003 = Teeth Tips and Defining Decades

**Teeth Tips and Defining Decades** is the third episode of A Problem Squared.

* When does the new decade start?
* The best system for brushing teeth.
* How many orders are there for Bec's show?
* Top travel tips.

Get in touch if you have any more travel tips!

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#### When does the new decade start?

The first problem tackled in this episode concerned an internet argument about whether 2020 was the end of the old decade or the start of the new decade. Bec got an angry reply to her re-tweet of someone quoting a video as "the best video of the decade" relating to the spread of fake news that it was the new decade. She then forwarded the tweets to Matt, who tackled the issue.

Matt started by mentioning that this issue was also brought up in 1999. People back then wondered if the year 2000 was the end of the old millennium or the start of the new one. Yet, it wasn't as big an issue in 2000 and 2010 probably due to lack connectivity and social media sites like Twitter.

He then mentioned that there is no year of 0 CE. In the middle of the first millennium, people started backdating time to the birth of Christ, putting the year 1 CE one year after the year 1 BCE, which causes numerous issues, as goes against the counting of ages (a newborn baby isn't 1 year old, it's 0 years old.)

Because of this arbitrary starting point, as Matt put it, this meant that at the start of year 2000, only 1999 years of the Common Era had passed. This is due to the first decade lasting from the start of 1 to the start of 11, the second decade lasting from the start of 11 to the start of 21 and so on, making 2020 the end of the decade and 2021 the start of the new decade. The other argument relates to the naming of the decade, which puts 'the 20s' as 2020 to 2029, which is the more common understanding by laypeople.

For expert understanding, Matt contacted the International Organization for Standardization (ISO), which, based on Regulation 8601, the year 1 BCE = 0 CE, which means that the decade starts in 2020.

#### Systems for Brushing Teeth

As a follow on from the "How much pizza is too much pizza?" question in the previous episode, someone on Patreon asked about the optimal way to brush one's teeth, like "Upper before Lower" or "Left before Right". They also asked 2 follow-up questions, one about if electric toothbrushes would change which system is better, and if the toothpaste's viscosity mattered. Bec tackled this set of questions.

Beginning with the first question, she commented that it didn't really matter which method you use. As long as you brushed equally on all sides, it would take the same amount of time. She also found out that the best way as recommended by dentists is brushing in quadrants, as one could get a better sense of timing (30 sec per quadrant = 2 min of tooth brushing).

Recommended analog toothbrushing methods include light circular motions over teeth and gums, or a 45° angle pointing towards the gums. Electric toothbrushes simulate the light circular motions, so it is less work, since you only need to brush over the teeth. It would does require less effort from the brusher.

Matt had his own follow up question based on the quadrant brushing. He suspects that the quadrant he brushes first might be cleaner than the rest since there's less toothpaste near the end. So, he asked Bec if anyone has looking into changing the starting quadrant every day. However, according to Bec, it seems that not many people care, so little research has been done in this regard. She says that the toothpaste is just there to provide a protection of fluoride after the germ ridding, so the difference would not be noticable.

With the last question, Bec says that using more toothpaste doesn't seem to make much difference, except costing more. The recommendation by dentists is a pea-sized amount. Most of the ingredients don't matter either, so viscosity would not be a factor optimally. The main thing recommended by dentists is fluoride toothpaste.

In terms of tips for brushing, Bec mentions not rinsing your mouth after brushing (just spit, rinsing your mouth could wash off the protective fluoride), brushing your tongue (due to bacterial build-up) with a toothbrush or tongue scraper, use mouthwash at least 30 minutes after your brushing, preferably floss before brushing and wait 20 minutes after eating before brushing (you may brush away your enamel that was softened by food acid).

Optimising for speed, Bec found all-mouth brushes work like a mouth guard, brushing each teeth individually. This means that one could brush for just 10 seconds and clean optimally. However, it is hard to implement in reality, since mouth shapes and sizes differ between people. Matt's recommendation is having 2 electric toothbrushes.

Finally, referring to Bec's Australian dentist friend, toothbrushes work to get rid of the plaque from your teeth, so brushing different quadrants earlier makes little difference. The main thing she recommended was to learn to brush properly, and remember to brush the gum line (the place where the tooth and gum meet), and also recommends eating at least 30 minutes after brushing.

#### Orders of Jokes

Bec posed a question to Matt regarding her newest stage show. The premise of it was that she had 25 jokes on post-its, and the audience got to decide what joke they wanted to hear. Her question was about how many shows she could theoretically do before the order of the show would repeat a previous one.

Matt did the math and came up with 15.5 septillion (or 1.55 x 10^25). He arrived at this by imagining that the audience first has 25 options for a joke, then 24 as one of the jokes is removed, then 23 and so on. Thus, the number of possible shows is 25 x 24 x 23...3 x 2 x 1 = 25! = 1.55 x 10^25.

He also worked out the average number of shows it would take before an audience would repeat, and found that it was more likely to repeat than not after 500 billion shows (or 5 x 10^11).

Bec has found, however, that audience tended to choose certain notes in certain orders, so she will log the orders of her 2020 shows and analyse them with Matt.

#### TL;DR

Q: When does the new decade start?

* According to the ISO, 2020.

Q: What is the optimal brushing method? Do electric toothbrushes matter? What about viscosity of toothpaste?

* Optimal brushing method: Quadrant method
* Electric toothbrushes reduce the need for physical effort, but require electricity.
* Viscosity doesn't matter, but fluoride is the best.

Q: How many of Bec's shows could she do before repeating an order of a previous show?

* Maximum number: 15.5 septillion shows. Most probable number: 500 billion shows.

### AOB & Updates

002- In the previous episode, Bec was tasked with helping Matt get over jetlag. Matt attempted the solution of drinking lots of water before and during the flight, and it seems to weaken some of the effects of jetlag. He also gave a bit of travel advice: bring electrical tape to tape over bright LEDs in hotel rooms. Bec's tip is getting some slipper socks to put on in the person's room, since it puts her in a comfortable mood.