Thanks to @[email protected] for the links!
Here’s a link to Caltech’s press release: https://www.caltech.edu/about/news/thinking-slowly-the-paradoxical-slowness-of-human-behavior
Here’s a link to the actual paper (paywall): https://www.cell.com/neuron/abstract/S0896-6273(24)00808-0
Here’s a link to a preprint: https://arxiv.org/abs/2408.10234
A bit in the data sense is just an element of the set of booleans. A bit in the entropy sense is the amount of information revealed by an observation with two equally probable outcomes. These are not the same thing because the amount of information contained in a bit is not always equal to one bit of entropy. For example, if a boolean is known to be 0, then the amount of information it contains is 0 bits. If it is known that the boolean is equally 0 or 1, then the information content is 1 bit. It depends on the prior probability distribution.
In some contexts, a bit can refer to a boolean variable, a flag. In other contexts, it may refer to the voltage at a certain point, or any number of other things. But when you are talking about bits/s then it’s a measure of information.
Yes, but as you know, this implies that the information is already available. You can use that knowledge to create a compression algorithm, or to define a less redundant file format. That’s very practical.
We can also be a bit philosophical and ask: How much information does a backup contain? The answer could be: By definition, 0 bits. That’s not a useful answer, which implies a problem with the application of the definition.
A more interesting question might be: How much information does a file contain, that stores the first 1 million digits of the number π?