I’m back from my Trans-Michigan Road trip in my $800 beater Exploder; I am glad I brought tools, I needed them.

Vaguely a week ago I made a post asking for some advice on what I should do to prep for my 5-day long trip from industrious Detroit, all the way up to Michigan’s gorgeous Pictured Rocks State Park. The link can be found here

Admittedly, I was a bit nervous to take my 196K mile 2002 Ford Explorer that was purchased for $800 on an 800+ mile (it actually ended up being closer to 1000 miles) after having only owned the car for ~6 months, and knowing what common problems cause these trucks to… stop moving. The 5R55W transmission is known for some common weak points, the 4.0L SOHC V6 also commonly likes to jump timing and send a valve kamikaze style straight and the pistons, causing catastrophic failure.

Based on some of the comments of the aforementioned thread, I decided to go through all consumables and service related items prior to my trip. I changed the oil and filter in the transmission with genuine Ford stuff, thankfully the fluid looked relatively in good shape, still red but not pink anymore, so it was due for a changing. I also did coolant, spark plugs, plug wires, rear brake rotors and pads, and the rear diff oil, oddly I neglected to do the front diff oil, but since the 4 wheel drive still works stupendously (it doesn’t), I decided it could go on the backburner.

My SO and I decided that camping was the way to go, we wanted to get some good exercise in the form of bike riding and kayaking, so I purchased 2 kayaks from a local sporting goods store, a pair of roof rack mounts off of Amazon, and BAM! I have successfully added a giant windbreak to my already fuel-inefficient 5700 pound SUV.

Driving on the expressway was fine although it was completely obvious there were two kayaks on the roof, every time I approached even the slightest grade the cruise control decided I needed to be in 3rd gear and sent the engine revs soaring to 3000 RPM, it also liked to stay there after the crest of the hill when the truck was clearly going downhill and needed no throttle applied. I frequently had to turn the cruise control off, wait for it to shift back to top gear, and re-engage it, this happened literally hundreds of times during the trip, I was wishing it had the V8 during these times, until I made it to the gas pump for the first time and discovered my fuel economy; 16. 16 Miles to the gallon; yikes. That would mean I was going to chew through 60 gallons of fuel at an average cost of $3/gal over the whole trip, let’s just round up to $200 for my fuel budget. It was also at this time that I discovered that my fuel fillter neck is leaking, and wouldn’t let me put fuel at full speed, so I had to hold it at a slow stream every time I needed to put gas in. Whopee.

After about 300 miles there was an extremely loud crash noise accompanied by a loud and repetitive banging noise coming from the passenger side of the roof, after pulling over I found that 2 of the screws holding the front of the roof rack had walked themselves out, causing the roof rack and thusly the kayaks to happily bounce rhythmically on the roof of the Explorer. Thankfully; I brought my Husky Mechanics tool set along for the ride, which had a T-30 Torx bit which was needed to thread the screws back down and secure everything back in place, crisis averted.

It was at this time pulling back onto the expressway, the explorer decided to surge-shift from 2nd to 3rd and 3rd to 4th gear, this made my heart palpitate a bit, as surge shifting a notorious problem of the 5R55W transmission. Oddly, my stress was unwarranted because it never did it again over the next 500 miles, and it seemed the gearbox only wanted to shift better as the trip went on, im guessing the transmission fluid and filter service I did ended up doing some good because a lot of the other hard shift issues I encountered prior to the trip were all but completely gone, and when the gearbox did downshift to 3rd during the uphill jaunts, it was hardly noticeable (aside from more engine noise). Maybe some old fluid still going through the system? I might consider another drain and refill just to see if that clears things up better going forward.

We ended up staying at a quiet campground in a tiny town called Grand Marias; for anybody unfamilar with Michigan history, this area was founded as a logging trail in the late 1800s, but later turned into a tourist spot because of the nice weather and adjacent great lake and state park. Instead of tenting I had brought about 6 inches of memory foam to lay out in the back of the truck, it measured out to about the same as a full size bed, and my girlfriend and I were plenty comfortable sleeping in the back.

After 2 nights of outdoor activities, exploring the area, and just general rest and relaxation, we packed up on a very foggy wednesday morning, I start the explorer and am greeted with an engine running on 5 cylinders. Still a bit hazy from having just woken up, I ended up putting it in gear anyway and took off from the camp ground to find a diner to grab some breakfast and coffee, after which I would deal with the problem. Spoiler alert; there is no breakfast joint in Grand Marais, everything opens at noon.

After the misfire did not clear up (unless the engine was over 2000 RPM), I pulled over, popped the hood with the engine still running, and decided to start wiggling spark plug wires. After getting electricuted by the ignition coil, many many many uses of swears, I reseated the loose plug wire, and the engine was back to roaring on all 6 cylinders.

