Can We Accurately Express Our Thoughts?
The speed and complexity of our thoughts exceed our abilities of language and communication, specifically our ability to convey complex ideas. We can use symbols as shortcuts, but we still have to deal with “the economics of words“. 
Why is it Hard to Communicate Complex Ideas (and Sometimes Even Simple Ones)?
Our communication woes arises from the discrepancy between the way our brains work (an electro-chemical computer storing sensory information in a matrix of synapses), and the types of communication tools we have (like symbols, body language, numbers, equations, 26 english letters, spoken language etc). Simply put, we have a limited number of tools to express a large array of complex concepts, and that can be frustrating (trust me).
Keeping it simple can be tricky, but arguably, less is best. It has been shown that body language, tone of voice, and simple words are actually more effective communication tools than long rambling sentences.  Perhaps this is why xkcd, “for Dummies”, and “explain it like i’m 5” are so popular.
Before we move on to pondering why we struggle to communicate our thoughts clearly, an excellent introduction to language by Harvard professor Steven Pinker.
TIP: Learn more about the complexities of communication.
Steven Pinker: Linguistics as a Window to Understanding the Brain. What is language?
Why Can’t We Say What We Mean? Why Don’t We Always Mean What We Say?
We can’t say what we mean, because we lack the words to express abstract and complex concepts. We don’t always mean what we say, for the same reason. To understand what another person means we must look at context, subtext, and non-traditional symbols like body language and other less obvious cues.
Why Can’t We Communicate Complex Ideas Easily?
Complex ideas can make sense in our heads, but yet, they commonly seem elusive when we try to speak them or put them to paper.
Human communication problems are rooted in the limitations of our written and spoken language, the way our memory works (big storage capacity, but a lack of accuracy), the many connections between different non-verbal types of information (neural connections and their plasticity), our limited attention spans as humans (our inability to concentrate on what is being communicated), and the general limits of both our biology and the communications tools we currently have at our disposal.
We have amazing long term memories to store lots of data, but getting it out of storage isn’t always easy. Think of trying to explain your love from someone, or the meaning of excellence and virtue, or morality, or even many simpler things.
The following video is a simple overview of how we make memories. See our section on memory for more details.
How We Make Memories – Crash Course Psychology #13
FACT: We can’t even have new ideas without copying, combining, or transforming old ones. Facts like this point to the wide array of reasons “saying what we mean” can feel so frustratingly out of reach sometimes.
Sensory Perception, Sensory Memory, and Semantics
Our brains are more complex than our systems of communication, and this becomes obvious when you take a look at sensory memory.
We pick up on countless sensory signals at almost all times (although our brain factors out most of the signals for us, like our nose for instance). We perceive vastly more than we can consciously think about, we consciously think about more than we express with our syntactic, symbolic, semantics, and the way our brain stores, compresses, and transform sensory information to be useful for everyday life adds another layer of complexity when trying to communicate complex and abstract things.
TIP: See consciousness and the Brain: Deciphering How the Brain Codes Our Thoughts from Amazon or read it online.
How Many Thoughts Does the Average Human Have Per Day?
Another thing that makes it hard to communicate is the sheer amount of thoughts we have per day. Even though there isn’t an exact count, it has been estimated that we have somewhere in the range of 15,000 – 65,000 thoughts per day.
Our short-term working memory can hold about 5 – 7 thoughts at a time, and thoughts stick around for about 20 seconds max.
As one source concluded: “70,000 thoughts per day, that is 3000 per hour, or 50 per minute, or just under one per second”.  
NOTE: There is no solid study on how many thoughts people have per day. As far as I can tell the story goes like this: Deepak Chopra was once quoted as saying that humans had about 15,000 – 65,000 a day. It has been rounded up to 70,000. I’ve traced the 70,000 number back to a sci.psychology Google forum from 1993 where students are playing “he said, she said.” So the 70,000 thoughts factoid should be taken with a grain of salt.
Symbols as a Form of Communication
Luckily, despite our limitations, we can employ many different types of symbolism as communication tools to help us express deep meaning. We also have our favorite ace up the sleeve, technology. Humans can build tools that compensate for our weaknesses. We aren’t the strongest animal on the planet, but we compensate with technology. Cognitive computing and collective intelligence can break through the barriers that our individual minds can not.
The more communication tools we employ, the better we can communicate our wide array of thoughts. That said, even using multiple languages, cognitive ai, internet, symbolism, song, the arts, technology, math, sciences, equations, emojis, mirror neurons, dancing, crowd-sourcing, social media, marketing campaigns, and all our modern tools we can still find ourselves struggling to “organize our thoughts” and “say what we mean” in a simple and clear way on a individual, social, collective, or especially spiritual level.
FACT: Humans are amazing thinkers and we can store a great deal of information in our subconscious, but we struggle with refining and communicating that knowledge. Luckily cognitive AI like Watson shows off our strong point, building tools to do what we can’t.
Charlie Kaufman on Screenwriting. One simple mission – to explain screenwriting to students in 45 minutes. Surely an expert in his field could do such a thing in only a few words. Surely.
Example: I want to express to someone with no background in physics what the nature of mass-energy is. This should be simple, but it isn’t. I can say E=mc2, or I can say mass is potential energy and energy is kinetic energy. Or I can talk about rolling a cold bowling ball down a snowy hill and talking about how the extra snow is relativistic mass. Or I can say everything is energy and vibrations. I can show a video, draw pictures, sing a song. Show a speeding train or a rocket ship and a light clock. I can explain the nature of light, the nature of electromagnetic energy. I can write a poem, or tell a story only using emoji. I can show examples of calculating mass and energy mathematics-wise using light speed as a conversion factor. I can explain square roots. I can talk about Einstein the man, or the history of special relativity. I can use many tools, but I struggle to convey the deep but ultimately simple nature of mass-energy… despite my relative understanding of it.
How to Improve Effective Communication
We may never be able to “say what is on our mind” perfectly, but we can get better at it. Here are some tips:
Learn another Language
Interestingly those who speak more than one language seem to have an advantage.
With English, you get 26 characters to convey everything that is stored in your 86 billion neurons, each with many synaptic connections. There are some concepts that we understand as humans that aren’t represented by words or phrases in English (schadenfreude, areté, and hygge come to mind). Other languages offer different opportunities to make sense of information and convey concepts using words and phrases specific to that language. When we say languages, we mean languages like code, music, and other non-traditional language types as well as verbal languages.  
Humans can’t focus on more than one thing at once; rather our attention is “time-shared” by quickly going back and forth between ideas (multitasking). We also have a limited short-term working memory. This means that sorting out our own ideas and communicating them aren’t just fighting against a limited vocabulary, we are also fighting against limited short-term memories and limited attention spans.
Symbols are your Friend 😀
Luckily, in practice, we get more than 26 characters and the English language to combat our limitations. In a way, we can think of language as symbolism with everything from body language, to math, to emjoi being used to symbolically express ideas.
We can use symbolism, analogy, metaphor, art, music, body language, emotion, etc. to convey what we really mean. The more styles of communication we employ, the more effectively we can communicate to others. Our brains can store ANY stimuli, we aren’t limited to words. It’s harder to convey non-verbal stimuli with words, but we can use the aid of symbolism to take us beyond written or spoken languages. 
Keep it Simple
Just do it, KISS: When it comes to thinking, speaking, and writing less is best. Keep it simple stupid (KISS), and explain it to me like I’m 5. The fewer symbols you can use to convey meaning, the better the communication. People get burned out reading or listening. Our attention is limited; our memory is limited. We can learn a lot about the impact value of brief sound bites from the world’s most effective advertising campaigns.