What do small children and infants know about music and math? Practically from birth, babies start thinking both mathematically and musically; humans come hardwired for both music and math…
You might wonder how we know something like this: After all, infants can’t talk. We infer it in part from how long infants look at something. If infants see the same thing over and over again, they tend to look away quicker the more they see it. That is called habituation. If they see something unexpected and something changes, they look longer and that is called fixation.
When babies are just three or four days old they can distinguish three dots from two dots. Researchers discovered this by showing babies two dots repeatedly until they get habituated and stop looking for long periods. When the researchers switch to three dots, the babies are fixated; they look longer than if they had just been shown two dots. This is evidence of something that mathematics educators have a word for. It’s called subitizing: Instantly counting without counting out the individual elements.
This is a transcript from the video series How Music and Mathematics Relate. Watch it now, on The Great Courses.
Subitizing comes from the Latin subito, a musical term. Subito forte means to play suddenly loud. Adults subitize three, four, even five items. In my classrooms, I can look at the students and count out groups of five very quickly. If you try to do this with three, four, or five you have virtually no errors and incredibly fast reaction time. But, if you try to do this with more than five, most adults have more errors and a much longer reaction time.
Infants are subitizing at three or four days old, indicating they have some innate numerical ability. If they can sort of count in some sense, or subitize, can they add? Can they combine groups and count them? You would think that would be much harder, but by five months infants can tell that 1 + 1 is 2. They can do basic addition. This is known because of the work by Karen Wynn, a psychologist at the Infant Cognition Center at Yale. The tests she performed involved the violation of expectation. Again, babies will look longer at unexpected images, objects, or outcomes.
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Her tests seemed deceptively simple. Children were shown dolls behind a screen that could rise and fall. First, only one doll was shown, then the screen lowered to hide it. Next, a second doll was shown going behind the screen to join the first doll, still hidden. Naturally, when the screen came back up the children would expect to see two dolls. But when only one doll was revealed behind the screen, children as young as five months old spent longer amounts of time looking at the unexpected result.
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If you’re skeptical you might ask, how do we know it is really about the numbers and not just some innate counting of dolls? They tested to eliminate that possibility as well. They have switched objects and with five-month-olds, if you have one doll plus one doll and then drop the screen and show the baby two blocks instead of dolls, they do not look very long. There’s a shorter gaze. On the other hand, if you have one doll plus one doll and then drop the screen and there is one block, there is a longer gaze. That is unexpected to them. These young babies do not know the difference between a doll and a block, but they somehow know that 1 + 1 is 2.
Older babies look longer at both. Older babies by about a year know that a doll and a block are different. They know that one doll plus one doll should not equal two blocks. This is a sort of addition that these infants are doing that at 12 months old; addition is nearly innate.
The Tie to Music
What about music? Are there musically innate structures in the brain? What we know is that there are early preferences about music — babies like fast, loud, and familiar music. To understand this, they have developed what is called a conditioned head turning experiment. This work was performed in the early 2000s by Alexander Lamont in the UK.
In the study, a baby’s head controlled what music was being played. When the baby looked left, he heard one song. When the baby looked right, he heard a different song. Babies at about a year old quickly learn how to control the system—how turning their heads tells them what music they’re going to hear. When they control the music, they prefer upbeat, loud music.
But what about familiar music? To test for that, they had mothers play music in utero for the last three months of their pregnancies. Then the babies did not hear that music again for a full year after birth. That one year they put these babies in this head turning experiment and the babies preferred the music that they had heard in the womb over similar styled and similar tempoed music. This research showed that infants have musical structures in their brains that can store musical memories. This research got taken out of context and we heard about the Mozart effect, which was not entirely well-reported in the media.
What’s the big picture message from all of this? It points to an obvious connection between math and music. Infant’s brains are structured in ways that allow them to process fundamentally important aspects of both. Before language—before walking even—infant brains can process, remember, and maybe even understand both math and music.
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Music can help with studying math for many reasons: enjoyable music puts one at ease and helps set remembrance points based on the song and additionally, as music is mathematical with repeating rhythms, frequencies, and octaves, the formulas are similar and work together.
Pythagoras from the 6th century BCE is credited with the propagation of a mathematical understanding of music throughout Europe, based on his studies with Kemetic scholars.
Math was understood for millennia in ancient Kemet (Egypt), but the European era of math truly began when Euclid formulated an axiomatic study of math.
While zero was considered a placeholder as far back as the Sumerians, it was in India around AD 458 that the concept was derived from the Buddhist Sunyata doctrine.