--- The Arduino adventure ---

From now on, I'll be doing a lot more technical hikes. I've already done some - the early Bear Creek hikes, where I measured distances and recorded an altitude profile, the smile experiment when I counted how many people smiled back at me when I smiled at them and when I did not smile at them, and the Lookout Mountain hike recording of altitudes, temperatures, and barometric pressures. Beginning with this years explorations of mathematics, I'll be looking at the pure and applied sciences regularly, so I need to make sure that my tools are all in order.

On 1/19/19, I checked the Altitude app (created by Pygdroid and available as an Android app on the Google Play Store) I use to record altitudes and distances to see if I could use it and my camera at the same time. I just wandered around the house with my phone this time and it seemed to work fine but I'll try it later on a walk to the library.

I also checked my Arduino to make sure that it actually works the way I want. I've had it for a couple of years and have not powered it up. I did so today and was happy to see that it works.

I bought my Arduino 101 from SparkFun, a local business that supplies electronic parts, equipment, and kits to hobbyists at great prices. They also offered a plastic carrying case that seemed like a good idea for my adventures. It required a little modifying. The compartments are well divided and I wanted to be able to run wires between them, so I cut some notches into the dividers.

                                                                 [Arduino case]

Now, I can keep all my Arduino equipment in a case that I can keep in my backpack, or on me.

                                                                    [Arduino rig]

I also bought a plastic cover for the microcomputer. It fits nicely into a smart phone holder that will attach to a camera tripod. I will be making one more alteration of the Arduino case - a bolt in one compartment that I can screw the clip to. That should keep my equipment from moving around in the case while I'm hiking.

                                                               [Arduino and clip]

When I attached the microcomputer to a 9 volt battery, it lit up.

                                                            [Arduino powered up]

and when I opened up my Science Journal app and looked around for the Bluetooth, I found this screen...

                                                         [Arduino on Science Journal]

I am set.

It's sorta frustrating that it wouldn't do you much good for me to go into a lot of depth about using the Arduino 101 since, soon after I bought it, Intel, it's manufacturer, decided that they didn't want to be in the microprocessor business and the Arduino 101, which is set up from the get-go to work with Science Journal, is no longer available.

The good news is that, if you want to play around with a microcomputer on the trail, SparkFun has other Arduino (and other microcomputer) options with Bluetooth.

If you want to check out SparkFun (and I highly recommend them), here is the address of their website...

https://www.sparkfun.com

I then went about testing to make sure that my Arduino would accept external inputs. Here's a photo of my setup.

                                                        [Arduino with photocell]

There are two items on my plugboard. Right on the gutter in the middle is a photocell. Just to the right is a resistor. An electronics hobbyist would immediately recognize this as a voltage divider. Let me explain.

Electricity is very much like a fluid. If you have water running through a hose and you narrow the hose (say, by crimping it), two things happen. First, less water gets through. Second, the pressure at the end of the crimp away from the faucet has less pressure. In other words, pressure is dropped by the crimp.

For electricity, the pressure that drives the electricity is called voltage and it's provided by the source of electricity (battery, generator, etc.). The amount of electricity that flows through the wire over a period of time is called current. The resistor and photocell in this circuit are the crimps. They resist the flow of electricity.

In this circuit, both "crimps" in the line drop a certain amount of pressure. That pressure drop could be measured across either element with a voltmeter. If the two resistors (in a circuit, that's what a crimp is called) have the same value - resistance, the amount the flow of electricity is impeded - then the voltage drop would be the same across each. The voltage would be divided equally between the two. In this circuit, one of the resistors reacts to light. As more light hits the photocell, it resists the flow of electricity more and creates more of a voltage drop. The resulting shared voltage drop across the resistor, then, has to be less. That change can be measured by a voltmeter across either the photocell or the resistor. Here, you can see that I have three wires going to the circuit. The black and green wires run to the Arduino so that it acts as a voltmeter.

The red wire feeds electricity from the Arduino to the circuit through the photocell. The photocell and resistor are connected in series so that all the electricity must run through both to get out through the ground (the black wire). the green wire runs to the voltmeter input to the microprocessor (called an analog input - there are several). So, the Arduino is measuring the voltage drop across the resistor.

The Arduino broadcasts what it measures to my phone via Bluetooth and my Science Journal app records it for me. I waved my finger back and forth across the photocell and this is what Science Journal recorded.

                                                          [Science Journal screenshot]

When I placed my finger over the photocell, the voltage decreased and when light hit the photocell, the voltage increased. The values are "raw" because they show voltage level across the resistance (not in volts). The measurement are not in any standard units but, if I knew the relationship between the values and, say, lumens, I could calculate the actual amount of light, but that wasn't my intention.