Along the route I had selected to go back, we would be going by Tahquamenon Falls, this is a must see for anybody visiting Michigan’s Upper paninsula, I hadn’t seen it in over 20 years, so it was a bit nostagic to go back and remember going with my family as a kid.

I also took the obligatory photo of my jalopy parked just outside of the Mackinac bridge.

10/10 would do again, road trips in beaters has a certain level of excitment that a new car just doesn’t give; you become drunk with excitement when you actually make it to your destination, and euphoric when you make it home.

submitted by Nevin Manimala Nevin Manimala /u/iamnotcreativeDET
[link] [comments]

Negative effects of mathematical education in everyday life and in mathematics itself

I really don’t know where should I’ve posted this, but this is becoming a very serious issue for me.

The first problem is about mathematics itself. I’ve delved so deep into a very narrow field of mathematics (in order to do research), that is becoming more and more painful to even think about say calculus or even high school geometry problems, and this has two aspects: 1- I have forgotten a lot about the techniques and also the knowledge needed to tackle such problems, 2- I have become incapable of concrete thinking. I cannot consider a problem for what it is, and my mind wanders around to reach a more abstract formulation or variants of a problem, and I drive people nuts because of this.

I’m forcing myself to look through the simple question in this subreddit, both to refresh (and I must humbly admit sometimes to learn) basic mathematical knowledge, and also to strengthen my (concrete) problem solving skills, but this could only do so much.

My problems in real life, which encompass my problem in mathematics itself to some extent again, are even more serious.

I have developed a horrible memory and possibly bad thinking habits. I cannot think or memorize without some kind of a method. It might have something to do with becoming excessively conscious about the way I memorize and think, or it might simply be due to the ways I’ve been using my brain for a long time. Regarding thinking, I’m very prone to make weird mistakes when I go on autopilot mode; As a cure, I try to stay focused all the time and think way more than necessary on every simple daily problem and decision. It’s sometimes very embarrassing to see how “normal” people can immediately see a solution to a problem without any kind of consideration. When I ask them to explain how they reached a particular solution, I almost never get an answer beyond “it’s obvious”; It seems people don’t even know how they do these things, and it makes me think, perhaps I’ve lost some of the “brain modules” any human must have due to studying mathematics. I used “lost” instead of “lacked”, because I wasn’t like this as a teenager, or in my early 20s.

I guess by posting this, I’m looking for both sympathy, and also possible ways to ameliorate the situation.

submitted by Nevin Manimala Nevin Manimala /u/chasesdiagrams
[link] [comments]

Existence of bi-measurable function between two measurable sets

Lets say A and B are two lebesgue measurable subsets of the real line, both of positive measure. Is it always true that there is bi-measurable function f mapping A to B? If so, how do we prove that?

By bi-measurable I mean that there are measurable subsets A’ and B’ such that AA’ and BB’ are null sets and f restricted to A’ is a bijective function from A’ to B’ such that the function and its inverse are both measurable.

What about a general measure space? It’s easy to construct a counterexample using a discrete space with counting measure. However is there anything we can say about when a general measure space does have the given property and when not? What if we additionally assume that A and B have the same measure?

If that makes a difference you may additionally assume at any point that A and B have finite measure.

submitted by Nevin Manimala Nevin Manimala /u/whatkindofred
[link] [comments]

Test whether one variable perfectly predicts another

Let’s say I have a dataset with 2 variables and I want to test whether one variable can be perfectly predicted by the other (i.e. Rsquared=1, linear only) in the population although not necessarily in the sample due to possible measurement error. How do I test this? (what test statistic) Some additional info: In the usual case, using a regression model, we test whether Rsquared (or R, or Bz) is equal to 0 or not. Now, however, we only want a positive if it’s exactly equal to 1, taking measurement error into account though. submitted by Nevin Manimala Nevin Manimala /u/minimalattentionspan [link] [comments]

Power calculations to determine number of interventions possible in a trial?

Hi all, ​ I’ve come across the above question and I am a little stumped. I presume this is a trial that has determined a set sample size. ​ I had always thought it was best practice to first determine number of interventions necessary and then work out necessary sample accordingly and am a little unsure how to do this process backwards (especially as usually I have only done calculations with one intervention). ​ If anyone could shed some light on this problem, I would be very grateful. Thanks submitted by Nevin Manimala Nevin Manimala /u/Sef_ [link] [comments]

Parametrisation for “Generic potato shaped” simply/multiply connected bounded domain in R2

I am trying to produce a “generic potato shaped” simply/multiply connected bounded domain in R2 (e.g. https://en.wikipedia.org/wiki/Simply_connected_space#/media/File:Runge_theorem.svg) with Tikz and pgfplots. The generic potato shape has, despite its name, a quite specific shape, which I fail to reproduce. Does anyone know a parametrisation of the potato shape (or whichever lump one prefers)?

submitted by Nevin Manimala Nevin Manimala /u/Raibyo
[link] [comments]