Reality. That which is ultimately real is beyond words. Words are always one step removed from what is real because they are a method of description, not the thing itself. For example, you may describe your experience right now as sitting in front of your computer or holding your smartphone, browsing net and being calmly aware of the ambient sounds, smells and sights of your home (or wherever you are).

However, if you think about that for a minute, it’s actually an extremely impoverished view of what is really happening. At best, it’s a broadly accurate skeleton and at worst a vague regurgitation of someone else’s description of a similar experience. If you were to become fully aware of what is actually happening right now in your immediate experience, you would find it impossible to describe. Indeed, you would find yourself sitting within an entirely original and infinitely nuanced experience.

Is this useful to know? Hell no. Kind of interesting though to think that the only reality we all share is something that exists beyond all our interminable narratives of difference, power, law, blame, praise etc., simply being, as it always has done and always will do, regardless of the language games we humans play with each other. We spend so much time and energy attempting to forge conditional, sandcastle relationships with each other by creating flimsy linguistic binds when it would be so simple just to stop and recognise the only reality we all already share. Still, where’s the fun in that?

However, words in general are like a shared life raft we all sit on in order to maintain the pretense that our methods of description, however refined they may be, actually have some fundamental ground in reality. We do this because it creates the illusion of control and of a shared-known. The truth is that all language is, strictly speaking, baseless. Nobody in the history of human communication has ever spoken one meaningful word about what is real.

This is because reality, the world of direct experience, is infinite, as is most obviously demonstrated by the electromagnetic spectrum. It cannot be contained by linguistic classifications because it is immeasurable, and language is essentially, ‘the world as measured,’ by conscious thought. Whatever we experience, it can be put into words. Though this is against all that has been said in this thread. Words are symbols. They symbolize things in the world, but they are not the thing. A lot of people seem to mistake the word for the thing, but they are not the same. Words were invented to enable communication. Well, that's not quite right. Symbols were invented to enable communication. Words can be symbols, but so can sounds and drawings and movements.

To my mind, the most problematic thing that can't be expressed in words are things like zen concepts. Oneness, for example. Nonattachment. Presence. They words symbolize something, but it isn't close to the experience we employ them in order to communicate the experience to others. That's why meditation and yoga are so important. You can experience oneness, but it's impossible to explain it very fully in words. You might give another person a few hints about it, but you won't get close to the full experience.

Also, God is something that most people have a difficult time explaining in words. I'm an atheist, so the concept doesn't mean much to me, but I understand that a lot of people refer to some experiences of oneness that I have had, as being close to God. Words are useful, as are many other forms of symbols. However there are things the conscious brain has difficulty apprehending. These things are better understood by the parts of the mind that don't have words. Of course, not having words, or any other symbols, these parts of the mind can't express themselves very clearly. As a result, a lot of people don't think there is any other kind of thinking besides the kind you do in words or symbols. But all that other thinking cannot be expressed in words.

There are quite a few things that fit this criteria but I would like to point out a couple of the common ones that can help you derive all the possibilities for unexplainable ideas. For something to be unexplainable through vocabulary, it would require the audience to be incapable of understanding. This can be compared to trying to explain the atomic theory to a dog. No matter how many words you know or how intelligent your dog is, your dog will never be able to understand what an atom is.

For humans, the number one cliché is the hypothetical situation of describing the color purple to a person that was born blind. In order for him to understand this, he would need to know the foundations of color. It doesn't matter how many ways you try to explain it.. The man will never be able to understand color because he has never experienced it. This can even apply to colorblind people. I personally have tried to discuss the differences between red and green with my father, but since he does not have any foundations for those colors, he will never understand them.

From a mathematical perspective, there are a couple things that cannot be truly explained to a point of complete understanding. The idea of infinity is used so often in calculus courses, but does anyone really have a full understanding of it? Try to picture the quantity of infinity for a second. Let's say you have infinity amount of money. The fact is, you can't. There is no way to comprehend this quantity because it essentially doesn't exist.. But how can it not exist when there are numerous infinite limits and series that all have a solution? This also applies the same way to division by zero and that nasty imaginary number.

Everything we ever learn in life is a comparison to something else. Everything needs a foundation to be understood. When there is nothing to compare something to and there is no foundation for it, than it cannot be understood. You can never explain what it feels like to be in love to a person who never has loved.. What it feels like to have your best friend die to a person who has never experienced loss.. Wisdom and understanding is built on experience, so how can one understand that which they have not experienced? Cheers!