So, now, I know that I can take the Arduino on the trail with me to measure things I can't measure otherwise with the internal sensors in my phone or another instrument like my weather meter.

Technical hikes involve measurement. There's a lot that you can do with some really inexpensive equipment and learning to use it is a lot of the fun.

--- Mathematics in the colleges ---

Just looking at the websites of the colleges and universities in the area, it's hard to see any real focus in their mathematics departments. They seem to have a broad range of interests. I think I see a strong leaning toward discrete mathematics (combinatorial mathematics, graph theory, fields that deal specifically with whole numbers) and theoretical math at the Denver University. There are a few faculty members that share my interests in educational mathematics and statistical tools.

Statistics seems to be a big topic in the Colorado School of Mines. They make their areas of research more explicit on their website. There seems to be a lot going on with wave phenomenon, spatial statistics, computational math and analysis, and mathematical biology. For a school that focuses on applied technology, those topics don't surprise me much.

I walked up to the Denver University campus last Friday to sit in on a presentation and subsequent reception. It was a nice day and I got some nice pictures of the school of mathematics and science, which is spread across several buildings along Illif Avenue.

The water garden nearest the Newman Center, one of three on campus, is named Dan's Garden after Daniel Ritchie, a major donor to the university. It is in front of the Daniel Felix Ritchie School for Engineering and Computer Science, which is named after his father.

                         [Dan's Garden and the School for Engineering and Computer Science]

The three buildings to the west are all named for the philanthropic Boettcher family - the East and West Boettcher Buildings and the Boettcher Auditorium. Charles Boettcher was born in Kolleda, Germany in 1852 and his son, Claude, established the Boettcher Foundation in 1937, which supports education and research in Colorado. The park between the East and West Boettcher Buildings has several sculpture including busts of Charles, Claude, and Charles II Boettcher.

                                                     [The Boettcher Buildings and park]

The other building that houses the School of Natural Sciences and Mathematics is the Clarence M. Knudson building.

                                                                   [Knudson Hall]

The Robert and Judi Newman Center for the Performing Arts stands to the east. This cyclopean building sports a sundial on the south wall and, not a rose window, but an embossed rose, on the western facade.

                                                                 [Newman Center]

After wandering around this southern strip of the campus, I headed to Knudson Hall and the lecture. It was presented by Florencia Orosz Hunziker of Yale and was entitled "Fusion Rules for L(25,0)".

I enjoyed the lecture and... in truth, I didn't understand a single word she said. Actually, I did understand two words. I knew that there is something called a "tensor" and I understand "isomorphism". It was way above my head, but that was pretty much what I expected.

So, why did I go? First, I wanted to meet the mathematics faculty and, second, I wanted to push myself beyond my boundaries. Although I didn't understand the principles that Ms. Hunziker presented, I found that I could follow her thoughts and I recognized the method that she and her colleagues were using in their research. Afterward, in the reception, i had a brief conversation with her and was gratified when she didn't look at me as though she thought I was an idiot.

Actually, the all the attendees were friendly and very human. The conversations after the lecture were not at all above my head.

And as a bonus, the lecture rang bells.

I've dipped into theoretical mathematics a few times but it tends to be about three graduate courses further than I've been but I recognized a few things. Ms. Hunziker talked about Virasoro algebras. I had never been exposed to Virasoro algebras before but she kept drawing triangles on the board representing three-way isomorphism. Not really enjoying the feeling of ignorance, I looked up the topic at home. I can't say I understood much better but I noticed a recurring connection with particle physics and string theory.

One of the much cherished principles of physics has been supersymmetry, a belief hat there has to be an underlying, unifying pattern in the universe. From what I have gathered, supersymmetry has been rather disappointing. For instance, matching subatomic particles have failed to appear where they were expected. This pattern they that have been searching for seems to be a two- or four-fold pattern - sort of, "everything has a mirror image".

But I remembered reading a book in school by Sir Arthur Eddington, "New Pathways in Science". One of the chapters discussed Dirac's "Theory of Groups" and his idea that the universe is governed by pentads of operators. I don't see much about pentads anymore. It looks like it was one of Dirac's ideas that didn't really catch on. I wonder if the three-way operators are one side of a pentad.

So although I still don't have the foggiest, I did enjoy the seminar.

I've noticed that most progress comes from stretching beyond your limits. My memory has never been great but in memory tasks, I could never move forward until I put down the text and pushed myself to recite. I couldn't use new problem solving techniques until I moved past the examples into the exercises.

I once read a book on differential equations and came away as ignorant as when I started. Then, about a year later, I read the book again and, magically, I understood everything. I say, "magically" because I had done nothing mathematical in the interim. Obviously, my subconscious had been working in the meantime.

Adventuring is moving out into uncharted territory. The excitement of adventuring is the novelty.

