Did the moon appear larger 4 million years ago?

Not to any significant extent.

Even at 4 cm a year, over 4 million years, that's about 16 million cm. That sounds like a lot, but 16 million cm is only 16 km.

At present, the average distance from the Earth to the moon is 385 000 km. A difference of 16 km is very minute and would not significantly affect its appearance.

Also, for what it's worth, the distance from the Earth to the Moon varies by tens of thousands of kilometers over the course of the year (like most objects, its orbit is not a perfect circle). Its maximum distance is about 405 400 and its minimum distance is about 362 600 km. Even these differences only make a marginal difference to its appearance. A 16 km difference in its average distance is virtually inconsequential.

Although you are correct, over very long time periods, this would be significant. 4 million years is just not long enough.

If you were to be magically chronotransported 4 million years ago, you would not notice the difference, although you could measure it with relatively simple instruments.

It is 4 cm per year.

times 4 million, that's 16 million cm,

=16,000,000 cm = 160,000 m = 160 km

4 million years ago, the Earth was just as much covered by oceans as it is today (and the rate of recession of the Moon's orbit is tied to the tides). The tidal effect is inversely proportional to the CUBE of the distance, so that as the Moon was a bit closer, the rate of recession would have been a tiny bit more than 4 cm per year.

So, just for the fun of it (and to make calculations easier), let's say that it was closer by 192.2 km

The average distance is presently 384,400 km so that the Moon was then 1/20 of 1% closer

(in fraction = 0.0005); measurable but not observable.

Of course, the difference in appearance between the Moon at perigee (closest to Earth on its elliptical orbit) and the Moon at apogee (furthest point on its orbit) is a lot more than that (it can be as much as 12%, with one happening a mere 2 weeks after the other) and still most people don't notice unless you point it out to them. Therefore, to measure a difference of 1/10 of 1 %, you'd need to take precise measurements over a period of many lunar orbits (many months) to get it accurate enough.

Observer a quarter taped to a wall 9 feet away. Next move closer by 1/32 of an inch. Does it appear bigger to you?

<QUOTE>moves aaway from the earth at a rate of 2 cenemeters every century.</QUOTE>

At the current time. It doesn't mean that rate has always been the same.

<QUOTE>would it just be known through mathematics</QUOTE>

You don't know distances "through mathematics" any more than you know how to paint through color. If you want to measure distances or velocities, you still have to make measurements; "using mathematics" is not enough.

Yes it did.

The moon is moving away from the earth at rate of 3.8 centmers PER YEAR, NOT CENRY..

"..The Moon's orbit (its circular path around the Earth) is indeed getting larger, at a rate of about 3.8 centimeters per year. ..."

http://curious.astro.cornell.edu/about-us/37-our-s...

Yes, the moon DID appear larger 4 million years ago, but that was BEFORE the species homo sapiens had evolved.

Your facts are wrong. 3.8 centimeters = 1.625 inches PER YEAR, NOT PER CENTURY.

It's moving away at 2 cm/century TODAY, which is a big difference than saying that it's moving at some constant 2 cm/century away from us.

Yes, the moon was closer in the past and like all objects it appears larger when it's closer to the observer.