“GK: Thanks for the positive statements here! But I would say “stance” rather than “idea”.”

Once again you send me to the dictionary, Greg, let’s see
[Merriam-Webster online]

STANCE

“Etymology: Middle English stance, staunce, from Middle French estance position, posture, stay, from Old French, from Vulgar Latin *stantia…”

(yes, it sounds like vulgar latin)

“..the position of the feet of a golfer or batter preparatory to making a swing”

What can I add? Swing, GREG, swing !!!

(Anyway your nice idea/stance of “non-commutative probabilistic method”, Greg and Scott, deserves a separate discussion sometime.)

If a PhD was about what you understood,believed and knew what happens if that research your PhD was based was found to be incorrect? Would we have to revoke everybody’s PhD’s that were based on science later found to be incorrect? Since science should be impartial and apply the same standards to everybody.

A naive person would therefore assert that they believe that there aren’t such things as belief.

In a way, the probabilistic method does not really exist in mathematics. It is technically valid to say, “oh, that is really a counting argument” when you see the probabilistic method in use. In any of these results, probability theory is just one way to explain the real proof. Some people do not like this scaffolding. I disagree with them, but the equivalence to non-probabilistic explanations is valid.

The presence of non-commutative probability in mathematics is similar, but even more hidden because most mathematicians do not study non-commutative probability. There are a lot of non-quantum results in mathematics whose proofs can be phrased quantumly, but traditionally aren’t. People generally won’t be convinced unless you use quantum probability to prove something new, and even then someone else might rephrase the proof in non-quantum terms. That is a high hurdle. If everyone were equally conservative about classical probability, the probabilistic method would not be a standard concept either.

Thanks for the positive statements here! But I would say “stance” rather than “idea”. If anyone can be credited with the idea, it would be von Neumann.

Some reason for skepticism is the insight from statistical mechanics that models based on ordinary probability and on non-commutative probability behave overall in a very similar way.

There is no such insight from statistical mechanics. The experience in both statistics mechanics and field theory is that classical and non-commutative probability are similar in some ways. But in other ways, they aren’t. For example, there is no explanation of superconductivity and lasers in classical probability. Although there is no strict impossibility theorem in the classical setting, the mere existence of lasers is significant evidence in favor of quantum probability.

Or to pick a more initial example, one of the paradoxes of physics a century ago was how electromagnetism, which is an attracting force, can possibly lead to the existence of rigid structures in chemistry. For comparison, there are no rigid structures in astrophysics. The answer is Pauli exclusion, which is purely a statement of quantum probability and not a new force law.

The amazing success of the “probabilistic method” in so many areas of mathematics (even in proving theorems which seem completely unrelated to probability) make this idea of Scott and Greg very appealing. However, results in this direction are still very sparse. Some reason for skepticism is the insight from statistical mechanics that models based on ordinary probability and on non-commutative probability behave overall in a very similar way. I suppose we will have to wait and see.

Actually, the more I think about it, the more I realize this Marcus Ross story is optimally designed (intelligently designed?) for being blogged about.

I mean, look. We’re talking about a story that’s got

(1) evolution vs. creationism (always a winner),
(2) a slightly new twist, but not so new that everyone won’t immediately have an opinion about it,
(3) a compelling human-interest angle, and
(4) an academic ethics question, which even those who accept the fact of evolution can argue about till the sun goes cold (or for Dr. Ross with his mortarboard off, the Rapture).

So, on behalf of all of us bloggers: thank you, Dr. Ross!

I can’t really put myself in the shoes of deeply religious people, but here is what I think anyway. I think that the guy believes creationism not for any empirical reason but out of loyalty. But he is also reasonably smart, and even interested in evolutionary biology despite his loyalties. He therefore also understands empirical scientific truth, just as a different mode of “truth” than literalist Christianity.

Now I think that believing things out of loyalty amounts to either stupidity, or dishonesty, or denial (which is just self-dishonesty). I also think that it’s too fashionable in the United States, especially in national politics. For example, the polls tell me that most Republicans still believe that the US is “winning” the war in Iraq. I interpret most of this sentiment as sheer nationalist loyalty. It bugs me. But the problem is not just conservative ideology. I have heard people say, “in this country, you ARE innocent until you ARE proven guilty”. I.e., it’s not just a legal presumption, it’s an injustice if we don’t personally believe that all acquitted defendants are innocent. This bugs me too, because it’s stupid.

So okay, belief for the sake of loyalty is a brain malfunction. But it is also only human. Undoubtedly I also believe some things just because I’m supposed to, and maybe social pressure also prevents me from identifying these false views.

But he was truthful in his thesis. His thesis has a series of true statements about paleontology. They aren’t statements about his own beliefs, they are statements about the history of the planet. The real issue is that he’s untruthful at other times, when he promotes creationism.

Maybe this discussion has moved from Ross himself to what a PhD means or should mean. I think that it should mean that you have done valid research in the field. You’re describing it as a description of what people understand. Even aside from political controversies such as creationism, your suggested interpretation bothers me. I would prefer that people see my own PhD as a demonstration of achievement, or at the most that I master(ed) certain skills, rather than that I know, believe, or understand any particular thing.

I might have attributed this difference in interpretation to a difference between physical sciences (or mathematics) and biology, but I’m not sure that that’s fair. Certainly in mathematics, I’m perfectly happy to credit people who, for whatever reason, reject their own valid contributions. If you have a good idea, it doesn’t really matter if you also disavow it. I would suppose that biology should be the same.