omenti

remote learning laboratory kits

a mini-post you can have fun with

 

I managed to survive a bit of remote online instruction.  While it doesn't fit my teaching style, it seems clear it's going to be with us for awhile.  Labs are a big issue for science and engineering courses. Watching videos and running simulations isn't a rich experience, but what is?  A few of us have been thinking about that recently.  The fact that most students have access to a smartphone opens up some real possibilities.  A smartphone is basically a computer with a lot of sensors and a network connection.  The trick is to get raw data from the sensors and devise experiments students can run or - better yet - design on their own.  You need an app with a good interface. 

 

I know of a  few projects working on apps to get at sensor data.  They tend to fill different niches, but  there are some existing apps.  

recommendation

Get phyphox from Apple's AppStore or GooglePlay.  (if you have a choice I recommend the iPhone version as the variety and quality of sensors is well-defined).  It's a free download from Bergische Universität Wuppertal.  Their webpage (English and German) has some experiments including some videos and forums. It's a great starting point.  

 

Chemistry seems more difficult and I think biology needs real samples if you're going to get serious, but I'm confident we'll see some inventiveness.    We'll probably see other sensors and adaptors that attach to phones.  Microscopes are naturals and I have an ultrasound adaptor that is a dandy bat detector.  Some would be easy - like a simple  spectrograph and others would take some design and manufacture.  Many could be vastly cheaper than current lab gear if enough units were sold. A school system or university could just give them to students.  Also old smartphones can be donated to kids who don't have one - you don't need a network connection for most of this. 

 

Engineering has huge possibilities with Arduino kits and simple sensors and actuators. So much exists - it's a question of crafting projects and instruction. 

 

I would love to see inexpensive, easy to calibrate environmental sensors.  Environmental work would be a lot of fun and could engage students socially and politically.  Imagine mapping out toxic substances at the block level around the country. Collaborative student science. 

 

And all of this works for the amateur at home.  Perhaps someone needs to restart SciAm's old Amateur Scientist column or create and Amateur Technologist... and I'm particularly interested in the intersection of this and art (folks like Shuli would probably be or already are all over it as she's already in the space).  

 

And I'm working on an amateur project of my own. (although that's usually the case)

 

exciting times

 

 

yet another confusing word

These days we're hearing and talking about a future that is suddenly very difficult to predict.  Uncertainty is frequently invoked.  I know what it's supposed to mean, but the scientific context is very different.  It's one of those words - theory, hypothesis, work, energy, power, model, significant, natural, ...  - with a very specific scientific meaning at odds with their popular meaning.  (science communication is hard)

 

Who knows what's going to happen? frequency comes to mind,  while uncertainty is well defined in the context of science.  It's the quantification of how tightly we can constrain what we don't know.  That's a very powerful concerpt.  Being the simplest of the sciences, physics has the most rigid requirements.  In order for a discovery to be accepted by particle physicists uncertainty that it could be something else has to be lower than one part in three point five million - the five standard deviation level.  People living in this world spend much of their time thinking about what could go wrong and devising other measurements to disprove their original hypothesis.   We speak in terms of confidence levels.  

 

Henry Cavendish was one of the first to work at understanding and minimizing uncertainty when he weighed the Earth to determine the gravitational constant.  Even today the measurement is difficult as gravity is incredibly weak as forces go.  Without going into details,  Cavendish built an exquisitely sensitive  torsion balance that measured the attraction between small lead spheres and a much larger lead sphere.  His early measurements made sense, but was it just gravity?  Perhaps there was a bit of a magnetic effect .. he rebuilt the experiment with a large magnetic ball replacing the lead ball.  This wasn't to rule out magnetism as much as to set a quantitative limit on how large the effect was.  Then he turned to thermal effects heating and cooling different parts of the experiment.   He was left with his best measurement and the level of confidence that he had removed all other controllable effects (including human error).    

 

The game becomes trying to make a more precise measurement and perhaps seeing something new in the process - some measurable effect that can't be explained conventionally.  A good deal of science advances in this way.

