CLOSE
iStock
iStock

Letting Eyewitnesses Sleep Could Make For More Accurate Testimony

iStock
iStock

Despite what watching Law & Order might have taught you, eyewitness accounts of crimes are far from trustworthy. Human memory is fallible, and in fact, eyewitnesses are notoriously bad at providing accurate evidence. Misidentification by eyewitnesses has played a role in 70 percent of convictions overturned by DNA evidence in the U.S., according to the New York-based Innocence Project. But a new study suggests one way to help eyewitnesses provide more accurate evidence: sleep.

Published in the journal PLOS ONE and spotted by Futurity, the study finds that witness testimony is more accurate during police lineups if the person is well-rested.

In the study, Michigan State University students watched a video of a staged crime in which a man planted a bomb on a rooftop. They were then asked to look through several black-and-white lineups of six people, some of which included the perpetrator from the video, and some of which only had look-alike fillers. The participants had to wait 12 hours between watching the video and picking out the criminal from the lineup, but not all of them spent it the same way. Some watched the video in the morning and looked at the lineup at night, while others watched the video at night and then looked at the lineup in the morning, after they had slept.

The researchers found that when participants slept between seeing the “crime” and being presented with potential suspects, they were less likely to pick someone out of lineups that only included fillers. In other words, they were better able to reject innocent lookalikes, noting correctly that the perpetrator they had seen wasn’t present at all. People who had not slept misidentified an innocent person as the perpetrator 66 percent of the time compared to 42 percent of the people who had slept. That doesn’t seem like a huge difference, but even one misidentification in real life can have serious consequences for innocent people accused of crimes. The results track with existing research on sleep that has found that it plays an important role in cognitive processes like learning and memory.

However, sleep didn’t make the participants any better at identifying the correct suspect when he was in the lineup. Both groups could pick him out with about 50 percent accuracy. Essentially, sleep isn’t going to solve crimes, but it could help ensure that the wrong person doesn’t go to prison.

Previously, a 2016 study in Psychological Science found that it’s relatively easy for police to nudge witnesses into picking their prime suspect from a lineup by making sure that they’re the only person in the group with a particular distinguishing feature, like a beard. These unfair lineups not only resulted in misidentification, but participants who chose from them were more confident about their (incorrect) choice than people who saw more fair lineups.

Taking a long nap isn’t the only way to improve lineup accuracy. The criminal justice advocates at the Innocence Project recommend several methods to make sure that witness testimony is more accurate, such as making sure that the people shown in the lineups all roughly match the description of suspect (beard and all), having the lineup administered by an officer who doesn’t know which person in the lineup is the police’s suspect, and making sure the witnesses know that the perpetrator might not be in the lineup at all, and that the investigation will continue even if they don’t pick anyone.

[h/t Futurity]

nextArticle.image_alt|e
John Phillips, Getty Images for Tourism Australia
arrow
Animals
New Plankton Species Named After Sir David Attenborough Series Blue Planet
John Phillips, Getty Images for Tourism Australia
John Phillips, Getty Images for Tourism Australia

At least 19 creatures, both living and extinct, have been named after iconic British naturalist Sir David Attenborough. Now, for the first time, one of his documentary series will receive the same honor. As the BBC reports, a newly discovered phytoplankton shares its name with the award-winning BBC series Blue Planet.

The second half of the species' name, Syracosphaera azureaplaneta, is Latin for "blue planet," likely making it the first creature to derive its name from a television program. The single-cell organisms are just thousandths of a millimeter wide, thinner than a human hair, but their massive blooms on the ocean's surface can be seen from space. Called coccolithophores, the plankton serve as a food source for various marine life and are a vital marker scientists use to gauge the effects of climate change on the sea. The plankton's discovery, by researchers at University College London (UCL) and institutions in Spain and Japan, is detailed in a paper [PDF] published in the Journal of Nannoplankton Research.

"They are an essential element in the whole cycle of oxygen production and carbon dioxide and all the rest of it, and you mess about with this sort of thing, and the echoes and the reverberations and the consequences extend throughout the atmosphere," Attenborough said while accepting the honor at UCL.

The Blue Planet premiered in 2001 with eight episodes, each dedicated to a different part of the world's oceans. The series' success inspired a sequel series, Blue Planet II, that debuted on the BBC last year.

[h/t BBC]

nextArticle.image_alt|e
iStock
arrow
science
5 Ways You Do Complex Math in Your Head Without Realizing It
iStock
iStock

The one thing that people who love math and people who hate math tend to agree on is this: You're only really doing math if you sit down and write formal equations. This idea is so widely embraced that to suggest otherwise is "to start a fight," says Maria Droujkova, math educator and founder of Natural Math, a site for kids and parents who want to incorporate math into their daily lives. Mathematicians cherish their formal proofs, considering them the best expression of their profession, while the anti-math don't believe that much of the math they studied in school applies to "real life."

But in reality, "we do an awful lot of things in our daily lives that are profoundly mathematical, but that may not look that way on the surface," Christopher Danielson, a Minnesota-based math educator and author of a number of books, including Common Core Math for Parents for Dummies, tells Mental Floss. Our mathematical thinking includes not just algebra or geometry, but trigonometry, calculus, probability, statistics, and any of the at least 60 types [PDF] of math out there. Here are five examples.

1. COOKING // ALGEBRA

Of all the maths, algebra seems to draw the most ire, with some people even writing entire books on why college students shouldn't have to endure it because, they claim, it holds the students back from graduating. But if you cook, you're likely doing algebra. When preparing a meal, you often have to think proportionally, and "reasoning with proportions is one of the cornerstones of algebraic thinking," Droujkova tells Mental Floss.

