The iPhone apps my cold, dead hands would cling most rigidly to
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Instapaper - combine this with the Instachrome extension, and whenever I see a webpage I want to read later, it'll be waiting with me as I wait for a train
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Light - it's bright! No more torches. If you lived in Hanborough, you'd need this too.
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Trainline - faster than my laptop and/or a speeding bullet for checking train times in the UK
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PlainText - write notes on your laptop, have them appear on your phone instantly through Dropbox and vice versa. Oh, and Dropbox of course, too.
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Dictionary.com - etymologies, pronunciations, the works.
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Remote - control Keynote presentations from your phone.
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Glympse - let other people know where you are.
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Skype - I can call Mia for free while walking the streets
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iTrans Tube and Tube Status for planning London Underground journeys
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Snaptell - red laser black magic. Point at a book, and have elves whisper about it to you.
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Angry Birds - the most popular mobile game of all time.
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Spotify - all the music in the world on the go. Requires a Spotify subscription.
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Shazam - tells you the name of songs that are currently playing.