Friday, October 19, 2018

The Baader-Meinhof effect and flying over the southwest United States


The frequency illusion... 

... aka the Baader-Meinhof effect, happens when you learn something new, and then suddenly start to see it everywhere.  This happens when you finally decide to buy a new car and after weeks of agonizing, you finally pick that very special one, the very distinctive car that speaks to only you.  You're so happy.  

And then you start to see that car everywhere. It's not distinctive at all, but actually pretty common.  

That's the Baader-Meinhof effect.  It happens because you don't notice all of the cars that are just like it before you made the choice--it's an illusion of the frequency of the item.  

It also happens with words.  If I use the term whale shark and you learn that as a new concept, suddenly you'll see it everywhere.  Trust me, you'll start to see whale shark everywhere now.  

So when Regular Reader Ramón wrote it with a Washington Post article, it was a nice example of this effect.  He found a real, live example of our Challenge from last week:  How can I make a movie of my flight?  In that post, I show you how to make a video by using Google Earth to capture a flight path.  

Ramón noticed that the Post article "Flying over Trump's wall" used the exact same technique (although they did some great post-production video editing).   In an early part of the fly-over, it looks like this: 



Thanks for the find, Ramón!  Now we all know how this brilliant piece of visualization was created.  

Search (and visualize) on! 


Thursday, October 18, 2018

SearchResearch Challenge (10/18/18): How can you find lists of things?


I often find myself in the position of looking... 

... for a list of things.  It's a natural way to try and get your mind around a given topic--if I can give you a list of items in that category, you'll get a sense of how that category of thing is defined (or at least how it looks).  People often do this when it's hard to define something precisely.  The difference between a vegetable and a fruit is tricky, but if I tell you that apples, strawberries, bananas, and grapes are all fruits while potatoes, carrots, corn, and peas are all vegetables, you'll start to get the idea. This doesn't give you a technical definition (difficult question: is a cucumber a fruit or a vegetable?), but it gives you a working intuition.  

This came up for me a few weeks ago when I went to see an art exhibition of the Pre-Raphaelites.  I love their artwork, and while I knew a few of the artists (Dante Gabriel Rossetti, John Everett Millais, and John William Waterhouse, I couldn't name any others, although I know I'd recognize their names).  Who are these folks??   Here's the kind of thing I wanted to get from a search:  



This week's Challenge is to figure out the best way to search on Google for a set of things that share a common property.  That is, to find a way to create this image above.  The Challenge: 

1.  Can you find a way to find a set of each of the following:  
      a.  Pre-Raphaelite artists 
      b.  fictional works written in the Regency era
      c.  clans in Scotland
      d.  trees that are evergreen throughout the year 
      e.  Canadian Prime Ministers   

Once you figure out how to do this, you'll be able to this, and much more!

As always, be sure to tell us how you do it. 

AND... if you find a particularly interesting set of things, be sure to leave a comment telling us about the great set you found (and what it is!).  

Search on! 




Wednesday, October 17, 2018

Answer: How can I make a movie of my flight?

My goal was simple...  

... I just wanted a movie that's a scan of the flight path.    

Why?  Because as I was looking out the window, I saw beautiful things, extraordinary things, and I wanted to be able to stop the plane and look around a bit.  How could I do that?  


So this became a search for a tool that would let me do exactly this.  I set up the Challenge like this:    



1.  Can you make a movie that recreates the experience of flying from San Francisco to Austin?  Obviously, you don't want it to take all 4 hours.  How about a 2 minute version of the flight that just shows off the really interesting parts between Arizona and West Texas? 

This isn't an ordinary SearchResearch Challenge--this is really a Challenge about (A) How to find such a tool?  and (B) How to use the tool to create a video that follows the flight path.   (You'll get to choose your own tool, along with your altitude and camera angles.)  


How can I find a tool that could do this?   I started with a bit of a question to Google: 

     [ make a movie flight over the earth ] 

The results were pretty interesting--here's the SERP:  




Just looking at this suggests that I can make a video like this with Google Earth Pro.  Great!  

After a few queries of the form:  [ how to make a video in Google Earth ], I was able to piece together a way to create the video.  Here's how I did it: 

1.  Open Google Earth Pro and draw a path.  Here I approximate it with 2 segments--one starting at SFO airport, bending slightly in New Mexico and then continuing on to Austin. Just use the "path tool" in the toolbar at the top.   Two clicks, and then I gave the path a name:  SFO/AUS path. Click on the path tool (shown below) to make it:  



In the image below, I created a path, and added to yellow push pins (just to make the start/stop locations more visible).  This is the flight path.  



