mathematical strategies to increase vaccination rates

Lately the focus in public health has been getting people to get a vaccine for Covid-19. There's been advertising around it. Also an incentive game of "if this percentage, 70,80, etc. gets vaccinated by this date, then some of these restrictions might be considered to be lifted". Which is also pressure and punishment if the goal is failed to be reached, to identify and deal with the wreckers.

I got thinking about ways to increase the vaccinated rates for a population. Two basic tactics come to mind. Somehow persuade the unvaccinated holdouts to get a vaccine. Or remove the unvaccinated. I thought about it purely from which approach is mathematically more effective at increasing overall vaccination rates.

At first I thought this might be a hard to describe mathematically or set up an equation. However after a bit I realized if you describe the groups the right way, then it is easy to understand and the more effective strategy is clear.

So assume you have some kind of population, P. Within this population are vaccinated and unvaccinated persons. So the starting percentage S, is more than 0 and less than 100 percent.

The trick is to treat a target group of unvaccinated as "outside" the main population. Then apply each strategy and determine the effect.

With the conversion strategy, people in the outside target group choose to get vaccinated. In this case a subgroup of 100% vaccinated is added to the initial population P, which is under 100%. it should be clear that adding a 100% vaccinated group to P will increase the overall vaccinated rate of the combined group from S to a bit higher than S.

Now with the removal strategy, then the holdouts are just somehow removed, eliminated. In this case P is the same, and S is also the same. So the overall vaccinated percentage does not increase when the groups are set up this way.

So it is then mathematically clear that motivating holdouts to get vaccinated is a more efficient way to increase the overall vaccinated percentage than, ahem, removing the holdouts.

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An example will demonstrate. This could actually be used as a junior high or high school math question on fractions, setting up a model, and reasoning.

Suppose there is a group of 10 people and 6 are vaccinated. Is it more effective to cast a holdout from the group, or to convince a holdout to get a vaccine. Which would be more effective to increase the overall vaccinated percentage.

In this case we would treat P as 9, with 6 vaccinated. So the starting point S is 6 of 9 vaccinated, or 67%

If you add a vaccinated to P then it becomes

6 of 9 + 1 of 1 = 7 of 10 = 70%

if you remove a holdout then it just remains as P

6 of 9 = 67%

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So it should be clear that converting holdouts to get vaccinated is a more effective strategy than removing them to increase the overall population vaccination percentage.

how to fix Sonicare iPhone disconnect

I got a Philips Sonicare toothbrush last Christmas. I'd been with Oral-B before that. I'm glad I switched to Sonicare and I consider it a better product.

One thing Sonicare does that takes some getting used to is the smartphone app with the toothbrush. I wasn't used to turning on my iPhone and clicking on an app to brush my teeth - I still only use the phone at night. Still the app is handy and pretty well designed.

One problem I've noticed is that on iPhone at least, the Sonicare app can become "disconnected" from the toothbrush. This has happened twice in the three months I've been using it. When the problem occurs the app does not detect that the brush is turned on. Clicking retry or troubleshoot from the Sonicare app did not seem to help.

The solution is this for iPhone

go to Settings

select Bluetooth

cycle Bluetooth off, then back on

under My devices, for the Philips Sonicare device, click the information icon at the right

click Forget This Device

 

with the Sonicare toothbrush turned on, off the charger, and nearby, iPhone Bluetooth should then show it as an available device. click to pair with the Sonicare device and the Bluetooth connection should be good again for a few weeks. 

if it loses the connection again in a few weeks or so just repeat this process of forget device / re-pair and it should fix it

Philips Sonicare toothbrush

Sarah Silvervan leaves the democratic party

 

In recent news Sarah Silverman has left the democratic party.  I'd only vaguely heard of her. I knew her as a loudmouth blue checkmark ani-Trump. how original. 

It appeared her political career had stalled or regressed. In 2016 she was a speaker up on stage at the DNC convention. In 2020 she was replaced, no longer a speaker at the convention. like Sandra Fluke.

As far as I follow it, her tireless work and crude stunts for the Democratic party didn't seem to especially lift her entertainment career either.

