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Now, I know what you must be thinking: How can all of these estimates produce a reasonable answer?Well, it's rather simple.In any Fermi problem, it is assumed that the overestimates and underestimates balance each other out,and produce an estimation that is usually within one order of magnitude of the actual answer.In our case we can confirm this by looking in the phone book for the number of piano tuners listed in Chicago.What do we find? Pretty incredible, given our order-of-magnitude estimation.But, hey - that's the power of 10.

With this many pianos,how many piano tuners are there?We could begin the process of thinking about how often the pianos are tuned,how many pianos are tuned in one day,or how many days a piano tuner works,but that's not the point of rapid estimation.We instead think in orders of magnitude,and say that a piano tuner tunes roughly 10 to the second pianos in a given year,which is approximately a few hundred pianos.Given our previous estimate of 10 to the fourth pianos in Chicago,and the estimate that each piano tuner can tune 10 to the second pianos each year,we can say that there are approximately 10 to the second piano tuners in Chicago.

While this doesn't tell us exactly how many people live there,it serves an accurate estimation for the actual population of just under three million people.So if there are approximately 10 to the sixth people in Chicago,how many pianos are there?If we want to continue dealing with orders of magnitude,we can either say that one out of 10 or one out of one hundred people own a piano.Given that our estimate of the population includes children and adults,we'll go with the latter estimate,which estimates that there are approximately 10 to the fourth,or 10,000 pianos, in Chicago.

At first, there seem to be so many unknowns that the problem appears to be unsolvable.That is the perfect application for a power-of-10 estimation,as we don't need an exact answer -an estimation will work.We can start by determining how many people live in the city of Chicago.We know that it is a large city,but we may be unsure about exactly how many people live in the city.Are the one million people?Five million people?This is the point in the problem where many people become frustrated with the uncertainty,but we can easily get through this by using the power of 10.We can estimate the magnitude of the population of Chicago as 10 to the power of six.

Fermi problems are named after the physicist Enrico Fermi,who's famous for making rapid order-of-magnitude estimations,or rapid estimations,with seemingly little available data.Fermi worked on the Manhattan Project in developing the atomic bomb, and when it was tested at the Trinity site in 1945,Fermi dropped a few pieces of paper during the blast and used the distance they traveled backwards as they fell to estimate the strength of the explosion as 10 kilotons of TNT, which is on the same order of magnitude as the actual value of 20 kilotons.One example of the classic Fermi estimation problems is to determine how many piano tuners there are in the city of Chicago, Illinois.

We can use the power of 10 as a tool in making quick estimations when we do not need or care for the exact value of a number.For example, the diameter of an atom is approximately 10 to the power of negative 12 meters.The height of a tree is approximately 10 to the power of one meter.The diameter of the Earth is approximately 10 to the power of seven meters.The ability to use the power of 10 as an estimation tool can come in handy every now and again,like when you're trying to guess the number of M&M's in a jar,but is also an essential skill in math and science,especially when dealing with what are known as Fermi problems.

Whether you like it or not,we use numbers every day.Some numbers, such as the speed of sound,are small and easy to work with.Other numbers, such as the speed of light,are much larger and cumbersome to work with. We can use scientific notation to express these large numbers in a much more manageable format. So we can write 299,792,458 meters per second as 3.0 times 10 to the eighth meters per second.Correct scientific notation requires that the first term range in value so that it is greater than one but less than 10,and the second term represents the power of 10 or order of magnitude by which we multiply the first term.

Today, the test is still controversial,and many people assume it has been disproven.But a massive 2013 review of all the existing Rorschach research showed that when administered properly the test yields valid results,which can help diagnose mental illness or round out a patient psychological profile.It hardly a stand-alone key to the human mind test is.But its visual approach and lack of any single right answer continue to help psychologists paint a more nuanced picture of how people see the world.Bringing us one step closer to understanding the patterns behind our perceptions.

Without its inventor to keep it on track,the test he had methodically gathered so much data to support began to be used in all sorts of speculative ways.Researchers gave the test to Nazi war criminals,hoping to unlock the psychological roots of mass murder.Anthropologists showed the images to remote communities as a sort of universal personality test.Employers made prejudiced hiring decisions based on reductive decoding charts.As the test left clinics and entered popular culture its reputation among medical professionals plummeted,and the blots began to fall out of clinical use.

