Ah. Fair enough. That's a rather interesting case, and what I assume is not what people think of when you say random number. I assume that people think of a uniform distribution (i.e equally likely numbers).
You're probably right that people who haven't taken a course in probability are likely to use "random" to mean "uniformly at random". And of course, most people haven't taken a course in probability.
I would assert that people don't even know how to conceptualize the question in these terms ("random number" == "uniform distribution").
After you do study probability (by gambling, by lab work, by quantitative programming, or, least fun, in coursework), you get introduced to the "right questions to ask", like:
"what's the distribution",
"are the samples independent",
"what are you conditioning upon"
For instance, many people don't know that the distribution of the sum of two dice looks very different than just one die. They're both random, but not both uniform. Often people know something's weird, but can't formulate the question because they don't have the language.
Speak for yourself. Gaussian distributions are ubiquitous (thanks to the Central Limit Theorem), while uniform distributions only exist in the realm of pseudo-number generators and little else.
I think that the point you're trying to make is that a random variable with a uniform distribution is more "random" than a random variable with a gaussian distribution. The metric you're implying is called entropy, as a uniform distribution is maximally entropic.
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Ah. Fair enough. That's a rather interesting case, and what I assume is not what people think of when you say random number. I assume that people think of a uniform distribution (i.e equally likely numbers).
You're probably right that people who haven't taken a course in probability are likely to use "random" to mean "uniformly at random". And of course, most people haven't taken a course in probability.
I would assert that people don't even know how to conceptualize the question in these terms ("random number" == "uniform distribution").
After you do study probability (by gambling, by lab work, by quantitative programming, or, least fun, in coursework), you get introduced to the "right questions to ask", like:
"what's the distribution", "are the samples independent", "what are you conditioning upon"
For instance, many people don't know that the distribution of the sum of two dice looks very different than just one die. They're both random, but not both uniform. Often people know something's weird, but can't formulate the question because they don't have the language.
Speak for yourself. Gaussian distributions are ubiquitous (thanks to the Central Limit Theorem), while uniform distributions only exist in the realm of pseudo-number generators and little else.
I think that the point you're trying to make is that a random variable with a uniform distribution is more "random" than a random variable with a gaussian distribution. The metric you're implying is called entropy, as a uniform distribution is maximally entropic.