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.

if you forget your mask

 Many areas including Nova Scotia have COVID-19 restrictions and requirements around masks. 

So the local rule is indoor masks. Now when you are outdoors there's no mask. As stated you would have to put on a mask on going to an indoors public place.

Now if you have a mask with you, say ready in your pocket. Then on going in forget to put the mask on, an unfortunate but completely understandable oversight.

So what might then happen? I see four possibilities

• nobody who works at the place notices. it's pretty easy to overlook
• someone notices but decides to give the benefit of the doubt and choose to assume that there's a no mask medical exemption; and not say anything
• someone notices, believes they could or should say something, but chooses not to say anything
• someone notices and mentions it

Now in polite society, if reminded of this confusing new rule amidst all of the many changes and rules and restrictions, etc. of course if someone mentions it; quickly apologize for the error and put on the mask which is conveniently right at hand.

one of the millions of discarded masks polluting the environment

got my Parler badge

So I'm now a verified user on Parler. I got my badge. For some reason this pleases me. It's not difficult for regular users like myself to get verified on Parler. The process is straightforward.

the dysfunctional culture of the blue checkmark

Regular user verification is a good feature with Parler. Back on twitter there was a "blue checkmark" culture. This is elitist and ultimately toxic.

Everything seemed to revolve around the blue checkmark people and their posts. A distinct vibe that only the blue checkmarks really mattered, blue checkmark opinion was more important, only blue checkmarks are worth following. The blue checkmarks were of course presented as prominent, and some fraction of them I'd heard of in real life. Over the years the percentage of twitter blue checks whose names I recognized in real life declined.

followers and following

I'm up to 80 followers now on Parler, 11 days after joining. I am happy with that, find it pretty good. In 9 years on twitter I had 80 followers. Parler is a better site, friendlier and more outgoing, and no blue checkmark culture. There seems to be more of a followback convention there. Many people I'm following followed me first. I generally follow back.

Overall I follow a few more people than follow me. Mathematically this is how it should be. It was a twitter culture thing that it was somehow bad to be following more than follow you. twitter followers were often low quality: scammers, adult clickbait, spam, bots, business promotion.

In general, I'm pretty sure Parler and twitter followers are governed by Price's Law. That is, the square root of Parler accounts have garnered half of the followers. It's just the way it is. These are the big accounts with many thousands, or millions, of followers. These prominent accounts are unbalanced, with far more followers than they follow.

Now overall "following" and "followed by" have to balance out. The total of followed and followed by across the site is of course the same. So the natural result for us regular folks is then to be following a few more people than we are followed by.

COVID-19 and life expectancy

There's some interesting data now out of Florida around COVID-19 and life expectancy. With COVID-19, Florida Phoenix

The average age of death is 76.57, according to the data analyzed Sunday, with more men than women dying. More than 80 percent of deaths were those aged 65 and over.

Now outside of COVID-19, the average life expectancy is per Florida Sun Sentinel

Florida’s average life expectancy is 79.6 years old. That’s a little older than the national average of 78.8 years.

Finally some usable data.

so it appears the result on life expectancy from COVID is a decline from 79 to 76. Overall it's not actually that bad, as 76 is the COVID-19 number, thus it only affects those who die of COVID-19. Many elderly won't, and they will still get their 79 years average. So the 3-year decline in life expectancy from 79 to 76 actually only affects those who die of COVID-19. So the overall decline in life expectancy due to COVID will be less than three years.

The biggest issue with the decline in life expectancy and COVID is that it just appeared here in 2020. Thus the 2020 mortality will include

• those who were going to die in 2020 anyway, with or without COVID-19
• some people who would have died in 2021, but died in 2020 because of COVID-19
• some people who would have died in 2022, but died in 2020 because of COVID
• some people who would have died in 2023, but died in 2020 because of COVID

now in 2021 if nothing changes it should get better. the 2021 expectation becomes

• those who were going to die in 2021 anyway
• minus the 2021 who died in 2020
• plus some COVID who would have died in 2022
• plus some COVID who would have died in 2023
• plus some COVID who would have died in 2024

Now by 2024 all of the new excess mortality due to the sudden introduction of COVID and a 3-year life expectancy decline into the elderly population should have worked their way through. it should start improving in 2021, and be to the steady state by 2024. COVID-19 will just be another condition that old people die of, one of many.

old people get die. they just do

There are many serious conditions that affect the entire population. however they primarily affect the elderly, and can be a cause of death. This short list includes

