> What is this notion of "pure randomness" that this article and many comments seem to be eluding [sic] to?
First, s/eluding/alluding/
Second, although the topic is complex, one test of randomness is that an ideal compression method, one able to find and exploit any repetitive pattern, cannot compress a random sequence.
Third, the term "entropy" as used in information theory is tied to randomness, as explained here:
A quote: "The entropy rate for a [fair coin] toss is one bit per toss. However, if the coin is not fair, then the uncertainty, and hence the entropy rate, is lower."
I think you're fudging what is supposed to be uniform here. In your example, the unigrams (i.e. single digits) may be uniform, but the n-grams for n > 2 are not.
Comments
> Perhaps I'm just not using the same definitions of terms, but I thought a uniform distribution is still considered random.
No, a uniform distribution is not evidence of randomness. Consider the digits 0 - 9 repeated endlessly:
0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789 ...
Uniformly distributed? Yes. Random? No.
> What is this notion of "pure randomness" that this article and many comments seem to be eluding [sic] to?
First, s/eluding/alluding/
Second, although the topic is complex, one test of randomness is that an ideal compression method, one able to find and exploit any repetitive pattern, cannot compress a random sequence.
Third, the term "entropy" as used in information theory is tied to randomness, as explained here:
http://en.wikipedia.org/wiki/Entropy_(information_theory)
A quote: "The entropy rate for a [fair coin] toss is one bit per toss. However, if the coin is not fair, then the uncertainty, and hence the entropy rate, is lower."
Based on that, high entropy -> high randomness.
Not to oversimplify a complex topic.
>Uniformly distributed? Yes. Random? No.
I think you're fudging what is supposed to be uniform here. In your example, the unigrams (i.e. single digits) may be uniform, but the n-grams for n > 2 are not.
Actually, the n-grams are periodic and repetitive also. They certainly aren't random.
They may be periodic and repetitive, but they aren't uniform. For example, there are lots of "01"s and no "02"s.
Could you edit that long line somehow? It makes reading harder in my phone.