Sunday, December 11, 2022

Population Dynamics in the Harry Potter Universe

 In Harry Potter and the Chamber of Secrets Hagrid makes an interesting comment. He says

"Most wizards these days are half-blood anyway. If we hadn’t married Muggles we’d’ve died out."

This comment got me thinking about the genetics and population dynamics of the Harry Potter universe. This topic prompted a lot of questions.  

Why is the magic population so small relative to the non-magic population? 

Hagrid's comment implies that there is something inherent in magic users that puts downward pressure on their population. There are a few possible explanations:

  • A genetic effect associated with the same genes that allow magic use also reduces fertility.
  • Certain magic users face cultural pressure not to have children (for example, witches might face pressure not to have children, resulting in more magic using men choosing non-magical partners). 
  • Hagrid could be referring to a specific event, rather than a general trend (for example, say there was a catastrophic event in the past which eliminated a critical mass of magic users).
Let's see if we can isolate one of these potential causes. 

Size of the Magical Population

The size of the magical population is hard to gauge, but it is clearly fairly small. Let's work out an estimate. We know that Hogwarts is the only school of magic in the UK, and that attendance at Hogwarts of another school of magic is (effectively) mandatory for magic users. Based on the size of the great hall, which ostensibly contains all of the students and staff at once, Hogwarts likely has about 200 students ages 11 - 18. 

According to the UK office of statistics, people ages 11-18 made up about 10% of the total population in 1998 (about 5.9m out of 58m people). We know that witches and wizards can live longer than regular people, so let's generously assume people 11-18 make up 5% of the magic population. Based on these assumptions, the total magical population is the UK in 1998 was approximately 4,000 people, or about 0.007% of the total UK population. The UK accounted for approximately 1% of the global population in 1998. This implies a global wizarding population of about 400,000. 

The quidditch world cup is said to have 100,000 attendees in Harry Potter and the Goblet of Fire. The 2002 Football World Cup had about 2,700,000 attendees (27x as many) [5]. The world population in 2002 was 6.2 billion [6], meaning 0.04% of the world population attended the Football World Cup. One could extrapolate that the global wizarding population is 100,000 / 0.0004 = 250,000,000. However, I believe the ease of transportation in the wizarding world means a much higher percentage of the world population attends the quidditich world cup, likely as high as 25%, based on a a global wizarding population of 400,000. 

This population estimate aligns nicely with the apparent scale of the magic economy: magic users in the UK are effectively a small town. The ease of transportation enabled by magic (apparition, flue powder) means that the population can be geographically distributed over a large area without losing the cultural cohesion of a small community. A variety of observations seem consistent with the magical population existing as a distributed small town (or perhaps small nation-state):

  • They have their own currency.
  • They have a small number of businesses (one bank, several restaurants, several specialized stores).
  • They have a single government.
  • Most Magic users seem to prefer (or are limited to?) magic-specific occupations. It is implied that this is a cultural preference, rather than law. 
There a some potential inconsistencies with this view. For example, In 1998 approximately 5% of the UK population was employed in Education. [2] The magical community does not seem to follow this employment demographic, since the staff at Hogwarts is only about 0.25% of the magical population. 

Regardless, I think there are metrics to this concept that deserve more thought. Are there aspects of a small-town culture that put downward pressure on population? 

Magical Ability Propagation

There's general consensus in the literature that magical ability is inherited, though it's unclear whether the trait is expressed on a single gene or multiple, or whether it is dominant or recessive. [3] [4]. This is consistent with the potential for non-magic users to have magical children (e.g., Hermione) and the ability for magic users to have non-magical children (squibs, like Mr. Filch).

Birth Rates Among Magic Users

We don't get to meet many magical families, but with the exception of the Weasley family almost all magic families have only one child. This sample set is also likely skewed toward a higher birth rate, since most of the characters are children. 

