Critical Thinking for Voters update

For those following the Critical Thinking for Voters Ebook, I have corrected some past typos and added a chapter about fallacies. It isn't a manual on fallacies, basically a "what to look for" briefer with references to deepen your knowledge. I try not to be partisan or judgmental and try to stay away from contemporary illustrations (but sometimes it's just to tempting.)

Actually, fallacy watching would make a great family hobby right now. Turn on the latest political debate, pull up the wikipedia List of Fallacies article and start marking them off as you hear them.

"That's a red herring."

"Ah, too common. Not worth many points. That one was an interesting slippery slope, though."

"Wait a minute. Was that a fallacy of ambiguity? I think it was!"

"What kind is it?"

"Wait. I'll check.....Equivocation......That's an ambiguity in the middle term! Wow! That's an ambiguity in the middle term! That's gotta be worth 75 points at least! High five everybody!"

They ought to have a television kit for sale somewhere!

Can I trust my phone?

Recently, I was checking some of my past measurements and I found the latitude and longitude I recorded at The Bluffs to be off by about 130 miles. (I checked the GPS recording from the Physics Toolbox Pro with the latitude and longitude from Google Maps.) That's a tiny error in respect to the circumference of the earth. I still calculated that to within 1.01% on the same hike. But it would be pretty bad if I were telling someone where to meet me!

So I wondered how my other phone sensors perform. After all, the inside of a smartphone is a noisy place with so much electronics packed into such a tiny space building up heat, and so much energy swirling around in my urban setting. I decided to check my magnetometer so I set my phone in a quiet place (in my bedroom) using the Science Journal to record magnetic fields and left it for about an hour.

Here's the recording.

Not a lot of detail here but there are a few things that jump out at me. The first, oh, 23 minutes are rather "fuzzy" and then the tracing settles down into a nice flat line. After that, there are a few spikes somewhat larger than the earlier fuzz; then, at the end (maybe give minutes), the tracing drops and suddenly jumps up).

I don't see any drift. In other words, the tracing doesn't seem to drift up or down over time.

I am going to guess that the early fuzziness is internal noise as my magnetometer adapts to internal noise in the phone. Is the noise enough to worry about? Well, all instruments have errors, even manual tools like rulers and scales react to environmental noises like changes in heat and drafts. To check how much the tracing moved around, I saved the tracing as a comma separated values (cvs) file and loaded it into my DANSYS statistical spreadsheet. All I needed to check was the range of values in a section of the tracing.

The range here is 0.0165 μT. The average field strength is 52 μT (these figures are x10). The standard deviation is 0.028 μT. That last figure indicates that 66% of the samples will deviate from the average of 52 μT by only 0.028 μT, and 98% will deviate by 0.056 μT. I can live with that!.

The 52 μT background field strength is very close to what I found and reported in the Earth Specs blog. That's pretty close to the normal field strength of the Earth's magnetic field (25 to 65 μT).

By the way, background magnetism isn't constant over the Earth's surface. Dense rock and metal content in the Earth's crust can concentrate the magnetic field in certain areas much like iron cores in transformers and electromagnets can concentrate the magnetic field produced by an electric coil. This fact can be used by prospectors to find ore deposits and the magnetometer has long been in the prospector's tool chest. This close to the Front Range of the Rocky Mountains, it doesn't surprise me that the magnetic field strength is toward the upper range of Earth's background magnetism.

As for the spikes in the last half of the tracing, those do not surprise me either. The air system clicked on a couple of times while I was recording and electric relays and motors can kick out some heavy fields.

You always have to be concerned about the accuracy and reliability of your instruments. Different phones will have different sensors and driver circuits. You might want to check out your sensors. NASA has a cool book called "A Guide to Smartphone Sensor." It's a free download and you can get it here:

https://spacemath.gsfc.nasa.gov/Sensor/SensorsBook.pdf&ved=2ahUKEwi_y8XM-tnpAhWoHzQIHd3dDlwQFjAAegQIARAC&usg=AOvVaw3Jdvl70h9QILRRQ2U99Yol

Earth's specs

Somewhen in the 200s BC, a Greek named Eratosthenes measured the circumference of the Earth. He worked and lived in Alexandria, Egypt and knew of a place in Syrene, Egypt where, on the summer solstice, the image of the sun could be seen in a deep well, meaning that the sun was directly overhead. That placed Syrene on the equator. 

