Common sense tells us that one's sense of hearing is important for safely navigating traffic. The problem is, common sense isn't reliable. It's common sense that tells people that it's safer to bike on the sidewalk or the left side of the street. It's common sense that tells people that cycling is inherently more dangerous than other forms of transportation.
It is this same common sense that seems to be the only thing used to support the argument against headphones. I have not seen a single scientific fact or statistic listed to the same effect. I encourage any headphone opponents to list them though.
Furthermore, most people telling us how unsafe headphones are probably don't even have personal experience with the issue. They have likely not worn headphones while riding. If they had for any length of time, I suspect their views on the subject would be different. It may be true that your ability to hear traffic is decreased, but the usefulness is highly dubious in the first place. Hearing the sound of traffic is probably a psychological comfort for these people. If there are 15 cars near you, can you really identify the position and speed of each one using sound? Getting any useful information from sound in moderate to heavy traffic is near impossible.
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Bring the pain.