While it is easier to think of large numbers in terms of logarithms, cause it makes unfathomly large numbers much more palatable, I disagree that it makes scales more intuitive.
1 billion is a very large number, and thinking of it as 10^9 make it seem smaller.
1 trillion is "just" 3 orders of magnitude above 1 billion, and "only" 9 orders of magnitude less than the number of atoms in a mole.
I don't know the answer to making the mind understand scale. I don't think things like "it 's about 2000 football pitches" help either. I don't think "a billion is the number of cubic milimeter in a cubic meter" work either. I don't think the logarithm based "zoom visualization" work either. I just think the brain just cannot picture what those numbers mean. We're not wired to understand those things very well, just as we aren't wired to work with 4+ dimensions
(Author of Mag World here) I'm here to attest that it's worked for me! I see now that I had a fractured collections of number lines in my head (thousands, millionths, billions, and of course all the various units). Since using mag notation and integrating it into my thinking, it has absolutely helped create a grounded "magnitude line" in my head. So I'm not proposing this idly. Notation is a tool of thought (as per Ken Iverson), and using mag notation consistently, turned the advanced method of "logarithms" into a basic perspective of magnitude for me.
Maybe give it a few weeks or months and see if it gets easier for you too.
Focusing on the magnitude instead of the value of a number, changes the perspective when we're talking or thinking in these scales.
From the site:
> The universe is very large, but it is not infinite. All quantities in the universe (distance, time, energy, mass, etc) exist within 50 to 100 orders of magnitude.
> The human species interacts with only 25 of these magnitudes.
Reminds me of the work of Neal Agarwal, e.g.:
https://neal.fun/size-of-space/
https://neal.fun/size-of-life/
https://neal.fun/space-elevator/
https://neal.fun/deep-sea/
While it is easier to think of large numbers in terms of logarithms, cause it makes unfathomly large numbers much more palatable, I disagree that it makes scales more intuitive.
1 billion is a very large number, and thinking of it as 10^9 make it seem smaller.
1 trillion is "just" 3 orders of magnitude above 1 billion, and "only" 9 orders of magnitude less than the number of atoms in a mole.
I don't know the answer to making the mind understand scale. I don't think things like "it 's about 2000 football pitches" help either. I don't think "a billion is the number of cubic milimeter in a cubic meter" work either. I don't think the logarithm based "zoom visualization" work either. I just think the brain just cannot picture what those numbers mean. We're not wired to understand those things very well, just as we aren't wired to work with 4+ dimensions
(Author of Mag World here) I'm here to attest that it's worked for me! I see now that I had a fractured collections of number lines in my head (thousands, millionths, billions, and of course all the various units). Since using mag notation and integrating it into my thinking, it has absolutely helped create a grounded "magnitude line" in my head. So I'm not proposing this idly. Notation is a tool of thought (as per Ken Iverson), and using mag notation consistently, turned the advanced method of "logarithms" into a basic perspective of magnitude for me.
Maybe give it a few weeks or months and see if it gets easier for you too.
Very interesting.
Focusing on the magnitude instead of the value of a number, changes the perspective when we're talking or thinking in these scales.
From the site:
> The universe is very large, but it is not infinite. All quantities in the universe (distance, time, energy, mass, etc) exist within 50 to 100 orders of magnitude.
> The human species interacts with only 25 of these magnitudes.
> The universe is very large, but it is not infinite.
We actually don't know this, it's still an open question.
s/universe/observable universe/