

Back of the Envelope Calculations [pdf] - jasim
http://www.yorku.ca/bquine/ENG1000/lectures/ENG1000_6_2_BOTE_BQ_rev2.pdf

======
tokenadult
When hiring engineers for my company, I might ask, what are the trade-offs in
using PowerPoint-style slides to make a technical presentation? And I would
expect an astute engineer who has thought about technical communication to
refer me to either serious

[http://www.edwardtufte.com/bboard/q-and-a-fetch-
msg?msg_id=0...](http://www.edwardtufte.com/bboard/q-and-a-fetch-
msg?msg_id=0001yB)

or humorous

<http://norvig.com/Gettysburg/>

discussions of the defects of PowerPoint slides as a communication tool.

The slides shown here cover some interesting ground, and I was glad to see the
specific reference to Enrico Fermi, who popularized the kind of estimation
question discussed here in certain circles. Certainly, it is beyond dispute
that

"Although most engineers remember key numbers related to their field, no-one
has every detail at their fingertips

"Hence we need to estimate not only the values of numbers we need, but which
numbers are appropriate, and how to perform the calculation

"the emphasis here is on 'order of magnitude' estimates – to the nearest
factor of 10

"it is also important to remember that these are rough estimates and to place
only appropriate reliance on the results"

The last point is the most crucial. It is vital to remember how much
uncertainty there is in your estimates, or overall in your model that includes
both exactly measured and estimated values. The model is not reality. It is
not easy to get engineers to remember that they have to look into the
mechanism of the model to understand how it works. That's why a NASA Mars
probe failed when one part of the engineering team used United States
customary units while another used metric units to design modules of the probe
that were supposed to communicate values to each other.

<http://edition.cnn.com/TECH/space/9909/30/mars.metric.02/>

~~~
notaddicted
What are the alternatives though? (to powerpoint)

I love chalk and talk but it puts a lot of load on the speaker. My Electricity
and Magnetism professor basically pushed it to the limit I think. He had a
carefully cultivated temper that was bad enough to keep 100 students totally
silent for 50 minutes and he used about five different colors of chalk, but
there are limits to what you can scrawl out on a blackboard.

You can distribute written documents, this gives you maximum opportunity to
convey information, but you can't force people to actually read them. Going
from a paper memo to email exacerbates this I think. Best case scenario, you
can present very clear and well structured information but if you go past two
pages you have to wonder if anyone is really paying that much attention. As a
"best case example" I'd look at something like this memo that Robert McNamara
wrote to LBJ about a month after LBJ took office:
<https://www.mtholyoke.edu/acad/intrel/pentagon3/doc156.htm> . A benefit of
written work is that you are committed to your words. But: creating a concise
and readable written document that will effectively spread your thoughts is
excruciatingly difficult. You can't write a book of background info every time
you have a staff meeting.

...

About remembering that you have a rough model though, I think the key thing is
that when you realize that there is something you are interested in measuring
and once you have a model then you can start looking for quantities you can
actually measure to (in)validate and tighten the model. Always be model
checking.

~~~
jperras
I spent four years studying physics and mathematics, and I only had one
professor that used transparent acetate sheets with notes pre-written and
examples on them. All my other professors wrote out everything with chalk.
Heck, we were _excited_ when they used more than one colour of chalk, because
that meant there was something exciting about to come up.

Additionally, having chalk & talk meant that many students showed up to class,
instead of just relying on "reading" printouts of slides that the professor
made available. I would venture a guess that I would have performed rather
poorly in a class that had powerpoint slides, due to my inherent laziness in
my early 20s.

~~~
hp50g
Acetate rocks, especially when its well written and you can pop into the
prof's office and have a tea and chat and do some photocopying. I learned much
more this way.

Chalk, we spent more time dictating and deciphering the babbling fool who
can't communicate it all concisely from memory.

------
GabrielF00
The Bureau of Labor Statistics says that there were 6,300 Musical Instrument
Repairers and Tuners (code 49-9053) in the United States in 2010 and 320 in
New York State in
2008.[http://www.acinet.org/occ_rep.asp?next=occ_rep&Level=...](http://www.acinet.org/occ_rep.asp?next=occ_rep&Level=&optstatus=111111111&jobfam=49&id=1&nodeid=2&soccode=499063&stfips=36&x=68&y=17)

~~~
rquantz
But that's a broad category. There are a lot of instruments that need repairs
and maintenance that are not pianos, and they tend not to cross instrument
categories, or even individual instruments. A flute repair person will not
likely also repair oboes, for instance. Also, piano repairs and piano tuning
are not always done by the same people.