2.  Save the path as a tour.  First select the path on the left; then click on the "Play Tour" button.  This will make the Play Tour toolbar appear like this: 




The Play Tour controller will popup to the right of that menu item in the lower left of the window.  This will let you save the SFO/AUS path as a Tour:  



Once you've got that, you can click on the floppy disk icon (far right in above diagram--no, I don't know why they show a floppy disk icon as the "Save" button).  

That will create a new item in the list in the upper left--here I named it "SFO/AUS Tour."  





3.  Now... Open the Movie Maker tool.  It's in the menu pulldown list Tools>Movie Maker.  Note: You need to close the Play Tour controller first!  This will make the tour playback automatically and will create a video as a side-effect. 



Here's an example of what that Tour video looks like (this isn't the entire flight from SFO to Austin, it's just a sample of the path... it gives you a good idea).  URL: https://www.youtube.com/watch?v=c0sRxmPoRWo



There are lots of options you can do to make it fly in the way you want.  In particular, you could move the view position manually to fly over the entire route quickly.  Here's what that video would look like.  It's kind of jerky because I'm actually pulling the viewpoint along moment to moment, and I wasn't super careful.  



My original goal, remember, was to be able to fly along the flight path and stop wherever I wanted.  As wonderful as YouTube is, the UI for YouTube isn't the best way to inspect the terrain as you fly overhead.  For that, you want a downloadable MP4 file that you can open with a video controller (like Quicktime Player).  Here's the link to that video.  Try right-clicking the link to download it, open in your favorite video controller,  and then try zipping back and forth like a boss--you can easily pause, go forward, go backward.  It's a very different experience than YouTube (or any online video system) can do.  Direct manipulation is really handy sometimes.  This is one of those times.  


Search Lessons 


Finding the right tool is often a prerequisite to satisfying your search goals.  In this case, we had to find the right tool, and a simple search found that Google Earth could do this.  After figuring that out (and downloading Google Earth Pro), it was a process of figuring out how to actually make a movie that would follow the flight path of the plane.  THAT involved a bit of futzing around, but once I figured out the sequence of button clicks, it was straight forward.  

And now I have my video... on my computer, ready to zip back and forth along the flight path. 

Search on!  

(A new Challenge tomorrow to get us back on track!) 




   


Wednesday, October 10, 2018

Delay of game... (Oct 10, 2018)


I hate to do this to you... 

... because the answer to last week's Challenge is fun..  but I'm doing a tour of upstate New York this week.  I'm teaching at Cornell today and the University of Rochester tomorrow.  

"Far above Cayuga's waters..."  
Cornell University

As a side-effect, I've had no time to write up my answer to the "Can you make a video?" Challenge. 

BUT... I'll have time this weekend, so I'll post my solution next Monday, October 15.  

Keep searching (and making those videos) until then! 

In the meantime, I'll be teaching (and occasionally looking for the color changes in the fall leaves... which I have to admit, seem rather muted this season).  

Search on! 




Thursday, October 4, 2018

Fermi Estimation again (Part 2)


Estimation is an art... 

... that deserves practice.  And by practice, I mean that you very deliberately look at your mistakes and learn from them.  

In an earlier post about Fermi Estimation, I showed how I estimated Enrico Fermi's height by this method.  Here's an infographic showing what I did.  



That's great.  

HOWEVER... As good as estimation is, it's worth checking your work from time to time in order to learn where you can be better.  

In that earlier estimation post, Regular Reader Chris wrote in with a great comment.  Here's what he wrote: 

As Jon said in an earlier post, the average size Italian was 5 feet 6, but I would say he is below average height. My estimates would make him between 5 and 5"3"
Using this image and assuming an bench height of about 30 inches, this would make him only 60 inches tall (5 feet). Using this image with Robert Oppenheimer (on the left)  I estimate him [Fermi] at about 5'2". According to the NY Times Obituary, Oppenheimer was 6 ft...  Likewise in this photo he [Fermi] is a good foot shorter than Chancellor Hutchins (right) who was 6'3" according to Commentary Magazine

Aside from being a GREAT example of using photos to estimate height (rule of thumb: use more than one photo to verify; also get the heights of other items in the photos), this also bring up another valuable estimation heuristic:  Always double check your work.  