Listing all of the adults of an age to have had children:
  • Weasleys - 7 Children
  • Dumbledores - 3 Children
  • Hagrid's Parents - 1 Child (his half brother is not a magic user and does not count)
  • Potters - 1 Child
  • Malfoys - 1 Child
  • Lovegoods - 1 Child
  • Longbottoms - 1 Child
  • McGonogal - 0 Children

Unfortunately there are a lot of characters about whom we don't know enough to make a robust data set.  For example, we aren't told whether McGonogal has siblings or children. There is not enough data to make a meaningful statistical statement about magical birth rates. Anecdotally we can only observe that many adults in the Potter books are childless (or have children that are never mentioned). Only one Hogwarts teacher ever has a child (Lupin). The rest have no mention of children:
  • Dumbledore
  • Hagrid
  • Lockhart
  • McGonogal
  • Slughorn
  • Snape

Education and Autonomy

It is well established that increases in education and (and presumably the resulting autonomy), particularly for women, lead to overall decreases in birth rate [7]. Although the wizarding world seems to have maintained some aspects of the patriarchy of the world at large (the ministers of magic are all male, for example), women in the wizarding world clearly have education and autonomy at a level on par, or ahead of, most modern economies. The birth rate has been steadily decreasing for many years [8].  Was Hagrid making a veiled sexist comment about witches preferring to have fewer children than their muggle counterparts? 


Further Research

There is a lot of research yet to be done. Some ideas:

  • Set up population simulation to try to determine approximate rates for the wizarding world. 
  • Analyze the supply chains for magic users - how do they differ from those of non-magic users? 
  • Is in-breeding a problem among magic users? The preference for "wizard blood" among some users could lead to such situations. 

[1] UK Office For National Statistics

[2] UK Office For National Statistics

[3] Live Science

[4] Muggle Net

[5] Statista

[6] Census

[7] Worldbank

[8] Macrotrends

Thursday, May 13, 2021

Building the Mega Drop

Figure 1: Mega Drop (With Ramp)

About a year ago we took down a beautiful old box elder in our backyard. It grew on a hill behind our sandbox and swingset. It was big, wide, and had lots of large dead limbs that, unfortunately, were a safety risk for our kids (Figure 2). We had the tree cut down, and were left with a large (approximately 3' diameter) stump on our hill. 

Figure 2: The Box Elder


For this project we used almost exclusively either scrap wood or wood from Home Depot's 70% off pile. I don't have a detailed price list, but I'd guess we spent about $40. 

At first we wanted to build a tree fort, so we used some two by fours to make a level building surface on top of the stump, then we added treated decking boards to build a base. Almost immediately we realized that the "floor" we had created would make an awesome drop for our backyard singletrack trail. We extended the surface so that we had a deck leading from the nearby hillside path to the top of the stump. Soren dubbed this setup the "mega drop."

We used a variety of rocks, logs, and assorted backyard construction materials to shore up the design, then we tried it out. 
Figure 3: Ouch

Although the drop was a reasonable height, the hill on which we had to land was sloped in two directions, which made landing rather tricky. After a mix of successful and unsuccessful attempts, we went back to the drawing board. We decided to change from a drop to a steep ramp, which would maintain the excitement of the descent without the frustration of the sketchy landing. 



Saturday, May 8, 2021

How to Fix a Broken XPower Dump Truck Drive Switch

 My son got an XPower "Pulls up to 50 Lbs!" dump truck for his birthday, but within a week it had stopped working. It would turn on and make noise, but would only drive sporadically. It turns out the problem is a somewhat flaky button design with an easy repair: Add a spring to the button

Figure 1: The XPower Dump Truck Power Button Stopped Responding

Disassembly

There are only two kinds of screws used, both with Phillips heads, so disassembly is easy. You have to remove the wheel drive assembly to get to the circuit panel on which the problem switch is located. 

  1. Remove the bottom plate, which includes the battery pack.
  2. Remove the wheel assembly (all four wheels come off in one large assembly). This will reveal the two screws noted below (Figure 2)
  3. Slide the cab off of the gear and motor assembly. The cab slides "up" from the truck's perspective. 
  4. Remove the circuit board, speaker, and bed-closure button (Figure 3). There is no need to disconnect any wires. 
  5. Remove the button (Figure 4)

Figure 2: Remove these Screws to take off the Cab and Circuit Board

Figure 2.5: Configuration of the Gears

Figure 3: The Circuit Board

Figure 4: The "go" Button is the Problem

Figure 5: The Go Button Switch on the Circuit Board

Repair

The problem is that this button can get stuck in the up or down position. To solve this problem, I added a little spring to the button. I used a metal shears to make a little more room inside the button head (Figure 6), then added a small spring (Figure 7). Make sure that the spring is small enough that the button can still make contact with the switch. 

Figure 6: Making a Little Room for the Spring


Figure 7: Positioning of Spring


Figure 8: Success!


Saturday, January 23, 2021

How to Teach your Kids not to Beg

I'm a proponent of the Ross Greene approach to to parenting (and teaching, disciplining, etc). If you're not familiar with Dr. Greene, one of his core arguments is that the behaviors we want to see from kids are skills that needs to be taught and practiced. Scolding or punishing a child do nothing to help him or her learn the skill they are lacking. 