Eratosthenes assumed the Earth to be a sphere. If that were true, he reasoned that, if he stuck a rod in the ground vertically, it's line could be extended straight to the Earth's center to form an angle with a similar line from Syrene and that angle could easily be calculated. All he had to do was measure the angle formed of the line from the tip of the sun's shadow to the tip of the rod with the ground, subtract that from the 90° angle of the vertical rod with the ground, and he would have it...and "it" would also be Alexandria's latitude. It worked out to be about 7°.

By that time, everybody knew that the Earth was round and that the angular measure of any circle was 360°, and Eratosthenes knew that Alexandria was 5000 stadia from Syrene, he could figure out the circumference of a great circle on the Earth and, therefore, the Earth. His result was 250,000 stadia, or 39,385 kilometers, which is 1.4% off from the accurate circumference, 39,941 kilometers. Not too shabby!

So, on my recent hike to The Bluffs, I decided to do a modernized version of Eratosthenes' calculation.

The summer solstice was still a ways in the future so, not trusting nature to provide me with a good shot of the sun on demand, I measured the latitude and the distance between Arapahoe and Ridgegate Stations on the RTC southern light rail lines. I used Veiyra Software's Physics Toolbox Pro for the measurements. Here are the readouts.

Arapahoe Station

Ridgegate Station.

The distance, measured as the crow flies using Google Maps, is 5.6 miles or 9 kilometers.

"As the crow flies" is another way of saying "along a great circle on the globe," so I now have a way of converting degrees along the circumference of the Earth to kilometers and vice versa. By the way, I have it from a reputable source, namely, a crow, that crows do not always fly in straight lines.

The two stations are at almost the same longitude, so I can ignore that. The difference in latitude is .08 degrees.

But what about the stick in the ground? Well, that's another thing. It's called a gnomon and was a primary tool of ancient astronomers. It simply measured the angle of inclination of an astronomical object. Today we have astrolabes (basically a protractor with a plumb bob and a pointer) and the more advanced theodolite used by surveyors. I have a theodolite on my phone, the Dioptra app by Workshop512.

Since I really had all the information I needed, and I didn't know how far I was from the equator, I just wanted to do a modern version of Eratosthenes' trick to find my latitude by the sun. True to course, it was so cloudy on the summer equinox that I couldn't even tell which quadrant of the sky the sun was in, but I slapped a welder filter on my phone and took this shot from Dioptra the next day.

The angle of inclination was 51.1°, which was close to the actual measure on the equinox taken from the Time and Date website:

https://www.timeanddate.com/astronomy/usa/denver

Solar noon was at 1:07.

Angle of inclination was 50.5°, which placed my latitude at 90°-50.5°=39.5° . Looking at the Toolbox measurements above, I'm off by less than a tenth of a degree. The Dioptra measurement, which is also GPS is 39.58, so it's close.

But back to the real thing. The difference in measured latitude was 0.08° which is 4 minutes and 48 seconds (There are 60 minutes in a degree and 60 seconds in a minute). If 0.08 degrees is the same as 9 kilometers, 1 degree is 112.5 kilometers.

Okay, breath held, the moment of truth….112.5 kilometers times 360 degrees is 40,500 kilometers. The actual value is 39,941 kilometers. I was off by 1.01% Wow! I just impressed myself!

Of course, along with all the measurement error and such, the Earth is only approximately a sphere. The radius at the equator is larger than the radiuses at the poles.

We know the circumference of the Earth. The approximate volume is easy. The volume of a sphere is π\6 times the diameter cubed. The diameter is the circumference divided by π. Working backward, the diameter is 12,714 kilometers. So the volume is right at 10 to the 12th power cubic kilometers.

Okay, mass...mass is a bear. You measure mass with a balance and standard mass (remember the blog about mass and weight?) But Earth does have a mass. How in Sam Hill would you figure it out?

