How math predicts life on Earth and the universe beyond

Math doesn't suck. It is one of humanity's greatest and most mysterious journeys.

  • There is a pervasive cultural attitude against mathematics, but it is actually a mind-blowing tool for analyzing and predicting the world around us—and far beyond. We asked mathematicians Edward Frenkel and Po-Shen Loh, and physicists Michio Kaku, Michelle Thaller, Janna Levin and Geoffrey West to explain the wonders of math.
  • West explains the rule of 'quarter-power scaling' in biology—there is a mathematical equation that predicts how much food an organism needs to eat to survive and it's remarkably consistent, whether you're looking at ladybugs, cats, elephants, and even trees and flowers. Math underpins our lives in incredible ways.
  • Infinitesimal calculus—the math that describes how moving bodies change over time—turns out to predict not just phenomena on Earth but far out in the universe. The 11-dimensional math used by physicists turns out to predict the exact results of particle physics experiments. Humanity is on an incredible journey with mathematics and every day it opens up the world and universe in eye-opening ways.
Keep reading Show less

Learn to think like an engineer with the help of these courses

Math can become intuitive with a little practice.

  • Engineering is the foundation of society, from physical infrastructure to every device in your possession.
  • Electrical engineering is one of the most in-demand occupations in the technological age.
  • The Mathematics for Engineers Prep Bundle teaches you how to think like an engineer.
Keep reading Show less

Every calculator you'll ever need, for free

The Omni Calculator site is a stunning treasure trove of free calculators.

Image source: Dusit/Shutterstock/Big Think
  • 1,175 calculators attempt to solve every everyday math problem for you.
  • All free to use, it's amazing how many aspects of life get a calculator.
  • Bookmark this collection — it's hard to imagine you won't someday need it.

It's true that high-school calculus teachers torture their students with them, but it's also true that once some degree of mastery is in hand. Mathematicians love a good — efficient, clever, and useful — formula.

These things aren't just for classrooms or advanced scientific applications, either. While it's amazing that formulas predict what will happen if we slingshot a spacecraft around some distant celestial body, they can also be part of our earthly lives calculating all sorts of everyday things.

In any event, for many math heads (carefully typed), slinging formulas together and inventing new calculators is just plain fun. Last week, for example, UK physicist Steven Wooding sent us the link to a calculator he and a friend constructed that predicts contactable alien civilizations. That was fun, but the site to which he directed us is nothing short of dazzling: It's called Omni Calculator, and it's a mind boggling repository of 1,175 calculators whose purpose is to help everyone get to the right answers in their personal and professional lives.

A mathematical treasure chest

floating math equations

Image source: Alexey Godzenko/Shutterstock

Want to know exactly how many balloons it would take to send your house airborne, as in the Pixar's "Up"? No problem. Hate running unexpectedly out of toothpaste en route to bed? Live your best life. Ditto toilet paper.

Some of the calculators are pretty profound, too, such as the Every Second calculator that shows just how much happens in the world every 60th of a minute — it's an enthralling set of numbers.

Fun stuff aside, Omni Calculator is an absolutely staggering collection, an incredible resource for normal people and professionals—from doctors, to chemists, to financial advisers, to construction teams, and more.

Who is behind Omni Calculator?

color blocks with the four basic math symbols

Image source: rawf8/Shutterstock

Omni Calculator is the project of a Polish startup of 24 people dedicated to helping others solve all of the small math problems in their daily lives. The company manifesto:

"In a surprisingly large part, our reality consists of calculable problems. Should I buy or rent? What's my ideal calorie intake? Can I afford to take this loan? How many lemonades do I need to sell in order to break even? Often times we don't solve these problems, because we lack knowledge, skills, time or willingness to calculate. And then we make bad, uninformed decisions?"

Omni Calculator is here to change all that — we are working on a technology that will turn every* calculation-based problem trivial to solve for anyone.

The asterisk says, "within reason."

It all started when founder Mateusz Mucha built a unique web calculator. It could calculate in any direction without a fixed input or output. He invested $80 in translating his Percentage Calculator into 15 languages and stood back as the app was downloaded 4 million times, and counting.

At some point Mucha changed his goal: "Instead of calculating one thing, we'll calculate all of them — for everybody." To serve this aim, all of Omni Calculator's calculators are free to use, developed by the company in collaboration with all sorts of experts.

Go spend some time looking around and bookmarking tools for your own use. You're pretty much guaranteed to find something that solves a problem with which you're struggling. At the very least you'll come across some amazing calculators that will get you thinking about unexpected things.

COVID calculators

Omni Calculator also provides a special set of calculators that allow you to crunch COVID-19 numbers for yourself, from a social distancing calculator to one that can predict when your next stimulus check should be due.

