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Magnitude
The Scale of the Universe
Contributors
By Megan Watzke
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In Magnitude, Kimberly Arcand and Megan Watzke take us on an expansive journey to the limits of size, mass, distance, time, temperature in our universe, from the tiniest particle within the structure of an atom to the most massive galaxy in the universe; from the speed at which grass grows (about 2 to 6 inches a month) to the speed of light. Fullyillustrated with fourcolor drawings and infographics throughout and organized into sections including Size and Amount (Distance, Area, Volume, Mass, Time, Temperature), Motion and Rate (Speed, Acceleration, Density, Rotation), and Phenomena and Processes (Energy, Pressure, Sound, Wind, Computation), Magnitude shows us the scale of our world in a clear, visual way that our relatively mediumsized human brains can easily understand.
Excerpt
INTRODUCTION
We want to take you on a journey
to explore some of the lightest and heaviest, fastest and slowest, hottest and coldest, largest and smallest, loudest and quietest phenomena in the Universe.
It can be difficult for us to conceptualize the magnitude of such phenomena at both the largest and smallest ends of the spectrum, because these sizes, speeds, masses, and quantities are so far outside the realm of our own experience. The notion of the tiniest particle within the structure of an atom or the vastness of a black hole at the center of a galaxy is impossible for us to truly fathom. But, while the concept of magnitude can be challenging, it’s not insurmountable. Understanding magnitude in the extreme just requires the right tools: not hammers and screwdrivers, but rather the intellectual tools that allow us to explore these concepts in a clear way. That’s where the language of science comes in.
In a world such as ours, it would be impossible to cover every example or aspect of magnitude. Also, we couldn’t possibly include or define every type of unit that magnitude is measured in, but, thankfully, the Internet is full of helpful conversion calculators if you take a look. We hope, however, that you enjoy our selection of what we think are some of the most interesting ways to picture the scale of our Universe.
Orders of Magnitude
In everyday language, “orders of magnitude” connotes the idea of the expansion of size in some significant way. In science, there is a more precise definition.
Scientifically speaking, an order of magnitude of a number usually refers to the approximate value of that number, measured in powers of ten—in other words, where that number sits on a scale that measures ones, tens, hundreds, etc. So 10 and 20 are the same order of magnitude, but 100 is one order of magnitude larger. Between 10 and 1,000, there are two orders of magnitude, and so on.
Let’s think of this another way. If you recall a number line from school, it looks something like this:
Each step you take on this number line involves the change of one (move to the right to add one to your value, or subtract one if you move to the left).
With orders of magnitude, the math is a bit different. Instead of adding (or subtracting) a set amount for every step you take on the number line, you multiply (or divide) by a prescribed amount. It looks something like this:
This is powerful. On the first number line, we went up by a value of 5 in 5 steps. Simple enough. But in the second number line, we moved up by a value of 100,000 in the same number of steps. We need this turbocharged way of changing values in order to depict the awesome range of magnitudes, both large and small, that we’ll be exploring in our known Universe.
Linear versus Logarithmic Scales
Because scientists, engineers, and other technicians so often need to present values that stretch over many orders of magnitude, they have developed a visual way to show this. It’s called the logarithmic scale.
Let’s look at a runofthemill ruler like the one you used in elementary school. For every big dark line on the ruler, you are taught to add one inch or centimeter. If you move the same distance again, you add another inch or centimeter. Three steps equal three inches or centimeters, and so on. This is called a linear scale, meaning one move is the equivalent of adding—or subtracting—one unit of distance (in the case of a ruler, that is one inch or centimeter).
In a logarithmic scale, you don’t add or subtract for every step, you multiply or divide depending whether you are moving to the right or to the left. The most common form of a logarithmic scale uses the number ten as the base, multiplied by itself one, two, three, etc., times.
So the first step on our logarithmic ruler represents 10 × 1, which is 10. The second step on this logarithmic ruler is 10 × 10, or 100. The third step is 10 × 10 × 10, which equals 1,000, which means we’ve moved up three orders of magnitude. In other words, after only taking three steps on a logarithmic scale, we’ve quickly reached 1,000, as opposed to the thousand steps that would have been required on a ruler using a linear scale.
This is what makes logarithmic scales so helpful when depicting the magnitude of things or behaviors that have a huge range. In this book, we will make it clear whether we’re talking about a linear or a logarithmic scale with each different phenomenon.
