Green Eggs and Zipf's Law

 In the 1930s and 40s American linguist, George Kingsley Zipf wrote about a pattern found in written texts.  Now known as Zipf's Law, the pattern shows an eerie similarity in the distribution of word frequencies across essentially all documents whether they are books, essays, short stories or letters.  If you take a given set of words, count up all the words and order them by frequency you will find that the second most common word occurs almost exactly half as often as the first.  You will also find that the third most common occurs one third as often as the first, the fourth most common occurs one fourth as often, the fifth one fifth and so on with each word occurring 1/n as much as the most common word where n=its place in the order.  

Pretty neat and pretty weird but as researchers from different disciplines began to look for distributions in other data sets we started seeing the same pattern everywhere.  City populations, website traffic, citations of scholarly articles, deaths in wars, TV ratings.  How long you remember things follows this pattern.  Even randomly generated texts follow Zipf.  

We don't fully understand why language follows Zipf's law but the basis of why all these very deliberate, human systems follow the same pattern is somewhat simple: human behavior, even the extremely complex nature of cities and global societal behavior, are still governed by natural laws, and ultimately, math.  Even something like the population of a city which is governed by what feel like very personal decisions like taking a job, moving to be closer to family, etc. are subject to the ebbs and flows of pure numbers: the means and variances of statistics will, given time, determine the number of people living in a distribution of cities either in a country or in the world.  

This is similar to another statistical idea: the Pareto principle, named for Italian economist, Vilfredo Pareto.  It states that 80% of a given system's consequences are due to only 20% of that system's causes.  More concretely, Pareto discovered that 80% of land in Italy was owned by 20% of people.  This too has been applied to countless human systems: business managers will tell you that 80% of revenue will come from 20% of clients, IT departments and software engineers know that 80% of computer crashes come from 20% of the bugs, and 20% of your carpet endures 80% of the wear.  

When I first learned about Zipf and Pareto my mind eventually went to the stark wealth inequality that exists in the US and in the world.  Do these seemingly ubiquitous natural laws mean that we are locked in to the current state of affairs with roughly 20% of people controlling 80% of the world's resources?  But that's when I found a way out: Dr. Seuss.  

Famously, Theodore Geisel, known better by his pen name, Dr. Seuss, wrote the book Green Eggs and Ham on a bet that he couldn't write a book using only 50 words.  This bet produced one of the great children's author's most enduring classics.  I wondered: could this fairly extreme constraint get around Zipf?  I counted up all the words and plunked them into Excel.  And this is what I found:  

Green Eggs and Ham does not follow Zipf!  Just looking at the first few words "not," "I," and "them" you can pretty clearly see that the second and third appear much more frequently than the 1/2 and 1/3rd that of the first.  It's not even really close.  Another way to look at these data is that a Zipf distribution should be an almost perfectly straight line with slope = -1.  This line, especially after you get to "could" is no where near a straight line, it's a gentle slope towards the last word at that point.  

Green Eggs and Ham gives me hope.  If we just let systems motor along as they are, we'll inevitably end up with Zipf.  But if we manage to figure out a way to put some creative constraints on our larger systems, it looks like we may actually be able to push them towards equity.  I'm not remotely saying that will be an easy task but with the right tweaks, the right concerted effort in the right direction we might be able to pull a Zipf distribution into something a little more even.  I do so like green eggs and ham!  Thank you!  Thank you, Sam-I-am!

Sources:

https://upcommons.upc.edu/bitstream/handle/2117/180136/Ferrer-i-Cancho_EPJB_2005.pdf;jsessionid=0AA5762D175B3844791253058CFB645F?sequence=1

http://pdfs.semanticscholar.org/5a9a/0438af964d00249bafff11f0e85ef924a61a.pdf

http://pages.stern.nyu.edu/~xgabaix/papers/zipf.pdf

https://www.researchgate.net/profile/Wentian_Li/publication/253290454_Zipf's_Law_Everywhere/links/5cf59ef9299bf1fb185617ff/Zipfs-Law-Everywhere.pdf

https://www.biography.com/news/dr-seuss-green-eggs-and-ham-bet

https://betterexplained.com/articles/understanding-the-pareto-principle-the-8020-rule/

Vsauce: https://www.youtube.com/watch?v=fCn8zs912OE

Seuss, Dr.. (1960). Green Eggs and Ham. New York, NY: Beginner Books.

A Very Brief History of Earth and its Water

This story begins about 4.5 billion years ago.  Things were pretty boring in our solar system for a while.  Space dust had been floating around, gravity slowly gathering it into slightly larger clumps, for a time but what we needed to get things moving was some external kick.  Probably a nearby star exploded, or some large object came whizzing in to stir things up but whatever it was gave a nudge that allowed gravity to pull all that dust into the major objects that we recognize today: the sun, the planets and most importantly for this story, the large rocky object where eventually some apes would evolve and name "Earth" (among other names).