Well, obviously, you can't use a balance so any measurement has to be indirect. The first measurement to within 1% was made in 1798 by Henry Cavendish as a spin off of his accurate measurement of the gravitational constant. He used a torsion balance to do that and I can't even approach that kind of precision at home, so I'll just tell you how he did it. 

Isaac Newton figured out that the force of attraction (gravity) between any  two masses is directly proportional to the difference between their masses, and inversely proportional to the square of the distance between them. But to come up with an actual measurement, a proportionality constant was needed. He called it the Universal Gravitational Constant and never found it's value.

About 70 years later, Cavendish did it. Imagine a long, vertical, thin, flexible rod. At the bottom end is another rod forming an inverted T. At the end of that rod are two balanced heavy masses. His masses were  .73 kilograms each. He could set the bottom rod spinning back and forth and measure a slight force inhibiting the motion by comparing the frequency of oscillation with and without the force. The force, of course, would be another large mass close to one of the chunks of lead on the torsion balance. He knew the masses he was working with, the separation between them, and Newton's formula, so he was ready to calculate the Universal Gravitational Constant.

It was 6.67408 x 10^-11 m^3kg^-1s^-2 .

Believe it or not, that's what we need to calculate the mass of the Earth. Using Newton's formula we need the acceleration due to gravity (we found that approximately fooling around with the smartphone's accelerometer), multiplied by the radius of the Earth squared (we know that), divided by the Gravitational Constant.

So let's do it. Square the Earth first. The diameter is 12714 km so the radius is 6357 km. We need that in meters so 6357 x 10^3 meters. Square that to get 4.04 x 10^13 meters squared. The acceleration due to gravity is 9.18 meters per second square so the numerator is 3.71 x 10^14. Now we divide that by our Gravitational Constant, 6.67408 x 10^-11 m^3kg^-1s^-2  to get 5.56 x 10^24 kg (the accurate figure is 5.972 x 10^24 kg).

Actually, Cavendish didn't report the mass of the Earth. He stopped one step short by publishing the density of Earth which was 5.45 grams per cubic centimeter. He probably figured that, from there, it was easy to multiply that times the volume of Earth so, eh, let someone else do the easy part. 

If we look around and figure out what proportion of Earth is made of light rocks, heavy rocks, water, air... and come up with an average density we would say that it's around (and people before Cavendish had done just that) 2.7 grams per cubic centimeter, so where does all that mass come from?

Well, obviously, there's more underneath our feet than meets the eye. In fact, the deepest we've ever been is 12,262 meters and, although that's pretty deep, it barely scratches the surface. Still, the researchers expected temperatures around 212 degrees Fahrenheit and what they got was 356 degrees. It's hot down there.

But two things convince us that the core of the Earth is iron-rich molten metal. One is the surprising density of Earth. The other is something you don't see a lot of in the solar system...magnetism.

Earth is a magnet. The sun and gas giants like Jupiter and Neptune have strong magnetic fields. Mercury has a weak field. Some of the moons (but not ours) seem to be magnetic, but most of the smaller planets are magnetically inert.

We've used compasses that rely on the Earth's magnetic field for a long time. It wasn't until 1600 that William Gilbert proposed that Earth is a magnet. In fact, Earth is not a permanent magnet. It's an electromagnet.

Moving electrons (current) generates magnetic fields and our rotating molten metal outer core is one humongous magnetic field generator.

Our planet is special. We are just the right size. If we were too big, gravity would squash us. Too small and we wouldn't have enough gravity to hold onto our atmosphere. We get just enough sunlight for a healthy biosphere. We have plenty of that rare commodity - water. A nice balance of plants and animals conditions our air. And we have an effective magnetic shield that shunts dangerous solar radiations around the planet and out into space.

When I bought my current phone, I made sure it had a magnetometer in addition to the other regular sensors. Phones with GPS receivers will provide fairly accurate compass readings, but a magnetometer is more accurate and you can use it to measure both magnetic fields and electrical currents.

