Numbers, especially the very large and very small, can be deceiving. It’s almost impossible for our brains to compute the immense scale in the fields of astronomy or microbiology. Nevertheless, understanding and being able to visualize the incredibly large scale of our universe is valuable.

Let’s take a look at time and distance, and translate smaller units of time into understandably larger units:

1 second equals 1 second
1 million seconds equals 12 days
1 billion seconds equals 30 years
1 trillion seconds equals 30,000 years!

1 millimeter equals 1 mm
1 million mm equals 1 km
1 billion mm equals 1000 km
1 trillion mm equals 1,000,000 km! (this is like going around the world 25 times)

Here’s what $10k, $1 million, and $1 billion looks like:

1 Billion Dollars Visualized

And here’s $1 Trillion:

1 Trillion Dollars Visualized
Understanding these large scales can help us visualize numbers that we might read or hear about.

For example, when you hear that something is “99.999% reliable”, it means there is an error rate of 10 out of a million. Using our references from above, that’s like being offline for only 10 seconds out of 12 days. Or, looking at it from the perspective of “distance”, you can have a tolerance of 10mm (about the width of your pinky finger) for every kilometer.

The phrase “One part per million” is often used by chemists to measure concentrations of substances. One ppm is like having a presence of 1 second in 12 days. And a part per trillion? Only 1 second every 30,000 years!

To help humanity visualize the large scale of our universe, the American Museum of Natural History has produced a movie that begins with a view of the Earth’s Himalayan Mountains and then zooms out: showing the orbits of Earth’s satellites, the Sun, the Solar System, the extent of humanity’s first radio signals, the Milky Way Galaxy, galaxies nearby, distant galaxies, and quasars. Every object in the video has been rendered to scale using the best scientific research available in 2009. The film has similarities to the famous Powers of Ten video, which you can also see below:

And here is the famous Powers of Ten video:

So how does estimating scale and magnitude apply to skepticism and critical thought?

The pseudoscience of Homeopathy is a great example.

The “law of infinitesimals” in homeopathy states that dilution increases the curative power of homeopathy medications. This means that a part-per-million solution of a substance is more medicinally powerful than a part-per-thousand solution, which has in turn more curative power than a part-per-hundred solution. In contrast, many of our modern drugs are ineffective in small quantities and the efficacy increases with dosage.

Let us put modern medicine aside and consider the dosages involved in homeopathy.

Homeopathic medicines often come in 12x, 24x, 28x dilutions (“28x” means the solution has been diluted 28 times) . If a substance were to be diluted 30 times, this means that there would be one part medicine to one trillion quadrillion parts water (or other inert ingredient). That’s a 1 with 27 zeros, or 1,000,000,000,000,000,000,000,000,000. Going back to our “time” example, that the equivalent of being offline 1 second in 10,000,000,000,000,000,000 years!

What does this mean? It means that a homeopathic solution is effectively water. Nothing more. Yet, it is sold, and people buy it. Homeopathy defies the laws of physics and chemistry, but due to effective marketing and a proper lack of FDA involvement, homeopathic “remedies” continue to be sold alongside legitimate medications.

One more reason to think twice before you consider purchasing Snake Oil.


  • JamesDc

    Homeopathy is complete and utter rubbish. Nuff said.

  • Tadej

    Just a friendly reminded: fix the Wikipedia link under “References”; the last (2nd or closing) parenthesis is not included in the actual link.