The observable universe is billions of light years wide, and expanding in such a way that it’s difficult to even discuss its size in a simple way. As a result, it can be difficult to visualize the universe as a whole.

From the big bang to now.

One popular representation is to show a kind of timeline, starting with the big bang, and showing the evolution of the universe from then to now. It’s a nice way to represent the time scale of the cosmos, but visualizing the shape is a bit more difficult. One way this can be done is to use a logarithmic scale. Perhaps the most famous use of this scale is the Charles and Ray Eames video Powers of Ten, which showed the universe at ever increasing and ever decreasing logarithmic scales.

If you map the universe on a logarithmic scale, then you can create an image of the cosmos with the Sun in the center and the cosmic microwave background as a bounding circle. It looks a bit like a pre-Copernican view, but that’s just a trick of logarithms. Rather than a linear scale, where each step away from the Sun is the same, if the first step is a light year, the second is ten light years, then a hundred, a thousand, and so on. With logarithms you can fit the entire universe on a meaningful scale.

The one big disadvantage of such an image is that it gives the impression of a “center” to the universe as well as an “edge.” The one advantage is that it clearly shows why we see the cosmic background radiation coming from all directions, and how looking deeper into the sky gives us a view of the early universe.

Any graphical representation of the cosmos will have strong and weak points, but a logarithmic view is a great way to show the universe in a nutshell.

The post The Universe in a Nutshell appeared first on One Universe at a Time.

We generally think of numbers as a linear progression from 1 to 2 to 3, etc.  We also tend to measure things around us on a linear scale.  A ten hour road trip, for example, is very different from a one hour trip.  In the sciences, however, it is often more useful to look at things on a logarithmic scale.

A logarithm scale is one that focuses on the overall size, or  “order of magnitude” of objects.  For example, if something has a mass of 100 kilograms, then on a log scale it would be 2, since 100 = 10 x 10.  Likewise, 1,000 would be 3 on a log scale, since 1,000 = 10 x 10 x 10.  In general, you can base your log on any number you want.  The number 128 is 2 x 2 x 2 x 2 x 2 x 2 x 2, so you can say its log is 7 in “base 2.”  Perhaps the most common base in the physical sciences is the so-called natural log, which is a log of base e, where e is an irrational number about equal to 2.71818…

Log scales are so deeply rooted in physical phenomena that even our eyes and ears operate on a logarithmic scale.  This is why the loudness of sound is measured in the logarithmic decibel scale, and the brightness of stars is measured in apparent magnitude, which is a logarithmic scale of luminosity.   Even young children tend to perceive numbers on a logarithmic scale before we teach them linear counting.

Perhaps the most famous demonstration of a logarithmic scale is the short movie “Powers of Ten,” by Charles and Ray Eames.

While it’s a bit outdated, it shows how the universe can be viewed on a logarithmic scale, and how on such a scale humans exist roughly in the middle of the very large and the very small.

The post Logs of Nature appeared first on One Universe at a Time.