I titled this post How to Teach your Kids not to Beg but in the Ross Greene way of thinking, an alternate (but wordier) title would be How to Teach your kids the skill of seeing something they want and walking away from it

Humans (big and small) do not learn new skills well while under emotional stress. Our brains simply do not take in new information when we're angry, scared, tired, etc. Trying to teach a skill to a child during a tantrum is all but certain to fail. Instead, you need to intentionally practice the skill when the child's brain is in a ready-to-learn mode. 

With my children, we do lots of practice walking through toy aisles and not buying anything. Whenever we go to Target I tell my kids, "we can look at toys, but we will not be buying anything." Almost every time we go shopping, we spend 5-10 minutes looking at toys and not buying them. This process gives my kids practice walking away from things they really want. 

This practice has paid off over and over. My six year old has been saving money for a new bike for months, but was willing to go to the bike shop, look at bikes, and walk away empty handed multiple times. 

If you're interested in our bike purchase story, check out the video below!


Thursday, December 31, 2020

My LEGO Statistics from 2017-2020

Continuing this month's statistics theme, I also spent some time looking at my LEGO purchases over the last few years. During each of the past few years I've purchased between one and four thousand LEGO bricks. 

Bricks purchased per year

I am a very price-driven LEGO buyer, and it is rare that I purchase a set with a price-per-brick higher than $0.09. My per-brick expense has not varied much since 2017. I included some low-piece-count Technic and Duplo sets in this dataset, so the average skewed high in most years (this is why, in general, median is a better datapoint than average). 

Average and median LEGO brick price from 2017. 


LEGO pretty regularly turns over their product offerings, which means that popular sets become scarce a year or two after their first release. I compared my initial purchase prices for my sets to the the current lowest price on Amazon (not including shipping). 

Price change for sets purchased in a given year to current lowest price on Amazon. 

This chart makes it look like LEGO would be a great investment, but note that what I'm comparing is the asking price on Amazon, not the actual sale price. There are also significant fees when selling items on Amazon or eBay. Here's another look at the price change, this time by series. 

Price change for sets purchased in a given year to current lowest price on Amazon, by series.

LEGO Star Wars, Harry Potter, Technic, and BrickHeadz increased in value most consistently. The highest price increase, 885.30%, was actually for a Harry Potter branded BrickHeadz set, Harry and Hedwig (the only Harry Potter set I purchased in 2017). 

This is a relatively small data set, but it does not appear that LEGO sets increase in value significantly in the years following their retirement. Sets from 2017 that are now retired are not consistently listed for higher prices than sets from 2019. I suspect this trend will continue until the ten or twenty year mark, at which the nostalgia factor will kick in

If you're curious to see the individual set details, you can see the full spreadsheet here. I am really pleased with Google's improvements to their pivot table implementation. 

If you enjoyed this post, you should subscribe to our YouTube channel, Bricks and Bikes!




Friday, December 25, 2020

My 2020 Reading Statistics

2020 was a strange, stressful, and busy year, but our family did quite a bit of reading. The year isn't quite over, but it felt like a good time to assemble some statistics.

Words read/listened in 2020

Like many people, I worked from home much more in 2020 than in prior years. This cut my audiobook time down considerably (I listened to the a substantial portion of The Wheel of Time, approximately 2.5 million words, in 2019). 

2020 was also the first year my kids got really into chapter books. We read every evening before bed, and in 2020 we transitioned from re-reading the same children's books over and over to reading chapter books. (a transition that brought me much joy!) We worked our way through 18 books.


Words read with my kids, by genre

The total word count of Pok√©mon books is likely skewed high, because the word count from readlinglength.com for most of the Pokemon book series is based on page count. 

We read The Hobbit in 2019, but this year showed that books with kids (or dogs) as protagonists really appeal to my family (we tried to start The Fellowship of the Ring, but the kids weren't into it). 


Words read/listened by myself, by genre

My preference for personal reading is clearly fantasy, though my stats are skewed a little. First, I read a lot for work, which is not reported here because I often read parts of reference books (rather than reading cover-to-cover) and such books do not always have word counts available. I also opted not to include word totals for books I have not finished, which is why Non-Fiction/History is at zero (I am about 60% done reading The Defender).




Monday, December 7, 2020

Week Three Themes

 We had some amazing submissions last week! This week's themes are Warm and Fuzzy and Where do you see yourself in five years?