Spacial Dimensions

The other day, I was having a spirited conversation with my brother, and although I have no idea what we started off talking about, we eventually ended up talking about the fourth spacial dimension. We all know about the first dimension, which consists of a perfect line, and the second dimension, which consists of perfect plane, but we never get past the third dimension, which consists of three dimensional objects, like everything in your room. My brother and I decided that it was impossible to perceive of the fourth dimension. Much like a being in the second dimension can't perceive of someone in the third dimension. Do you follow so far? In general, although we can hypothesize about a hypothetical fourth dimension, there is no way we can understand how to perceive it. That's where most people would end the conversation. Sure, we can't perceive the fourth dimension, so let's stop talking, right? I don't know why, perhaps because of our thirst for knowledge or because we were bored, we continued on the topic. This is when it started to get tricky. We decided to look back on the first and second dimensions, and realized that there was no physical evidence of the first or second dimension, only a conceptual model that is accepted and unquestioned. In essence, although we know that the first dimension is a single point, there is nothing in our universe (yet) that truly represents a single point. A single point is always three-dimensional, because we live in a three dimensional world! For example, even a dot the size of a single atom is still a three dimensional model of matter. Draw the smallest point with a pencil, and you will still have a three dimensional object of granite. This blew my mind! The only logical conclusion that my brother and I could come up with is this: There is no physical first, second or fourth dimensions. It cannot exist in our three dimensional reality. Instead, we have an idea of the first and second dimensions, that cannot be verified with actual observation. Similarly, even if the fourth dimension were to exist, it would be unable to make true contact with us, much like we cannot truly observe the second dimension. Additionally, we cannot perceive of a fourth dimension much like the second dimension cannot perceive of the third. The fourth dimension would be able to perceive of a third dimension but not be able to observe it. We live in a physically three dimensional world, and our three dimensional brains developed ideas of other spacial dimensions that can only be represented using three dimensional models. Crazy, no? Tell me what you think about this conclusion. Did I make a mistake in my logic? Does the first and second dimensions exist only within our minds?