It could even diagnose some conditions difficult to pinpoint with other available methods.In 1921,Rorschach published his coding system alongside the ten blots he felt gave the most nuanced picture of people perceptual approach.Over the next several decades,the test became wildly popular in countries around the world.By the 1960s,it had been officially administered millions of times in the U.S. alone.Unfortunately, less than a year after publishing the test,Hermann Rorschach had died suddenly.

Others gave unusual and delightful descriptions.Responses were as varied as the inkblots,which offered different kinds of perceptual problems ome easier to interpret than others.But analyzing the test-taker overall approach yielded real insights into their psychology.And as Rorschach tested more and more people,patterns began to pile up.Healthy subjects with the same personalities often took remarkably similar approaches.Patients suffering from the same mental illnesses also performed similarly,making the test a reliable diagnostic tool.

Did the color on some inkblots help them give better answers,or distract and overwhelm them?He developed a system to code people responses,reducing the wide range of interpretations to a few manageable numbers.Now he had empirical measures to quantify all kinds of test takers:the creative and imaginative,the detail-oriented, the big-picture perceivers,and flexible participants able to adapt their approach.Some people would get stuck,offering the same answer for multiple blots.

And when he started working at a mental hospital in eastern Switzerland,he began designing a series of puzzling images to gain new insight into this enigmatic process.Using his inkblot paintings,Rorschach began quizzing hundreds of healthy subjects and psychiatric patients with the same question:what might this be?However, it wasn what the test subjects saw that was most important to Rorschach,but rather, how they approached the task.Which parts of the image did they focus on or ignore?Did they see the image moving?

Invented in the early 20th century by Swiss psychiatrist Hermann Rorschach,the Rorschach Test is actually less about the specific things we see,and more about our general approach to perception.As an amateur artist Hermann was fascinated by how visual perception varies from person to person.He carried this interest to medical school,where he learned all our senses are deeply connected.He studied how our process of perception doesn just register sensory inputs,but transforms them.

Take a look at this image.What might this be?A frightening monster?Two friendly bears?Or something else entirely?For nearly a century,ten inkblots like these have been used as what seems like an almost mystical personality test.Long kept confidential for psychologists and their patients,the mysterious images were said to draw out the workings of a person mind.But what can inkblots really tell us,and how does this test work?

And the more they melt, the less sunlight they're able to reflect,making the oceans warm even faster.Sea levels rise, coastal populations are threatened with flooding,natural ecosystems are disrupted,and the weather becomes more extreme over time.Climate change may effect different people and places in different ways.But, ultimately, it's a game that we're all stuck playing.And unlike in Tetris,we won't get a chance to start over and try again.

But burning these fuels also injected new carbon blocks into Earth's Tetris game.At the same time, we cleared forests for agriculture,reducing the Earth's ability to remove the blocks.And since 1750, the amount of carbon in the atmosophere has increased by 40%,and shows no sign of slowing.Just like in Tetris, the more blocks pile up,the harder it becomes to restore stability.The extra carbon dioxide in the atmosphere accelerates the greenhouse effect by trapping more heat near the surface and causing polar ice caps to melt.

Though the amount of carbon in the atmosphere has varied through ice ages and astroid impacts,over the past 8,000 years the stable climate we know took shape,allowing human civilization to thrive.But about 200 years ago,we began digging up that old carbon that had been stored in the soil.These fossil fuels, coal, oil and natural gas are made from the buried remains of plants and animals that died long before humans evolved.The energy stored inside them was able to power our factories, cars and power plants.

What's the connection to climate?Well, when that carbon dioxide is in the air,waiting to be reabsorbed,it traps a portion of the sun's heat,which would otherwise escape to space.Earth has played a version of this game with blocks of carbon.It creates a blanket of warmth,known as the greenhouse effect,that keeps our Earth from freezing like Mars.The more carbon dioxide blocks hang out in the atmosphere waiting to be cleared,the warmer Earth becomes.

To understand climate change,think of the game Tetris.For eons, Earth has played a version of this game with blocks of carbon.They enter the atmosphere as carbon dioxide gas from volcanoes,decaying plant matter,breathing creatures and the surface of the sea.And they leave the atmosphere when they're used by plants during photosynthesis,absorbed back into the ocean,or stored in soil and sediment.This game of Tetris is called the carbon cycle,and it's the engine of life on Earth.