 

Here's a cute introduction to uncertainty that I almost really like - the bear in the moonlight - almost as it doesn't touch on fundamental uncertainty.

 

There's another deep form of uncertainty - you've probably heard of Heisenberg's uncertainty principle and Schrödinger's poor cat.  Broadly stated Heisenberg showed that it was impossible to perfectly know both the position and momentum of anything.  He called it ungenauigkeit (inexactness) or unbestimmtheit (undeterminedness). Niels Bohr called it unsicherheit (unsureness).  Even today German physicists (like their Prime Minister, Angela Merkel) will call it unschärfe (fuzziness).  All of these terms are more descriptive of the physics than uncertainty.  The use of uncertainty suggests to some there is an exact value and we just can't measure it.  Instead there is just a probability distribution.  It is indeed fuzzy - at a microscopic level all of the atoms that make us up are fuzzy - it's just our world is mostly too large to notice.

 

In some parts of my life I try to avoid what is usually thought of as uncertainty, but when you want to really understand something diving in and reducing your uncertainty and increasing your level of confidence is a powerful tool. 

 

medical tests and probabilities

a mini post

 

There are many references in the news to how good viruses tests are and what conclusions you can draw from them.  Unfortunately some are wrong and I haven't seen any easy to understand explanations of how to figure these things out.  It's all conditional probability. The standard approach is to use Bayes' Theorem.  Unfortunately most people have never heard of it or vaguely recall a formula with P's and |'s they once memorized without knowing what it really did  

 

Here's an easy way to think about it in the form of an example.  Imagine a population, say a city, where 1% of the people have a viral disease (I'll call the disease 'virus').  There's a test with a 90% chance of returning a correct result.  So if you have the disease there's a 90% chance the test returns a positive, and if you don't have the test there's a 90% chance the test returns a negative.   So what's the probability that someone who has just been tested has the disease?

 

For simplicity imagine an unbiased group of 1000 people in the city.  Let's screen them and see what happens. Ten people will have the disease, 990 will be disease-free.Of the ten people with the disease the test will correctly identify nine of them and incorrectly identify one.   Looking at the people who do not have the disease 90% of 990 or 891 will correctly test negative, but 10% of the 990 or 99 will incorrectly test positive.

 

 

 

 

So the probability a person who tests positive actually has the disease is the number who test positive and have the disease divided by the total number who test positive:  9/108 or about about an 8% chance.

The example has nothing to do with the specifics of CV-19, but maybe will give you a way to think about how to sort out what the real tests are saying when an accuracy is published.   Going deeper really requires tools like Bayes' theorem, but hopefully this is clear.

 

Armed with this technique perhaps this otherwise well-written piece in the NY Times will make sense.  Also note this is for an unbiased initial sample.  If you're screening on existing conditions before testing (which is common outside of Iceland), additional complications appear. But at least this should give you an idea.

 

 

 

 

sometimes you need one heck of a butterfly

In the early 60s Edward Lorenz was working on one of the first computational weather prediction models.  Many of the early explorers, new to computer programming, were getting bitten by limits of the machines and software.   Lorenz, the story goes, was running a numerical computer model to redo a weather prediction from the middle of the previous run as a shortcut. He entered the initial condition shortening it in a way he didn't think would matter given the accuracy it was measured to (say 0.504 rather than 0.504103)

 

"At one point I decided to repeat some of the computations in order to examine what was happening in greater detail. I stopped the computer, typed in a line of numbers that it had printed out a while earlier, and set it running again. I went down the hall for a cup of coffee and returned after about an hour, during which time the computer had simulated about two months of weather. The numbers being printed were nothing like the old ones. I immediately suspected a weak vacuum tube or some other computer trouble, which was not uncommon, but before calling for service I decided to see just where the mistake had occurred, knowing that this could speed up the servicing process. Instead of a sudden break, I found that the new values at first repeated the old ones, but soon afterward differed by one and then several units in the last decimal place, and then began to differ in the next to the last place and then in the place before that. In fact, the differences more or less steadily doubled in size every four days or so, until all resemblance with the original output disappeared somewhere in the second month. This was enough to tell me what had happened: the numbers that I had typed in were not the exact original numbers, but were the rounded-off values that had appeared in the original printout. The initial round-off errors were the culprits; they were steadily amplifying until they dominated the solution." ¹

