Colorado (2018)

In 2018 I visited Colorado, giving talks at the University of Northern Colorado and Colorado State, and traveling into the Rocky Mountains.

The trip began with an ominous license plate sighting at the airport in Connecticut. Who knew the Sith Lord was an environmentalist?

Shortly after arriving in Colorado, I had lunch at a Japanese restaurant in Denver called Domo, and adjacent to the restaurant is a small Japanese antiques and crafts museum.

           

Through one wall of the museum you can enter an Akido training center. It was empty when I was there, but here is a video of it being used (shot from within the museum) on YouTube.

After lunch, my next task was to purchase a Colorado Rockies baseball hat. Here is the model I got.

Although the baseball team was in the playoffs at the time, that wasn't why I wanted the hat. The font in which the letters C and R are written by the Colorado Rockies looks just like the blackboard bold font that is often used in mathematics to denote the sets of complex numbers and real numbers: ℂ and ℝ. Another connection between the Rockies and math is that they celebrated Pi Day in 2017 by posting a nice image on Twitter.

(A comparison of this Photoshopped lineup photo with the original version, where the player numbers are nothing like the digits of pi, is here.)

When I went up to the cashier to buy my hat, she asked me if I was aware that it was a women's hat. Take a look at the hat again. It's obviously for a woman, right? In case, for some reason, you are not convinced, inside the hat I found the telltale "W" on the label and this webpage calls it a women's hat. The Rockies men's hat being sold at the Major League Baseball online store here looks pretty similar. I am as baffled about how a hat can specifically be for a woman as I am about how a pen can specifically be for a woman, as Ellen DeGeneres discusses in the video below.

The place where I bought the hat (in Johnstown, Colorado) was the sporting goods store Scheels. There was a working ferris wheel inside, which is a feature in many of the store's locations (do a Google image search on Scheels). I was the only passenger during my ride, which went around four times.

           

The University of Northern Colorado was a short drive down the road, and I gave a lecture there to the undergraduate math club.

The following day I gave a talk at Colorado State, where the math department is located along the beuatiful tree-lined Oval, which is the historic center of campus. These elm trees, shown below on the left, were planted in the 1920s. Their arrangement reminded me of the tree-lined drive into Princeton. Those elm trees, shown below on the right, were also planted in the 1920s.

           

The math department has a display case of many geometric sculptures, made from both wood and a 3d printer. Jeff Achter showed me his 3d-printed set of "mod p" glasses, which a student made for him because in his number theory class he talks about reducing equations modulo a prime p as "putting on your mod p glasses". Now he can really do it.





           




In the main office of the Colorado State math department I found the amazing old photograph below hanging above the copy machine. The math faculty I pointed out the photo to did not realize there is something interesting in it (mathematically): the person at the board is writing power series expansions using the obsolete corner notation for factorials instead of exclamation points. While I have seen the corner notation for factorials in old books, I've never seen a photo of a person using it. This is discussed in more detail on my other page.

On my third day in Colorado I visited Rocky Mountain National Park. The last town I went through on the way to the park was Estes Park, which is located near the park's entrance. Its most famous building is the Stanley Hotel, which was the inspiration for the Overlook Hotel in Stephen King's novel The Shining. The staff at the hotel knows that many people want to visit it without staying there, so they charge money simply to park and walk around. That wasn't worth it. I had lunch elsewhere in Estes Park, at Notchtop Bakery and Cafe, which is named after Notchtop mountain.

My host Anton Dzhamay was wearing a Russian t-shirt, and when the waitress gave us menus she saw the shirt and started talking to us in Russian. She is from Ukraine and it turns out a lot of the staff is foreign (Uzbekistan, Romania, etc.) since the owner is as well. Anyway, the food was fantastic. If you want to have a meal in Estes Park, definitely consider going to Notchtop.

The next 6 photos were taken before the road started going into the mountains.

           
           
           

The route up Trail Ridge Road led to the Many Parks Overlook, which is where the next 4 photos were taken.

           

           

Because of snowstorms farther ahead, Trail Ridge Road was closed beyond the overlook. Of course there is not just one road in the park. The next group of photos were taken on the return drive, heading toward Bear Lake Road.

           

           

           

The trees in the park have been devastated since the mid-1990s by the mountain pine beetle. Park rangers cut down the trees that have been killed by the beetle (at least those trees that are in danger of falling on areas where people are) and collect them into huge piles, as shown below, and burn them during winter months when the fires are less likely to spread out of control.

From the the Bear Lake trailhead there is a trail that passes 3 lakes connected by Tyndall Creek: Nymph Lake, Dream Lake, and Emerald Lake. The two photos below were taken at Nymph Lake. The prominent peak in both photos is Hallett Peak and the small people on the right side of the second photo, standing on the smaller of the tall rock formations, are on the path to Dream Lake from Nymph Lake.

Here is the view looking back toward Nymph Lake from that rock formation where the small people were.

           

I was walking slowly on account of the precipitation and uneven trail, but sometimes I had to stop to catch my breath since the trail was at over 9000 feet above sea level.

On the route to Dream Lake, here is a view of Glacier Gorge and my crossing of Tyndall Creek.

           

Finally I was at Dream Lake, where Hallett Peak was more striking.

           

I did not continue on to Emerald Lake. Turning back, at the start of the trailhead I visited Bear Lake.

The view at Bear Lake was not as impressive to me as Dream Lake, but I learned later that from Bear Lake you can see Longs Peak, which is the highest point in the park and is featured on the Colorado state quarter.

On my last day in Colorado I visited the Shambhala Mountain Center, a Buddhist meditation retreat. The drive there was through Poudre Canyon.

Along the route I could see damage in the canyon from fires in 2012 (many burned trees, as shown below) and floods in 2013 (large sections of the lower canyon wall had been carved out, but I did not get photos of that).

           

Once out of the canyon, the road went high up, and at one viewing area I saw some flowers near rocks (first photo below). Getting closer, I found it was a burial spot for Timothy Harvey (1975-2009). There was a second grave nearby.

           

Finally I was at the Shambhala Mountain Center.

Somewhere at the site is an enormous stupa, but it took a while even to see it. (It's not either of the buildings on the left or right side of the first photo below.)

               

The golden top of the stupa actually can be seen in the first photo above, as a yellow vertical strip behind my right shoulder, but soon after walking from that spot I lost sight of it again until I was much closer.

Finally the trees fell away and the building was clearly visible.

Each of the four sides has a similar design, but they do not all have working entrances.

           

           

Inside I saw an enormous Buddha statue and one person meditating.

Along each wall were many display spaces. I did not try to sit in the comfortable-looking chair.

           

After my visit was over, I looked out towards the parking lot, which was as invisible in the distance as the stupa had been at the start of my walk.

That's it!