You're also thinking algebraically whenever you're adjusting a recipe, whether for a larger crowd or because you have to substitute or reduce ingredients. Say, for example, you want to make pancakes, but you only have two eggs left and the recipe calls for three. How much flour should you use when the original recipe calls for one cup? Since one cup is 8 ounces, you can figure this out using the following algebra equation: n/8 : 2/3.

algebraic equation illustrates adjustment of a recipe
Lucy Quintanilla

However, when thinking proportionally, you can just reason that since you have one-third less eggs, you should just use one-third less flour.

You're also doing that proportional thinking when you consider the cooking times of the various courses of your meal and plan accordingly so all the elements of your dinner are ready at the same time. For example, it will usually take three times as long to cook rice as it will a flattened chicken breast, so starting the rice first makes sense.

"People do mathematics in their own way," Droujkova says, "even if they cannot do it in a very formalized way."

2. LISTENING TO MUSIC // PATTERN THEORY AND SYMMETRY

woman enjoys listening to music in headphones
iStock

The making of music involves many different types of math, from algebra and geometry to group theory and pattern theory and beyond, and a number of mathematicians (including Pythagoras and Galileo) and musicians have connected the two disciplines (Stravinsky claimed that music is "something like mathematical thinking").

But simply listening to music can make you think mathematically too. When you recognize a piece of music, you are identifying a pattern of sound. Patterns are a fundamental part of math; the branch known as pattern theory is applied to everything from statistics to machine learning.

Danielson, who teaches kids about patterns in his math classes, says figuring out the structure of a pattern is vital for understanding math at higher levels, so music is a great gateway: "If you're thinking about how two songs have similar beats, or time signatures, or you're creating harmonies, you're working on the structure of a pattern and doing some really important mathematical thinking along the way."

So maybe you weren't doing math on paper if you were debating with your friends about whether Tom Petty was right to sue Sam Smith in 2015 over "Stay With Me" sounding a lot like "I Won't Back Down," but you were still thinking mathematically when you compared the songs. And that earworm you can't get out of your head? It follows a pattern: intro, verse, chorus, bridge, end.

When you recognize these kinds of patterns, you're also recognizing symmetry (which in a pop song tends to involve the chorus and the hook, because both repeat). Symmetry [PDF] is the focus of group theory, but it's also key to geometry, algebra, and many other maths.

3. KNITTING AND CROCHETING // GEOMETRIC THINKING

six steps of crocheting a hyperbolic plane
Cheryl, Flickr // CC BY-SA 2.0

Droujkova, an avid crocheter, she says she is often intrigued by the very mathematical discussions fellow crafters have online about the best patterns for their projects, even if they will often insist they are awful at math or uninterested in it. And yet, such crafts cannot be done without geometric thinking: When you knit or crochet a hat, you're creating a half sphere, which follows a geometric formula.

Droujkova isn't the only math lover who has made the connection between geometry and crocheting. Cornell mathematician Daina Taimina found crocheting to be the perfect way to illustrate the geometry of a hyperbolic plane, or a surface that has a constant negative curvature, like a lettuce leaf. Hyperbolic geometry is also used in navigation apps, and explains why flat maps distort the size of landforms, making Greenland, for example, look far larger on most maps than it actually is.

4. PLAYING POOL // TRIGONOMETRY

people playing pool
iStock

If you play billiards, pool, or snooker, it's very likely that you are using trigonometric reasoning. Sinking a ball into a pocket by using another ball involves understanding not just how to measure angles by sight but triangulation, which is the cornerstone of trigonometry. (Triangulation is a surprisingly accurate way to measure distance. Long before powered flight was possible, surveyors used triangulation to measure the heights of mountains from their bases and were off by only a matter of feet.)

In a 2010 paper [PDF], Louisiana mathematician Rick Mabry studied the trigonometry (and basic calculus) of pool, focusing on the straight-in shot. In a bar in Shreveport, Louisiana, he scribbled equations on napkins for each shot, and he calculated the most difficult straight-in shot of all. Most experienced pool players would say it’s one where the target ball is halfway between the pocket and the cue ball. But that, according to Mabry’s equations, turned out not to be true. The hardest shot of all had a surprising feature: The distance from the cue ball to the pocket was exactly 1.618 times the distance from the target ball to the pocket. That number is the golden ratio, which is found everywhere in nature—and, apparently, on pool tables.

Do you need to consider the golden ratio when deciding where to place the cue ball? Nope, unless you want to prove a point, or set someone else up to lose. You're doing the trig automatically. The pool sharks at the bar must have known this, because someone threw away Mabry's math napkins.

5. RE-TILING THE BATHROOM // CALCULUS

tiled bathroom with shower stall
iStock

Many students don't get to calculus in high school, or even in college, but a cornerstone of that branch of math is optimization—or figuring out how to get the most precise use of a space or chunk of time.

Consider a home improvement project where you're confronted with tiling around something whose shape doesn't fit a geometric formula like a circle or rectangle, such as the asymmetric base of a toilet or freestanding sink. This is where the fundamental theorem of calculus—which can be used to calculate the precise area of an irregular object—comes in handy. When thinking about how those tiles will best fit around the curve of that sink or toilet, and how much of each tile needs to be cut off or added, you're employing the kind of reasoning done in a Riemann sum.

Riemann sums (named after a 19th-century German mathematician) are crucial to explaining integration in calculus, as tangible introductions to the more precise fundamental theorem. A graph of a Riemann sum shows how the area of a curve can be found by building rectangles along the x, or horizontal axis, first up to the curve, and then over it, and then averaging the distance between the over- and underlap to get a more precise measurement. 

SECTIONS

arrow
LIVE SMARTER
More from mental floss studios