a closer approximation than saying "g is 10", which we did all the damn time.
http://kisrael.com/ - quotes and links daily

User avatar
smq
Posts: 6
Joined: Thu Dec 13, 2007 9:12 pm UTC
Location: MI, USA

Re: 1047: "Approximations"

Postby smq » Wed Apr 25, 2012 1:09 pm UTC

Using several different calculators, I'm getting the Whitehouse Switchboard # as one digit off: .2024561414923965799[...] which works of you truncate but not if you round as would be expected. (The Whitehouse switchboard is 202-456-1414.) But then, I guess it is an approximation...

--SMQ

amod00
Posts: 1
Joined: Wed Apr 25, 2012 1:11 pm UTC

Re: 1047: "Approximations"

Postby amod00 » Wed Apr 25, 2012 1:13 pm UTC

pi^2 is a pretty good approximation for g already

User avatar
addams
Posts: 10336
Joined: Sun Sep 12, 2010 4:44 am UTC
Location: Oregon Coast: 97444

Re: 1047: "Approximations"

Postby addams » Wed Apr 25, 2012 1:31 pm UTC

Math is a beautiful and poetic language.
Math has elegant rules, like all languages.

To bend the rules and not break them is a skill, to be sure.

It must be very difficult inside his head. He can do that AND be normal?

Good Him!

How long do you think that takes? Can he sit down and blow through a thing like that from memory? In what? Ten minutes?

Or; Does he doggedly move from one system of measure to the next, until a circuit blows in his head?

A thing like that makes me wonder. I like watching people do that kind of work. Computers sure make it easier. Less entertaining for me, but, easier for the person doing the work.

Yep. Think about it children.
What were Mathematicians like before the computer?

Just like, now. Not all were the same.
Life is, just, an exchange of electrons; It is up to us to give it meaning.

We are all in The Gutter.
Some of us see The Gutter.
Some of us see The Stars.
by mr. Oscar Wilde.

Those that want to Know; Know.
Those that do not Know; Don't tell them.
They do terrible things to people that Tell Them.

OP Tipping
Posts: 262
Joined: Thu Dec 13, 2007 6:23 am UTC

Re: 1047: "Approximations"

Postby OP Tipping » Wed Apr 25, 2012 1:35 pm UTC

At least two of the "accurate to within" margins are lower than the uncertainty in the value estimated: the ocean's volume and the age of the universe.
a) Please explain the specific MEDICAL reason for ordering this MEDICATION !
b) Please state the nature of your ailment or injury.
c) One a scale of one to ten, how would you rate your pain?
d) Please state the nature of the medical emergency.

User avatar
jqavins
Posts: 96
Joined: Fri Apr 18, 2008 2:50 pm UTC
Location: Eastern panhandle, WV

Re: 1047: "Approximations"

Postby jqavins » Wed Apr 25, 2012 1:43 pm UTC

mistapotta wrote:My favorite one is π=355/113, just to irritate my students who insist π is irrational.

355/113 is 3.14159292, so much better than 22/7.

That's my favorite as well. It's good to better than 1 in 10^7, which makes it as good as perfect for very nearly all real world purposes. (For instance, in 1e-7 hours, an object moving at mach 2 covers less than ten inches.)
-- Joe
"[Some people don't believe in coincidence, but] I believe in coincidence. Coincidences happen every day. I just don't trust coincidence."
Elim Garak

tomsing
Posts: 4
Joined: Sat Feb 26, 2011 3:06 pm UTC

Re: 1047: "Approximations"

Postby tomsing » Wed Apr 25, 2012 1:45 pm UTC

smq wrote:Using several different calculators, I'm getting the Whitehouse Switchboard # as one digit off: .2024561414923965799[...] which works of you truncate but not if you round as would be expected. (The Whitehouse switchboard is 202-456-1414.) But then, I guess it is an approximation...

--SMQ


If you just keep dialing digits, only the first 10 will be used by the phone system, I believe.

beav
Posts: 16
Joined: Wed Aug 04, 2010 1:11 pm UTC

Re: 1047: "Approximations"

Postby beav » Wed Apr 25, 2012 1:51 pm UTC

THIS ep is why I read this comic. And come to this forum.

>sniff< it's BEAUTIFUL.

User avatar
VectorZero
Posts: 471
Joined: Fri Nov 02, 2007 7:22 am UTC
Location: Kensington

Re: 1047: "Approximations"

Postby VectorZero » Wed Apr 25, 2012 2:15 pm UTC

jqavins wrote:
mistapotta wrote:My favorite one is π=355/113, just to irritate my students who insist π is irrational.

355/113 is 3.14159292, so much better than 22/7.