I noticed she waited a few weeks after Joe Biden was installed to make this announcement. I guess at this point the political appointments are all done, and she didn't get one of them. Finding herself used up and discarded like a Bill Clinton mistress, Sarah makes this attention-seeking move for herself on the democrats.

so you're leaving? okay, sure, whatever. shrug. good luck. I suspect there are a decent number of C and D list Hollywood entertainers willing to take her place, her role, in the democrat party to see if they can increase their entertainment career, or launch a political career.

speaking of which, remember that thing with Hollywood and the UN? haven't heard much from Angelina Jolie or Emma Watson around that of late. meh w/e. I wonder what tolls they may have paid to get in at the UN. It just didn't have much impact, Ms. Watson among the wealthiest, highest paid persons in the world, harping about underpaid women.

a plea for ties in NHL hockey

I'm tired of the NHL shootout. It has run its course. It should just end. I cringe whenever I see it in a box score. I turn off the game if it goes to shootout. I avoid watching shootout highlights.

Maybe the shootout had a purpose back in the reforms introduced in 2005. That was a generation ago now. Hockey can change, as it changed when the shootout came in.

My proposal is to bring back the tie in regular season NHL hockey. I never minded tie games. One point each team, an honourable and hard earned split. Shootout does not increase excitement or fan satisfaction. Shootout is mathematically distorting, as some games award three points, and some award just two. 

Shootout messes up and distorts the standings. It's hard to tell if a team is really a winning team or a losing team. At least if nothing else, as a start, fix the standings. The won-lost-overtime/shootout lost is so unsatisfactory. You look at a team like LA Kings, 12-11-6. that doesn't look that bad, 12-11 a winning team. the third number means they lost those 6 games, so does that make them 12-17?

if there must be shootout then properly distinguish clean regulation wins from lesser overtime, and even lesser cheesy shootout wins. so 4 numbers, regular time wins, regular time losses, OT-SO wins, OT-SO losses. it would at least highlight how a team is really doing. we effectively can't really tell now.

the format of overtime is now also lacking. I'm sure the 3-on-3 overtime was meant to create action and excitement. what I've observed is there is often a lack of intensity to the overtimes, players not seeming to skate or defend all that hard. also 3 on 3 limits the number of players who can participate, making half the team spectators; same problem as shootout, not a team effort.

so getting to my point. a solution. I'll call it 4:4:4. four-on-four overtime for four minutes. winning team two points, losing team zero points. ties are back, one point each. I think this would restore intensity to overtime, get rid of shootout which has run its course, get more skaters involved in overtime, still more room to skate and score in overtime

Canada universities financially failing

I'd missed the story a few weeks ago. Laurentian University is insolvent. I just heard about it from some who are close to the academic scene. I guess a factor was a dangerous reliance on foreign students. With Covid-19, apparently a lot of that dried up. Regional high school enrollment has been in decline for a number of years, so there are fewer grade 12s incoming each year. 

They were heavily in debt was well apparently from a construction spree. Still, I'd heard of Laurentian, it's a first-tier university in Canada. So to declare insolvency, with the future by definition in doubt, seems like an important story. 

One news story from the time mentioned 60 years of history at Laurentian. that's not that much actually for a university. there are plenty of people alive today who were there the day Laurentian opened. it's probably the case that the number of universities opened in Ontario in the baby boom years of the 1960s is more than are needed today. Really, if Laurentian just closed its doors in May after exams what difference would it make. Students who are mid-degree could be easily absorbed into the numerous other Ontario universities.

the academics mentioned that here in Nova Scotia, Cape Breton University (CBU), is also highly reliant on foreign students, and their tuition. I don't have any visibility into CBUs finances as a result of Covid and travel restrictions, what if any shortfall there may be.

for CBU though, and the rest of Nova Scotia's universities, if it came to it (again I have no visibility into their finances and there have been no news stories, as far as I know everything is fine), there is a well established tradition when universities get into financial trouble. 

in 2011 NSCAD was bailed out. they were facing closure apparently after a bad real estate deal. in 2017 alone Acadia University was bailed out for over $10 million after a mysterious, massive hole apparently appeared in their budget. the running total for Acadia is now over $24 million. I've never seen an explanation over the $10 million shortfall. I guess the taxpayers are supposed to just shrug and accept it.

the truth is both NSCAD and Acadia should have just been left to close their doors due to the financial mismanagement. As with Laurentian, there is plenty of capacity to absorb any displaced students. there have been too many universities in Nova Scotia for a very long time now. if some just closed by their own mismanagement then its for the best in the long term.