Scientific Notation
You can see that as the logarithmic scale continues to grow, we will quickly be awash in a sea of zeroes representing huge numerical values. Fortunately, science has a simpler system for expressing these values.
Let’s say you have a million dollars. You could choose to express your vast fortune in writing as $1,000,000. Likewise, a billion dollars could be written as $1,000,000,000, and a trillion would be $1,000,000,000,000, and so on.
What happens if you want to multiply your trillion dollars by another million? That amount turns out to be $1,000,000,000,000,000,000. Writing out all those zeros starts to become a real pain. Although with a million trillion dollars on hand, you could probably hire someone to write it for you, there is another way.
Enter scientific notation. In our example, when a trillion dollars (a one followed by twelve zeroes) was multiplied by one million (with six zeroes), the amount came out to be the number 1 followed by 18 zeros. Another way to write that is this:
10^{18}
The 18 in this example is called the exponent, and it means that the number 1 is followed by 18 zeroes. If the exponent were 999, it would mean that the number you were expressing is a one followed by 999 zeroes.
So one million can be written as
1,000,000, or as 10^{6}.
A billion is
1,000,000,000, or 10^{9}.
A trillion can either be
1,000,000,000,000, or 10^{12}.
And so on.
The key to understanding scientific notation in this book is that for every number the exponent goes up, you are multiplying by a factor of ten. Conversely, if the exponent goes down by one, you are dividing by ten.
Multiplying with Exponents
You might have noticed that when we multiplied a million by a trillion, we ended up with the exponent of 18. This is also the same as adding the exponents (10^{6} and 10^{12}) of the million and trillion. That’s the way to quickly and accurately multiply two numbers in scientific notation—simply add the two exponents together to get the new value.
There will be times in this book that you will see numbers in scientific notation in which the exponent has a negative sign in front of it like this:
10^{−18}
When that negative sign appears, it means we have to move the other direction on our orderofmagnitude number line, which is to say we divide by ten. Once again in this example, there are 18 zeroes, but the decimal point is to the left of them and the one is on the right. This value, therefore, translates into
0.0000000000000000001
There are many examples in this book where things with very tiny values may surprise and interest you. Note that, no matter how large the negative exponent gets, the number never becomes negative. It just gets closer to zero.
Units, Equations, and Other Fun Stuff
Another very important tool for understanding and expressing magnitude is units.
We use units all of the time in our daily lives, even if we aren’t fully aware of it. How fast is your car going? (Typically we think in miles or kilometers per hour.) How long has it been since something happened? (Given in the number of seconds, minutes, hours, etc.) What is the temperature outside? (Degrees in Fahrenheit or Celsius, most often.) A unit is a way to quantify something in a reliable and consistent form. To put it another way: it’s how we measure things.
Systems of units developed in various pockets of discipline and geography over a wide span of time, which led to the cornucopia of units for practically every physical measurement. Recognizing what a mess this can make, some experts got together in an international consortium to sort it all out.
The current system is called the International System of Units, but is better known by the initials SI (for the French version of the name, Le System International d’Unites). At the heart of the SI is the metric system. The building block for measuring distance or length is the meter, and for mass it’s the kilogram, and so on. There are seven “base” units, each of which covers a singular physical property: length, mass, time, electric current, temperature, quantity of substance, and intensity of light.
SI Units
Throughout this book, we will use SI units. This will allow you to know that we are comparing the proverbial apples to apples instead of apples to oranges and let you appreciate the differences in magnitude at a relatively quick glance.
LENGTH: METER (m)
The official definition of a meter is the distance light—a ray of electromagnetic energy—travels in a vacuum in 1/299,792,458 of a second (in exponential form that would be 3.33564095 × 10^{−9} second). Other ways to think of a meter are that it’s 100 centimeters (cm), 1,000 millimeters (mm), or 1/1000th of a kilometer (km). In the United States you might think of it in terms of the more familiar inches: about 39.37 inches, or a little longer than a yardstick.
We can also go much smaller in size, from the micrometer or micron at 0.000001 (10^{−6}) m, to the nanometer (nm) at 10^{−9} m, to the Ångström (or Å) at 10^{−10} m, or 0.1 nm.
Everyday examples in meters:
5 km race,
1meter stick,
height of door (2 m),
diameter of AAA battery (10.5 mm),
thickness of a dime (1.35 mm).