For a long time the Earth looked like this:

Image: Tim Bertelink CC BY-SA 4.0

There are a few theories about where all the water on our planet came from.  One is that during the time depicted above, known as the Hadean, the water was already there.  It would have been entirely in the form of water vapor because it was extremely hot but it was around.  As the Earth cooled it would have condensed into a liquid, formed clouds, precipitated out of the atmosphere and started to do all the great things we can rely on water today for.  

Another theory is that when the Earth formed there was little to no water and we got it from some external source.  It might have come from a comet or an asteroid or a series of smaller asteroids.  This probably all happened pretty early on in the Earth's history.  We can find clues to where the water on Earth came from by looking at the percentages of the isotopes of hydrogen in the water molecules.  An isotope is a chemical element that has a different number of neutrons in its nucleus and in this case the stable isotopes of hydrogen can have either zero or one neutron.  Scientists today are still collecting samples, analyzing the data and running statistics to try to understand where all the water on our planet came from.  

Regardless of where it came from eventually Earth did get water on it, most of it in our one large ocean covering about seventy percent of the surface.  Side note: I did say "one ocean."  This may be splitting hairs but while most of us are taught that the Earth has a few separate oceans there is only one big body of water that covers the planet.  Check out this ArcGIS render of a map by the artist Athelstan Spilhaus:

Everything is connected and you could, in theory, take a boat to any point in the ocean without having to hop out onto dry land.  

Anyway, one of the next major events in the history of Earth's water is how it got salty.  It did not actually come that way!  This bit is fairly straightforward: as the water cycle started to get revved up and rain became a thing we got lakes, ponds and also rivers.  All those rivers meant a lot of runoff into the ocean.  As water flowed down river it brought sediment with it and in that sediment were a bunch of different salts.  Over the millions (and millions) of years that this process continued we eventually ended up with the salinity we currently see in our ocean.  Thanks runoff, now I can do a full body float when I go to the beach!  

While salt water plays an absolutely enormous role on the Earth's biosphere and climate, its the fresh stuff that we humans and other terrestrial animals need to survive and unfortunately it's much more limited.  

You can click to embiggen: the big blue blob represents ocean water, the little blob to its right is all the liquid fresh water and the every tinier blob next to that (which is...really hard to see) is fresh water in lakes and rivers.  This water, known as "surface water," is all that is available to us to use as drinking water and water to cook and clean with.  It's not very much!  

So it's important for us to get together and conserve and protect our fresh water resources.  One fun thing you can do is check out your local watershed conservancy, association, council etc.  Pretty much wherever you live there is a river near you.  A lot of these organizations host clean ups and fun events like festivals and bike rides to get people out there appreciating and connecting with their local waterways.  While a lot of those kind of events may be on hold right now, you can still get out there and appreciate the nearest river, lake, pond or stream.  

https://www.livescience.com/33391-where-did-water-come-from.html

https://www.iflscience.com/physics/origin-earths-water-discovered-0/

Why Are Planetary Orbits Elliptical?

I hope everyone enjoys my Extremely Fancy images on this post.  I built most of this myself and I a) don't have the best technical art skills and b) lack any actual graphics software.  Someday hopefully we can afford a graphics department.  :)

It may seem like planetary orbits and orbits of other objects should be circular.  Circles are simple and many patterns in nature adopt a roughly circular shape.  However there are two factors that dictate a planet's orbit that will help us understand why orbits are elliptical and not circular. 

Just be sure we're on the same page, an ellipse is what we usually call an oval.  This is an ellipse:

The two dots are the ellipse's foci (I just sort of ballparked it here).  The exact math and concept of what foci are is a bit outside the scope of this post but you can think of it this way: a circle is a special case ellipse in the same way that a square is a special case rectangle.  In a circle the two foci overlap and are at the center.  The more stretched an ellipse is, the further away from the center of figure they will be (yes, this is a simplification).  You can also check out this neat little demo to get a sense of how the placement of the foci dictate what the ellipse will look like.

Let's also get a little bit of possible confusion out of the way.  The way you often see Earth's orbit drawn in text books or diagrams looks a bit like this:

There was a time when I was hearing people talk about the idea that Earth's orbit was actually circular and that the way it's drawn in textbooks is highly exaggerated.  This is sort of half true.  The way it is drawn is often exaggerated but the orbit is elliptical.  It's just not all that elliptical.  How elliptical an orbit is can be described with a measurement called eccentricity which goes form 0 to 1 with 0 being a perfect circle.  Earth's orbit has an eccentricity of about 0.0167. So rather than the very noticeably elliptical path in the image above it's closer to something like this (again, ballparked):

To see why planets have elliptical orbits we need to take a look at what happens when two massive objects interact in space.  We're going to keep the systems to two objects for simplicity and we're also going to imagine one object is stationary and the other is moving towards it.  Neither of these things is really what you see in space as objects are all hurtling around towards and away from one another constantly but it gives us a nice clean system that should hopefully make things relatively straightforward.

