The Science of Comprehension

How We Understand Abstract Concepts

Part II

Beethoven's 5th Symphony

Consider the concept of “Beethoven’s 5th Symphony”. We may have a copy of this symphony on sheet music, or we may have an audio recording of the symphony on a CD, or we may know a musician who has memorized the symphony. In each case the media itself isn't the symphony — the sheet music itself isn't the symphony, the plastic CD itself isn't the symphony, and the musician herself isn't the symphony. Instead, the symphony is the notes represented on the sheet music, or the sound recorded on the CD, or the sound the musician and her fellow musicians in the orchestra make when they play the notes that Beethoven wrote.

The sheet music itself has ink on it arranged in a particular way to form symbols which describe the notes of the symphony. The paper and ink itself are physically real and tangible, and the symbols on the paper are physically visible, but the notes which the symbols represent are considered to be a pure abstract concept. The note “middle C sharp” is the same here as it is over there, and it will be the same tomorrow as it was yesterday. Time and location are irrelevant.

That is why we can make copies of the sheet music, and even though each copy is itself physically unique, the notes represented by the symbols on each copy are considered to be the same. We may photocopy the sheet music, enlarging it so we can better see the notes, or shrinking it so it will better fit in our pocket. We could even use different colored paper and ink. Yet even though the copies themselves may be different sizes and colors, and each copy is physically unique, still each copy represents the same symphony, because the symbols on each copy represent the same notes.

Now consider the audio CD recording of Beethoven’s 5th Symphony. The CD itself has billions of pits etched into it which describe how to recreate the sound. There may exist thousands of copies of this CD recording, and even though every CD is physically unique, they are all considered to be identical because they all describe how to reproduce the same sound.

And consider the musician who has memorized the symphony. The memory is physically stored in her brain, somewhere, somehow.1 Even though every musician in the orchestra has their own brain, and each brain is uniquely different, still they all have memorized the same symphony.

We have an abstract concept of “Beethoven’s 5th Symphony” as being a series of notes, and even though the media on which the notes are recorded may be different, it’s the notes themselves which comprise the symphony.

Here’s a diagram of various ways we can store “Beethoven’s 5th Symphony”:

Media → Symbols → Notes

Media
• Paper
• Plastic
• Brain

Symbols represented by:
• Ink on the Paper
• Pits on the CD
• Neurons & Synapses in the brain

Symbols represent:
• Beethoven’s 5th Symphony
• Beethoven’s 5th Symphony
• Beethoven’s 5th Symphony

Now consider what happens if all the sheet music in the world of Beethoven’s 5th Symphony is burned in a huge bonfire by religious fanatics who believe music is the work of the devil, and every audio recording of Beethoven’s 5th Symphony is melted down and recycled to make a huge army of plastic cows, and everyone who’s memorized any part of Beethoven’s 5th Symphony is inexplicably killed in a tragic trolley car accident.2

Suddenly Beethoven’s 5th Symphony no longer exists. Not only have all physical records of Beethoven’s 5th Symphony been destroyed, the pure abstract concept itself of Beethoven’s 5th Symphony is also gone. Can abstract concepts be destroyed? How can an abstract concept cease to exist?

The new 21st Century Enlightenment emerging from the field of Cognitive Science is telling us abstract concepts don't exist apart from the material world. An abstract concept must be physically etched somewhere in the material world in order for it to exist.

Abstract Concepts Do Not Exist Abstractly

If this is so, then what happens to other abstract concepts, like gravity and numbers and mathematics? Where is the abstract concept of the number 5 etched into our universe?

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Endnotes:

[1] The brain has approximately 100 billion neurons interconnected at approximately 500 trillion synapses.—David J. Linden, The Accidental Mind: How brain evolution has given us love, memory, dreams, and god. (2007) pg. 28,32


[2] Moral philosophers love thought experiments involving runaway trolley cars. They ask, "What would you do in this situation? If you do nothing then five people ahead on the tracks will get run over and killed by the runaway trolley. But you can flip a switch which will divert the trolley onto a different track, saving those five people, but killing a sixth person on the other track. Would you flip the switch?"
        Instead of wondering, "What would I do?" my first thought as an engineer is always, "Who designed and built this defective trolley car? Who signed off on it? Who inspected it? What went wrong with our system of trolley car safety oversight? If I flip the switch to divert the trolley how do I know the trolley won't derail and end up killing everyone!?" That's what you get when you ask an engineer to ponder these moral thought experiments. My final response is, "That's what you get for letting moral philosophers design your trolley cars".