Take the Milky Way, containing 100 to 400 billion stars (let’s take 250 billion).
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Incidentally, the number of US citizens is higher than the number of stars in the Milky Way, so if you find yourself a good way of visualizing the former, you can transfer that understanding to the latter.
The point is that a few orders of magnitude can be visualized / grasped just by adding another step to the ladder, chopping off only as large a step as you can take at a time.
Then even a whole lotta orders of magnitude just become a short sequence of steps, going off of concepts you find more familiar.
I often start with 10^3 as “number of students in my high school”, I have a distinct image of some school photo in the school yard where everyone was on there. After that e.g. the number of images (each showing one yard-full of students) in a photo album. Number of photo albums that could fit in an Ikea shelf. Number of Ikea shelves in a library. Etcetera, though that alone should get you to 10^10 or so.
Suddenly the steep mountain slope has a stairway, and doesn’t seem quite so daunting anymore.
I often start with 10^3 as “number of students in my high school”, I have a distinct image of some school photo in the school yard where everyone was on there. After that e.g. the number of images (each showing one yard-full of students) in a photo album. Number of photo albums that could fit in an Ikea shelf. Number of Ikea shelves in a library. Etcetera, though that alone should get you to 10^10 or so.
Imagining grains of sand can get you to bigger numbers faster.
So, there are more than 100 billion US citizens?
Thanks for noting, corrected.
You’re welcome.
To clarify:
The point is that a few orders of magnitude can be visualized / grasped just by adding another step to the ladder, chopping off only as large a step as you can take at a time.
Then even a whole lotta orders of magnitude just become a short sequence of steps, going off of concepts you find more familiar.
I often start with 10^3 as “number of students in my high school”, I have a distinct image of some school photo in the school yard where everyone was on there. After that e.g. the number of images (each showing one yard-full of students) in a photo album. Number of photo albums that could fit in an Ikea shelf. Number of Ikea shelves in a library. Etcetera, though that alone should get you to 10^10 or so.
Suddenly the steep mountain slope has a stairway, and doesn’t seem quite so daunting anymore.
Imagining grains of sand can get you to bigger numbers faster.