That's my favorite as well. It's good to better than 1 in 10^7, which makes it as good as perfect for very nearly all real world purposes. (For instance, in 1e-7 hours, an object moving at mach 2 covers less than ten inches.)
And so elegant, to boot. 2 1's, 2 3's, 2 5's. Write them in order, bisect and assemble the fraction, you'll never forget it.
Van wrote:Fireballs don't lie.

User avatar
deoxys9
Posts: 3
Joined: Wed Mar 05, 2008 11:32 pm UTC

Re: 1047: "Approximations"

Postby deoxys9 » Wed Apr 25, 2012 2:35 pm UTC

This would make an excellent poster. I'd buy it in a heartbeat. They're just so elegant and cool!

kafkadog
Posts: 9
Joined: Wed Aug 12, 2009 8:42 pm UTC

Re: 1047: "Approximations"

Postby kafkadog » Wed Apr 25, 2012 2:48 pm UTC

Shidoshi wrote:
ptorquemada wrote:
Shidoshi wrote:The gas constant is expressed in J/gmol.K and not J/kgmol.K which would be the SI unit.


I've never seen the abbreviations "gmol" or "kgmol", but the SI units of the gas constant are Joules per mole Kelvin, and moles are defined as if they were based on grams instead of kg. Probably because the chemists threatened insurrection otherwise... grams are a much more convenient laboratory unit.


I've been recently through ChemEng and now they are starting to use "kilogram moles" and "gram moles", that way everything can be expressed in kg without much problem. Carbon12's molar mass is 12g/gmol or 12kg/kgmol (or even 12lb/lbmol if you swing that way). It's a somewhat new concept yeah, but it sure helps putting everything to SI and making less confusion.

The SI unit for "amount of substance" is the mole:
http://www.bipm.org/en/si/base_units/
"The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12."

And the current Wikipedia article on the mole says:
"In the metric system, chemical engineers once used the kilogram-mole (noted kg-mol), which is defined as the number of entities in 12 kg of 12C, and often referred to the mole as the gram-mole (noted g-mol), when dealing with laboratory data.[17] However modern chemical engineering practice is to use the kilomole (kmol), which is identical to the kilogram-mole, but whose name and symbol adopt the SI convention for standard multiples of metric units."
[Reference 17 is to an engineering text published (as its 6th Ed.) in 1996.]

So the kg-mol is 1. not new, and 2. not SI.

User avatar
da Doctah
Posts: 997
Joined: Fri Feb 03, 2012 6:27 am UTC

Re: 1047: "Approximations"

Postby da Doctah » Wed Apr 25, 2012 2:58 pm UTC

bitwiseshiftleft wrote:Also, e^(pi * sqrt(163)) ~ 640320^3 + 744. But that one is famous. And was found by a method other than brute force.


Damn, you beat me to it.

I once had parking permit number 163 at work. One weekend, the hang tag somehow got lost from the driver's door pocket I had been keeping it in and I had to apply for a replacement. Although I asked for a re-issue of the same number on the grounds that the number was easy to remember (citing the near equality above), they couldn't give it to me.

I had to settle for the boring 31416 instead.

Sinnombre
Posts: 2
Joined: Wed Oct 26, 2011 3:07 pm UTC

Re: 1047: "Approximations"

Postby Sinnombre » Wed Apr 25, 2012 3:06 pm UTC

How could he miss the best approximation of all?

pi^2 = 9.8696
g = 9.78 to 9.82

That one is actually useful in basic physics, since the period of a small angle pendulum is:
T=2 pi sqrt(L/g) --> T = 2 sqrt(L)

anchises868
Posts: 2
Joined: Wed Apr 25, 2012 3:19 pm UTC

Re: 1047: "Approximations"

Postby anchises868 » Wed Apr 25, 2012 3:26 pm UTC

My personal favorite, or at least the one I use with my math students, is [math]\pi \approx \sqrt[4]{\frac{2143}{22}}.[/math]I found it by accident.
Spoiler:
Well actually, while playing with a calculator while on the toilet...

cburke
Posts: 28
Joined: Fri Jun 27, 2008 3:58 pm UTC

Re: 1047: "Approximations"

Postby cburke » Wed Apr 25, 2012 3:51 pm UTC

I had a problem with Jenny's constant until I realized that that was a minus sign in the exponent, not a "dot" for multiplication.

User avatar
San Fran Sam
Posts: 228
Joined: Tue Nov 15, 2011 5:54 pm UTC

Re: 1047: "Approximations"

Postby San Fran Sam » Wed Apr 25, 2012 3:55 pm UTC

alextrabec wrote:Randall wins again. P.S. You are all nerds fact checking a web comic. Great Job, make your professors proud! Also, your mom plus me makes a "That what she said joke" - Enjoy

Love the comics and nerds, keep it up bitches!


Or the comic could have been titled "Pedantry Test". You know who you are.