What went wrong in my original post?  That's easy to spot:  My original estimate of his head size was 9.4 inches (21.9 cm).  Where did THAT number come from ?  From two sources:  (1) my estimate of his head size by comparison with the control panel behind him.  I know the size of those control knobs, and I estimated from that.  (2) I measured my own head size.  Since the two numbers were close, I went with that number. 

Thing is, I'm taller than Oppenheimer and a bit shorter than Hutchins.  So it's not a surprise that my head measurement would produce a fairly tall estimate.  

Chris showed us a great estimation validation method--Look at the person side-by-side with known people (and known heights).  




Here's another picture showing three famous physicists:  E. O. Lawrence, Enrico Fermi, and Isidor Isaac Rabi standing side-by-side.  A quick search for Lawrence shows his height at 6 feet (182.8 cm).  A quick search for Rabi shows his height at 5' 4" (162.5 cm)  So this estimate by photograph is probably pretty accurate.   Fermi was a bit shorter than his friends, right around 5' 3" or so.  


Estimation Lesson 


1.  If you take an initial estimate and multiply it by 7.5, then any error you have in your initial guess is going to be magnified by 7.5!  Caution:  Make sure your initial data is pretty close before you go multiplying it by a fairly large facto.  

2.  It's always good to have two very different ways of estimating.  In this case, a quick photo check would have shown that my original estimate was off.  I'll do that next time for sure!  



Estimate on! 




Wednesday, October 3, 2018

SearchResearch Challenge (10/3/18): How can I make a movie of my flight?


Last week I flew from San Francisco to Austin, Texas... 

... as usual, I had a window seat to I could see the landscape slowly rolling past the window.  In my opinion, this is one of the most wonderful things you can do: look out the window at the glorious southwestern geology.  

At some point in my flight, I saw many extraordinary things... forests, craters, mountains, brilliant white salt flats, and center-pivot irrigation systems that defined small communities in the middle of a vast loneliness.  

What I really wanted to do was to make a film that would capture all of the beauty of the country we were passing over.  Alas, I didn't think to tape my video camera to the outside of the plane.. and have it run for the 4 hour flight.  

Here's the path we took from San Francisco, over Phoenix, over El Paso and over West Texas into Austin.  


After I landed, I thought that there MUST be a way to do this with a bit of online research.  After all, we know that there's a lot of aerial imagery out there.  So... this led to this week's Challenge:  


1.  Can you make a movie that recreates the experience of flying from San Francisco to Austin?  Obviously, you don't want it to take all 4 hours.  How about a 2 minute version of the flight that just shows off the really interesting parts between Arizona and West Texas? 

This isn't an ordinary SearchResearch Challenge--this is really a Challenge about (A) How to find such a tool?  and (B) How to use the tool to create a video that follows the flight path.   (You'll get to choose your own tool, along with your altitude and camera angles.)  

Be sure to tell us how you did it (and what searches you had to do).  AND, if you would, please post your video to YouTube so we can all see what you made.  

Of course, once you've made the video, be sure to tell us what interesting and wonderful things you found along the way.  

Here's one of the things I found--a huge patch of white sand (naturally enough, this is White Sands National Monument).  It's a big white sandy beach in the southern part of New Mexico.  It's really obvious--once you see it and learn where it is, you won't be able to NOT spot it on any aerial photo of New Mexico.  

After this, you'll literally see the world differently. 

Search on!  


Thursday, September 27, 2018

Answer: Mysteries from Mozart's time

How many pianos in Salzburg...  

... can you Ferminate and answer the Challenge?   

Well... okay... let's just jump into it.  The Challenges from last week, please...  


1.  As you know, Wolfgang Amadeus Mozart had a famous sister--also a performing prodigy.  Maria Anna Walburga Ignatia Mozart, called Marianne and given the nickname "Nannerl, was his older sister.  But in nearly every picture of her, she's got a remarkable head of hair.  See this picture below: 



Nannerl and Wolfgang Mozart playing two-handed duets at the piano


The question I had was How do you sleep with hair like that?  Or, I suppose, the other way to think about it would be How much time do you spend on hair like that?  Any ideas?  

