This is a fascinating concept: proving the reality we exist in from within said reality.

It generally can only be conceptualized from a perspective outside that reality or perception of it.

Where-in lies my perspective, in that there are multiple ways to perceive this reality and what it means to each of us as individuals.

While I, like many others, cannot personally relate to the ‘dream experience’, it is no less real to those of you that DO dream, than this reality is to all of us.

I certainly could not convince you that you did not dream, since you yourself had the experience of a dream, and are already convinced of its’ having occurred.

My understanding of what people describe as dreams is something much different than what we experience as this reality.
If not for the simple fact that they can tell the difference between when they are dreaming and when they are not, dreams are also described as having a different perception of the 5 senses.
Smells don’t quite smell right, things don’t appear or feel the same. Pain is often described as non-existent in the dream state. “pinch yourself to see if you are awake”, and whatnot.
Events that occur in dreams are often described as unrealistic events.

Not everyone dreams, and not everyone has the same dreams.
Therefore, we can definitively say that dreams are not reality.

For those of us who do not dream, we go to sleep and instantaneously awaken later to find our reality just as intact as we left it. Quite frankly, the thought of having to experience some “non-reality” between the end and beginning of each consecutive day seems like more of a “nightmare” than any scary non-real dreams I have heard people describe.

But what of this reality? The one we all experience together and can, for the most part, agree on aspects of the experience?

For instance, our ability to communicate with one another by various means.
We can send information to one another through any of our 5 primary senses, or even use extensions thereof such as digital communications or radio broadcast.

Is reality real?

Well we first must define what we perceive as reality. At which point we can discuss how real or not real it may or may not be.

If you describe your perception of reality in every minute detail I could only agree up to the point at which your perception of reality differs from my own. Doing this across a wide number of human specimens can give us an idea of the consistencies and inconsistencies in our various perceptions.

But I think the real question is:
Is reality really what we think we are perceiving?

We can feel and object and determine its shape and physical dimensions and in most cases our sense of vision concurs. We can agree on the shape and size of physical objects, and even their weight. I can prove that each of these perceptions is merely subjective and no more real than the dream you claim to have had. But let’s take an example that’s a little easier to understand.

Color

I will exclude for the purpose of discussion, those that we consider color-impaired or those that do not always agree with the common perception of a particular color, and focus on people that do agree.

We can select from various colors a color with an associated nomenclature, let’s say green.
For us, all things green appear to be “green”.
What is green? Well we point at it and say that is green. But what of the actual color each of us see? Do we see the same green? Or do we simply associate whatever color we see as being green because we were told that is green?

The latter is the correct answer. We do not all see the same green, or any color for that matter.
Each eye perceives color differently. But those differences are consistent such that the true color has the same effect when viewed from the same eyes. In other words, we see a color that we associate as green whenever we seen something green, but your green is not the same as my green. And I have no way to communicate to you what those differences are, other than to allow you to see through the lenses of my eye.
Then you can say “oh, that’s what you see as green”. You will quickly want your eyes back because you are used to your own color set.

Each aspect of our perception is experienced differently by each of us. Reality, wether it is real or not, is not exactly what we perceive it to be.