My Android has a AK09918 triaxial magnetometer. Since it's triaxial, it measures field strength in three directions (like the accelerometers). There are two common kinds of magnetometers in smartphones: magnetoresistive and Hall Effect. The AKM is a Hall Effect sensor that uses a flat conductive plate. A magnetic field causes electrons to deviate from their path and polarizes the plate. That can be sensed as a potential difference across the plate.

About a week ago, I hiked down a mile of  Little Dry Creek trail and used the Physics Toolbox Pro to record magnetic fields. I walked almost due west so I was cutting across the magnetic field lines.

The strength of a magnetic field is measured in teslas (in this case, in microteslas). A tesla is equal to a weber per square meter, and a weber is a kilogram per square second. If you understand induction (it makes transformers work), webers involve how much voltage you can crank out with a magnetic field. So with microteslas, don't expect geomagnetic electric generating stations any time soon.

I recorded the magnetic field in three directions at a rate of one measurement per second. Since I had the phone in my shirt pocket, the x direction was right-left, y was up-down, and z was forward-backward. I then saved the several thousands readings in a csv (comma separated values) file that I could pick up with DANSYS, my statistical spreadsheet.

Here's a graph of the tracings.

The tracings are pretty fuzzy, indicating a lot of noise. The inside of a smartphone has lots of electrical components crowded together and heat from those and the outside. Noise is to be expected and when you're measuring on the order of micro-anything, you can expect noise to blur the lines. 

All the lines have big spikes but the z component has the most. That is my forward and backward direction and I was walking in an urban environment, so power lines, underground cables…. yeah. So that's not the Earth's magnetic field, right? 

Many scientists call this the anthropocene epoch because the biggest influence on the Earth's environment, for the first time, is a single species - humanity. Every stray magnetic field alters Earth's magnetic field locally. Have you ever tried to get a compass to work in a house? You're likely to find it somewhat off the magnetic north.

But, we can sense some trends. There is a noticeable difference between the start of my recording and the latter part. That's because I started at my home and walked a ways more or less north before turning west on the trail.

The green line gives us the total field strength. It's measuring around 50 to 75 microteslas. The normal background magnetic field strength runs around 25 to 65 microteslas, so we're well within that range (once we get away from the houses.) The local residue from residences doesn't seem to spread out very far. The trail is generally about 200 to 300 feet (as measured by Google Maps) from the nearest houses.

Geophysics is the study of the physical attributes of our planet. After the barriers between East and West came down in 1957, scientists took the opportunity to focus on Earth and instituted the International Geophysical Year. You can learn a lot more with a team than you can alone. Perhaps you can join with some interested neighbors and have a Geophysical Year of your own!

Critical Thinking for Voters

I don't and never have intended this blog as a place for political commentary, but the last presidential election and local elections since then have caused me concern on several points not the least being the disturbingly low turnout of eligible voters in the 2016 presidential election, evidently because voters in the United States do not believe that their votes matter.

I believe that their votes do matter - or can if they vote critically, and am working on an ebook, Critical Thinking for Voters. It's a work in progress but I am making it available as I finish chapters. It can be downloaded via the link in the sidebar of this blog.

Let me know what you think.

Photos during the time of ...

(With apologies to Mr. Gabriel Garcia Marquez)

Avoiding everything is getting old and is certainly cramping my style, but slowing the transmission of a novel virus has its points.

I've mostly been wandering around close to home. People are out socially distancing. It is certainly a time to be out observing social behavior under atypical circumstances.

How are people behaving around you? How are you reacting to the different situations?

I've been back to Fiddler's Green to see more of the statues and I walked down Little Dry Creek Trail to look at Holly Reservoir. Here are some photos.

A reminder of the old west in modern Arapahoe County.

That odd little mound near Arapahoe Station.

An ensemble at Plaza Tower One, Village Center. A bear, plates falling down and some logs.

The elephant puzzled me until I saw the mouse on the pavement in front of it.

Denver likes murals.

This wild boar looks like a matching statue over near Englewood Station. Much of the art in this area is also part of the Denver Museum of Open Air Art. 

This piece of modern art...well, I'll let the artist explain it….

Giraffes!

They're still working on Marjorie Park.

