Author: Nat

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Do I Really Need to Use Unsalted Butter?

TL;DR 1 stick of salted butter (8 tbsp) has about 1/3 tsp of salt.

Maybe the same thing happens to you: you want to bake something. The recipe calls for unsalted butter. You have all the other ingredients. You have salted butter. You just don’t have unsalted butter. You look at the recipe. It calls for salt. Are you really going to go to the store and get unsalted butter? Should you just use salted butter? Maybe it will end up too salty! Why do they do that anyway!? Since we don’t eat that much butter at this point, it’s kind of a pain to keep two kinds on hand just in case.

This happened to me recently, and I finally decided it’s time for me to figure out how much salt there is in salted butter.

One tablespoon (14g) of Kerry Gold butter (one brand we had on hand) has 100mg of sodium. One tbsp of Whole Foods organic salted butter (the other one we had) has 80mg of sodium. It seems like 90mg is a pretty good average guess. According to Rose Beranbaum’s blog, the National Dairy Council says that salted butter is 1.6-1.7% salt, which works out to 90mg of sodium.

One stick of butter = 8 tablespoons. At 14g/tbsp, that is 112g per stick of butter. Taking 1.65% of 112 gives 1.8g of salt. Most sources will tell you that a tsp of salt is 6 grams, so this is about 1/3 tsp. So you can use salted butter and reduce the salt you add… or, this guy on reddit suggests you just leave the recipe as is and the extra salt will enhance the flavor of your dish. For example, Senga commented on the Rose Beranbaum post, “I usually make my shortbread with salted butter. Last time I used unsalted and frankly I find it’s missing taste. Will go back to salted although real shortie should be made with unsalted.”

The other consideration: my recipe called for Kosher salt, which comes in larger crystals so that when you take 1 tsp there is more air. It weighs about 5g. But 1/3 tsp still comes in in the right ballpark. However, I think the salt is supposed to be a bit crunchy in the recipe and give you little “salt bombs,” so it’s reasonable to stick with unsalted butter and add in the Kosher salt. Rose B likes the scent of unsalted butter better, but I’m not sure it makes a difference in the final product.

When I worked this out, I didn’t have the NDC figure, so I took this approach: 1 stick of butter = 8 tbsp. At 90mg of sodium per tbsp, that is 720mg of sodium per stick. How much sodium is in a tsp of salt? Only part of salt is sodium; the rest is chloride. What part of salt (sodium chloride) is sodium? Let’s go back to high school chemistry: the atomic weight of sodium (Na) is 23, and chlorine (Cl) is 35.5. The total is 58.5. Dividing, the sodium is 23/58.5=.39, so salt is 39% sodium. You will see people say 40%, which is definitely close enough. 40% of one tsp of salt (6g) is 6×0.4=2.4g of sodium per tsp of salt. That is 2,400mg. 720mg of sodium in stick of butter divided by 2400 mg of sodium in a teaspoon of salt is 0.3… so a stick of butter is (again) about 1/3 tsp of salt. Checking online, people seem to say 2,300+ mg of sodium in a tsp of salt. Close enough!

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Changes to Wordle that didn’t get much attention

tl;dr After the NY Times purged some solutions and available guesses back in February, they quietly reintroduced them as available guesses, and they also shuffled around some of the solutions, without eliminating any.

Wordle was born on June 19, 2021. Perhaps Josh Wardle wanted to celebrate the birth, because the first answer was “cigar.” Being birthed of a nerd, this was known as “Wordle 0.”

Joy often comes with pain, and Wordle is no exception. Wordle was pre-programmed with 2315 answers, so the last Wordle was to have been Wordle 2314, on October 20, 2027. (If you’re into spoilers, you can find all of them here.)

Around Feb 15, 2022, shortly after the New York Times purchased Wordle, they eliminated some words that they felt were obscure or offensive. People noticed because some folks had the original version in their browser cache, and they got a different answer (“agora”) from the folks who wound up with the revised NYT version (“aroma”). “Agora” was the first of six solutions that were eliminated. The other five were “pupal,” “lynch,” “fibre,” “slave,” and “wench.” With 6 fewer words, Wordle will draw its last breath on October 14, 2027.

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E&M Codes 2021: Good News, for a Change

Just about exactly eight years ago, I wrote a series of posts that began with this paragraph:

If you’re a psychiatrist (or psychiatric RNCS) in the US reading this, you are almost certainly aware that all of our billing codes changed on Jan 1, 2013.  If you are like most of the psychiatrists I know—at least in private practice—you are at least somewhat freaked out by this.  If so, keep reading.  If not—for example, if you’re not a psychiatrist in the US—stop reading this immediately and go do something more interesting, like… well, like just about anything other than memorizing a phone book.  (There used to be things called phone books…  never mind.)

