Narrow opening

Managed to prove a theorem today that I'd been working on this week. Turns out the statement of the theorem wasn't true. I found a counter-example while trying to prove it this morning. Fortunately, the counter-example made it clear what the correct statement of the theorem should have been. Once I fixed the theorem, the proof came relatively easily. It's definitely easier to prove true theorems than false ones, haha.

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I went for a walk with Laura this afternoon. We went to a "cycling in Sevilla" exhibit, but it wasn't that interesting. On the way home, we passed by a park that has been under construction since we got here last summer and is now open. Honestly, it's not clear what they actually did. It looks like any other park. My guess is that they were busy doing something to the infrastructure under the park, not to the park itself. That said, it's a pretty space:

On the way home, we passed by Plaza de San Francisco to see the progress on bleacher construction for the Semana Santa processions. The aisle that all of these procession have to pass through seems surprisingly narrow. Also interesting to note, the bleachers in this plaza are custom fit around lightposts, trees, fountains etc. They are clearly for this purpose and this purpose only:

Itálica

Today we took a tour of the nearby Roman ruin of the city of Itálica. The city was founded in roughly 200BC, but really usurped an existing village of indigenous people. Initially, the city was down in the Guadalquivir river plain, but regular flooding forced its relocation up into the nearby hills. The part of the city we visited today was actually added later, a mere 400 years later, in 200AD. Itálica was the first Roman city on the Iberian peninsula. It seems to have thrived for about 600 years and then sort of faded away, though there have been people living around it through to this day.

It was initially unearthed in the 14th century by monks of the nearby Monasterio de San Isidoro del Campo. It didn't become a protected archeological site until the early 20th century. There's not much left above ground. The site consists mostly of foundations of homes and businesses and avenues. There are some replicas of Roman statues that have been unearthed at the site. This Venus-like statue was found half buried in a nearby village being used as a doorstop.

Entering Itálica, you hit the main avenue with the original stone pavers:

Some of the stones bear graffiti:

The first of many intricate mosaics we encountered was in the bathroom:

Here's a row of nearby toilets. I guess the Romans were a little more comfortable than us with their normal bodily functions, haha:

The rooms of various homes were easily discernible by their outlines in the foundation stones. Most remarkable were the floors of the bedrooms and other rooms that had beautiful mosaics. These intricate mosaics were like the Persian rugs we use today:

It's hard to see here, but I was most impressed by the use of different color stones. There were blue, yellow, green, red and lots of other color stones. Impressive because paint would not have lasted 2000 years:

A row of smaller rooms in a poorer section of the city:

Also impressive was the Anfiteatro de Italica. This stadium seated 25,000 people and hosted regular gladiator bouts. This site has also been used several times in the filming of Game of Thrones:

Underneath the stadium, these tunnels let service personnel and competitors get around:

After the ruins, we visited the aforementioned Monasterio de San Isidoro del Campo. Established in 1301, it has been a Catholic monastery up until recently:

The typical mix of moorish and christian art of southern Spain is in evidence here:

The style of this painting of the last supper was unusual. It is not know who painted this:

The woman in this crypt is reported to have been burned at the stake for some transgression (though it's not clear to me why she would then be buried in the church). The legend goes that during her burning, the heat from the flames lifted her skirt immodestly. Her loyal lady in waiting, jumped into the flames and died protecting her lady's modesty. She too is named and buried in this crypt:

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We got home and Diego's Bar was going strong. Here you can see the last of the patrons and then closed and cleaned premises an hour later:

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Putting the Whitman VPN to good use this evening watching UK play in the second round of the NCAA Men's Basketball Tournament:

Bean Burritos

Laura made some refried beans and we had bean burritos for lunch:

Interestingly, the best salsa you can find here in Sevilla is at the Costco.

We've been meaning to check out this market across the river from us for a few weeks now. We finally made some time for a walk through today:

It's nice space, but there's not much here that isn't in the closer Triana Market. Some of the prices on the produce were perhaps a bit lower.

Preparations continue here for Semana Santa (Holy Week before Easter). Every Catholic brotherhood in Sevilla will have a procession to the Cathedral. Each procession follows a different route from its home neighborhood, but they all have to pass through the Plaza de San Francisco. Crews are setting up bleachers here so that spectators can see each of the processions that occur during this week-long event in a single place. The seats are like "box seats" in a stadium and are not cheap:

Spring

On this first full day of spring, I went to Parque de Maria Luisa to see what I could see. Turns out, there are a lot of flowers in full bloom here in Sevilla this time of year other than the azahar (orange blossom). I sat by this reflecting pool for a bit and read a book:

The smell of the orange blossoms was quite strong. When I got up and turned around, I saw why:

This tree is well on its way to having its leaves back:

The purple bougainvillea on this trellis were going strong:

The statue of Maria Luisa herself presided over a varied display of flowers:

The sun was so bright, it washed out this photo of the north tower of the Plaza de Espana:

In one of the lesser parks on the way home, I noticed these red/orange flowers:

It was pleasantly cool today.

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I mostly read elementary probability and statistics today. I'll get back to working on the paper tomorrow.

Density

I'm still working on my paper. I'd been mulling over adding an important generalization to the results, but was a bit afraid of how hard it might be. This morning, in a fit of energy, I decided to just start at the beginning of my notes and start incorporating a density function into the narrative, theorems and proofs. It took most of the day, but I got it done. The proofs didn't need too much fixing and all the results still held. With a density function, the results are more useful to a couple of other areas of math and also more useful in applications like image compression. Sometimes the dread of something is way worse than the actual something.

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Happy first day of spring (which doesn't officially start for another hour at the time of this writing)! It was actually a bit cool here today, but still wonderfully sunny. My run along the river was actually more pleasant in the cool breeze.

Walla Walla seems to be emerging from its long, cold winter too. It's 56F there right now. Probably the warmest temperature of the year so far there. I hope next winter is much milder than this one was.

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I've mentioned before that there are thousands of orange trees in Sevilla (and throughout southern Spain). The trees are now starting to bloom. The blossoms look a bit like honeysuckle blossoms. Even better, they smell like honeysuckle blossoms. Walking around the city the past 10 days or so, you often get strong wafts of the orange blossom smell. The orange tree is such an important part of Spanish culture that the language has a word specifically for "orange blossom", azahar.