# The Universe of Discourse

Fri, 31 Dec 2021

I doubt this story will be of interest to anyone but me, but it's the best thing that happened to me this month.

Back in October I bought a new house and arranged a homeowners’ insurance policy for it. The main purpose of such a policy is that if your house is destroyed by fire or some other calamity, the homeowners’ insurance people will arrange to build you a new house in the same place. If you have a mortgage, the lienholder will require a policy as a condition of the mortgage, but it's a good idea to have one even if you aren't required to. Usually the rebuild-the-house coverage is bundled with theft insurance, in case your house is robbed, and personal injury insurance, in case someone slips on your sidewalk.

I called the company that had brokered the policy for my previous house, and they assigned me to Brenda Wyman. Brenda presented me with one option: Company S. I said I was surprised at how high Company S's premium was. Brenda told me that Company S had by far the lowest premium. I asked if she had called the company that provided the insurance for my previous house. She said she had. I asked how much their quote was for. She told me, and the number was indeed larger than the quote from Company S. At this point I was tired of trying to extract information from Brenda and let it drop.

The insurance coverage is contingent on the insurer doing an inspection of the house to make sure it is not a hazard and is not about to fall down. Company S did their inspection in mid-November, but didn't notify me of the results until December. On December 6, they sent Brenda a letter: they had found seven things wrong with the house. I had until January 7 to fix them or they would cancel my insurance.

I was upset by this. Some of the seven things were minor, but two were not. The company wanted major roof work done. I was already in negotiations with roofers, but it might take me more than 31 days to select the roofer, sign the contract, and schedule and complete the work. There were major holidays coming up: roofers wouldn't work on Christmas. Roofing work is contingent on dry weather and I don't control the weather. Company S also demanded that I tear up and repour the cement in the alley that adjoins the house.

I could think of three ways to proceed:

1. Attempt to schedule the work and get it all done by January 7
2. Attempt to negotiate with Company S to get an extension, should it be impossible to complete all the work by January 7
3. Arrange a new insurance policy with a different company

I started work on (1) and (2) and made a to-do item to proceed with (3) in a week depending on how things looked.

For (2) I immediately wrote back to Brenda to point out that the demands were unreasonable and might be impossible to satisfy. Was there any flexibility in the date? I also asked if there was a way to contact Company S directly.

Brenda's reply was reassuring. She claimed that Company S wouldn't require that all work be completed by January 7. It was enough for them, she said, that forward progress was being made, and if I had signed contracts by January 7 that would satisfy them.

Nevertheless I contacted Company S's customer service number, hoping to get something in writing. The customer service guy was brief and to the point: they didn't care that the holidays were coming up. They didn't care that I had only been given a few weeks to fix major items. They wouldn't give me an extension. But I could write to the inspections department and see if they said anything different.

I emailed the inspections department to see what they said, laying out the situation in detail: I had already addressed two of the seven items; I had verbal agreements to get three more finished by January 7, and I was working on the two major items. But I couldn't be certain the work would be complete by January 7 and if they insisted, I would have to obtain coverage elsewhere. The inspections department had promised to reply in 24 to 48 business hours.

Meanwhile I continued to talk to contractors about the major plumbing, cement, and roofing work that Company S had demanded.

I had emailed the inspections department midday Wednesday December 8 and been expecting a reply later that week. I didn't hear back from them until late Tuesday the 14th. At first I was only somewhat irritated, but then I realized: they had only promised a response in 24 to 48 business hours. There are only 40 business hours in a week, and they had replied 36 business hours after receiving my message, well before their promised deadline. That was even more irritating than when I thought they had replied late.

But at least their reply was brief, clear and direct:

We are unable to offer an extension. Please place the insured home with another carrier by 1/07/22.

I reported to Brenda:

I talked to Company S about this, to see if there was any leeway on the deadline. They told me there wasn't and suggested I should get different insurance.

Please hook me up with someone else.

Brenda continued to insist that Company S would give me an extension:

When I discussed with Company S, they advised me that as long as you are making progress with this and show contracts they could extend it. I would need this information to contact them with it.