This is a pretty open-ended question, and it's worth noticing that while I asked the question about Nannerl, a simple image search for: 


     [ 18th century big hair ] 

quickly tells us that florid, extravagant hair was the rage in the late 1700's.  Here's what you get if you look at the images from that query: 



Sure, some of these are modern recreations, but clicking through some of the obviously older images quickly leads to images like this, for both men and women:  




One of the blogs that appeared with this query was Two Nerdy History Girls with their great post on this topic.  In part 2 of their post, they spoke with hair dressers at Colonial Williamsburg living museum who actually practice this craft and asked the relevant question, "How long does it take?"  


Their answer?  Not as long as you think--around 10 minutes for an "ordinary" pile of hair as seen in some of the images above.  

In reading their blog, I learned a new term:  pomatum (a kind of scented pomade applied to hair to give it some structure and scent).  Using this in a query, such as:  [ pomatum 1700..1799 hair style ] leads to books about fashion, and to the inevitable Wikipedia article about hair styles.  All of which agree:  These hairstyles can be relatively straightforward (around 10 - 15 minutes) to build a relatively simple coif, but the larger, more impressive and elaborate hair-dos can take a long, long time.  

And yes, you don't sleep in these things.  You take them down in the evening and comb out the hair.  (Whew!)  
  


2.  When I visited the Mozart residence at No. 8 Makartplatz (the so-called "Dance Master's House," aka Tanzmeisterhaus), I was struck by the odd appearance of one of Mozart's pianos--the key colors are reversed!  The accidentals are white, while the naturals are black.  Here's what I mean; Mozart's piano keyboard is on the left, while a current piano keyboard is on the right. 



So... when did the colors change from black naturals to white naturals... and why? 


I started this Challenge by looking for a history of the piano.  I figured any such account would probably cover the key color shift, and give some references to boot.  I started with this query: 


      [ history of the piano key color ] 

All of the resources found on this SERP told me that the piano was invented by Bartolomeo Cristofori, and that his original pianos had black keys with white accidentals (those keys that are shorter and raised above the keyboard).  That's certainly the case for Mozart's pianos (see above). 

As with many things, there are a number of stories about why the colors changed.  

Even on the Question-Answering (QA) site Quora, there are a number of hypotheses on the post Why are colors of piano keys reversed on certain Viennese pianos

a.  Cristofiori's friend convinced him to change the color.   
b.  It was cheaper to do it that way.  Elephant ivory became cheaper than the black ebony wood that was being used for the black keys.  Since a keyboard is composed of 52 type naturals and 36 accidentals, it was cheaper to use the expensive ebony for the accidentals.
c. It's easier to see.  No accidentals are adjacent, but there are many places where naturals are adjacent. If the naturals are white, it's easier to see the gap between them because it's dark.  See below: 




(As a piano player myself, I will also add that ivory keys are very robust and have a great touch--they have just the right amount of friction and absorb sweat well.  They're just much nicer to play than wood.)  

Reading more of the results from this single query, I found that:  

Piano maker Yamaha believes, Living Pianos, and the Joshua Ross website believe (c).  And I as read through many of the results, that seems to be the dominant belief.  

More importantly, I could not find a solid justification for the color switch.  Without finding a design document or standard (that says something like "henceforth, all accidentals shall be black and the naturals shall be white"), and given that so many early pianos, clavichords (a precursor instrument), and harpsichords have black naturals, it's more likely that it's just the fashion of the time that turned into standard practice.  

Not all questions have clear, unambiguous answers--and this might be one such question.  

We'll leave this Challenge marked as "open for more research."  After looking at at least 100 different sites (including history books about pianos), this is as far as I got.  Maybe we'll find a better answer in the future! 



3.  Speaking of Fermi Estimation and Mozart's piano (we were, weren't we?)... What would you estimate as the total number of pianos in Salzburg during the year when Mozart left Salzburg for Vienna?  How would you do this estimate?  


Austrian pianos over the years

This is another Challenge that could consume a LOT of time. I know I had to keep resisting the urge to answer this definitively... Our goal is to estimate the number of pianos. 

I started with a basic question:  How many people lived in Austria in 1781, the year Mozart left Salzburg for Vienna?   

By checking the Wikipedia entry on Salzburg, I know that Salzburg had 27,858 in 1869.  But by searching for [ Salzburg population 1770..1800] I found a book (surprisingly entitled Pilgrimage to Crete) that tells us that the population in 1771 was around 16,000.  