 

Small changes to an input that was iterated many times created a big change in the output. He presented it at a conference causing someone in the audience to comment a single flap of a seagull's wings could change the weather forever.  Lorenz started using that in his talk changing it to the more poetic single flap of a butterfly's wings in Brazil setting off a tornado in Texas.

 

The image resonated with many existing notions about complex systems including science fiction where a time traveler steps on a bug and returns to a vastly changed future.  From there it has managed to become an embedded concept - usually used to describe chaotic and large inefficient systems.  The problem is it isn't always true. In fact it's usually false.

 

Chaotic systems are often less sensitive to change than other systems.  Run a stream of water in your sink.  The motion in the flow is extremely chaotic - no computer could keep up with the details.  Stick your finger in for a second.  The overall flow changed while your finger was present, but quickly returned to its normal chaotic level almost immediately after you took it out. 

 

The climate system is extraordinarily complex. Predicting weather in advance has made incredible progress thanks to better models, hardware, and software.  It turns out there's probably a limit to how far models can predict based on fundamental changes in the atmosphere.  They aren't butterflies.  Butterfly wing flaps are quickly dampened out by thermal motions of the surrounding air.  To make a change you need big butterfly - a really big butterfly ..  the equivalent of several massive thunderstorms taking place in areas you can't predict ahead to the necessary accuracy.  A butterfly flap equivalent of several thermonuclear explosions.²

 

Inefficient complex systems tend to heal themselves.  The Internet, the way food used to be grown and distributed .. almost any large scale process before it was made "efficient" .. tend to be much more robust than efficient systems where "wasteful" redundancy has been removed.  I worry we're witnessing some of that now as the result of a large perturbation to numerous systems.

 

People often come away with the idea that you can manipulate a large complex system if you only can figure out what breed of butterfly to use and exactly when and where to turn it loose.  It's a fool's errand.  Instead you need to study these systems to learn if it is possible to steer them and how you might do it.  The real insight may be you need to change the system itself rather than its inputs.  

 

The same is true for complex efficient systems.  A very small change can crash them.  High efficiency can be the enemy of robustness. Of course systems can be too inefficient - the trick is to find the right balance to build robust systems.

 

________

It's easy to build simple systems where butterflies are very effective.  Lorenz's weather program was simple and easily influenced and it's really easy to find simple expressions that are hair trigger sensitive.³

 

__________
 

¹ E. N. Lorenz, The Essence of Chaos, U. Washington Press, Seattle (1993), page 134

² a few times 10¹⁵ J - several hundred kilotons to one megaton.  A large thunderstorm is in the ballpark.

³ I won't spell it out, but if you're comfortable with differential equations consider y'' - y = 0  (say y(t) is position as a function of time) with the initial conditions y(0) = 1 and y'(0) = -1.  The solution is simple and predictable.  

Now imagine you have a measurement error and y'(0) = -1 ± ε  where ε is small.  Different, eh?  :-)

 

 

the problem of where

a minipost

 

Wandering around in a field we seem to know roughly where we are and can make a plan to get from here to there.  This sense of location takes place deep in the hippocampus and the neighboring entorhinal cortex (full disclosure - I couldn't remember that one and had to look it up).  The hippocampus has place cells that fire individually at different locations.  Grid cells and head direction cells are in the entorhinal cortex and create a virtual map of triangles that provide the hippocampus with additional information of location and heading.  It's a full navigation system that receives additional sensory information from sight and hearing.  

 

Some of us make better use than others.