In most cities and towns, many of the streets, buildings, and parks are named after people - people that, at least at one time, were important to the history of that place. What are the place names in your area and where do they come from?

--- Terminus: California Street ---

A circuit around California and Stroud Streets from 15th Street to 19th Street in Downtown Denver forms the terminus of several of the light rails  - F, H, D, and L. A hike around the circuit is short but there's a lot there. I wasn't that interested in food or shopping but there is plenty of that.

I left the train at the Convention Center/Theater District Station and walked around to the Convention Center entrance. I've shown the big blue Bear ("I See What You Mean") in a past blog. Here he is looking into the Convention Center lobby.

                                                                  [Big Blue Bear]

The Convention Center is near the south end of 16th Street Mall, the southern end of old Denver, and the Civic Center Park. Denver is really a fairly small city. I would not attempt a hike across downtown Atlanta in a day but it would be easy  to start at the Convention Center, walk down 16th Street Mall and see the capital and other government buildings at Civic Center Park, return to California Street to complete the circuit around Stout back to 16th Street, and then take the 16th Street Mall Flyer bus to Union Center, look round there and Commons Park, then walk back down to the Conference Center in a day. For those that like city life, that would be a good day trip.

                                                     [Denver from the Conference Center]

The Conference Center/Theater District complex is cyclopean. The Conference Center itself is modernist sculpture of glass and steel. Characteristic of Denver, the interior is adorned with art.

                                                      [Conference Center and wall art]

There was a garden show opening in a couple of hours, but I didn't want to wait around so I started up California Street.

                                                    [California Street and the light rail]

The Colorado Information Center is just down the street on the right (north side of the street). They have a gift shop where you can buy, among other things, replicas of the blue bear (not quite as big as the original) for less than $30 - two sizes, even. The staff is friendly and informative.

The buildings along the circuit are a mixture of old and new. The old tends toward ornate.

                                       [Rose colored building with decorative pilasters and plaques]

Older buildings in Denver often affect a Greek Classical style. If a wall doesn't need columns, columns are suggested anyway with the use of ornate pilasters.

An interesting assemblage of buildings, the Holy Ghost Catholic Church literally rests under a cantilever projection of a skyscraper. Beautiful as a combination of new glass and old stone, there is also a humor here. I say "old" but the church building was dedicated in 1924 with less than a third of is original plan completed. The present building displays the largest collection of colocreme travertine in the United States, over 300 tons of decorative stone.

                                                     [Holy Ghost Catholic Church]

The Federal Custom House at California and 19th Street has an impressive portal. There's a lot of brass in Denver.

                                                          [Federal Custom House]

This is where I turned down 19th Street to follow the light rail over to Stout Street. At 19th and Stout is a collection of buildings, old and new, that house the Federal 10th Circuit Court. The new building to the east is an ornamented block of concrete.

                                              [New Byron White United States Courthouse]

These buildings were names for Byron Raymond White (1917 - 2002) the first Coloradan to serve on the United States Supreme Court.

Across 19th Street is the old building, a classical style building of the same Yule marble that adorns the state Capitol, the Lincoln Memorial, and the Tomb of the Unknown Soldier. Consistent with Denver's love of monumental architecture, the front of the courthouse has a porch with 16 (count 'em) columns. The side walls don't need columns, so they have pilasters to be consistent.

The inside is similarly spectacular with barrel vault ceilings in the lobby and Federal District Courtroom and richly paneled ceilings in other rooms. Being a federal courthouse photography isn't allowed, but you can visit and be wowed. They also have an informative brochure in the lobby.

                                               [Old Byron White United States Courthouse]

The west side of the courthouse is adorned by these two bighorn sheep. The sheep were the work of Denver sculptor, Gladys Caldwell Fisher. Their official names are "Rocky Mountain Sheep" and "White Ram".

                                                                  [Courthouse sheep]

Across 18th Street from the Byron White Courthouse is the Ghost Building. You can look at the outside but you can't go in - it's very posted.

                                                                [Ghost Building]

It was named after Allen M. Ghost, who was a real estate tycoon. The 1700 stone blocks were moved to the current location in 1985.

Almost back at the Convention Center, I spied another purple building, this one the La Boheme Gentlemans' Cabaret. Again featuring ornate pilasters, it is, as they say, a strip club. I see on the Internet that they consistently get good reviews.

                                                                  [La Boheme]

After the train ride back to University Station, I walked across campus to home, stopping along the way to take a few pictures of the construction being done on the west side of the Driscoll Building. This is scheduled to be finished next fall.

                                                             [Driscoll construction]

Some cities favor a monumental style, others like small town American aesthetic. How would you describe downtown in your city? Have many of the buildings been relocated? A lot of Selma, Alabama, where I used to live, was originally in Cahaba, Alabama but was moved upriver because of flooding.