Why we can stop worrying and love the particle accelerator

By delving into the mysteries of the Universe, colliders have entered the Zeitgeist and tapped the wonders and fears of our age.

Peter Macdiarmid/Getty Images
What would happen if you stuck your body inside a particle accelerator?
Keep reading Show less

New algorithm computes how to find those lost at sea

Researchers devise an effective new predictive tool for maritime first-responders.

Image source: PHOTO JUNCTION/Shutterstock/Big Think
  • Predicting the locations of objects and people lost at sea is devilishly difficult.
  • MIT and other institutions have developed a new algorithm that identifies floating "traps" that can attract floating craft and people.
  • The new TRAPS system has just completed a successful first round of testing.

When the first pieces of Malaysian Air Flight 370 finally turned up in July 2015, they were found on Réunion Island off the eastern coast of Africa in the Indian Ocean, thousands of miles from the best-guess location of where the plane went down. Experts weren't especially surprised at the drift, given the complexities of the ocean.

Finding a missing craft or person at sea in a hurry is a nightmare for first responders, and the math involved in tracking survivors — and debris — is anything but simple, given the sea's ever-changing mix of wind, weather, and wave conditions.

Researchers at MIT, the Swiss Federal Institute of Technology (ETH), the Woods Hole Oceanographic Institution (WHOI), and Virginia Tech recently announced the first successful trials of their new "TRAPS" system, a system they hope will provide faster, more accurate insights into the floating locations of missing objects and people by identifying the watery "traps" into which they're likely to be attracted. The team's TRAPS research is published in the journal Nature Communications.

According to Thomas Peacock, professor of mechanical engineering at MIT, "This new tool we've provided can be run on various models to see where these traps are predicted to be, and thus the most likely locations for a stranded vessel or missing person." He adds that, "This method uses data in a way that it hasn't been used before, so it provides first responders with a new perspective."

A Eulerian approach

Image source: MIT

The TRAPS acronym stands for "TRansient Attracting Profiles." It's an algorithm based on a Eulerian mathematical system developed by lead study author Mattia Serra and corresponding author George Haller of ETH Zurich. It's designed to discover hidden attracting fluidic structures in an onrush of changing data.

The traps the researchers seek are regions of water that temporarily converge and pull in objects or people. "The key thing is," says Peacock, "the traps may not have any signature in the ocean current field. If you do this processing for the traps, they might pop up in very different places from where you're seeing the ocean current projecting where you might go. So you have to do this other level of processing to pull out these structures. They're not immediately visible."

The new algorithm crunches through data representing the most reliable available wave-velocity snapshots at the last-known position of the missing item, and rapidly computes the location nearby traps in which a search is likely to be productive. As velocity data is continually updated, so is TRAPS.

Comparing the new Eulerian algorithm with previous Langrangrian predictive methods, Serra says, "We can think of these 'traps' as moving magnets, attracting a set of coins thrown on a table. The Lagrangian trajectories of coins are very uncertain, yet the strongest Eulerian magnets predict the coin positions over short times."

At sea

Image source: MIT

Theory is one thing, and functioning out on the real, maddeningly complex ocean is another. "As with any new theoretical technique, it is important to test how well it works in the real ocean," says Wood Hole's Irina Rypina.

The study authors were pleased — and surprised — at how well TRAPS worked. Haller says, "We were a bit skeptical whether a mathematical theory like this would work out on a ship, in real time. We were all pleasantly surprised to see how well it repeatedly did."

The researchers tested TRAPS off Martha's vineyard in the Atlantic Ocean in 2017 and 2018. WHOI sea-going experts assisted as they attempted to track the trajectories of a range of floating objects — buoys and mannequins among them — set into the water at various locations.

One challenge is that different objects may behave in their own ways in the ocean. "These objects tend to travel differently relative to the ocean because different shapes feel the wind and currents differently," according to Peacock.

"Even so," says Peacock, "the traps are so strongly attracting and robust to uncertainties that they should overcome these differences and pull everything onto them."

In their experiments, the researchers tracked freely floating objects for hours via GPS as a way to verify the TRAPS system's predictions. "With the GPS trackers, we could see where everything was going, in real-time," says Peacock. Watching the objects move via GPS, the researchers, "saw that, in the end, they converged on these [predicted] traps."

Anchors aweigh

The researchers now have sufficient faith in TRAPS that they plan on sharing it soon with the U.S. Coast Guard. Says Peacock:

"People like Coast Guard are constantly running simulations and models of what the ocean currents are doing at any particular time and they're updating them with the best data that inform that model. Using this method, they can have knowledge right now of where the traps currently are, with the data they have available. So if there's an accident in the last hour, they can immediately look and see where the sea traps are. That's important for when there's a limited time window in which they have to respond, in hopes of a successful outcome."

Quantcast