------
zeteo
This method breaks rather quickly because, when you multiply two order-of-
magnitude estimates, you get a two-orders-of magnitude estimate. (And so
forth.) In the piano tuners example, there are some five independent
quantities being estimated. Of course, the answer "I think there are 500 piano
tuners in NYC" doesn't sound as impressive when you add "within five orders of
magnitude"...

~~~
pmiller2
This is strictly true, but doesn't account for the fact that errors tend to
cancel one another. For instance, if 2 of the 5 independent estimates are
high, one is right on, and 2 are low, you can end up with a number very close
to the actual number. And, by "very close," I mean usually within 1-2 orders
of magnitude, depending on the quality of the component estimates.

------
alanlewis
15\. Source:
[http://www.yelp.com/search?find_desc=piano+tuner&find_lo...](http://www.yelp.com/search?find_desc=piano+tuner&find_loc=New+York%2C+NY)

~~~
shanelja
If this was Reddit this would pretty much be /thread, however I propose the
following question:

While this may be a good estimate, what about businesses not on Yelp?

"Professional Piano tuner" doesn't seem the most technologically advanced
profession, so I think it's safe to assume that there are several, if not
dozens more in existence in the NY area.

~~~
ambiate
This is correct. In my town, there are four used game stores. Two of these
stores do not exist online in any shape or form (One locally owned, one a
subsidiary of game exchange).

Searching for a seamstress in my town turns up a few results for dry cleaners.
A look on craigslist returns a much larger result.

------
rquantz
NYC is a weird place to estimate in exactly this way. It has more of a lot of
types of people who have pianos other than families. NYC has a
disproportionate number of wealthy people, and also a disproportionate number
of professional pianists, and I would expect both those categories get their
pianos tuned rather more often than a typical family.

NYC also has lots of concert halls, and any decent concert hall will tune the
piano to be used in a performance on the day of. A hall like Carnegie hall
would have several pianos tuned every day.

I no do math, so maybe those things aren't enough to have a material effect on
the number of piano tuners.

------
jonsen
Book: <http://mitpress.mit.edu/books/street-fighting-mathematics>

Free PDF edition available there.

------
gyepi
Jon Bentley has a chapter on this topic in the performance section of
_Programming Pearls_. This is a very useful skill for reasoning about problem
boundaries. All too often, our performance estimates are on the order of
"fast" and "crazy fast". Worse yet, we build systems without understanding how
they will scale under load.

------
gus_massa
_> A well-known curve of a calculation’s accuracy versus mental effort goes
like_

    
    
      \
       \
        \    __
         \__/  \
                \____ 
    

Have anyone really measured this bump or it's only folklore / myth?

~~~
tinco
It's the well known 'this graph is true because it has unexplainable data in
it' bump.

~~~
gus_massa
The problem is not that it is unexplainable, or yet unexplained. The problem
is if it is measurable and if it really exists.

(For example gravity is "unexplained" in some way. You have two masses, they
deform the space, and with some approximations you can use the formula
F=GmM/R^2. But, for example, why do masses deform the space?!?!?!?!?! But
luckily you can measure it, just drop a stone or find a gravity lens, so
gravity exists.)

------
Irregardless
One problem: He assumes that the market is being adequately served, i.e. that
supply and demand are relatively equal. What if tuners have a 1 year backlog
and they're charging triple what you'd pay in other cities because there
aren't nearly enough of them? This one piece of information could drastically
affect the accuracy of any response.

Not exactly relevant when all you're concerned with is determining whether or
not someone can "estimate the answer without any specialised knowledge". But,
then again, why would you only be concerned with something so trivial?