I was not going to trust Brenda's say-so when I had it from the horse's mouth that the situation was the exact opposite. What if I proceeded with Brenda's plan, provided the documentation she suggested, and then on January 7, Company S refused to give me the hoped-for extension that they had already told me they would refuse to give me? Even Brenda had only said “they could extend it”, not “they would extend it”.

I said:

That's the opposite of what they told me. I got email yesterday from Company S that says:

We are unable to offer an extension. Please place the insured home with another carrier by 1/07/22.

If it's sufficient for me to be making progress and show contracts, I want it in writing from them this week.

Brenda did not seem to appreciate the situation, that on one hand I had a vague, secondhand suggestion that I could maybe get an extension, and on the other hand I had a clear commitment directly from Company S to cancel my policy on January 7.

Brenda talked to Company S again but did not get any actual commitments. Her contact said:

Hello Brenda, you can have the insured call customer service to discuss the issues.

The best way to resolve this is to email photos of any corrections made to the inspections inbox for review…

I reminded Brenda that I had already spoken to customer service and they had told me they would not negotiate, and that I similarly had a written reply from their inspections group saying the same thing. I also pointed out:

I emailed them at 1PM on Wednesday Dec 8th and didn't hear back until the following Monday. That is not an effective way to communicate when the situation is changing day-to-day as it is here.

Brenda and I were also having some difficulty communicating, it seemed:

You can send me the things you have right now and I can contact them and see what can be done.

I understand your frustration with this, but when it comes to what they are wanting I am also stuck trying to resolve it for you but I do have to present the proof of repairs for them to even consider.

I made one more attempt to communicate with Brenda. I summarized the progress I had made and when work was scheduled.

I told them all this in the email I sent their inspections department last week, and their reply was “we are unable to offer an extension. Please place the insured home with another carrier by 1/07/22.”

So that is what I am asking you to do.

To me that seems clear, direct, and unambiguous. But not to Brenda, who said:

If you can change those verbal agreements to actually written up agreement on their letterhead that would show you are doing it but can’t be done til after 1/7. Especially since you put a deposit down with the cement person.

Definitely send me the pictures of the trees trimmed and vines removed.

Brenda wanted me to contact the barely-literate cement guy and have him write up the agreement on “letterhead” (that he surely didn't have), and for what? To send to Company S, which had already told me twice that they didn't want it.

That seemed to be the end of that road. I hate repeating myself and I wasn't going to ask Brenda a third time. If Brenda wouldn't find me another insurer, I would find one without her. My first couple of tries didn't bear fruit but the third one did. The new agent (not Brenda or anyone who works for Brenda's company) told me:

1. Brenda had arranged too much insurance for me; I was paying to have the Company S agree to spend up to $X to rebuild my house, but rebuilding the house couldn't possibly cost more than$⅔X.

2. Most homeowners’ insurance companies would have given me a six-month grace period to make the necessary repairs. Company S was notoriously inflexible.

The new guy was able to arrange new coverage for me with an insurance premium 15% lower than the one Brenda had gotten me. I notified Company S the next day that I was ending my coverage and wanted a refund. (To their credit, this was completely painless, and the refund check arrived timely.)

I didn't bother to inform Brenda. Maybe I'll hear from her again, maybe I won't. She has all the information she needs to figure out what happened, if she cares to.

Okay, why have I written down this long story? Because it made me really happy. It is a distillation of my growth as an adult.

Faced with a difficult and complicated situation, I was able to deal with it constructively and timely. I didn't crawl under the covers. I didn't procrastinate. I didn't take the superficially easy way out, of crossing my fingers, hoping that Brenda was right and that I wouldn't get screwed on January 7.

I pursued a three-prong approach. I'm bad at long-term planning, good at short-term improvising, and the key to being a successful improviser is to leave as many options open for as long as you can. I did that this time. When Brenda wouldn't help me find new insurance, I found it myself. But if I hadn't found new insurance, maybe it would have turned out Brenda was right and I could get an extension. Or even if Brenda had been wrong, maybe I could have completed the repairs by January 7. There were a lot of ways this could have gone, a lot of ways it could have turned out okay, and I pushed everything forward in parallel until I found a way through.