Now, how to estimate the fraction of the population with a piano??  (Not organs, clavichords, or harpsichords, but honest-to-God pianos.)  

With a search in Google Books for [ piano social history Salzburg ] I found the book Men, Women and Pianos: A social history, which points out that in Vienna, during Mozart's time, around 2% of the population had a piano at home. If that number holds for Salzburg (only a couple hundred miles away), 2% of 16,000 would mean there were approximately 320 pianos in private homes.  If we add in a few for schools, churches, etc -- that would bring the number to around 350.  

Things changed a few years later when piano manufacturing started in Salzburg and Vienna on a large scale, but at this time, in the late 18th century, there weren't that many!  

Search Lessons 


There are a couple of things to learn from this Challenge.  

1.  A simple query often leads to a number of results which are collectively quite good.  In the "big hair" Challenge, not all of the results were superb... but when reading them en masse, you can learn a bit from all of them--in particular, terms of art like pomatum that let you dig more deeply and precisely into the topic.  That is, the collection is more valuable than any one item. 

2.  While it's tempting to dig deeply into a research topic, when estimating, you want to find just the essentials to make your case.  In the Challenge about numbers of pianos in 1781 Salzburg, all I wanted to do was to find the population of Salzburg AND a reasonable estimate of the number of pianos in an Austrian city.  I found the number for Vienna, and transposed that to Salzburg.  Just be careful when doing an estimation search as opposed to finding a definitive answer.  

3.  Sometimes... you can't find a definitive answer!  Yes, my friends, there are some Challenges for which a definitive answer lies somewhere in the mists of history.  So why DID piano keyboards reverse their colors?  We might never know.  We have hypotheses, but I wasn't able to find a clear cut answer.  


Thursday, September 20, 2018

New search-by-image method on Bing.com


My brother is a pilot... 

... and every so often he sends me a picture from somewhere in the world asking "So, smart guy, where is THIS photo taken?"  

Here's one such photo he sent me recently: 


Nice pic.  Of course, I took up the Challenge and did my usual Search-By-Image search tricks

But searching for this on Google didn't give me anything.  

So I tried the Cropping-the-Image trick, cropping it to this close-up, and then re-doing the Search-By-Image.  


But that didn't work either.  I kept cropping it in different ways, but I didn't get very far.  It takes time to crop the image, save it, then re-load it into Image search. 

So I tried this on Bing's image search tool

  

Like Google's Image search, Bing also has the camera icon, which lets you upload an image to Search-By-Image.  

When I uploaded this image, the UI looks like this: 

Bing's search-by-image UI.

And.. as you can see on the right-hand side, this didn't work either.  

HOWEVER... if you roll your cursor into the image area, you'll see a "crop symbol" popup in the upper right corner.  (Pointed to by the yellow arrow I added to the screen grab.)  


When you select the crop tool, the UI changes to let you do live cropping.  


At this point, you can drag the corners of the sub-image box to create a cropped search of the image. 

The really nice thing about this is that when you let go of the corner widget, Bing re-runs the query with the cropped area.  This means you can very quickly search through many cropped versions of the image!  (You can read Bing's announcement of this--they include a nice demo.)  

With Bing's cropping tool, I played around with this for about 5 seconds before I found the right crop that located a near-match of the image!  

Look at the image in the upper left of these results.... THAT's the image I was looking for... Now that I've got a matching image, it doesn't take long to look at that image and figure out that it's in Detroit, Michigan, just outside of the downtown YMCA.  


Here's a closeup--you can see it's clearly a picture of the same statue. 


It's a great tool... Highly recommended when you need to explore the possibilities of cropped images in a short amount of time.  

Search on! 





Wednesday, September 19, 2018

SearchResearch Challenge (9/19/18): Mysteries from Mozart's time


Salzburg was Mozart's home ... 

... in his pre-Vienna years.  It's where he was born, lived, and launched his career.  

When I was visiting earlier this year, I visited several of the places that Mozart lived and performed.  As you'd expect, as I looked around, I noticed a few things--things that struck me as funny/odd.  Of course, being a curious fellow, I had to look these things up with a bit of online research.  Can you answer these oddities as well?  

Here are three of the things I had to look up.  I was surprised at the answers to each of these.  


