Fighting the moderately good fight on probability

Recently I’ve been engaged in intense combat over probability theory (readers will remember my research in this area – here and here) at an unlikely venue, a blog called “Feminist Philosophers.” I’ve been debating views on probability with English professor David Wallace, who merely adds hominem to my criticisms.

This should encourage everyone! You need not be “officially” “expert” in “disciplines” in order to make discoveries in them. This applies to both Dave and me (though I obviously think I have the upper hand).

The Three Thousand Year Reich of Negative Numbers (part one)

The curious reader might be interested to know that Diophantus and the Greek thinkers rejected the concept of negative numbers (and irrational numbers, of course) as “patently ridiculous” and “idiotic.” And we are a Greek-based society. So to borrow David Hume’s plaintive question – Then whence Negative Numbers? The answer to this question lies in the Orient. If there was ever a “yellow menace,” negative numbers are it. The Chinese, the Indians, and the Muslims gave us negative numbers. Not the superior Greeks. Is this a coincidence? I think not. These countries have had a vested interest in the concept from the very beginning.

Fortunately, however, negative numbers are behind a very thin conceptual veil. Once removed, it is easy to see the “Chinaman behind the curtain.” I’ll just say QUED ahead of time. Observe:

I can have three horses, but I cannot have negative three horses. Some people, suffering from Cognitive Dissonance (CD), suggest that “debt” is a manifestation of negative numbers. But that’s really just arguing semantics. Wittgenstein and Derrida disproved semantics back in the 20th century. In any case, what’s really going on in the situation is not that I have negative horses; rather, I owe some positive horses (Positive horses=horses that exist; countable horses. Who would want to be owed imaginary horses?). We can get by just fine without negative numbers. Besides, the Universe is full of stuff, not -stuff. If you would like to confirm this, here is the relevant empirical experiment:

Turn your head this way and that, and look at things. You may if you wish do this in a lab, for a more sciencey feel.

This conclusion, in conjunction with the abolition of infinity, has pathbreaking – nay, watershed – consequences for the number line, which now looks like this:

numberline2

I constantly get compliments for how incredibly parsimonious my arguments are – well, this one perhaps beats them all!

If the abolition of negative numbers in the conceptual schema catches on in the West, we can expect an end to the Three Thousand Year Reich of the Neo-Zoroastrians who think that the number line is an exact balance between negative and positive (seriously, what are the chances anyway that it would be an exact balance? It’s even worse than 1/Penultimate. It’s zero!). Now some might say that empirically the Universe is symmetrical, and they might cite anti-matter as confirmation of this. But there is not room here to discuss anti-matter; I’ll leave that for a future post!

“0.9999…. = 1”

This is an essential assumption of Bayes’s Calculus. If you doubt that this is common, then just take a cursory look at the mathematical community here, here, here, and here.  And here and here. Do you know what this means? It means that Calculus, like probability (see my deconstruction of probability), is false. The argument goes something like this:

0.333… is 1/3, right? Well 1/3×3=1. But surely 0.333…x3=0.999…! Therefore, by one or another form of the transitive property, 0.999…=1!

In addition to being a near-blasphemous usage of the transitive property, it is just plain false. Think about it in the following manner. 0.1 is necessarily greater than 0.0X, where ‘X’ is any countable number. 0.1 is also necessarily greater than 0.0XX. And so on. No matter how many X’s you add to the series, it will never equal or be greater to 0.1. Therefore, by mathematical induction a la carte, no amount of repetition of 0.0XXX…. could ever equal 0.1, which is what is necessary to add to 0.9 in order to equal 1. Importantly, (0.9 x / x<0.1)≠1 Λ (0.9 x / x<0.1)<1. Therefore Calculus is false. A house built on sand cannot divide itself.

Notice that all I needed to disprove this foundation of calculus was mathematical induction.

Advice to all my readers: Don’t let “math wizards” intimidate you with technobabble. And note that I am not alone.

Imaginary numbers (part one)

This concept kind of shoots itself in the foot, so I don’t need to spend much time on it. Using an imaginary number in an equation is like intentionally using a false premise in an argument, which is of course totally inappropriate in scholarship.

In fact, the man who invented Imaginary Numbers was an ophthalmologist named Renes Descartes. He coined the term. And guess what. It was in a criticism of the idea. Orwell would have a field day.

Infinity (part one)

I don’t think I need to spend much time on infinity. Infinitus est numerus stultorum. It suffices to point out that you cannot show me infinity of anything whatsoever. Since everything is finite, including every number, putting them all together will still not get you to infinity. According to math (and also its feisty sidekick, the English language), the number before infinity would be known as the “penultimate” in the series of all numbers. So in my opinion, the last number in the number line is the penultimate.

There is also a convenient common sense method for refuting infinity. If there were infinite numbers, then the Universe couldn’t fit them all in. But clearly the Universe does fit them all in, by the transitive property. It fits our brains, and our brains fit all the numbers. Please see William Lane Craig on this point, for further discussion.