[.cnI redruM]

Eviscerate at your leisure. There is plenty here worthy of fulsome contempt.

[Numbers Guy]

I saw Derbyshire's link to this piece a few minutes ago. Since the author is so in love with fuzzy left-wing proofs, that means he must doubt his own argument.

[Dr. Frank fan]

Honestly my only reaction to this is eye-rolling. The more I read the more I roll my eyes, to the point where I doubt I'll be able to finish reading this.

For starters, I have no idea what the hell the things he is talking about have to do with "left-wing" and "right-wing". There is a real issue to discuss here but the author just seems obsessed with labelling things he doesn't like "right-wing".

[Luke Skyfreeper]

Frankly, I don't see it.

The author's point -- that even mathematical proof, traditionally regarded as quite objective, ultimately contains a subjective element -- is valid, and he does a good job of explaining it.

[BlueNgold]

Typical of the left ... using a circular argument to prove a circular argument is a circular argument...

[hellinahandcart]

If I'd stuck with math back in high school, would this article make sense to me now?

[sjmiller]

As a professional mathematician who knows all of the mathematicians mentioned but two (the author and one other), I feel somewhat suited to comment.

I'll leave the statement on "like right-wing policies" for others. For me, I consider the following "a proof". One has a set of definitions, axioms, and assumptions, and the rules of logical implication. For example, if I know that P implies Q (P --> Q) and I know that P is true, the Q must also be true.

I consider something to be proved if by applying the rules of logic it can be deduced from my axioms and assumptions. This leads us to the concept of relative proof, namely, we can show the result follows from our initial assumptions, but we don't know if our initial assumptions are valid.

I'll give two standard examples. Let one of my axioms be that A and not A are both true (A an arbitrary statement). Then it turns out that, using the laws of logic, you can prove ANY statement B is true. Why, it turns out that A and not A both being true is quite powerful. Thus, we have an inconsistent axiom structure, and it isn't surprising that we can deduce anything.

Another example is Russel's Paradox. Mathematicians used to think that given any property P, one can form the set of all x having property P. Russel considered the following: Let R be the collection of all objects x such that x is NOT an element of x. If R is a set, then R is an object having some elements in it. We can ask: is R an element of R? From the definition of R, an object x is in R if and only if x is NOT an element of X. So, if R is not an element of R, then R is in R; if R is an element of R, then R is not in R! Contradiction! Such a set cannot exist, we cannot just collect any group of objects to be a set.

The point to get from this is that there can be lots of surprising subtleties. Things that "look" or "feel" convincing are often false. I would say two major ways for something to be false is that (1) it just doesn't follow from the axioms / assumptions (and you made an argumentative mistake); (2) the original axioms / assumptions are bad / inconsistent, and what you are studying now highlights that.

For the proofs of Fermat and small prime gaps, we weren't finding mistakes with our axioms. We were finding deductive mistakes in very long, very technical, complicated arguments (at least for Fermat, I'm not too familiar with the small gaps paper).

There is a lot more to the subject. It turns out there are many results which can be proven to be undecideable from a set of axioms / assumptions.

But I hope this gives the general idea. He is right that there are different levels of proofs. We have much more "rigorous" proofs than a few centuries ago. We have lots of cases with strong heuristics indicating what "should" be true. The problem is the field is getting very technical. I know -- I write papers in the field, and referee. I've found mistakes by papers from big names where all the arguments are fine, but the lower boundary term of an integral was dropped, and that made all the difference. However, I don't DOUBT that papers like this COULD be successfully refereed, if people took the time. Hales' proof of the Kepler Conjecture (on sphere packing) is a lot harder, as the computer checked numerous cases. So, while some things can be done by hand, the universe may collapse before we finish.