I remember the Dr. Janet Halliwell years, a generation ago now. A good and smart woman. She noted there were too many universities in Nova Scotia. Alas she had little success consolidating campuses or programs. As in Northern Ontario, there are fewer grade 12s every single year in Nova Scotia too.

Universities tend to be long-lived. They cost a lot to establish, and once there, there is a sense of community, of generational continuity, of permanence. But they don't necessarily have to live forever. Maybe the public universities in Canada should move toward a model similar to private institutions. They can run well for a while, when they are most useful, when there are lots of students and opportunities for grads. Though they don't have to last forever. We have to recognize that even long-lived institutions can run their course.

flexible, opportunistic women

So there's a story out on Ellen Page this week. It made Time magazine. Did anyone see Time magazine? apparently it is still a thing. Anyway Ellen has had some kind of upper body surgery and is now identifying as a man and will go by Elliot Page. uh, sure. 

E. Page looked terrible in the Time photo, a 14 year old boy comes to mind. That's fine for a fourteen year old. In the next 4-7 years he will fill out properly, the trajectory is upward and good. Not so much for 34 year old Page.

It brings to mind some recent stories in and around this area over the years. Let's go over a few.

Amber Heard  when Elon Musk or Johnny Depp resources were available she was into men. Otherwise when it's in her interest for being lesbian or bi then she's cool with that.

Lindsay Lohan  remember in 2008 Lindsay was an international story for coming out as a lesbian in her sensational relationship with DJ Sam Ronson. The story was front page for weeks. Lindsay got an incredible amount of attention out of it. I wonder if the reason the relationship with Lindsay and Sam failed was it was a dispute over who was going to live off the others' paycheque.

Today Lindsay is apparently straight again, in a relationship with international financier Bader Shammas.

Lindsay understood that you can only shock people once. She was smart enough to get there first with the lesbian thing, along with Ellen DeGeneres. Every one since has had less impact. Today the typical reaction is shrug, yawn, whatever.

Miley Cyrus  she was prim and proper as a teen on Hannah Montana. Then she was wild for a few years with Wrecking Ball, VMA and all that. Then when advantageous back to prim and proper, on The Voice with clothes carefully concealing her tattoos, married to wealthy movie star Liam Hemsworth. oh then there's another wild Miley phase, took off on Liam with Kaitlynn Carter. Put her in the news for a while. Then she's straight again with Cody Simpson. yawn. Liam Hemsworth is A-list. Everyone since further down the list.

Ellen/Elliot Page  Ellen Page skillfully strung out the "is she a lesbian" thing for a number of years. Then in 2014 she made a splash coming out as lesbian. Helped her acting career, landing an X-Men role. She was gay married for a while when that was a thing. didn't have as much impact it seemed as the 2014 announcement. heh E Page puts the men in X-Men now. I don't know what the acting job market is for Marvel movies or any roles for Elliot Page. Could be the end of that career, who knows. Shame, she was a not unattractive woman, in movies.

Going through with actual surgery, there is the first time shock factor, as with Lindsay years ago. Though unlike the others, there's a permanence to this. It limits and closes off potential future options to switch back or whatever if the situation is advantageous. If some opportunity presents. The other ladies were smart enough to always keep their future options open, whatever they may be saying or doing in the current moment.

Got a Time magazine piece and photo shoot. I'm old enough to remember when being featured in Time was a big deal. I guess Ellen got there first on this one. I suppose there's Chaz Bono too, somehow that feels different, more genuine, from a different time

future price direction on baseball and hockey cards

I sold a couple of hockey cards this week on sportlots. Some early 1980s Edmonton Oilers o-pee-chee. A guy in Ottawa bought them. I hope they are to his liking. They were the highest individual priced cards I've moved on that site.