Unlike 2013, the billing codes themselves have not changed, but as of January 1, 2021, the documentation requirements for these codes have gotten significantly less complex and onerous. Like then, this post should be of no interest to you if your are not a US psychiatrist or psychiatric nurse. But if you are—and especially if a significant portion of your practice is psychotherapy—the situation is very different from 2013 because these changes are:

  • good news
  • not widely publicized
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Doomsday Calendar, Part 3

In the process of looking up John Conway’s “Doomsday Algorithm” for figuring out what day of the week “any” date falls on, I came across Chamberlain Fong’s description of a simplification of Conway’s algorithm that he and Michael Walters came up with, which they describe in a paper on arxiv. (“Any” is in quotes for reasons explained in Part 2.)

What does the Fong/Walters algorithm do differently? Let’s note what’s the same. Conway’s scheme of “Doomsdays” is still in place, and you still need to know the Doomsday for the start of the century. The difference is in computing the offset. There is no dividing by 12, remembering the quotient, dividing the remainder by 4, etc. (Apparently that part of the method was due to Lewis Carroll, as explained in Part 2 or in Fong’s Scientific American blog post.)

How does the alternate method , which they call “odd+11” work? If you love flowcharts, look here. But it’s pretty simple:

  1. Take the last two digits of the year.
  2. Is it odd? If so, add 11.
  3. Divide your number (which now must be even) by 2.
  4. Is your new number odd? If so, add 11 again.
  5. Reduce your number modulo 7.
  6. Subtract your number from 7 (“take the 7s complement”).
Continue reading “Doomsday Calendar, Part 3”
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Doomsday Calendar, Part 2

This internet thing, though. It seems to be all rabbit holes, all the way down. In my previous post, I wrote about John Conway’s “Doomsday Algorithm” for figuring out what day of the way “any” day falls on. It seems that there are quite a few people who have spent a lot more time thinking about calendars in general, and mental calendars in particular, than I have. Most of what’s in this post is based on this excellent piece by Chamberlain Fong.

The first helpful thing Fong does is to give some history. Conway’s method has two parts: the identification of particular days of the year as “Doomsdays,” which all fall on the same day of the week. Once you know what day of the week any give year’s Doomsdays fall on, it is easy to figure out the day of the week of an arbitrary date. The other part is to figure out what day of the week the given year’s Doomsdays fall on.

The first part of the algorithm seems to be entirely due to Conway. The second part, interestingly, was apparently worked out by Lewis Carroll—one of the few people in the orbit of mathematicians who may have been more playful that Conway. Martin Gardner, the legendary author of Scientific American’s Mathematical Games column, was a serious student of Carroll, and when he came across Carroll’s work on perpetual calendars, challenged Conway to come up with something simpler.

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John Conway’s “Doomsday Calendar”

[This wound up being Part 1 of 3. You can find Part 2 here, and Part 3 here. You don’t need to read all three parts, but Part 3 does actually describe a significantly simpler algorithm than the one Conway used.]

John Horton Conway, a great mathematician of unmatched playfulness, died recently at age 82 of Covid-19. His biographer, Siobhan Roberts, wrote an excellent New York Times obituary. Conway was something of a showman, in a good way, so I should give a spoiler alert up front, especially these days, that this has nothing to do with Doomsday as in the end of the world.

Photo by Denise Applewhite, Princeton University Office of Communications

I never met Conway, but in the mid-70s my math camp buddy Rob Indik had a summer in which he commuted to the UI Chicago campus “with Vera [Pless] driving, Conway in front, and me riding in the back and trying to ride along with Conway’s free flow of ideas.” I remember Rob regretting that he couldn’t remember a mental “perpetual calendar” that Conway had taught him. In the computer age we have no call for perpetual calendars, but back when dinosaurs roamed the earth they were novelty items: a small object with a few dials, which would let you figure out what day of the week any date falls on. A mental one sounded like fun, and I occasionally thought—not very hard—about how you might go about it. I never got very far. [I see that this is not the definition of “perpetual calendar” favored by Wikipedia, but that the American Heritage Dictionary has me covered.]

With Conway’s death, I decided to look it up, and found that it’s around the web in several places, but without a very clear explanation of why it works. So I thought I would explain both how it works and why it works.

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Fixing Up My Virtual Garage

In my last post, I told the story of reviving a moribund computer program from 15+ years ago.

In the process, I revisited my stash of moribund computer programs, including a little web page with links to some of them. It was dusty and pathetic and pretty much nothing worked. So I rolled up my sleeves and prettied it up, and if you want to look any of it, you can find it here.

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The Archeology of Computer Programming

TL;DR You can skip any time to the 20-second movie at the bottom of the post. Spoiler alert: the video will eventually reveal the solution to the puzzle.

Happy New Year! I just returned from a quick family trip to Seattle, and you would think that this post would be about my visit to the Living Computer Museum with my cousin Eric, and programming adventures now 50+ years ago in the RESISTORS. But it’s not, as worthy as those topics are.

Actually it all started when I read a post by Ben Orlin on his Math With Bad Drawings site about Evelyn Lamb‘s Page-a-Day Math Calendar, recently published by the AMS. One thing led to another, and my son Ben was kind enough to give me a copy for Christmas.

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