~~~
thatthatis
Knowing the correct order of magnitude is seldom trivial. Getting the correct
order of magnitude quickly will make you a better decision maker (not to
mention impress people whose opinion matters).

An imbalance of supply can increase/decrease the population by maybe as much
as 2x (or .5x). An order of magnitude can be the difference between a market
that's worth considering and one that's too small to currently be serviceable.

This is important because in business getting a right(ish) answer quickly is
often more important than getting a precisely correct answer slowly. While
you're measuring precise supply and demand, FermiCo has already concluded that
the market is too small and moved on.

p.s. irregardless is a great word.

------
leoedin
I use this type of calculation all the time. It's often applied to a more
scientific problem than piano tuners, but the key is round numbers,
approximations and simplified equations. It's an incredibly useful process if
you have an idea sloshing around but don't know whether it would yield
anything. 10 minutes and a few estimations and you know whether it's feasible
or not.

------
zwieback
I've asked out-of-town job candidates "How many gas stations do you think are
in this town?" but I've not had much success with that. I think for engineers
it's vital to be able to do order-of-magnitude estimations and I'm trying to
get my kids to learn that but it doesn't seem to come naturally to people.

~~~
tinco
I think it has to do with how you phrase the question. People go to job
interviews knowing that they're going to be tested for their knowledge, and
phrasing the question like that triggers a "how am I supposed to know that?"
response.

But you're not actually asking them to know it, you're asking them to reason
about it. So perhaps instead of asking "How many gas stations do you think are
in this town?" try asking "Could you give me a reasonable estimate of the
amount of gas stations in this town?".

I think a lot of people just lock up when they're asked something they don't
know in a synthetic situation even when in a real situation they would
actually make very good judgements since in any real situation the context is
often so much more clear, unless you like to keep your employees in the dark..

~~~
Terretta
> _I think a lot of people just lock up when they're asked something they
> don't know in a synthetic situation even when in a real situation they would
> actually make very good judgements since in any real situation the context
> is often so much more clear, unless you like to keep your employees in the
> dark._

I've had that mental block happen, not when asked to estimate something like
balloons in a gym, but when asked to estimate something I _knew_ for a _fact_
was a single search query away.

I was asked, "So how many travelers or trips in the US each year?"

Googling "how many travelers in us" gives [http://www.ustravel.org/news/press-
kit/travel-facts-and-stat...](http://www.ustravel.org/news/press-kit/travel-
facts-and-statistics) as the top result.

Knowing this is that kind of data, I was unable to put myself in a frame of
mind to make believe reasoning through it. The interviewer told me to just
pretend we were white boarding a marketing plan for a travel tool. I pointed
out that in such white boarding or brainstorming conversations, someone would
look that data point up because it's obvious a lookup would be more quickly
available and more accurate than running through a Fermi style reasoning
chain.

Partly because the best developers are "lazy", morally opposed to reinvention
of wheels, your point about performance in a _synthetic situation_ is dead on.

------
bprieto
I actually did this the other day to show a friend that a newspaper had
greatly exaggerated the number of prostitutes in Spain (300.000).

There are 40M persons in Spain, 50% are women, 50% of women have an age
suitable for the trade, it is impossible that 3%, or 1 in 30 are prostitutes.

------
ambiate
If only all requirements were up front and found in the initial discourse.

------
infinitone
Never thought i'd see my first year eng prof's lecture on HN. :)

This lecture note is credited to Professor Ben Quine, a popular and favourite
eng prof at York University, Canada.

~~~
TheLegace
Really, I had him a couple years ago. I'm in CompEng, what field are you in,
we might know each other ;).

~~~
infinitone
We do know each other. Very well :0

------
TheLegace
I was taught by the engineer who created those slides. Pretty interesting guy.
Has Professor Quine okayed the slides being posted?

