A Thanksgiving Recipe Puzzle
This Thanksgiving I'm planning to make my famous turkey gravy. Thankfully, I have a full 12-ounce container of turkey stock, which is hard to come by. For the recipe, I need exactly 6 ounces of stock. Unfortunately, I have only two measuring cups, one of which holds exactly 5 ounces and the other 7 ounces. What's more, the cups are so old that all of their markings have worn off. So, it appears that I can only measure out exactly 5 ounces or 7 ounces of stock.
Now, of course, I could just pour the stock into the 7 ounce cup and estimate when it is about an ounce less than full. Or, I could double all of the ingredients and make twice as much gravy. Or, I could run out to a store and buy a new and improved measuring cup. But is there any way, using only the two measuring cups I have, to measure out exactly 6 ounces of stock?
If you think you know the answer, click on the solution, below.
A Traditional Thanksgiving Thank You!
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Java Jive: A Refill
A recent headline reads:
Study: Coffee may help kidney disease patients avoid early death1
In a previous entry2, I discussed how three classes of words and phrases may help you understand science and health reporting. The above headline contains two of them: "may" and "help". "May" is one of a class of related words that indicates that the results of the study are less than definitive. Coffee may help; but, then again, it may not. No one now would say that cigarette smoking may cause lung cancer because this would suggest a reasonable doubt about it. "Help" is a word from a different class that indicates that the supposed healthful effect of coffee is weak.
The article beneath the headline begins:
Can caffeine help people with chronic kidney disease [CKD] live longer? That's the suggestion of a new study that found that among more than 2,300 Americans with chronic kidney disease, those who drank the most caffeinated drinks reduced their risk of premature death by 24 percent.1
"Suggestion" is another word, like "may", that indicates that the results of the study are less than conclusive. Also, we now learn that it is "caffeinated drinks", rather than coffee, that supposedly "reduced" the risk of death. So, presumably, you could get the same effect by drinking tea, or one of those highly-caffeinated "energy" drinks, instead of coffee.
When reading news reports of scientific studies, I strongly suggest reading the whole thing or at least skipping down to the end and reading the last few paragraphs: it's often there that we get the bad news. In contrast, in this article we get the bad news as early as the fourth paragraph:
"…[O]ur observational study cannot prove that caffeine reduces the risk of death, but only suggests the possibility of such a protective effect," [lead researcher Dr. Miguel Bigotte Vieira] said.1
This, despite the fact that a couple of paragraphs previously we were told that "those who drank the most caffeinated drinks reduced their risk " of death. Now, the lead researcher tells us that the study only "suggests" such a "possibility". It's a good thing that he didn't say that it may suggest such a possibility!
However, the study found a "dose-dependent inverse association"3 between caffeine consumption and death, which does indeed suggest a causal relationship between the two.4 However, since it was only an observational study, it cannot establish such a relationship, which is why Vieira goes on to note:
The findings also need to be replicated in a trial that compares caffeine consumption with no caffeine consumption before patients are counseled to drink more coffee or other caffeinated drinks….1
I think this is exactly right, but it comes close to contradicting what Vieira said in a press release:
These results suggest that advising patients with CKD to drink more caffeine may reduce their mortality. This would represent a simple, clinically beneficial, and inexpensive option, though this benefit should ideally be confirmed in a randomized clinical trial.3
This suggests that, while it would be ideal to have a randomized clinical trial, it's not too soon for CKD patients to increase their caffeine intake. In contrast, Dr. Leslie Spry, a spokesman for the National Kidney Foundation, is quoted at the end of the original article:
This is yet another observational study, Spry noted, where only an association was found, not cause and effect. Given the relatively small size of the study, and the small reduction in death risk, Spry said he's not willing to tell kidney patients that the more caffeine they drink, the longer they'll live. "I would rather say that compared to little or no caffeine intake, those people with the highest intake of caffeine as estimated by dietary recall, may have a lower mortality, but the reason for this lower mortality is not proven by this association research," he said.1
This is actually a better-than-average news report on a new study, for it includes something that most such articles leave out: a second opinion from an independent expert. Moreover, Spry's cautions are not included in the original press release, so this is not just a rewritten press handout, which is all too common nowadays.
- Steven Reinberg, "Study: Coffee may help kidney disease patients avoid early death", UPI, 11/4/2017
- See: Cuckoo for Cocoa Puffery, 6/11/2017
- American Society of Nephrology, "Caffeine consumption may help kidney disease patients live longer", EurekAlert!, 11/3/2017. This is the press release that probably started it all. A "dose-dependent inverse association" between caffeine intake and death means that the more caffeine the study's subjects consumed, the longer they lived.
- This is an application of John Stuart Mill's "method of concomitant variation", see: Philosophy of Scientific Method (Hafner, 1963), Book 3, Chapter 8, Section 6.
Here's how I did it: First, I filled the 7-ounce measuring cup with stock from the 12-ounce container. Then, I poured the 7-ounce measuring cup into the 5-ounce cup, filling it. After that, I poured the 5-ounce cup back into container of stock. I proceeded to pour the 2 ounces of stock from the 7-ounce cup into the empty 5-ounce cup, then refilled the empty 7-ounce cup from the stock container. I then filled the 5-ounce cup to the top from the 7-ounce cup, leaving 4 ounces in the 7-ounce cup. I emptied the 5-ounce cup back into the container, then transferred the contents of the 7-ounce cup to the empty 5-ounce cup. I refilled the empty 7-ounce cup from the container, then filled the 5-ounce cup to the top from the 7-ounce cup, leaving―Ta-Da!―exactly 6 ounces in the 7-ounce cup. Finally, I made the gravy.
Well, that was a lot of work! Next Thanksgiving, I think I'll just buy a new measuring cup.