Have a safe day.

top1214
Posts: 29
Joined: Wed Oct 17, 2007 6:06 am UTC

Re: 1047: "Approximations"

Postby top1214 » Wed Apr 25, 2012 3:57 pm UTC

mistapotta wrote:My favorite one is π=355/113, just to irritate my students who insist π is irrational.

355/113 is 3.14159292, so much better than 22/7.

This fails for Jenny's constant. :(

ttk
Posts: 2
Joined: Wed Apr 25, 2012 3:38 pm UTC

Re: 1047: "Approximations"

Postby ttk » Wed Apr 25, 2012 3:59 pm UTC

I'm loving this table. I spend a lot of time figuring out approximations (mostly for equivalence functions, like converting Rockwell Hardness-C to Brinell Hardness Number: bhn = 89.75 + 28.5125*hrc - 0.1905*hrc**2 + 0.00315*hrc**3, coming soon to a CPAN module near you), but Randall's are just awesome.

The error in the sqrt(2) formula bothers me a lot .. I've edited my copy of the image so the "-" is "+", but the edit looks bad. I don't suppose Randall ever reads these forums and might post a corrected image? That would be wonderful.

RyanfaeScotland - I give up. What's the punchline?

-- TTK

User avatar
San Fran Sam
Posts: 228
Joined: Tue Nov 15, 2011 5:54 pm UTC

Re: 1047: "Approximations"

Postby San Fran Sam » Wed Apr 25, 2012 4:01 pm UTC

Klear wrote:
Noir_Desir wrote:reminds me of my dad's easy way to do simple multiplications:

7*7? Just take 5*10 and subtract 1.


How is that better than "Just take 50 and substract 1", or even: "7*7? Just take 49 and you're done"?

Edit: Also 7*7 is trivial since everybody knows 6*7=42.


What do you get if you multiply six by nine?

Astari
Posts: 1
Joined: Thu Feb 16, 2012 2:18 pm UTC

Re: 1047: "Approximations"

Postby Astari » Wed Apr 25, 2012 4:16 pm UTC

deoxys9 wrote:This would make an excellent poster. I'd buy it in a heartbeat. They're just so elegant and cool!


I would as well - I'd hang it in my classroom, and try to find some fun way to incorporate it into my lessons. I'm sure the kids would get a kick out of it.

Dr. Tom
Posts: 2
Joined: Wed Apr 25, 2012 4:03 pm UTC

Re: 1047: "Approximations"

Postby Dr. Tom » Wed Apr 25, 2012 4:20 pm UTC

somebody_else wrote:The error in the first Protip is pretty big though. If only the fractions were added instead of subtracted. I am going to use the radius of the earth one from now on - just to confuse anyone reading my work.


It's a simple error. It should be plus, not minus. 3/5 + pi/(7-pi)

/a picogalyear is about 2 hours (galactic year/10**12)

Elirra
Posts: 18
Joined: Wed Oct 19, 2011 2:43 pm UTC

Re: 1047: "Approximations"

Postby Elirra » Wed Apr 25, 2012 4:28 pm UTC

San Fran Sam wrote:quote]

What do you get if you multiply six by nine?


42. I love base 13 jokes.

User avatar
Trickster
Posts: 89
Joined: Fri Sep 05, 2008 5:56 pm UTC

Re: 1047: "Approximations"

Postby Trickster » Wed Apr 25, 2012 4:31 pm UTC

I take exception with the joke about 1/140... 1/137 is a perfectly fine constant approximation.

:D

popman
Posts: 70
Joined: Sun Mar 07, 2010 7:38 pm UTC

Re: 1047: "Approximations"

Postby popman » Wed Apr 25, 2012 4:51 pm UTC

San Fran Sam wrote:
Klear wrote:
Noir_Desir wrote:reminds me of my dad's easy way to do simple multiplications:

7*7? Just take 5*10 and subtract 1.


How is that better than "Just take 50 and substract 1", or even: "7*7? Just take 49 and you're done"?

Edit: Also 7*7 is trivial since everybody knows 6*7=42.


What do you get if you multiply six by nine?

fourty-two.

only with stone scrabble tiles though.
www.crashie8.com

therenaissanceman
Posts: 11
Joined: Sun Aug 14, 2011 1:45 am UTC

Re: 1047: "Approximations"

Postby therenaissanceman » Wed Apr 25, 2012 4:55 pm UTC

My physics teachers are going to get a kick out of this one.

I also warned them in case a wiseass decided to try and use that on a test or homework.

aconley
Posts: 1
Joined: Wed Apr 25, 2012 4:58 pm UTC

Re: 1047: "Approximations"

Postby aconley » Wed Apr 25, 2012 5:06 pm UTC

The age of the universe approximation is more like 1/160 accurate for the current WMAP 7yr value (Komatsu et al. 2011,
ApJS 192, 18).