• heart attack
• stroke
• heart failure
• cancer (many forms)
• diabetes
• ALS
• Alzheimer's
• dementia
• Parkinson's
• Huntington's
• liver failure
• kidney failure
• COPD / respiratory failure / sleep apnea
  
• the flu
• falls
• natural causes

now in 2020 this new condition has unfortunately been added to the list of health hazards faced by the elderly

• COVID-19

so of course masks, lockdowns, all that, will fail. there was a lockdown just a few weeks ago, and what do we have to show for that? now the same authorities who demonstrated their incompetence in the first failed lockdown, want to go back into lockdown. the insanity of trying the same thing again and again and expecting a different result

the reality is COVID-19 will in the near term reduce life expectancy of people alive today by something less than three years. that's the bad news. the good news is that life expectancy has been rising for decades, centuries now. so this immediate three year decline due to the sudden appearance of COVID-19 will be made up soon enough. other good news is that there is active research into vaccine and treatment of COVID. So the occurrence of COVID should decline, while survivability should increase.

 

the conservative parties of Canada

 so the conservative party of Canada has a new leader, Mr. Erin O'Toole.

O'Toole replaces outgoing leader Andrew Scheer. in the fallout from the 2019 federal election where the Liberal Party won a minority government, Scheer was out as leader. I didn't really follow the conservative party story too closely, just occasional headlines from TV news. O'Toole seems like a decent fellow.

I was disappointed to see Scheer removed after just one election. Scheer won the popular vote, held the Liberals to a minority, and nicely increased the number of conservative seats. In Canadian federal election history a majority government is virtually never defeated after one term. So it was not realistic to believe or expect Scheer should have won, or he somehow cost the conservatives the win.

Scheer was well on track to follow the Stephen Harper 4-election strategy. When Harper became conservative leader he was facing a popular Paul Martin majority that appeared set to govern for a good decade or longer. In the Harper strategy

• election 1: hold the Liberals to a minority
• election 2: win a minority
• election 3: win a larger minority
• election 4: win a majority

In 2019 Scheer successfully completed step 1: nicely. But it is what it is. I understand some of the anti-Scheer faction want the conservative party to move toward the centre-left. If I'm following, the theory seems to be this is needed to win in urban Toronto (the GTA), Ottawa, Montreal, and the Maritimes.

With the rise of the Green Party, Canada already has three left-wing parties: Liberal, NDP, Green. the leftist worldview seems to be very well represented in Canada. I'm not sure if the left-leaning voter in Canada really needs or wants a fourth option, some kind of Red Tory, left-lite?? thing.

the other conservative party

The 2019 election featured the electoral debut of the People's Party of Canada (PPC). Maxime Bernier was able to get the new party launched, field a candidate in every riding, and win 1.6 percent of the vote. They cost Scheer a few seats, but not enough to tip the final 2019 result Liberal minority win.

Not too bad for a party only founded in 2018. How long and how many elections did the Green Party exist in Canada before they won their first seat? Bernier and the PPC don't seem to be going anywhere soon. PPC today is an option for the right-leaning voter in Canada. I'm guessing the legacy conservative party hopes PPC will turn out be this generation's National Party. Some good ideas, charismatic leader. Didn't form critical mass, failed and dissolved in a few years.

the long game in Canada

I'd suspect the PPC wouldn't mind following a trajectory broadly along the lines of the Reform Party of Canada. Reform was founded in 1987. By 2006, Stephen Harper of the conservative party, the merged Reform/Progressive Conservative Party entity, won a federal election. So 19 years, about a generation. The long game in Canada sometimes isn't all that long. In the mean time as I noted, there was generally fairly good government in Canada under Jean Chrétien / Paul Martin.

joined Parler

I've decided to give Parler a try. I'd heard about it for the last few months. I'd been on Twitter since 2011.

I signed up recently. It's been fun there so far. At the time of this writing I have zero followers on Parler, lol.

Parler does some things well. The site is a bit glitchy at times, so was Twitter in the earlier days, and through to today for that matter. What they are trying to build is a hard problem. On Parler a tweet is called a Parley, and a retweet is called an Echo. One of those good to know things.

Dilbert is there yay. some other unpersons who I used to enjoy following on Twitter before they mysteriously vanished are over on Parler. so it's a bit of a reunion. hopefully I've joined Parler during the fun time, the good time, while it lasts. I can remember when there was good time on Google, Facebook, YouTube, and Twitter too.

Well maybe you will stop by. My Parler username is same as on Twitter, @tookalito.