There are extravagant water features all around Denver. This one is at the apartments called "The Cascades". I suspect there's a little nose twerking of nature here in the high desert.

Pike's peak from Quebec.

Another consequence of the virus.

A photo I took of the sun through a welder filter. You know that photographing the sun directly will damage your digital camera, right?

Interesting tunnel under Arapahoe on Little Dry Creek Trail. It's blocked now but maybe later...

Little Dry Creek at Holly Park

Mount Evans from Holly Park. They're done nice views from this little park on Little Dry Creek Trail.

Holly Park

Although Little Dry Creek is almost never dry, Holly Reservoir usually is. Like many stream constructions in the area, Holly Reservoir is a buffer in case of flash floods.

If you want to hike the whole thing, Little Dry Creek Trail begins at Yosemite near Briarwood and Davies Streets and runs about 4 miles to the Highline Canal. It's a well maintained trail, easy at sections but the stretch along Arapahoe is a constant grade that can wear you out after a time. It grades up toward the east.

One of the socially acceptable activities during the time of The Virus is hiking. If you're into biking, that's okay, too.

Terminus: Ridgegate

Ridgegate station is the southern terminal for three lines of the light rail system in Denver: the E, F, R lines. It's just about as far south as you can go and be in the Denver area. Just south of there are the bluffs, a wild grassland.

I hear that there are companies wanting to build there, but there are also concerned citizens fighting them to keep that area wild.

Ridgegate is growing. The light rail extension from Lincoln Avenue to Ridgegate Parkway is new and I haven't been south of Lincoln on it. I visited someone at Sky Ridge Hospital near Ridgegate a couple of months ago.

Currently the terminus is isolated but in easy walking distance of the Ridgegate community, it's shops, and the hospital. My destination was The Bluffs Regional Park.

Like all train and bus stations in the Denver area, this one has been adorned by a known artist, in this case, two artists. The names are Erik Carlson and Erica Carpenter. Decidedly modern, the art incorporates local ranch brands and technological symbols into an exhibit called "End of the Line." I'll let them tell you.

Here's some of the art.

The station is large but sort of lonely out on the plains.

As near as it is to a dense residential area, it's separated by I-25. A short hike brought me there. The entrance to the town is guarded by a brass elk at Cabela's parking lot (I guess it's an elk.)

Long, long ago, in a land pretty darn close by (I live in a suburb of Denver), the Pacific Plate crashed into North America and buckled the continent forming the Colorado Plateau. Except for a few volcanoes that belched a lot of ash into the wind, it was a fairly well rounded plateau, but rains fell and, soon rivers formed (like they do) and the South Platte and Arkansas Rivers started carving out deep gorges and depositing silt and rock east of what would be the Rocky Mountains. Mixed with the mud that formed when the volcanic ash decomposed, there was a deep blanket of gunk sloping out across the plains. To the south of what is today Denver, quartz rich sands got washed down and formed a hard layer over the softer stuff.

Time and rain kept flowing and water flowed both west and east. Tributaries of the South Platte and Arkansas Rivers kept excavating. To the north of Denver, nature wore the land down to a nub, and today we have the gently rolling hills of the western plains. To the south, that hard capstone resisted erosion in places and now we have the mesas and buttes like Castle Rock. Between, the ridge of Palmer's Divide split falling waters apart to run into the South Platte to the north, and the Arkansas to the south. And right on the northern border of Palmer's Divide is this 

I'm sure the little Creek that flows through Lone Tree had something to do with forming the hills in Bluffs Regional Park but they look like wind might have played a big part, too.

The Bluffs are an island of grassland above the surrounding residential areas. The wind was strong and cold and I'm sure there was plenty of wildlife out of sight. Still wintery weather in the Denver area, it's too early for wildflowers to be blooming. The main draw today was the views of the mountains. Only four miles further south from where I live, the bluffs make Pike's Peak seem far closer.

Pikes Peak

Mount Evans and the Front Range

Devil's Head

At the overlook, there's a little circle of stones that serve as a place to sit. It served me as a place to eat my lunch.

A stone disk set in the center of the circle points out some of the surrounding mountains.

After a short hike, I headed back down to the station and took a train back home.