When one object approaches another in space there are two forces acting on the object: its own momentum and the force of gravity attracting the two objects.  There are a few different things that can happen depending on how strong these two forces are.  If an object has a very high momentum and the gravitational attraction between the two objects is fairly low, the path of the object will be bent but it will not be "caught" in an orbit.  The red arrow represents the object's momentum and the blue arrow, gravity, resulting in the purple arrow.  These arrows will change as the object proceeds on its path but hopefully this illustrates how this combination of forces will result in the path shown:

The second possible outcome is that the force of gravity is quite high and the momentum quite low.  This results in the smaller object crashing into the larger.

When we have a situation in between these two extremes, when the momentum and force of gravity are relatively in balance, this is when the smaller object is "caught" and falls into orbit around the larger.  We're going to visualize this to see why the orbit will be an ellipse.  We're going to look at a relatively extreme (high eccentricity) shape compared to Earth's orbit but this situation still applies to our planet.  I'm also going to change the orientation so we can visualize the formation of an orbit as the smaller object *falling* into the gravitation field of the larger.  This is not really a metaphor, as we'll see.  Orbits are a type of falling...they just don't end up in a crash.  At least for a great many billions of years.  I'm also going relabel the larger object "object A" and the smaller object "object B."  OK here we go!

I put numbers on a few points in object B's new orbital path to try to break down what's going on.  Imagine at point 1 that object B is hurtling along in space but it has begun to get close enough to object A that their gravitational attraction is going to start to change its course.  As it moves toward point 2 its initial momentum has it wanting to continue on its original path but gravity now has it on a path falling towards object A.  As B moves towards point 3 gravity is getting stronger, accelerating it, but because it maintains momentum, it does not crash here but instead moves on a curved path along the "bottom" of object A.  As it moves "up," away from the "bottom" of the orbit here gravity is now going to decelerate object B.  I removed the other force arrows at point 4 because the important point here is that its momentum is carrying it "up," away from object A but gravity is still pulling towards object A.  Object B decelerates until it reaches the "zenith" of the orbit at point 5 where it then begins to fall again back towards object A. 

You can think of this a bit like tossing a ball into the air in an arc from one hand to the other.  As you put a force on the ball it rises but is decelerated by Earth's gravity.  As it reaches a zenith it's upward velocity momentarily becomes 0, then it is accelerated by gravity, falling back down to your other hand. 

So why can't this system form a circle?  Well...actually it can.  It's just extremely unlikely.  In order for the orbital path to be a perfect circle the balance between the momentum and gravity need to be exactly matched and at exact right angles as it is caught in orbit.  This is what that would look like:

Imagine the smaller object moving towards the larger and it's position and momentum enter the orbit at the top of this diagram.  Right at this moment, the force of the momentum and the force of gravity would have to be exactly the same and exactly at right angles to one another to create the perfect 90 degree arc, bringing it to the point to the right of the larger object, at which point momentum and gravity are still exactly matched and exactly at right angles, continuing neat 90 degree arcs all the way around. 

Sorry for holding out on you: circular orbits can happen and do happen.  They're just very, very rare because the conditions you need for them to form are exceedingly unlikely.  Think back to the analogy of throwing the ball in an arc from one hand to the other.  Imagine how unlikely it would be for you to get that ball to go in an exact semicircle.  The force and direction you apply to the ball with one hand would need to be super precise for this to happen.  It's not hat you couldn't ever get a ball to fall into a perfect semicircle, it's just that you would have to be extremely lucky or try over and over again.  And remember, while Earth's orbit is an ellipse, it is actually pretty close to a circle. 

Except!  There is one little caveat.  I've simplified a lot here but one thing I've glossed over a bit is that gravity is a force that attracts two objects together.  It doesn't actually pull object B towards object A, it pulls them towards one another.  Now obviously with objects that differ in mass by extremes like the Sun and Earth or the Earth and a ball, the acceleration on the smaller object is going to be much, much more noticeable.  But there is a non-zero acceleration on the more massive object. 

One of the things that this means for orbits is that smaller objects don't actually orbit larger objects.  They orbit each other.  The point where they orbit one another is their center of mass.  You can think of this as the point at which the combined mass of both objects is equal on both sides.  The center of mass also represents one focus (remember our ellipse's foci at the very beginning?) of an elliptical orbit.  While the Earth is a large object, the Sun is much much more massive so for our orbit the center of mass is actually pretty close to the center of the Sun.  Again, I'm totally ballparking this and completely simplifying but just to illustrate:

Warning!  Not remotely to scale!

Even if Earth's orbit wanted to be a perfect circle (err...conditions were lined up exactly perfectly so the momentum and gravitational forces were balanced and at exact right angles), that tiny shift in where the objects orbit one another would mean it would still end up as an ellipse.  Just by being two massive objects orbiting one another and having a center of mass they introduce eccentricity into the orbit.  

