# Why Do Things Float in Water?

WHY? is our attempt to answer all the questions every little kid asksHave a question? Send it to why@mentalfloss.com.

I bet you know that wood floats but a rock sinks. But why? Let’s look deep inside each object at its molecules (MOLL-uh-kyools). Everything is made of molecules. Molecules are very, very tiny. You can only see them with a special microscope. In some objects, like a rock, molecules are squished tightly together. In others, like wood, the molecules are more spread out. How closely molecules are crowded together in a space is called density. Density is a big part of why some things float and others don’t.

Objects like coins, rocks, and marbles are more dense than water. They will sink. Objects like apples, wood, and sponges are less dense than water. They will float. Many hollow things like empty bottles, balls, and balloons will also float. That’s because air is less dense than water. This is one reason huge ships can float, even though they’re very heavy. Inside a ship, there’s a lot of hollow space filled only with air. But that’s not all: shape matters, too!

The outside of an object is called its surface. When more of the surface is touching the water, the object is more buoyant (BOY-ant), which means it floats better. When an object floats, it pushes water out of the way. That’s called displacement. But guess what? Water pushes back! So the more surface area an object has, the more water pushes back against it, helping it float. That's another reason why even big ships don't sink if they have the right shape.

You can test this out yourself. Try making a boat with a flat bottom using tinfoil. Does it float? What happens if you start putting pennies or pebbles inside your boat? What happens if you crumple your tinfoil boat into a ball? Using what you’ve learned about density and buoyancy, why do you think the empty boat floats best?

# 8 Ways Science Can Boost Your Halloween Fun

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Halloween is all about embracing the supernatural, but science shouldn't entirely fall by the wayside during the spookiest of holidays. Here are a few ways it can actually improve your holiday, from making trick-or-treating easier to fooling your brain into thinking you're eating tasty treats even though you're nibbling on candy cast-offs.

## 1. Slow the decomposition of your Halloween jack-o'-lantern.

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You don't have to be an expert gardener to keep your jack-o'-lantern looking fresh all Halloween season long. While scouting out pumpkins, pick hard, unblemished ones and steer clear of those with watery dark spots. These splotches indicate frost damage.

Hold off on carving until right before Halloween so your gourds won't rot—but if you can't resist, try squirting their exteriors with lemon juice after you're done slicing and dicing. The acid inhibits pumpkin enzymes, which react with oxygen and cause browning. A light misting of bleach solution will help keep fungus at bay. Some apply vegetable oil or Vaseline to prevent shriveling and drying. We experimented with various techniques in this video.

For extra TLC, you might even want to bring your jack-o'-lanterns in at night if temperatures dip; if you live in a hot and humid area, extend its life by placing it in the fridge overnight. Try using glow sticks or LED lights instead of flesh-singeing candles.

## 2. Use apps to plan a treat-or-treating route.

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Thanks to technology, trick-or-treaters (and their hungry adult companions) can now scout out which neighbors are doling out the best candy and which are sticking with Tootsie Rolls, apples, and toothbrushes. Simply download the app for Nextdoor, the neighborhood-based social network, to check out an interactive "treat map" that lets users tag whether their home is handing out treats, and what that treat is.

Since safety is far more important than sugar, guardians should also consider adding a tracking app to their arsenal come Halloween, especially if their kid's venturing out alone. The Find My Family, Friends, Phone app gives the real-time locations of trick-or-treaters, provides alerts for when they turn home, and also comes with a "panic" button that provides emergency contact details when pressed.

## 3. Optimize your candy's flavor (even if it's SweeTarts).

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Not crazy about this year's Halloween loot? Fool yourself into thinking those black licorice pieces and peanut chews taste better than they actually do by eating them after you scarf down the chocolate and Sour Patch Kids. According to a 2012 study published in Psychological Science, being aware that these items of candy are your very last candies actually tricks the brain into appreciating them more (and thus thinking they're tastier than they really are).

Meanwhile, a 2013 study from the same journal found that creating a candy-eating ritual enhances flavor and overall satisfaction. Nibble the ridged edges off a Reese's peanut butter cup before tackling the creamy center, sort the M&Ms by color, and take your time unwrapping a chocolate bar.

## 4. Create a DIY fog machine with carbon.

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Save money at Party City by creating your own fog machine at home. When dropped in water, dry ice—or frozen carbon dioxide—creates a gas that's a combination of carbon dioxide and water vapor, but looks like the fog you'd see rolling through a haunted graveyard [PDF].

