Frazz by Jef Mallett for October 02, 2022

Ouch that stung, especially since I was killed trying to solve the problems handed down from my parents’ generation. And before you say anything about how I’m posting, I didn’t STAY dead, I was just declared dead before telling the guys scraping me off the street to be careful of my broken leg/hip.

By the time Caulfield’s generation inherits our problems, there won’t be a solution.

 The Fly and Trains Problem

 The problem is this: Two trains are on the same line, 100 miles apart, heading towards each other, each traveling at 50 MPH. A fly that can travel at 60 MPH leaves one engine flying towards the other. Upon reaching the other engine, it instantaneously turns around, and heads back to the first engine. This is repeated until the two trains crash and the fly is crushed in the collision.

 Question: How far does the fly travel before the crash?

 The interesting story: According to several persons who were present, this problem was presented to the famous mathematician John von Neumann at a cocktail party. After thinking about it for a few seconds, he answered “60 miles”. The disappointed questioner said “Oh, you discovered the shortcut. I thot you were going to try to sum an infinite series.” Von Neumann then asked “What shortcut?”, because he had, in his head, summed the infinite series. (Hint: The shortcut is that the trains take exactly an hour to cover the 100 miles between them, during which time the fly has covered 60 miles at 60 MPH. Figuring out how to do it as an infinite series is left as an exercise for the student.)

La Crosse to Grand Rapids by rail via Chicago is about 484 miles. The Empire Builder takes about 15 hours, which is about 32 mph. There isn’t a trestle, but there is a car ferry that saves 120 miles, and four minutes of driving time, according to Google Maps. The car ferry no longer hauls trains.

Caulfield is still in training…

Welcome to the club. That’s every generation. We’re working on it.

Being dismissive about passenger rail is part of the problem.

I think the quicker route is through Chicago at this point.

Caulfield’s intelligence is the level that will devise solutions. Problem is many won’t accept the outcomes and will continue along their chosen paths.

I like the trains between the panels.

Don’t get too haughty, Caufiled – you will also have to face problems created by your own generation.

Lacrosse Indiana or Lacrosse Wisconsin?

Isn’t that what every generation does?

It’s never been otherwise lad. How about a tunnel UNDER lake Michigan?

“East is East and West is West, and never the twain shall meet…”

… unless they’re on the same twack.

Yeah, we thought we’d solve all our parents’ generations’ problems….

I seem to remember that the problem went like this: John is on a train traveling 42 miles an hour. Jane is on a train traveling 36 miles an hour. They both leave from stations 100 miles an hour. If the sky is blue, how many apples did Sarah eat?

the next generation is always solving problems left by the present generation

Those of my generation left need to heed this and do two things, stop creating problems, and don’t stand in the way of those (youngsters) solving problems.

I didn’t see the trains in between the panels, at first.

after next month’s election we will have a good idea what problems the future generations will face.

When do the trains leave and how far apart are they when they do start? DIRT. Distance Is Rate x Time.

Most of which have been handed down from previous generations for as long as we know.

Although come to think of it, using Conor Cruise O’Brien’s useful distinction, most of them aren’t problems but situations.

Ella just had a week about solving word problems in Mt. Pleasant. She too had a problem involving two trains meeting a few days ago.

Caulfield, think of these as samples at the grocery store on Saturday. Examples similar to the real problems your own generation will get themselves into soon enough.

Referencing the trains snippet…

I thought for a moment that I was looking at a Mad Magazine Sergio Aragonés “marginal” …

And the buck keeps moving.

As near as I can figure it, if the distance between the two train stations is 459 miles, then the two trains would meet at approximately 5 hours, 9 minutes, and 26 1/3 seconds, provided they left at the same time which is only implied.

“Every generation blames the one before …”

Easy. The trains meet at 7:23 pm on June 9th.

Meanwhile, my generation keeps trying to solve the problems invented by Caulfield’s generation.

It’s a little tiring hearing the younger generation complain about “problems” handed to them. If not for previous generations handing down knowledge they would be living in caves. Problems come with the vast benefits. It’s called life.

He is not wrong

Remember that word problems are given in math class. Math is all about abstraction – get rid of irrelevant details (irrelevant to THIS problem), and reduce to a purely abstract problem. As soon as you say “that isn’t possible”, you have missed the point.