Ask A Scientist The Elements team answers your most pressing questions!
Q: How big is infinity, really? A: The short answer is that infinity is unimaginably huge. List as many numbers as you can, and you will not have listed them all. Infinity is a concept, not a number, and trying to treat it like one doesn’t work. If you’ve ever taken a calculus course, then you’ll have seen it as a placeholder for getting very close to a value but never quite reaching it, as with limits taken to infinity. The longer answer is that there are actually different sizes of infinity. Take the natural numbers, i.e. 1, 2, 3, 4, etc. There are infinitely many natural numbers. Now take all the even numbers and all the odd numbers. You might think that you’ve split infinity in half, but these groups of numbers (sets) are actually the same size as the set of all natural numbers. If you take the double of every natural number, then you have the set of all even numbers: the number of values in both sets is the same. The same can be done with the odd numbers (1). Now for the weird part: the set of all real numbers, i.e. whole numbers, fractions, and irrational numbers (such as π), is larger than the set of integers (2). We were able to show that the set of odds, evens, and integers were all the same size by connecting every integer to every odd or even number, but that’s impossible to do with the set of all real numbers (2). Showing that is a much more complicated process, but if you’re interested, look up Georg Cantor’s Diagonal Proof to see it.
Q: What makes sunsets pretty? A: The color of the sky which we see is the result of selective scattering of sunlight by air molecules. Visible light includes a spectrum of wavelengths, from violet (shorter wavelengths) to red (longer wavelengths). Typical air molecules are slightly closer in size to violet wavelengths, and therefore reflect and redirect them in all directions and to our eyes more effectively than for longer, redder wavelengths (3). If our eyes weren’t more sensitive to blue light than violet, we would see the clear daytime sky as violet! At sunset and sunrise, however, sunlight takes a much longer path through the atmosphere than during the middle part of the day. The light that reaches our eyes during these times of day appears reddened. A nearly infinite number of scattering events have occurred by the time sunlight reaches us, which remove the violet blue light within the spectrum and leave predominantly red wavelengths! You can imagine the same blue light you see in the sky in the middle of the day becoming increasingly red as it travels to reach somewhere further away where the sun is setting.
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