## 5. Eat sort-of-heart-healthy Halloween candy.

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Halloween candy isn't always bad for you. While shopping for this year's trick-or-treat bounty, steer clear of sugary confections and milk chocolate mini-bars. Opt for dark chocolate treats instead. Research suggests that our gut microbes ferment the antioxidants and fiber in cocoa, creating heart-healthy anti-inflammatory compounds. Plus, dark chocolate or cocoa also appears to help lower blood pressure for people with hypertension, decrease bad cholesterol, and stave off cardiovascular disease and diabetes, among other benefits.

## 6. Analyze data on Halloween candy trends and give the people what they want.

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Thanks to data science, you can make sure you're giving out the best treats on the block. Bulk candy retailer CandyStore.com combed through 10 years of data (2007 to 2016, with a particular focus on the months leading up to Halloween) to gauge America's top-selling sweets. They created an interactive map to display their results, which includes the top three most popular Halloween handouts in each state and Washington, D.C. Be prepared for plenty of stoop-side visitors and adorable photo ops.

## 7. Bake better Halloween treats with chemistry.

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Cooking is essentially chemistry—and depending on your technique, you can whip up chewy, fluffy, or decadent Halloween treats according to taste.

Folding chunks of chilled butter into your dough will give you thick, cake-like cookies, as will swapping baking soda for baking powder. When butter melts, its water converts into gas, which leaves lots of tiny holes. If the butter flecks in question are colder and larger, they'll leave bigger air pockets. As for the baking powder, it produces carbon dioxide gas both when it's mixed into the dough and when it's heated. For an extra boost in texture, you can also try adding more flour.

Prefer chewier cookies? Start out with melted butter in the dough, and stick with plain old baking soda.

And for extra-fragrant and flavorful baked goods, opt to use dark sugars—like molasses, honey, and brown sugar—because they're filled with glucose and fructose instead of plain old sucrose. As cookies bake, they undergo two processes: caramelization, in which the sugar crystals liquefy into a brown soup; and the Maillard reaction, a chemical reaction between the dough's proteins and amino acids (flour, egg, etc.) and the reducing sugars that causes tasty browning.

## 8. Take deep breaths to stay calm in haunted houses.

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Halloween can be tough for people with anxiety or low thresholds for fear. While visiting a haunted house or watching a scary movie, remember to take deep breaths, which fends off the body's flight-or-fight response, and reframe your anxiety in your mind as "excitement." It's also a good idea to schedule spine-chilling activities after an activity that triggers feel-good endorphins—say, after a walk to check out your neighbors' awesome Halloween displays.

# Some Mathematicians Think the Equal Sign is On Its Way Out

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A growing number of mathematicians are skeptical that the equal sign, traditionally used to show exact relationships between sets of objects, holds up to new mathematical models, WIRED reports.

To understand their arguments, it’s important to understand set theory—a theory of mathematics that’s been around since at least the 1870s [PDF]. Take the classic formula 1+1=2. Say you have four pieces of fruit—an apple, an orange, and two bananas—and you put the apple and the orange on one side of a table and the two bananas on the other. In set theory, that’s an equation: One piece of fruit plus one piece of fruit on the left side of the table equals two pieces of fruit on the right side of the table. The two sets, or collections of objects, are the same size, so they’re equal.

But here’s where it gets complicated. What if you put an apple and a banana on the left side of the table and an orange and a banana on the other side? That’s clearly different from the first scenario, but set theory writes it as the same thing: 1+1=2. What if you switched the order of the first set of objects, so instead of having an apple and an orange, you had an orange and an apple? What if you had only bananas? There are potentially infinite scenarios, but set theory is limited to expressing them all in only one way.

“The problem is, there are many ways to pair up,” Joseph Campbell, a mathematics professor at Duke University, told Quanta Magazine. “We’ve forgotten them when we say ‘equals.’”

A better alternative is the idea of equivalence, some mathematicians say [PDF]. Equality is a strict relationship, but equivalence comes in different forms. The two-bananas-on-each-side-of-the-table scenario is considered strong equivalence—all of the elements in both sets are the same. The scenario where you have an apple and an orange on one side and two bananas on the other? That’s a slightly weaker form of equivalence.

A new wave of mathematicians is turning to the idea of category theory [PDF], which is based in understanding the relationships between different objects. Category theory is better than set theory at dealing with equivalence, and it’s also more universally applicable to different branches of mathematics.

But a switch to category theory won’t come overnight, according to Quanta. Interpreting equations using equivalence rather than equality is much more complicated, and it requires relearning and rewriting everything about mathematics—even down to algebra and arithmetic.

“This complicates matters enormously, in a way that makes it seem impossible to work with this new version of mathematics we’re imagining,” mathematician David Ayala told Quanta.

Several mathematicians are at the forefront of category theory research, but the field is still relatively young. So while the equal sign isn’t passé just yet, it’s likely that an oncoming mathematical revolution will change its meaning.

[h/t Wired]

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