Now, for an object the size of Earth, the eccentricity introduced due to the center of mass not being at the very center of the Sun is pretty small.  For something like an asteroid that is 100th or 1,000th the mass of Earth that eccentricity is going to be...not even measurable.  We're talking ten, thirty, fifty decimal places out.  It's not zero but it's tiny.  But it's always going to be there.  Even in a system where the momentum and gravitational forces are lined up just right, the center of mass of the system is going to introduce, at the very least, a tiny amount of eccentricity into the system.  So even in the most unlikely, perfect situations, we're never going to get an exactly perfectly circular orbit. 

This post was super fun and I did a ton of research.  I hope you enjoyed it!  As with other topics, I'm not an expert but this definitely took me out of my comfort zone.  If you have comments, corrections, questions etc. please drop them in the comments or tweet at me @paulsfenton. 

Thanks for reading!

Sources:

email correspondence: Richard Binzel, Professor of Planetary Science, Joint Professor of Aerospace Engineering and MacVicar Faculty Fellow, Massachusetts Institute of Technology

https://www.scienceabc.com/nature/universe/planetary-orbits-elliptical-not-circular.html

https://www.youtube.com/watch?v=DurLVHPc1Iw

https://www.youtube.com/watch?v=xaCyQvwJ_Vs

https://www.youtube.com/watch?v=59qniggFpFQ

https://www.quora.com/Why-are-planets-orbits-elliptical-Why-not-circular

https://www.windows2universe.org/physical_science/physics/mechanics/orbit/eccentricity.html&edu=high

https://www.education.com/science-fair/article/orbital-eccentricity/

https://gravity.wikia.org/wiki/Orbital_eccentricity

https://everything.explained.today/Circular_orbit/

https://everything.explained.today/barycenter/

https://physicsabout.com/keplers-laws/

https://www.quora.com/What-causes-comets-on-an-elliptical-orbit-to-return-to-the-sun-Theres-no-friction-in-space-and-the-comet-should-keep-going-out-of-the-solar-system

Are Viruses Alive?

I'm getting pretty tired of content about SARS-CoV-2/novel coronavirus/Covid 19.  I mean, we all need the best, most up to date public health information we can get so we can all do our part to keep one another safe and healthy and get through this thing.  But it feels like the radio and several TV shows are just...all Covid 19 now.

So while this post is going to be about viruses, it's not about SARS-CoV-2.  And while the title asks the admittedly click-baity question "are they alive?" I'm not actually going to try to answer that question.  I'm more interested in taking a look at what we mean when we say "alive."  I love to poke at what happens when we find things outside the neat categories humans try to put things into.  "Alive" may be the category nearest and dearest to our hearts and possibly one of the easiest to poke holes in.

What exactly is a virus?  I think we can safely define them like this: they are organic (regardless of whether they are alive or not) structures that can replicate using either DNA or RNA (a molecule similar to DNA used by most living things).  To do so, they "infect" a cell, basically breaking through the cell's membrane or outer layer of defense against the outside world.  They then hijack the molecular machinery the cell uses to replicate and begin to generate copies of themselves.

Like most things in biology (and probably all science), defining "alive" depends on who you ask.  But it seems that most of us agree on a few characteristics: 1. It can reproduce (on it's own) 2. It has cells 3. It obtains and uses energy 4. It grows and 5. It can sense/move in response to/adapt to the environment.

There are a couple of go to arguments against viruses being alive based on this list of characteristics.  Let's get the easy one out of the way: viruses don't have cells.  Cells always have some sort of barrier that creates an "inside" and separates it from the "outside."  For a lot of folks this is a dealbreaker: no "inside" and you can't be "alive," you're just a part of the environment.  I've got a few issues with this, two I'll handle now and one I'll come back to.  First, as organisms get more complex what is "inside" becomes less clear.  Think about this: there is a passage that goes straight from your mouth to your anus.  You aren't a a cylinder, you're a tube.  Secondly, though maybe this is more opinion than fact, I just feel that saying "cells or bust" is a bit arbitrary.  Imagine we found something that could reproduce, takes things in, spits things out but didn't have a cell (spoiler, we'll meet one of these things in just a bit).  I'd be inclined to at least consider that these things are alive.  Especially if you consider using DNA or RNA as a form of coding which not just allows it to reproduce itself but allows for mutations (changes due to the environment or a mistake in reading the code), that allows for changes across generations and therefore evolution.  I would not be at all surprised if when we find life on another planet it did not have cells.

Probably the most popular argument against viruses being alive is that they can't/don't reproduce on their own.  Again I've got a bit of a quibble with this: parasites.  Most parasites cannot survive, let alone reproduce without their hosts.  I have never heard anyone argue that because a parasite cannot survive or reproduce on its own this disqualifies it from being alive, yet it seems that many throw this line of argument out for viruses and expect the case to just be closed. 