The problem is that that measurement is a very model dependent value -- the current age estimate (13.76 +- 0.11 Gyr) makes
a bunch of assumptions (dark energy is a cosmological constant, a non running initial spectral index, purely Gaussian initial
conditions, number of relativistic neutrino species, no sterile neutrinos, etc.). There's a good chance at least one of those
will turn out to be wrong, although we don't know which one(s). None of those are likely to change the age that much
(so it won't suddenly become 11 Gyr or something), but you shouldn't believe that the age is currently measured to the
1 part in 70 that Randall claims.

praetor_alpha
Posts: 2
Joined: Wed Apr 25, 2012 6:15 pm UTC

Re: 1047: "Approximations"

Postby praetor_alpha » Wed Apr 25, 2012 6:22 pm UTC

Aw. My favorite isn't there:

φ ≈ -2sin(666°)

The golden ratio is the doubly negative sine of the beast.

Don't know exactly how accurate it is (or even if it's exact); a cursory calculation or two and comparison shows it's at least 8 digits accurate.

User avatar
Wnderer
Posts: 640
Joined: Wed Feb 03, 2010 9:10 pm UTC

Re: 1047: "Approximations"

Postby Wnderer » Wed Apr 25, 2012 6:29 pm UTC

He left off that the speed of light is (3+ln(20))/2 * 10^8 meters/second, correct to 1 part in 50000.
Last edited by Wnderer on Wed Apr 25, 2012 8:53 pm UTC, edited 1 time in total.

AnotherAngle
Posts: 2
Joined: Wed Apr 25, 2012 6:41 pm UTC

Re: 1047: "Approximations"

Postby AnotherAngle » Wed Apr 25, 2012 7:01 pm UTC

I have a 'proof' published about 60 years ago of why the proton/electron rest mass is [imath]6{{\pi }^{5}}[/imath],

It was publised in "Imperfect picture: An appreciation of the scientific and philosophic thought of Alfred Claude Jessup". I posted it at:

http://nigel.thedyers.org.uk/Jessup/Imperfectpicture.pdf

tangozulu
Posts: 1
Joined: Wed Apr 25, 2012 7:22 pm UTC

Re: 1047: "Approximations"

Postby tangozulu » Wed Apr 25, 2012 7:25 pm UTC

The value of second per/year approximation in the header of the page (just below the xkcd logo) is shown as pi * 10^6. The value of pi * 10^7 is 31,415,926. It's an off-by-one error, we all get 'em.

MichiK
Posts: 17
Joined: Thu Jan 17, 2008 9:34 pm UTC

Re: 1047: "Approximations"

Postby MichiK » Wed Apr 25, 2012 7:35 pm UTC

Hmm, I like e^π - π = 20. I already made people think their calculators have floating point errors like Intel CPUs...

rcox1
Posts: 112
Joined: Wed Nov 11, 2009 11:23 pm UTC

Re: 1047: "Approximations"

Postby rcox1 » Wed Apr 25, 2012 7:51 pm UTC

This reminds me of my applied physics class and error analysis. We would go through and work out the percentage errors assuming certain errors in our measurements. Of course we assumed the constants had no errors, and in fact the precision of the constants were much higher than the precision of the measurements, so error attributed to constants were negligible. It would be interesting to do such an analysis to see if any of these approximations would lead to significant increases in the error of the experiments.

Which of course is the real metric of an approximation. Constants do not exist by themselves. They are used to infer additional results. For instance, the gas constant allows us to convert the energy represented by temperature in an amount of ideal gas to the actual energy. The number itself is an experimental contrivance determined by a fit.

I guess it annoys me a little then to focus on these numbers themselves, since the numbers are not nearly as interesting as the process used to generate the numbers. I guess that is the experimental part of me rebelling against the ivory tower mathematicians, some who seem to be looking for cosmological significance in the fact everything can be approximated with pi or e or whatever is the constant of the day. Of course it is all in fun, and it is certainly enlightening to seeing the devine in e^(i*pi), but at the end of the day I would rather be looking for such things in a laser beam bouncing around the room, or an electron circulating a magnetic field, than in a bunch of numbers.

Leshy
Posts: 1
Joined: Wed Apr 25, 2012 7:50 pm UTC

Re: 1047: "Approximations"

Postby Leshy » Wed Apr 25, 2012 7:56 pm UTC

I this is the first time in have absolutely no idea what this comic means, and that the comments here don't help in any way, shape or form.
I mean, utterly clueless. (I get Jenny's number, but none of this math/science is remotely ineligible. Oh well. First for everything.


Return to “Individual XKCD Comic Threads”

Who is online

Users browsing this forum: Google [Bot], mscha and 83 guests