Do you know the geological history of your area? There are surprised there. Check it out and then keep your eyes open for clues to it's past as you hike.

Vectors

This first paragraph... you're either going to know what I'm talking about or you won't have the slightest idea. I didn't study tensors in college (or anywhere else except on my own time) and I suspect that they're still a graduate level subject. But they're not that complicated. Mathematicians use collections of values that can be handled as a single entity. They're called "matrices". A tensor is basically a multidimensional matrix of measurements. A zero order tensor is a scalar. A first order tensor is a vector. A second order tensor is a two dimensional matrix. A third order tensor is a three dimensional matrix, and so on.

The important thing about these things is that they are collections of many values but they can be handled as a single unit. It's like...you can buy a dozen eggs at the grocery store and bring them home separately - that's 24 trips to and from the store. Or you can put them into a carton and put the carton in a bag, and bring them home all at once. Just forget "eggs" and think "carton" until you get ready to make omelettes.

Tensors are advanced math and people generally think of advanced math as a kind of puzzle for folks that like that sort of thing. Well, abstract math is (sort of). But tensors are not abstract math - they're the other kind - practical math. In school, you study practical math. For most of us it goes like this: elementary arithmetic, algebra, geometry, trigonometry and precalculus (or college algebra), and then, in a college science curriculum there are differential calculus, integral calculus, and maaaaybe differential equations.

None of that involves tensors. You'll probably study some linear algebra ( that's matrices) and, in physics, you'll learn about vectors. But there's a lot (!) Beyond that….statistics, calculus of variations, numerical analysis, discrete mathematics…

The point is that all this stuff isn't abstract nonsense. It's all...and here's the kicker...it's all quick and easy labor saving devices. That's right. Advanced mathematics is there to make life easier for people that need to do certain jobs.

Take matrices from example. Let's say you had to figure out three values and you have three equations that contain them. Say, you overheard three people talking. One said, "I have 25, 7, and 43, so I have 490." Another said, "I have 13, 9, and 17, so I have 228." The third said, "I have 3, 23, and 37, so I have 488." You might reasonably think that they're talking about numbers of things with three different values, and you guess that they're naming the things in increasing value so you set up the following equations:

25X1+7X2+43X3=490

14X1+9X3+17X3=228

3X1+23X2+37X3=488

There are several ways to solve for the values of the three variables that make them all true at the same time. One is called elimination and it looks like this.

I counted about 27 (grueling) operations there. Here's the "advanced math" matrix method.

See, you can treat matrices like individual numbers so, once I had the coefficients of the variables packed safely away into one matrix (A) and the numbers on the right side of the equations packed into another (B), I just inverted A and multiplied it by B, two easy operations on the spreadsheet, and I had my answers.

It's pretty clear that the three were talking about money - pennies, nickels, and dimes.

It's a lot easier working with matrices than with individual numbers.

By the way, scalars are just individual numbers. A vector is a row (or column) of numbers. A two dimensional matrix has rows and columns, like the ones I used above. You can have a stack of two dimensional matrices to form a three dimensional matrix, and you can keep going adding more and more dimensions until your brain explodes.

When you're talking about tensors, you're usually talking about measured values and things can get pretty deep, but I won't here.

Many of the values that physicists work with have two parts, so they pack well into two valued vectors. Think back to all the things I measured in the playground.

I started at the trailhead and walked to the playground measuring the distance using AllTrails. It was 0.3 mile. That would not be enough for a physicist, though. They would also want to know the direction. My direction was almost due west or pi radians from an east-west line. The vector would be (0.3,3.15). It could also be represented by an arrow pointing west with a scaled length representing 0.3 miles. The vector would represent my displacement. Distance is a scalar; displacement is a vector.

The funny thing about displacement is that it's the distance traveled from start to finish. On a loop hike, displacement would be exactly 0, since, all told, I would have gone nowhere.

Speed is also a scalar. I walked about 1.8 mph. But physicists talk about velocity, which is a vector consisting of speed and direction. I walked 1.8 mph west.