If we take a look back at the list of characteristics of life I also think that 4. It grows may also be a bit arbitrary.  In fact single celled life doesn't really grow, at least not in the sense that multicellular life does.  Bacteria and other single-celled organisms reproduce by dividing one cell into two.  While there are stages in the processes that you might call "growth" it's definitely not the same as an organism being born, taking in nutrients, going through development and its body getting bigger.  

Let's go back to the idea that to be alive you need to have a cell.  Pretty recently we've found proteins that can, at least in lab settings, reproduce and create amino acids (molecules that are the building blocks of proteins which make up, well, most of everything alive).  I'm not going to argue that these proteins are living things but I am going to argue that they represent a possible glimpse into the beginnings of life on earth.  We know that in the history of earth there was a time when we went from no life to having life and that there was some process that allowed organic molecules like amino acids and proteins to eventually become "alive."  What I will argue is that this is a spectrum.  Rather than "alive" and "not alive" I think we can look at this as an evolution from inorganic molecules to organic molecules to RNA and DNA to cells to more complex organisms.  Even in the most complex vertebrates like ourselves, everything happening in our bodies is chemistry.  I don't necessarily know that you can draw a sharp line between chemistry and biology here.  [To be clear: I'm not trying to argue here that organisms like us with lots of cells and tissues and organs are "better" or "more advanced" necessarily; we just came later in the story].  So going back to viruses: they also contain organic molecules like RNA and DNA and so, I think, could be considered a part of this spectrum of organic structures.  

I think it's really interesting when one category starts to bleed into another like this: when inorganic becomes organic, when chemistry becomes biology.  Our human categories really start to break down almost every time we look at a transition in evolution between two groups.  When you look at the evolution of plants, for example, you have mosses which are considered plants by most but don't have stems or leaves which are generally considered things all plants have.  But we don't always see these rule breakers at the evolutionary transition points.  The platypus is a famous example of a mammal that does not give birth to live young.  It isn't an evolutionary descendant of other mammals, it's just a different branch on the tree.  Even the notion that all animals require oxygen has recently been overturned with the discovery of a species living in a completely oxygen-devoid part of the Mediterranean.  

As we've seen we can form categories for living things by coming up with a list of characteristics, looking to see if we've got all of them and then if it does, put it in that category.  As we've also seen, that doesn't always work.  The other way we can form categories is through evolutionary relationships.  If two things share a common ancestor (they evolved from the same species or, maybe in some cases, the same molecules) then we can put them in the same category.  That's why we consider platypuses to be mammals: they don't give live birth but they do share a common ancestor with other mammals.  Just like you and your cousins, platypuses and other mammals share the same stock, they're part of the same family regardless of characteristics.  Recently, some analysis of the shapes of proteins in viruses indicate that they may in fact share common ancestry with cellular life.  This is super preliminary but if more evidence starts to stack up and we become more confident that viruses and cellular life evolved from the same early organic chemical reactions on earth, I would be willing to say that viruses and cells are in the same category.  Maybe still not alive.  Maybe, the cousin of alive.   

Sources:

https://bmcbiol.biomedcentral.com/articles/10.1186/1741-7007-8-30

http://www.bbc.com/earth/story/20170125-there-is-one-animal-that-seems-to-survive-without-oxygen

https://www.popsci.com/new-evidence-that-viruses-are-alive/

https://www.sciencedaily.com/releases/2015/09/150925142658.htm

https://advances.sciencemag.org/content/1/8/e1500527

https://www.sciencealert.com/amyloid-protein-self-replication-abiogenesis-contrasts-rna-world

Exploring Nature at Home

We're only a few days away from the 2020 City Nature Challenge and obviously this year is going to be a little bit different.  You can visit their website, and specifically this page, to learn about what is changing and what isn't.

Unsurprisingly, while we are still going to try to get out and collect as many observations as possible, we will be doing this while social distancing.  For many of us this will mean observing the natural world in patches of green space in our neighborhood, our back yard or even just from our windows.  The other big change is that this year will not be a competition and some of the organizers are using the phrase "City Nature Celebration."  They also put together this guide on exploring nature at home.

I also recently wrote about exploring the natural world at home, even if it means you can't or don't feel comfortable going out into your neighborhood and wanted to share that here.

Even though we may be spending most of our time at home there are still ways to explore nature with your family!  Whether you are able to get outside to a park, green space, yard or you can only make observations through windows or from a porch there are lots of options for looking closely.   Here you will find resources, tips and ideas for you and the young people you care for to engage with the natural world! 

The Big Picture

No matter where you are exploring there are a few basic tips and tricks for helping young people explore the natural world you can always rely on:

•        Look closely and ask questions: what colors do you see?  What do you think this animal is doing?  How many legs does it have?  How many trees can you see?  What do you think we might find next?  What is the weather today? 

•           Record what you find: use whatever paper and writing tools you have available at home to keep track of what you find and notice.  If you have the ability to hang pieces of paper or keep your observations in the same notebook over time that can provide an opportunity to look back and talk about what patterns you see, what is always the same and what changes.  But if not, just the act of drawing or writing down your observations is a great way of focusing attention and solidifying observations in memory. 