There's a fair market it seems for o-pee-chee hockey cards from the 1970s through early 1980s, the era that I have some listed. I only listed my hockey relatively recently, years after I'd listed baseball cards.

On the buying side, my 1973 O-Pee-Chee hockey collection is under 60 cards remaining. I've been able to chip away at it with site credits from the baseball and hockey I've sold on sportlots.

I got thinking about collectors and prices and which way prices might move in the next few years. There was an Investors Group commercial where the prosperous client speculates about selling his coin collection to acquire an even nicer property. In the commercial the protagonist decides against it, at least for now.

So with baby boomers and baseball cards. A boomer born in 1950 or earlier would be over 70 years old now. Inevitably they have been and will be dying off in increasing numbers in the next 2-3 decades. You see it in the news now. 66 year old rock star dies of natural causes.

Now back in the 1980s the same boomers fueled the increase in demand and prices on baseball and hockey cards. Some were motivated by speculation, seeking to invest in future higher prices - not sure how that turned out. Some bought as genuine collectors, nostalgia for the players they cheered for as kids and teenagers in the 1950s through 1970s boomer era.

Gil Perreault 1973 o-pee-chee hockey card

So as these boomers die off, their card collections acquired in the 1980s will fall to their heirs. Many of the boomer estates and heirs may only wish to liquidate the collections for cash. So I expect in general some cards from about 1950-1980 will become less scarce. It may become easier to find Bobby Orr or Johnny Bench cards in the future than today. With more supply, and motivated sellers, I expect prices on this era may come down.

some math problems for students

I've pulled together some math things I've thought about in recent months that could be used as problems for students at different levels.

world distance away

Which is further away, halfway around the world or all the way around the world?

This is one for grade school, before junior high.

I took me a while growing up to grasp that one. A bit of geometry. I'd heard it growing up and it was some years before I grasped the answer and why the saying is "halfway around".


temperature in Halifax and Fredericton

Halifax is a coastal city, while Fredericton is a bit inland. As a result of geography Fredericton summer is hotter than Halifax summer, and winter in Fredericton is colder than Halifax winter. Is there ever a time when Halifax and Fredericton have the same temperature? At any given moment there is exactly one official temperature in both Halifax and Fredericton.

This one could be used in junior high or in high school to demonstrate the concept and power of continuous functions. The junior high could just explain with words while high school could be a bit more formalized with equations.

An outline of a solution goes something like
Let F(t) be the temperature at time t in Fredericton
Let H(t) be the temperature at the same time t in Halifax
Let D(t) = F(t) - H(t), the difference in temperature between Fredericton and Halifax at time t

winter snow in Halifax

increased voting share

In a two person election a candidate, Tim Tory, did not do well in one town. He only got 4 percent of the vote. The opponent, Larry Liberal, got 96 percent of the vote in that town.

In a later election Tim doubled his share of the vote in the town to 8 percent. Is Tim necessarily better off?

This one might be good in high or early high school. It's also useful as a practical math application, to avoid jumping to conclusion based on initial or incomplete information.

The answer is a bit subtle. On the face of it Tim seems better off. If the same number of people vote in both elections then Tim is better off. However with higher turnout Larry can overcome Tim's increased voter share and still win the town by a bigger margin.

Again the high school part might involve equations and expected value. It could be stated as (though it pretty much gives away the answer to the first question)

Suppose 1,000 people voted in the first election. How many people would Larry need to vote in the second election to overcome Tim's increase in voter share?

answer:
In the first election Tim had 40 votes and Larry got 960 votes. So the winning margin for Larry was 960 - 40 = 920 votes.

The question could then be restated as "At 92%, how many people does Larry need to vote to win by 920 votes" to equal his margin in the first election.

let x be the number of people who vote

0.92x - 0.08x = 920

x = 1,095.24, so need 1,096 voters

1,096 * .92 = 1,008
1,096 * .08 = 88
diff        = 920

So Larry needs a 9.6% increase in the number of people voting to overcome the loss in voter share and maintain a 920 vote advantage in the town in the second election.