1.  As you know, Wolfgang Amadeus Mozart had a famous sister--also a performing prodigy.  Maria Anna Walburga Ignatia Mozart, called Marianne and given the nickname "Nannerl, was his older sister.  But in nearly every picture of her, she's got a remarkable head of hair.  See this picture below: 

Nannerl and Wolfgang Mozart playing two-handed duets at the piano


The question I had was How do you sleep with hair like that?  Or, I suppose, the other way to think about it would be How much time do you spend on hair like that?  Any ideas?  


2.  When I visited the Mozart residence at No. 8 Makartplatz (the so-called "Dance Master's House," aka Tanzmeisterhaus), I was struck by the odd appearance of one of Mozart's pianos--the key colors are reversed!  The accidentals are white, while the naturals are black.  Here's what I mean; Mozart's piano keyboard is on the left, while a current piano keyboard is on the right. 


So... when did the colors change from black naturals to white naturals... and why? 


3.  Speaking of Fermi Estimation and Mozart's piano (we were, weren't we?)... What would you estimate as the total number of pianos in Salzburg during the year when Mozart left Salzburg for Vienna?  How would you do this estimate?  

Austrian pianos over the years

As always (and I hate to sound like an 8th grade math teacher), show your work!  At least tell us how you answered each of the Challenges!  

(And note that you don't need to answer all three of the Challenges.  If you don't have enough time, just do one.  But be sure to tell us HOW you figured out the answer. 

I'll write up what I found next week.  

Until then, Search On! 




Thursday, September 13, 2018

Answer: Can you be a Fermi estimator?


Being a good estimator... 

... requires two kinds of knowledge:  (a) facts about the world, and (b) basic math estimation skills.  Those skills let you work from the basic facts, combining the data and doing quick math estimates to get to some numbers that give you the information you seek.  



How tall was Enrico Fermi, the physicist?  How would you estimate?  Assume he doesn't have extraordinarily long legs.  

Fermi Estimation needs both kinds of knowledge--along with a bit of practice in figuring out how to go from point A to point B.  

Let's practice with a true Fermi estimation!  


1.  Can you estimate how tall Enrico Fermi was?  
In this example, I give you a piece of data: Fermi's head is 9.4 in (23.9 cm) tall.  

How would you estimate his height just from this information?  Ask yourself, What other information do I need to know?  

If you're an artist, you probably learned that when you sketch a person, their body proportions are often expressed in terms of head-heights.  Example:  An ordinary person is about 7.5 heads high--a tall, slender, elegant person is about 8 heads high. 



If you don't know that bit of data, you could look the relationship up quickly:  

     [ body proportion in heads ] 

Later edit (Sep 14, 2018):  In the original post I messed up the calculation with a typo... I wrote that 24 * 7 was 164, which is clearly wrong.  Once I had that typo, all kinds of errors followed.  Bottom line, check your math. Didn't your sixth grade teacher say that? 

So know you know Fermi's head is 23.9 cm tall.  To Fermi estimate, let's round that up to 24 cm.  You can probably guess that 24 * 7 = 168 cm.  If you then add in the half-head height (12), you can add 168 + 12 and get 180 cm.  Make sense?  

In this case, I did the mental math in metric because that value (23.9) could be easily rounded up to 24 without causing many estimation problems, whereas the English measurement (9.4 inches) was kind of a pain--if you round up OR down, you lose a lot of accuracy.  

Plus, I know how to convert from cm to inches pretty easily.  

I know (off the top of my head, OTTOMH) that 10 cm ~ 4 inches.  

(Here, the ~ means "close to" in value.)  

SO... to convert 180 cm  into inches, I would divide 180 by 10 and multiply that by 4.  My mental math was 180/10 gives me 18 --I then multiply 18  by 4 to get your Fermi estimate of 72  inches, or 6 feet.  

When I read that, it SOUNDS really complicated... but it's not.  Here are the steps laid out in a diagram.  


1.  I know 10 cm~ 4 inches.  So... I just have to divide by 10, then multiple the result by 4 to do that conversion. 
2.  180 cm /10 = 18
3.  18 * 4 = 72  inches...  

At that point, most English-unit-using people can convert that into feet/inches without any trouble: 6 feet tall. (Yes, I know that's a weird skill; so be it.  We grew up with it. Point is, it's not that hard.  