Window Observations

This is a simple, flexible activity you can use to connect with the natural world even if you don’t have access to green space at or near your home.  As written, you make observations through a window but you can also take a short walk through your neighborhood, go to a yard or park, if you are able, to make observations.  Try both and see what differences you notice between the window and your walks!

What you need: a window (optional: chart paper or any smaller kind of paper, pen/pencil/marker/etc, book or online field guides [see web links below], binoculars).

What you do: Choose a window, or several windows, where you can see a variety of plants, animals and weather.  This activity can be done with a single observation or over the course of days, weeks, months or even years.  No need to plan ahead if you don’t want to commit, though.  If you are using paper to record what you see, get out your paper and something to write. 

 Here are some things to look for and guiding questions as you observe:

·         

        Start off open ended: what natural things do you see?  What colors do you see?  Trees, animals,       weather, sky, clouds, rocks?  Start to get acquainted with your window or the section of your   neighborhood you have chosen to watch. 

·         What is the weather like?  Recording weather across a week, a month, or a longer period of time and   then going back and looking for patterns or trends (does the temperature go up each day, down each   day, up and down?  How many days were sunny vs. rainy vs cloudy?)  is a great but very simple   way  to engage with the natural world. 

·        What animals do you see?  Don’t worry about having to identify species at first.  Squirrels?  Birds?   Can you describe them?  What colors are they?  What do you see them doing?  Are they big,   medium or small? 

·         As you get to know the animals outside your window or in your neighborhood you can start to use   field guides to identify what species they are. 

·        What trees and other plants do you see?  Like animals, don’t feel you have to know the specific   species at first.  Are they tall or short?  Do their branches go up or out?  Do they have leaves or   needles? 

·        Don’t forget rocks!  Rocks will be a little trickier to identify from afar but go back to those open ended observations: what sizes do you see?  What colors?  Try to challenge your young people to get more specific than “gray” or “brown.”  Light or dark?  Greenish gray?  Try to get them looking and thinking as closely as possible. 

·        If you’re able to be up after the sun sets (and it is safe for you to do so), try making some observations after dark.  What are some things you notice that are different?  What’s the same? 

·        If you choose to continue making observations over many days, choose a time (maybe each week?) to go back and look and what has changed over time.  Are you noticing different animals across the weeks?  Do you notice different behaviors?  When do plants grow, lose their leaves, grow their leaves?  What patterns or trends have you noticed in the weather? 

Identification Guides for Window Observations

Mass Audubon Insects and Arachnids: https://www.massaudubon.org/learn/nature-wildlife/insects-arachnids

Mass Audubon Birds: https://www.massaudubon.org/learn/nature-wildlife/birds

Mass Audubon Mammals: https://www.massaudubon.org/learn/nature-wildlife/mammals

Tree Identification by Bark: http://www.trees-id.com/bark-1.htm

(For Plants) Go Botany Simple Key: https://gobotany.nativeplanttrust.org/simple/

Identifying Clouds: https://gewa.gsfc.nasa.gov/clubs/sailing/IMAGES/MISCELLANEOUS/CloudChart.pdf

Exploring for Nature Inside

What you need: you can explore inside or outside your house for insects and other invertebrates without using any special materials.  If you have a small jar or Tupperware container at home that can be helpful to place small creatures for viewing but it’s just as easy to observe them where you find them!

Just as with window observations, you can add a record, note-taking or drawing component to help your young people look closely, find patterns and ask questions about longer-term animal behavior. 

While not everyone agrees that they are the most welcome inhabitants, most of our homes are also inhabited by a range of insects, spiders and centipedes.  Hunting for these smaller animals in your basement, attic, bathroom or other out-of-the-way areas is another great way to engage with nature without leaving home!  While these creatures may not be the most popular, it is perfectly safe to explore for them.  There is only one potentially dangerous species of spider in Massachusetts, the very distinctive black widow.  While you are unlikely to encounter it (these spiders are much more common in the South and West United States) you can find information about identification and their behavior here. 

Identification and Resources for Bugs in Your Home

http://robdunnlab.com/projects/arthropods-of-our-homes/learn-more-about-your-arthropods/

https://www.vox.com/science-and-health/2016/1/23/10815572/insects-species-home

Exploring for Insects and Other Invertebrates in Your Yard

What you need: As with exploring inside, this can be a very engaging activity without any materials.  If you happen to have a small shovel for digging into the soil that can help find certain creatures, especially earthworms and insects that winter in the soil.  Again, a small jar can help keep creatures in place to view them but is not necessary for observing outside. 