I executed my plans timely. The whole business was over in less than two weeks: I got the inspection warning from Company S on December 6, and canceled their policy effective the 17th. There's a decent chance that, even had I not been able to get a new insurance policy, I would have been able to complete the repairs before the deadline; two of the seven items had been taken care of and four more scheduled on or before January 7. The cement guy demolished the old alley on December 21 and poured the new one on the 23rd. (The roof stuff is going to be more complicated and once I got my new insurance with the six-month grace period I stopped worrying about it.)

And I didn't lose my temper. I didn't insult Brenda or the innocent Company S customer service rep. I wasn't sarcastic. I didn't whine.

I solved an adult problem like an adult! I was grinning about this for several days around December 17–20. This is the sort of thing that only a middle-aged person can get excited about, but I like middle age, which has been really good for me in so many ways. I wonder, what would my 22-year old self have thought about this story? Would he have been surprised? Amazed? Astounded? (Horrified?) I don't think he would have forseen this degree of competence.

Happy new year, readers. May the coming twelve months be better for you than the previous.

[ Addendum: The insurance agent's name is not actually ‘Brenda Wyman’. Absolutely nothing in this post has any connection with any real person with that name. ]

Thu, 30 Dec 2021

[ This is a followup to In simple English, what does it mean to be transcendental? ]

A while back a Math SE user posted a comment on my simple explanation of transcendental and algebraic numbers that asked why my explanation had contained some redundancies:

Are there any numbers for which division is necessary? I can't think of any. Likewise, subtracting integers is redundant; I believe all you need is "you can add any integer; you can multiply by any non-zero integer; you can multiply by x."

This is true! I had said:

We will play a game. Suppose you have some number !!x!!. You start with !!x!! and then you can add, subtract, multiply, or divide by any integer, except zero. You can also multiply by !!x!!. You can do these things as many times as you want. If the total becomes zero, you win.

and you don't need subtraction or division. (The underlying mathematical fact that motivated this answer is that integer polynomials are the free ring over the integers. For a ring you only need addition and multiplication.) So why did I mention subtraction and division? They're not mathematically necessary, doesn't it make the answer more complicated to put them in?

I had considered this carefully, and had decided it was simpler this way. The target audience is a person with no significant mathematical training. To a mathematician, it's obvious that inclusion of integers includes subtraction as a special case because you can simply add a negative integer. But non-mathematicians are not used to thinking this way. They have been taught that there are four arithmetic operations. If I mention all four, they will understand that all the operations of basic arithmetic are allowed. But if I had said only "addition and multiplication" many people would have been distracted and wondered "why just those two? Why not some other two?". Including all four avoids this distraction.

I could have said only “addition and multiplication” and later on explained that allowing subtraction and division doesn't change anything. I think this would have been an inferior choice. It's best to get to the point as quickly as possible. In this case the point is that all the operations of basic arithmetic are allowed. The fact that you can omit two is not relevant. My version is shorter and clearer, and avoids the whole issue.

If my version were less technically correct, that would be a major drawback. Sacrificing correctness for clarity is a seductive but usually harmful choice. The result may appear more clear, when it actually isn't, because of the subtle errors that have been papered over. In this case, though, nothing was sacrificed. It's 100% correct both ways. Mathematicians might prefer the minimal statement, but whole point of this answer is that it is correct even though it is not written in the way that a mathematician would prefer.

I'd like to boil this down to a pithy maxim, but I'm not sure I can do it without being inane. There's something in it about how, when you write something for non mathematicians, you should try to write every part of it for non-mathematicians, not just at the surface presentation but in the deeper layers too.

There's also something about how you should be very careful to distinguish the underlying mathematical truth on the one hand, from the practices that mathematicians have developed to help them in their day-to-day business, or to help them communicate with other mathematicians, or that are merely historical accidents, on the other. The underlying truth is the important part. The rest can be jettisoned.