So yes, you have to know a basic conversion fact (10 cm ~ 4 in), and know how to break up a complex mental multiplication into parts.

(If you want to learn more about how to do this kind of mental math for estimation, there are many online videos that will walk you through the process.  One that's pretty nice is from the Khan Academy:  Estimating values.)  



2.  Can you estimate (without looking up the answer!) how many people in the United States are over 80 years old?  (For extra credit, how many people worldwide are over 80 years old?)   
This is an interesting question:  How would you go about estimating this? 

Again, you need to know a few things to start. 


1.  The population of the US.  (I know this:  It's around 325M people.) 2.  The population age distribution.  

Once upon a time, I remember seeing a chart like this.  They're sometimes called "age pyramids" or "age distribution" charts.  When I look at this chart in my mind's eye, the top couple of slices of that chart constituted around 3% of the whole.  

To check this, I also remembered that the average life expectancy is around 78 (which is lower than in some countries, higher than in some).  So 3% off the top sounds like a reasonable guess.  

So... 3% of 325 is easy.  Divide by 100 (3.25) and multiply that by 3.  That's 9.75 million people who are older than 80 in the US.  

When I look up the actual numbers to check myself, I see that there are 328.3M people in the US, and this is the age distribution: 



And, surprisingly, my estimate of 3% is pretty close to the actual value.  

Even more surprisingly, I also happen to know that the US is slightly above average for ages > 80 years throughout the world.  Since I know that the population of the Earth is 7.5B, 3% of 7.5B is 225M people, which is a lot of elder wisdom.  



3.  To do Fermi Estimates you actually need to know a few basic facts (e.g., about how many people live in the US).  This brings up a great meta-question for Fermi Estimation and sensemaking of data that you see presented in the news... What facts do you need to know to be a good Fermi Estimator? (There's no perfect answer for this; just tell us what facts you've used to do your own Fermi Estimates!)  

When I start thinking about how you do estimates in your everyday life, I think about all of the times I do the Fermi estimations on news stories that I read.  Usually, these days, these are stories about income, wealth, distribution, immigration, and science stories. 

To do any kind of Fermi estimation you need to know a few things.  I've been writing down some of what I'd consider core knowledge over the past week, just taking notes when I did my own estimates to see what core knowledge I used.  Here's my list (yours is probably different): 

- population of the US in 2017:  327M 
- population of the world in 2017:  7.5B
- area of California:  ~100M acres
- conversion from inches to cm:  1 inch = 2.54 cm 
- number of stars in our galaxy:  300B stars

And so on... 

The reality is that nobody can take the time to spend 5 minutes doing online research for everything.  But it's pretty simple to do Fermi estimates to see if what's being said actually makes sense.  

It's a really good skill to have.  I highly recommend you practice this whenever you see something that sounds a little off.  It just might be.  But with your Fermi estimator skills, you can see through the mistakes.  

Here's a short video by my friend Jevin West talking about Fermi estimation in his class at the University of Washington.  It's well worth watching--his examples are great!    (Video link.)  



Search Lessons 

A few lessons spring out at me... 

1.  You still have to know basic facts about the world.  Dates, places, quantities, names, sizes, durations...  For instance, how important are plastic straws as a source of plastic pollution?  (Can you estimate what fraction of the total plastic trash they are?)  Once you know how to do Fermi estimates, your reading and understanding of news stories  / current events changes.  Beyond just knowing facts--e.g., the population of Japan is around 127M--once you know things like this, you know what kinds of information can be derived from them. Example:  While 3% is a good estimate of the number of people world-wide who are older than 80, you might also know that Japan is an outlier in the age pyramid--they have many more older residents than most countries, so you should Ferminate a higher fraction for folks > 80 years of age.  

2.  Realize that you CAN do estimates that are pretty good, and use them to do basic fact-checking of a story.  If it doesn't add up, you have more research to do.  This more of an attitude about research than anything--but it's important.  Many people don't know how to do estimates, and so they don't know they can guesstimate what they're reading or hearing about. And that makes them more susceptible to incorrect data and news stories.   

3.  Of course, online search is handy to get to the basic facts and formulas.  This is really true for breaking stories where there simply isn't any good information yet.  Even if you can't determine a particular value for something you've read, there's a good chance that you can estimate it by looking up other information and combining the data together into a fuller picture.  


Keep estimating.  It's a great personal skill to have! 

Search on!