If you are able to explore a yard, park or other green space in your neighborhood you are likely to be able to find not only birds, squirrels and other vertebrates [animals like birds, mammals and reptiles that have  a backbone], but also a host of smaller invertebrates [animals without a backbone like insects, spiders and snails] hiding on plants, under rocks and logs and in the soil.  Here are some resources for how to best find these smaller creatures all around us. 

https://www.wikihow.com/Catch-Small-Bugs

http://www.bugcollectors.com/where-to-find-insects

Scientific Consensus and Uncertainty

There is a line of thinking, you may have encountered it, that says something to the effect of "there is no such thing as consensus in science."  The argument goes that in science we never prove, only disprove and we are always discovering, learning, tweaking and we should always be holding what we believe to be true, especially the theories and laws most dear to us, with skepticism.  Therefore, we should not or cannot ever have consensus.  There should always be room for debate in science and consensus is a tool of the powers of authority to stop those that would challenge this authority. 

The real difficulty with this line of argument is that it takes something that is true and good about science (that we only disprove, that we constantly amend our theories when new observations or information is collected, that we should remain skeptical) and takes its logical end creating such epistemological relativism that would dictate we can never know anything or ever do anything with that knowledge.  Which is demonstrably not the case.  We do know things and we do things with this knowledge. 

Let's think about how this applies to engineering.  We've studied steel.  Steel is great; it's fairly plentiful (rather it's components are), it's very strong, it's relatively easy if somewhat energy intensive to make stuff with.  So we have an idea: let's build stuff with it!  Let's use it to build some buildings!  Modest at first but eventually, maybe we can build some really tall buildings!  Now if your position is really that we cannot build scientific consensus you'll say: "No, no!  We need to continue to learn about steel!  Perhaps there is some hidden property that we're unaware of that would make it unsafe to build with!  What if there is an as-yet-undiscovered reaction that occurs when it reaches a certain elevation that makes it impossible to build tall buildings with?"  But we do build with steel.  We've reached a level of confidence that allows us to say "we know enough about this material, we understand its properties, let's move on and do some engineering with it." 

While it is true that nothing in science is ever proven in the strictest sense, confidence is a technical term for how statistically likely it is for future experiments or observations to hold with past experiments and observations.  So while we might not have proven that steel is a good building material, the statistics are very much in our favor. 

We also do have what we call scientific facts.  A fact is a piece of knowledge that, again, has been tested over and over and over to such an extent that statistically we have very strong confidence that it is for practical purposes "true."  One of the go to examples of this would be if you hold an object in your hand (that has greater density than air) and let go of it, it will fall.  Steel's high strength is a fact.  Atoms consist of protons, neutrons and electrons: fact.  Now could we discover new aspects of the natural world that counter these observations?  We could.  It's just very, very unlikely. 

"Ah!" Says the anti-consensus line of thinking.  "But in science there is no "truth."  We've been wrong before and we could be wrong now!"  Yes, many many scientific facts, laws and theories that were consensus for very long periods of time have not held up to the scrutiny of the scientific method and new evidence.  It's quite true.  We once believed in something called "the aether," a substance through which light waves could propagate.  It doesn't exist; we now know that light and other electromagnetic waves are self-propagating.  We once believed there was a substance called "phlogiston" within all combustible materials.  We had lots of evidence based on observation and experiment that such a thing existed.  It turns out we were wrong. 

Scientists and consensus can get locked into what is "accepted" and fail to pick up on evidence that would lead us to new theories, facts and laws that better explain our observations.  This is a very real aspect of the scientific method.  But saying that we cannot ever have enough confidence in our observations to do anything with them is throwing the baby out with the bath water.  And, again, demonstrably false.  Engineering is nothing but taking scientific facts, measurements, theories, etc and applying them.  We reach consensus whenever we build new infrastructure and technology.  Whenever we develop medicine (and yes, sometimes we make mistakes) we are reaching consensus.  When I know that jumping from a great height is a bad idea because gravity will accelerate me quickly to the ground and severely injure or kill me, I'm working with scientific consensus.   

You may see this argument applied to climate science and climate change.  That because science never proves anything, saying that there is a consensus is antithetical to the scientific method and merely serves to silence dissenters.  It prevents us from making new discoveries.  But here's what we know: it is a scientific fact (in the technical sense) that carbon dioxide and other gases trap heat in our atmosphere.  It is a historical and scientific fact that humans have added a bunch of rampant carbon dioxide to Earth's atmosphere.  Therefore, we can infer (and have measured) a rise in average atmospheric and sea surface temperatures.  We have observed ice that has existed since humans have melting.  We have a very, very high level of confidence in these things.  And we have a very high level of confidence that Earth's atmosphere will continue to warm and that this will have other effects on our climate. 

Do we know exactly what will happen with the climate?  No, of course not.  We have some decent models but there are a host of variables we can't predict very well (mainly the social variables, i.e. what are humans and governments going to do as we move into the coming decades).  Humans are notoriously difficult to predict.  But just because we don't have a perfect climate model with extremely high confidence doesn't mean we don't still have some basic facts that allow us to act in a logical, reasonable way. 

Good scientists are always skeptical, always open-minded.  Good scientists do their best to truly think critically and examine if their observations are in conflict with what they believe.  But good science also allows us to create, to heal, to feed, to protect.  Good science allows us to act and not only study. 