I'm rambling, so I'll stop here. Basically, I look at a "proof" as something that has been shown (step by step by step) to follow from a given set of axioms and assumptions and the rules of logical inference. Just because someone checks every step does NOT mean they checked correctly. Many times we have results that we "accept" as true, without having really done all the details (doing enough so we see the general picture, it looks similar to things we've seen before, so ....). As time is finite, often one reads papers and says "that statement seems plausible", and one keeps reading. If anyone wants to chat more, email sjmiller@math.ohio-state.edu.

[dead]

I understand his left wing approach to the essentially right wing problem of subjective vs. objective truth, but Euclid is only tangential to this theorem and have no idea why he would even be dragged, kicking and screaming, into this discussion.

On a more didactic level, the conundrum can be better expressed as a fluid rather than a concrete problem, for all that’s worth. Of course, one can easily envision a world where all liberal outlooks are expressed in liquid form and all conservative outlooks are expressed as solids, but of course that would depend on the average temperature of such a world, obviously.

I think the Hungarian physicist, Gotig Boldevitch, expressed it best, when he said, in his 1837 Theorem on Negative Intuity, “Sometime in the future, somebody named dead is going to invent me and thrust my imaginary self into some rambling but important sounding incoherence he posts on the internet, whatever that turns out to be.”

Despite his relatively fictitious nature, Boldevitch was very insightful and would only laugh at the evanescent state of truth in a world where political machinations constantly shift the meanings of words rendering “proof” profoundly ethereal, as it were.

[Cogadh na Sith]

Left wing proof:

Hypothesis "Y" is true because it makes me feel good to believe it is true.

Q.E.D

[Ernest_at_the_Beach]

Keywords seem about right!

[sirshackleton]

Uhhh....dude...could you repeat that?

[ShadowDancer]

There is plenty here worthy of fulsome contempt.

Your juvenile ad-libbed title is a good place to start.

[Sloth]

I disagree with the particulars of his 'right-wing' and 'left-wing' descriptions -- he seems to be equating them with 'concrete' and 'abstract', respectively, more than the 'perfect-to-the-letter' and 'warm fuzzy' way he describes them. I will say, though, that as a right-winger I feel uncomfortable espousing any position if I cannot document a methodical, objective means of supporting it, rather than mere intuition.

[Political Junkie Too]

Is this the reason why cartoonist Aaron MacGruder can say, "I believe that Condi Rice is a murderer, therefore I can call her a murderer?"

-PJ

[timydnuc]

It's left wing "logic" like this that gives me a headache. Excuse me while I get an excedrin and a martini.

[BlazingArizona]

In left-wing mathematics, on the other hand, proofs are unnecessary: just build a bomb in the privacy of your Montana cabin and mail it to those who hold opposing hypotheses. Ammonium nitrate beats logic anytime.

[Allan]

In order to be a mathematician it is necessary
though not sufficient
to suffer from a psychological disorder
which results in a total inability to communicate with normal human beings
in words they can understand.

[Congressman Billybob]

Here's a Euclidean Proof for you:

This author is a mathematician.

Based both on his occupation, and the evidence of this article, he knows diddly squat about politics.

Therefore, all of his references to "left" and "right" should be ignored, exactly as one of the proverbial monkeys should be ignored, when he typed out the opening lines of "Hamlet."

Quod Erat Demonstrum, or in its short form, Q.E.D.

Congressman Billybob

Click here, then click the blue CFR button, to join the anti-CFR effort (or visit the "Hugh & Series, Critical & Pulled by JimRob" thread). Don't delay. Do it now.

[weegee]

(a) Nothing is better than a good command of the English language.
(b) A college degree is better than nothing.

From (a) and (b) we get:
A college degree is better than a good command of the English language.

[moni kerr]

I thought it was rather simply stated. In mathematics, one test for a proof is it's logical validity (the 'right wing'definition). The other, 'left wing' proof is concensus. The first is rational, the second is fallacious. Citing popular opinion is not a valid test for truthfulness.

However, he leaves out another test; is it empirically verifiable. Most 'right wingers' deal with the world as it is whereas most left wingers tend to deal with the world as they want it to be. Leftist theories can be quite logical although I find that they most often skip the empirical test.