 

I've been wondering about the "court sense" seen in some elite athletes where it's important to know the position and motion of the ball as well other relevant players at any moment.  Soccer, hockey, rugby and beach volleyball come to mind. Using beach volleyball as an example the best players create an evolving mental map of the other three players including one that may be behind you.  They can't take the time to think about it.   It's interesting talking to a player.  They may be unaware of the uniform or other details of the other players, but are very aware of a few pieces of dynamic spatial information. 

 

Toddlers often take indirect paths getting distracted by any number of interesting waypoints on their path.  As adults we tend to take what we think is the easy path from A to B and these days that information comes from the GPS in our phone or car.  GPS navigation isn't infallible, but the same is true for human navigation.  Are we getting worse at human navigation by relying on these satellite consultations so much or is it just a computational extension of our brain?

 

fMRI experiments have been done with people navigating virtual cities and forests with and without GPS.¹   Compared to those who navigated using their own mental maps there was much less hippocampus activity in those who navigated by following external directions.   The virtual map generated by the hippocampus seems to appear only when you are actively engaged in the act of navigation.  It's like we're bypassing part of our brain when we use a GPS.  It has also been shown that enhanced use of personal active navigation increases the size of the hippocampus while inactivity causes atrophy.²  

 

Make it a game to turn off your GPS and navigation on your own for awhile.  There are numerous natural signs and signals that help you find your orientation and path.  Which side of the tree has moss? What is the sun angle and shadow direction?  Which direction is North at night? .. and hundreds more.  Try it in a city too.  If you get lost you can always pull out your phone for a quick look.  You might even find the fun of discovery that a toddler gets by observing their surroundings more carefully.    There's even some evidence that exercising the hippocampus by building up rich maps through cafeful observation lower dramatic stress.  Perhaps give up the GPS function, but sketch or carefully photograph was you see.  Straight up play and you might be doing your brain a favor. 

__________

¹ Several studies exist.  Here's a fascinating fMRI study taking place in virtual London.

² London taxi drivers have to spend a large amount of time building a mental virtual map of much of the city.  Brain scans show highly developed hippocampus regions.  Some preliminary work with people genetically disposed to early onset dementia has found people with highly developed hippocampuses may be protected from decline. 

the second order waffle house index

minipost

Waffle House is a mostly Southern restaurant chain offering your basic greasy American breakfast 24 hours a day.  Over 2100 locations. Any Southern town with over about 10,000 people has one.  I've visited one a few times when we were working with Disney and found at least their orange juice safe, but a lot of people love them. What makes them interesting to me is the Waffle House Index.  

 

Waffle House is deservedly famous for being open no matter what.  Power out? .. no problem .. that's the emergency generator.  Tornado cut through town?  Keep the place open for the disaster crews. There's even a central disaster control center to manage massive events like hurricanes.  They've become a legend - so much that FEMA publishes an informal, but often quoted Waffle House Index.  Immediately after a disaster they might report something like 3 of 14 Waffle Houses in the impacted area open.  A few days later progress might be summed up as 8 out of the 14 Waffle Houses are back online.  It's useful a measure of commercial and public resilience just under the level expected for first responders and front line medical people. 

 

Until yesterday all of the Waffle Houses were closed.  Now, in states like Georgia, they're allowed to open and some are.  COVID-19 is a new game.  The nature of the danger is ongoing rather than short-lived. Somehow the Waffle House Index doesn't seem appropriate.  I suspect a more interesting index might be the percentage of normal customers coming in for a normal sit-down meal staying the normal amount of time? Sort of a second order Waffle House Index.   What is the regional perception of danger and how does that play out in personal risk-reward calculations?  

 

As recently as this week national polls suggest over 80% of all Americans don't believe going to a restaurant worth the risk. Sporting events and concerts are over 90%.   How regional are these numbers and how do they change with function, social class, income, risk category,  etc. (football in Texas for example)   It's an interesting question as the economy attempts to come back given insufficient testing and a dysfunctional berserker executive. 

 

The evolution of this index would be most interesting.