Sources:

Kuhn, Thomas.  The Structure of Scientific Revolutions.  Chicago and London: The University of Chicago Press, 1962.

https://www.visionlearning.com/en/library/Process-of-Science/49/Uncertainty-Error-and-Confidence/157

https://eic.rsc.org/feature/the-logic-of-phlogiston/2000126.article

https://ncse.com/library-resource/definitions-fact-theory-law-scientific-work

The Speed of Light and Time Dilation

So light is fast.  But its speed isn’t necessarily special.  It just travels at the highest speed the universe allows.  Photons (the particles of light) have no mass so, like all things without mass, they have nothing to slow them down.  So off they go as fast as they can!  Why is there a universal speed limit?  The answer to this is, like other questions about the fundamental nature of the universe and laws of physics, we simply could not exist in a universe with infinite speeds.  There are two things that would go wrong for us:  1. It would take infinite energy to give something mass and so things with mass (like us) couldn’t exist.  2. Time (or to be more precise, really, space-time) wouldn’t exist.  Light travels at the fastest speed a signal can be sent in our universe.  Because we have a finite signal speed it means that events have distance and time between them.  This is quite odd to say, but an infinite speed of light or infinite signal speed would mean that there are not distances and times between events.  How would a particle with infinite speed actually behave?  A signal (or particle) with infinite speed would exist everywhere in the universe at once.  These particles would never take any amount of time to go anywhere and would never need to travel anywhere because they all would already be everywhere forever.  So while such a universe could exist we wouldn’t be around to observe it.  Nothing, really, would be around. 

Because the speed of light is always at the fastest possible speed the universe allows this has a weird byproduct: light’s speed is not relative to the observer.  It is always the same.  Here’s a little more detail about what that means and following, a little about why that’s weird.  Imagine someone on a train car going 100 km/h, you’re standing still watching the train car go by.  Now imagine they throw a ball at 50 km/h.  From their perspective the ball is going 50 km/h.  But from your perspective the train and the ball add their speeds together and the ball is going 150 km/h.  For most moving objects in the universe you have to measure their speed from a particular frame of reference.  That is, are we measuring the ball’s speed from your frame or from the person who is throwing the ball?  We will get different answers depending on which frame we decide to measure from.  But because light always goes at the maximum speed allowed by the universe, this does not happen for light.  Let’s go back to the train car only this time the person on board has a flashlight.  They’re traveling along again at 100 km/h.  They turn on the flashlight.  From their perspective the photons exiting the flashlight are going c (the speed of light, about 300,000 km/s). From your perspective the photons are traveling?  Also c, exactly the same speed.  Not c + 100 km/h.  

Here’s the weird thing…at least weird from our day to day experience:  the fact that light travels at the universal speed limit and its speed doesn’t change based on any frames of reference leads to time being experienced differently when travelling at different speeds.  Let’s go back to the train car.  This time, imagine there are mirrors inside the car and a beam of light bouncing between them.  The light beam is bouncing straight back and forth and takes some very small amount of time to make one bounce.  This is what it might look like, the back bars being the mirrors and the blue bar being the light beam:

Now, let’s set the train car moving.  Now the light beam must bounce at a diagonal and travel a slightly longer distance in order to “catch up” with the moving car.  Here’s what this looks like, again, the black bars are the mirrors, spaced out to show the movement of the train car:

Just like with the ball thrower, with most objects the train will just impart its speed on the object and we will see it go faster to keep up with the moving train across the slightly longer diagonals.  But here’s where things get weird.  Remember that light cannot go any faster and that it always goes at the speed c regardless of frame of reference (so its speed is the same if you are observing from outside the train or on the car).  If the speed can’t increase it seems we may be stuck with a problem: the light has to travel a longer distance in the same amount of time but it simply can’t because the speed of light is conserved no matter what.  Here’s the punchline: instead of adjusting the speed of light, the universe adjusts how much time passes for each frame of reference.  From outside the train time on the train actually slows down so the light has enough time to get back and forth from mirror to mirror.  From inside the train time appears to move at a normal rate.  But from outside, time is moving slower.

This is the phenomenon known as time dilation.  We don’t really start to see significant effects until we get pretty close to the speed of light but this happens every time you move with respect to someone/something else.  Every time you get in a car, train, plane, skateboard, bicycle, heck even walking, time slows down for you just a little bit.  So be wise, friends.  Choose something productive to do with all your extra nanoseconds. 

Some references:

Cox, Brian and Jeff Forshaw.  Why Does E=MC²?  Boston: Da Capo Press, 2009.  

PBS Spacetime:  https://www.youtube.com/watch?v=msVuCEs8Ydo

https://www.youtube.com/watch?v=Xo232kyTsO0

Khan Academy https://www.khanacademy.org/science/physics/special-relativity/lorentz-transformation/v/deriving-lorentz-transformation-part-2