Acceleration is also a vector consisting of change of speed and change of direction. When I was spinning the phone on the cord, I tried to keep the speed constant but there was still acceleration because the direction of the motion was constantly changing. (Actually, since I didn't do a very good job keeping the speed constant, both were changing.)

Most of the vectors in "undergraduate" physics are two-valued. More advanced physics and engineering get to use larger vectors because they're dealing with three dimensions (space) and four dimensions (relativistic space-time). But our universe is growing and some physicists think that we need ten, eleven, or, maybe, an infinite number of dimensions to describe it.

Are big vectors a problem? Well, they're hard to visualize but statisticians, social scientists, researchers, economists...they've had to deal with big vectors for a long time because every case in a dataset is a vector that might be described by two, fifteen, or thousands of values. Just think about what you look like in a census report: age, ethnicity, residence, number of people in your family, whether you're the head of your family - all values in a huge vector.

We will be talking about other quantities in the future: force, work, energy, magnetic fields. If you've never seen vectors in action, you'll get to see how they work.

Meanwhile...

I hope you don't think that the only things I do are what I report in my blog two or three times a month. Most of my activity is family and community business. I have a Carolina dog that keeps me busy at home and along with washing dishes and cooking occasionally, I make frequent trips to local grocery stores and there is the weekly trip to the old neighborhood where I am still the assistant librarian at the church I used to attend.

But I'm supposed to walk at least 20 minutes every day to keep my heart going. Almost literally, "if I stop, I stop." Luckily, even my local walks are interesting. Some of the neighbors like to talk and most of them have friendly dogs (Denver is dog territory). The scenery is even spectacular in the neighborhoods.

A while back, I walked over to the other side of Arapahoe to check out Fiddler's Green. It's at the north rim of the valley formed by Little Dry Creek. It's the southern border of the patch of tall buildings in South Denver called "The Denver Tech Center". I go there every week to the Arapahoe at Village Center light rail station, but I had not checked out the surrounding area. 

The big draw is Fiddler's Green Amphitheater, a major venue for stage shows in the area. But it isn't much to look at unless you're going in and that requires a ticket.

On the other hand, there is much more packed into the area. The other day, I noticed a bronze statue of an elephant near the rail station. It was so uncharacteristic that I couldn't quite figure out what it was from a distance. It's a reminder that there's so much up the hill (probably anywhere) that you always miss things, so you have to keep going back.

Adjacent to the amphitheater is Marjorie Park with it's collection of fanciful statues, including many from the Alice stories of Lewis Carroll. There was construction going on when I visited so I could only get a few shots through the gates.

The park was originally named Samson Park after the pet Yorkie of the Museum of Outdoor Arts founders John and Marjorie Madden. The name was changed in 2015. I'll have to return after they finish construction.

Luckily, nearby Tuscany Plaza was accessible with it's collection of statues.

There is outdoor art all over the place in the Village Center/Fiddler's Green area. On the way back from the train station, I got a picture of the bear outside Plaza Tower One, the prominent 22 story building at Village Center.

In fact, you could wander around the entire Tech Center for days looking at art and architecture. 

And, of course, the views of the Rockies in this area are stunning. It's easy to get so used to them here that you forget how breathtaking they are.

The little park running through Walnut Hills is a corridor for wildlife. I spotted this big redtail hawk a couple of days ago. If you have problems seeing it, it's because they are well camouflaged in their leafy surroundings.

Speaking of wildlife, last week, a friend and I hiked up Waterton Canyon to Strontia Dam. Groups of male bighorn sheep were lounging around. I guess the females are lambing. There were plenty of birds and we saw a herd of deer on the other side of the river. 

Not a great shot but incentive to go back sometimes with my telephoto lens. There is a big difference between optical and electronic enlargement.

The Corona virus is interesting from a sociological standpoint. It's a repeat of so many epidemics that I've been through over 66 years of life but this time it's close to mass hysteria. The electronic media has opened up the world to many exciting possibilities, but it has also become a tool for manipulating huge numbers of people who have adapted quite well to it and are very open to manipulation.

It is keeping me inside more to avoid all the mad dashing around and store emptying.

Stay safe and be a neighbor for those that are more vulnerable and we'll get through it all.