wendy.krieger @ Mar 25 2017, 09:07 AM wrote:What DoubleSharp is not seeing, is that the description i give is a fairly typical presentation of physics, where the 'depth' of the number is roughly as zipf's law.

The idea is that for small numbers you can 'know' their variations. For a number like 100,000, or the like, you can visit all the instances to it. For a number of thirty digits, you can know random examples, without being able to visit. And so on.

Once again, Wendy conflates concepts from linguistics (or more broadly, statistical behavior of data sets) with concepts from pure mathematics and physics. I'm tempted to characterize this habit of hers as a kind of

deepity, which is an attempt to sound deeply profound and wise, by making statements that at a literal level are true but trivial, but at a figurative level are false, but would be earth-shattering if they were true. Except that Wendy's utterances tend not to be true even at a trivial literal level.

Zipf's law was originally an empirical statistical observation about the frequency of

*usage* of words:

Wikipedia wrote:Zipf's law states that given some corpus of natural language utterances, the frequency of any word is inversely proportional to its rank in the frequency table.

This observation has

*absolutely nothing* to do with the mathematical concept of infinity, nor does it say

*anything* to either support or refute

Cantor's Theorem. She seems to believe that name-dropping something like "Zipf's law", without elaborating on it, might awe and impress the less discerning folks in the audience.

wendy.krieger @ Mar 25 2017, 09:07 AM wrote:The idea that Cantor proposes is that you can 'count' to any namable number, and that any number that has a name is countable. But the argument that the list that supposedly contains all numbers, can not do so, since it takes more numbers to express it, so the proposition they were trying to fill is false even before they commit the diagonal.

A small infinity of 10^80, would express in just eighty digits, and so the diagonal runs out well before the count does. And the further one extends the digits, one digit more gives ten times the examples.

Ten-to-the-eightieth-power is a finite number. Figuratively calling it a "small infinity" might make for a fun bit of poetry, but just because some bard might utter such a metaphor does not make ten-to-the-eightieth-power an "infinity" in any actual

*mathematical* sense.

Even if it is practically impossible for one human to recite the first ten-to-the-eightieth-power whole numbers (or even the entire human race, even if they had the entire history of the universe to do so), that set of whole numbers is still a

*finite* set, and is still

*countable* in principle. What Wendy doesn't get is that you cannot use the same reasoning that applies to finite sets to reason about infinite sets. Yet it is eminently possible for human beings to reason about infinite sets, and distinguish between

*countably* infinite versus

*uncountably* infinite sets. But because Wendy doesn't get Cantor's Theorem, she assumes that means that it can't possiby be true. That's a logical fallacy known as an

argument from personal incredulity, or more broadly an

argument from ignorance.

wendy.krieger @ Mar 25 2017, 09:07 AM wrote:It is interesting that Double-Sharp mentions 'germanic nationalism' in his comment on the first post. Much of this 'crank' stuff he goes on about is rather much the same as any other cultural superiorism, that is, the 'not invented here'.

Once again, Wendy is projecting her own faults on others. She's demonstrated quite frequently her pro-Germanic cultural bias, and her inability to accept anybody else's ideas unless she can somehow claim to have thought of them first. Several of us here have observed this behavior and criticized it. But instead of addressing the criticism, and amending her behavior, she seeks to deflect it back onto her critics.

wendy.krieger @ Mar 25 2017, 09:07 AM wrote:I have the foresight, to realise what i have done, is a different culture to the standard method, and understand that this is due to different perceptions, rather than right vs wrong.

Ah, and here we get down to it: the inevitable self-aggrandizement. What Wendy doesn't understand is that a population of "one" is not a "culture". While it is bigoted to make disparaging generalizations about an entire ethnic group (something Wendy apparently thinks she can engage in with impunity), it is completely legitimate to criticize the flawed thinking of one individual person.