MASS: KILOGRAM (kg)
A kilogram is the SI unit for mass. Originally, it was meant as the quantity of mass in one liter of pure water. Officially, it is the amount equal to a platinumiridium measure that resides at the International Bureau of Weights and Measures outside of Paris, France. In the United States you might be more familiar with its comparison in pounds (lb) at about 2.2 lbs.
It’s important to note that kilograms are a measurement of mass, while pounds are a measurement of weight. An object’s mass measures how much matter is in the object. For weight, you have to take into consideration the force of gravity. For example, on the surface of Mars, where the pull of gravity is only about 37 percent of that on Earth, a mass of 1 kg weighs only 0.814 lb. And out in space, if you’re orbiting Earth aboard the International Space Station, or perhaps speeding toward Mars in a spaceship, a mass of 1 kg would be effectively weightless. So if you want to lose weight, you can just go into space. But if you want to lose mass, you’ll have to stick with a healthy diet and exercise.
Grams are also commonly used when considering smaller objects, at about 1/1000th of a kilogram. On the larger side, 1,000 kg is equal to one tonne, or one metric ton.
Everyday examples in kilograms:
mass of a small car
1,000 kg
or 1 metric ton,
mass of a cow
400 kg,
average mass of a woman
55 kg,
mass of a liter of water or skim milk
1 kg,
mass of a bag of white flour
10 kg,
mass of a paperclip
1 g.
TIME: SECOND (S)
The second is familiar as a unit of time. In comparison to the minute or hour, it is 1/60th of a minute, or 1/3,600th of an hour. But how is the second officially determined? Originally, it was somewhat vaguely defined as 1/86,400th of a “mean solar day,” where the mean solar day is the time between successive passages of a hypothetical sun moving at a fixed speed across an imaginary line in the sky.
This recording of time was therefore not accurate enough in its existing format. Instead, we moved to the “atomic clock,” where properties of an atom are used to provide a definition of time, because excited atoms can produce light waves with welldefined frequencies (essentially, vibrational rates of atoms are very precise and can be observed and counted). So for atomic time, the second became officially defined as the amount of time needed for a single cesium133 atom to perform 9,192,631,770 complete periods.
Moving into smaller units, the millisecond (ms) is one thousandth, the microsecond is one millionth, and the nanosecond is one billionth of a second. Typically, larger units of seconds are used with exponents, and kiloseconds (1,000 seconds) are not often used.
Everyday examples in seconds:
blink of an eye 300 to 400 ms,
taking a breath in 3 s,
seconds in a minute 60 s,
seconds in an hour 86,400 s,
seconds in an average calendar year 365.25 days = 31,557,600 s.
ELECTRIC CURRENT: AMPERE (A or amp)
An electric current is a flow of electric charge, for example, in electric circuits. The ampere is the official SI unit, which is defined as the flow of electric charge across a surface at the rate of one coulomb per second. A coulomb (abbreviated C) is the charge moved by a constant current of one ampere across one second.
Genre:

"How big is big? How small is small? As an astronaut and citizen explorer, I love having someone explain some of the more puzzling aspects of our universe to me in terms that make sense. With Magnitude, my brain cried "Eureka!" every time I turned the page."
—Cady Coleman, PhD, former NASAAstronaut  "We live in a universe bigger and smaller than our brains can fathom. Magnitude is an enjoyable and essential guide to appreciating our place among it all."—Joe Hanson, author and host of It's Okay to Be Smart
 "Arcand and Watzke have crafted a masterpiece. A mustread for anyone wishing to appreciate the richness of the cosmos from its microscopic building blocks to its largest structures."—Avi Loeb, chair, Harvard Astronomy department

"Through clear text and illuminating illustrations, the authors tackle questions ranging from 'how does the mass of a human eyelash compare to the mass of the black hole at the center of our galaxy?' to 'how fast does a dentist's drill rotate?' A fascinating journey through the measure of all things."
—Marco Livio, astrophysicist, and author of Why?: What Makes Us Curious  "Magnitude brilliantly illustrates the relative scale of so many aspects of the universe that you will feel so much smarter about EVERYTHING after reading this!"—Curtis Wong, principal researcher, Microsoft Research
 On Sale
 Nov 21, 2017
 Page Count
 192 pages
 Publisher
 Black Dog & Leventhal
 ISBN13
 9780316502900
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