Now, it’s time for the final chapter in my “visits with old friends” series, which brings us
\nback to the Good Math\/Bad Math all-time reader favorite crackpot: Mr. George Shollenberger.<\/p>\n
Last time I mentioned George<\/a>, a number of readers commented on the fact that it’s cruel to pick on poor George, because the guy is clearly not all there: he’s suffered from a number of medical problems which can cause impaired reasoning, etc. I don’t like to be pointlessly cruel, and in general, I think it’s inappropriate to be harsh with someone who is suffering from medical problems – particularly medical problems that affect the functioning of the mind.<\/p>\n But I don’t cut George any slack. None at all. Because much of what spews from his mouth isn’t the <\/p>\n There’s been some great humor coming from George, particularly in the areas of math and logic.<\/p>\n George claims<\/em> to be a big fan of Cantor, and likes to babble about the transfinite numbers. Unfortunately, he doesn’t really have a clue about them – and in fact, in one of his comment threads, he \nThe discovery of new truths about a monotheistic God by modern philosophers and scientists are correcting the teachings of today’s religions. One discovery is the new truth about God’s infinity. Specifically, in the 15th century, Nicholas of Cusa spoke of the new infinity as ‘the infinite qua infinite’ beyond all finite things. In the 19th century, Friedrich Hegel called it ‘the ‘Absolute’ beyond all relative things and Georg Cantor called it ‘the genuine infinity’ beyond all bad infinities. In the 21st century, I call it ‘the determinate infinite’ beyond all indeterminate infinities.\n<\/p><\/blockquote>\n Did Cantor talk about bad<\/em> infinities? No. What Cantor did was define the basis of what became modern set theory, and then use it to construct two fundamentally different kinds of numbers using sets: Cardinal numbers (which measure size), and Ordinal numbers (which measure position). Then, looking at sets – like the set of natural numbers, he realized that there’s a cardinal (a size<\/em>) that describes George is incapable of understanding that. But he continually insists that he understands \nSince mathematicians cannot extend the number domain beyond the transfinite numbers and into some higher world of numbers, it seems time for them to accept the infinite qua infinite and start developing Cantor’s transfinite numbers. By developing the transfinite numbers, I expect science to uncover many hidden secrets such as new energy sources.\n<\/p><\/blockquote>\n Alas for George, modern math is virtually all done in terms of constructions built using the ideas of Cantor’s conception of the transfinite numbers wasn’t a religious thing. And it also was never
\nresult of an impaired mind: it’s the product of an arrogant, vile, awful person. Since our last contact
\nwith George, aside from the humorous idiocy, he’s also taken it upon himself to explain how we’ll never
\nhave a peaceful society in America until we get rid of all of those damned foreigners<\/a>, who have
\n“unamerican mindsets”. That post was where I really started to despise George. He’s not just a senile
\nold fool – he’s a disgusting, horrible person, just another of the evil ghouls who used a horrible
\nevent, committed by a severely ill individual, as a cudgel to promote a deeply racist agenda. <\/p>\n
\nadmitted to never actually reading any of Cantor’s work, but just having read a popularized biography of Cantor that briefly mentioned the idea of the transfinites. He continually comes up with new and ever-stranger ways of characterizing Cantor’s work. For a recent example, last month, in this post<\/a>, he said this:<\/p>\n
\nthe size of the set of natural numbers. But that number can’t possibly be finite. So there is at least
\none “infinite” cardinal number. Then moving on from there, he was able to show that there must be
\nmore than one<\/em> infinite cardinal; and in fact, that there can be different sizes<\/em> of infinities. But there’s no value judgement in Cantor’s studies: just the discovery of this seemingly
\nparadoxical (but fascinating) idea of infinite cascades of ever-larger infinities.<\/p>\n
\nCantor, and that we evil atheistic scientists and mathematicians (even the theistic Jewish ones like me),
\nare refusing to acknowledge the work of Cantor because of its supposed theological implications. For
\nexample, here<\/a>, he explains why we refuse to solve the worlds problems by ignoring the transfinite numbers:<\/p>\n
\nCantor, and no serious math student can get through school without seeing at least a little bit of
\nCantor’s transfinites – at least enough to see the famous diagonalization argument. But aside from
\nthe laugh value of that, it’s a demonstration of how profoundly he doesn’t understand Cantor – and how much he doesn’t understand why he doesn’t understand Cantor.<\/p>\n
\nintended to be a practical description of a real thing in the world. It’s an idea: a concept based
\non understanding the meanings<\/em> of numbers, and of understanding the different kinds of
\nnumbers. It’s a profound step to realize that even though the set of natural numbers is infinite,
\nit’s infinitely small compared to the set of numbers that can’t<\/em> be written as fractions. That’s an astonishing fact – even a useful<\/em> fact for understanding the world. But that doesn’t mean
\nthat we’re going to find a real-live infinite set with a transfinite cardinality – or that we’re
\ngoing to find an object that occupies a transfinite ordinal position in an infinite set.<\/p>\n